Fire-X: Extinguishing Fire with Stoichiometric Heat Release

H. Wrede, S. M. Mahfuz, A. Wagner, W. Pałubicki, D. L. Michels, and S. Pirk

ACM Transactions on Graphics (SIGGRAPH Asia 2025), ACM (2025).

We present a combustion simulation framework to model fire phenomena across solids, liquids, and gases. Our approach extends traditional fluid solvers by incorporating multi-species thermodynamics and reactive transport for fuel, oxygen, nitrogen, carbon dioxide, water vapor, and residuals. Combustion reactions are governed by stoichiometry-dependent heat release, allowing accurate simulation of premixed and diffusive flames with varying severity and composition. We support a wide range of scenarios including jet fires, water suppression (sprinklers, sprays), fuel evaporation, and starvation conditions. The system enables interactive heat sources, fire detectors, and realistic rendering of flames (e.g., laminar-to-turbulent transitions, blue-to-orange color shifts). Our key contributions include the tight coupling of species dynamics with thermodynamic feedback, evaporation modeling, and a hybrid SPH-grid representation for efficient combustion simulation. We validate our method through numerous experiments, demonstrating versatility in both indoor and outdoor fire scenarios.

Project Page

Autoregressive Generation of Static and Growing Trees

H. Wang, B. Zhang, J. Klein, D. L. Michels, D. Yan, and P. Wonka.

SIGGRAPH 2025 Technical Paper, ACM (2025).

We propose a transformer architecture and training strategy for tree generation. The architecture processes data at multiple resolutions and has an hourglass shape, with middle layers processing fewer tokens than outer layers. Similar to convolutional networks, we introduce longer range skip connections to completent this multi-resolution approach. The key advantage of this architecture is the faster processing speed and lower memory consumption. We are therefore able to process more complex trees than would be possible with a vanilla transformer architecture. Furthermore, we extend this approach to perform image-to-tree and point-cloud-to-tree conditional generation and to simulate the tree growth processes, generating 4D trees. Empirical results validate our approach in terms of speed, memory consumption, and generation quality.

SIGGRAPH Asia

Augmented Mass-Spring Model for Real-Time Dense Hair Simulation

J. A. Amador Herrera, Y. Zhou, X. Sun, Z. Shu, C. He, S. Pirk, and D. L. Michels.

International Conference on Computer Vision, IEEE (2025).

We propose a novel Augmented Mass-Spring (AMS) model for real-time simulation of dense hair at the strand level. Our approach considers the traditional edge, bending, and torsional degrees of freedom in mass-spring systems, but incorporates an additional one-way biphasic coupling with a ghost rest-shape configuration. Through multiple evaluation experiments with varied dynamical settings, we show that AMS improves the stability of the simulation in comparison to mass-spring discretizations, preserves global features, and enables the simulation of non-Hookean effects. Using a heptadiagonal decomposition of the resulting matrix, our approach provides the efficiency advantages of mass-spring systems over more complex constitutive hair models, while enabling a more robust simulation of multiple strand configurations. Finally, our results demonstrate that our framework enables the generation, complex interactivity, and editing of simulation-ready dense hair assets in real time.

ICCV

From Clouds to Cyclones: Physically Based Modeling and Simulation of Atmospheric Dynamics

Dissertation of J. A. Amador Herrera. Doctoral Advisor: D. L. Michels.
Committee Members: D. L. James, D. E. Keyes, I. Viola.

Applied Mathematics and Computational Sciences Program,
CEMSE Division, KAUST (2025).

Simulating weather remains a challenging research problem due to the intricate interplay of atmospheric, hydrological, thermodynamic, and electrical processes. This thesis introduces a novel physics-based framework that enables the real-time simulation of diverse weather phenomena with high visual and physical fidelity. Our approach models the complete hydrologic cycle by coupling atmospheric and pedospheric interactions, capturing the formation and evolution of various cloud types, including mammatus, hole-punch, and cumulonimbus, as well as their dynamic transitions. We incorporate a comprehensive microphysics scheme that accounts for different precipitation types, such as rain, snow, and graupel, and integrate the Wegener-Bergeron-Findeisen process into a Kessler-type formulation to simulate ice crystal growth in mixed-phase clouds. Additionally, we model ground-level water dynamics, including infiltration, runoff, and evaporation, while incorporating heat transfer mechanisms that drive diurnal temperature variations. Our results demonstrate the capability of our model to generate realistic 3D weatherscapes, showcase complex weather events, and even nowcast real-world weather by streaming live atmospheric data into our framework.
Building on this foundation, we present a physically based method for simulating large-scale cyclonic phenomena, capturing the interaction of heat, moisture, and turbulent microphysical dynamics of hydrometeors. Our model enables the realistic simulation of mesoscale cyclonic processes, planetary boundary layer interactions, and the development of hurricanes and tornadoes. By incorporating large-scale heat and water transport mechanisms, we reproduce the full evolution of cyclogenesis with visual and physical accuracy. We validate our simulations through quantitative comparisons with storm soundings and climatological data, as well as qualitative comparisons with prior modeling approaches.
Finally, we reformulate our framework to simulate atmospheric electrical phenomena by coupling cloud microphysics with air breakdown physics to model lightning. Our method enables the realistic generation of intra-cloud, cloud-to-air, and cloud-to-ground discharges by dynamically tracking charge separation and electric field development within convective systems. The resulting lightning simulations are physically plausible and visually compelling, supporting applications in visualization, forecasting, and synthetic data generation.
Together, these contributions form a unified and efficient multiphysics framework for the simulation of both everyday and extreme weather events, bridging the gap between visual realism and physically based atmospheric modeling.

KAUST Repository

Thunderstruck: Visually Simulating Electrical Storms

J. A. Amador Herrera, J. Klein, D. T. Banuti, W. Pałubicki, S. Pirk, and D. L. Michels.

IEEE Transactions on Visualization and Computer Graphics (TVCG 2025), IEEE (2025).

Thunderstorms are multi-physics phenomena resulting from intricate charge transfer processes in the atmosphere, which are driven by interactions between ice and water cloud particles. In this work, we present a physically-based model for simulating cloud electrification and discharge processes, enabling the simulation of emergent lightning phenomena, i.e., our approach automatically generates different types of discharges in response to dynamic atmospheric changes, relying solely on a minimal set of atmospheric parameters without requiring additional user input. We model charge separation at the microphysical level using a statistical mechanics approach to describe atmospheric electrification. Additionally, we introduce a gauge-invariant dielectric breakdown model capable of describing multiple bipolar channels, dynamic electric fields, and the electrical resistance of air, offering a comprehensive representation of lightning discharge processes. We validate our model through extensive comparisons with real data and prior state-of-the-art methods, demonstrating its capability to simulate distinct lightning types and the complete life-cycle of thunderstorms. Furthermore, we explore various applications of our framework, including real-time nowcasting, assessments in civil engineering, the generation of virtual environments featuring thunder and lightning, and the simulation of complex dielectric breakdown across diverse domains.

TechRxiv

Stressful Tree Modeling: Breaking Branches with Strands

B. Li, N. Schwarz, W. Pałubicki, S. Pirk, D. L. Michels, and B. Benes.

SIGGRAPH 2025 Technical Paper, ACM (2025).

We propose a novel approach for the computational modeling of lignified tissues, such as those found for tree branches and timber. We leverage a state-of-the-art strand-based representation for tree form, which we extend to describe biophysical processes at short and long time scales. Simulations at short time scales enable us to model different breaking patterns due to branch bending, twisting, and breaking. At long-time scales, our method enables the simulation of realistic branch shapes under the influence of plausible biophysical processes, such as the development of compression and tension wood. We specifically focus on computationally fast simulations of woody material, enabling the interactive exploration of branches and wood breaking. By leveraging Cosserat rod physics, our method allows us to generate a large variety of different breaking patterns. We showcase the capabilities of our method by performing and visualizing numerous experiments.

Project Page

FlameForge: Combustion Simulation of Wooden Structures

D. Liu, J. Klein, F. Rist, W. Pałubicki, S. Pirk, and D. L. Michels.

Proceedings of the ACM on Computer Graphics and Interactive Techniques (SCA 2025), ACM (2025).

We propose a unified volumetric combustion simulator that supports general wooden structures capturing the multi-phase combustion of charring materials. Complex geometric structures are represented in a voxel grid for the efficient evaluation of volumetric effects. In addition, a signed distance field is introduced to query the surface information required to compute the insulating effect caused by the char layer. Non-charring materials such as acrylic glass or non-combustible materials such as stone can also be modeled in the simulator. Adaptive data structures are utilized to enable memory-efficient computations within our multiresolution approach. The simulator is qualitatively validated by showcasing the numerical simulation of a variety of scenes covering different kinds of structural configurations and materials. Two-way coupling of our combustion simulator and position-based dynamics is demonstrated capturing characteristic mechanical deformations caused by the combustion process. The volumetric combustion process of wooden structures is further quantitatively assessed by comparing our simulated results to sub-surface measurements of a real-world combustion experiment.

Paper Video Cover Image SCA

Harmony: A Joint Self-Supervised and Weakly-Supervised Framework for Learning General Purpose Visual Representations

M. Baharoon, J. Klein, and D. L. Michels.

Transactions on Machine Learning Research, JMLR (2025).

Vision-language contrastive learning frameworks such as CLIP enable learning representations from natural language supervision and provide strong zero-shot classification capabilities. However, due to the nature of the supervisory signal in these paradigms, they lack the ability to learn localized features, leading to degraded performance on dense prediction tasks such as segmentation and detection. On the other hand, self-supervised learning methods have shown the ability to learn granular representations, complementing the high-level features in vision-language training. In this work, we present Harmony, a framework that combines vision-language training with discriminative and generative self-supervision to learn visual features that can be generalized across different downstream vision tasks. Our framework is specifically designed to work on web-scraped data by not relying on negative examples in the self-supervised learning path and addressing the one-to-one correspondence issue using soft CLIP targets generated by an EMA model. Moreover, Harmony optimizes for five different objectives simultaneously, efficiently utilizing the supervision in each data example, making it even more suited in data-constrained settings. We comprehensively evaluate Harmony across various vision downstream tasks and find that it significantly outperforms the baseline CLIP and outperforms the previously leading joint self- and weakly supervised methods, SLIP, MaskCLIP, and DetailCLIP. Specifically, when compared against these methods, Harmony shows superior performance in linear-probing, fine-tuning, and zero-shot classification on ImageNet-1k, semantic segmentation on ADE20K, and both object detection and instance segmentation on MS-COCO, when pre-training a ViT-B on CC3M. We also show that Harmony outperforms SILC on detection, linear and fine-tuning classification, and outperforms other self-supervised learning methods like iBOT and MAE across all tasks evaluated.

arXiv Code

Perm: A Parametric Representation for Multi-Style 3D Hair Modeling

C. He, X. Sun, Z. Shu, F. Luan, S. Pirk, J. A. Amador Herrera, D. L. Michels, T. Y. Wang, M. Zhang, H. Rushmeier, and Y. Zhou.

Spotlight, International Conference on Learning Representations, ICLR (2025).

We present Perm, a learned parametric model of human 3D hair designed to facilitate various hair-related applications. Unlike previous work that jointly models the global hair shape and local strand details, we propose to disentangle them using a PCA-based strand representation in the frequency domain, thereby allowing more precise editing and output control. Specifically, we leverage our strand representation to fit and decompose hair geometry textures into low- to high-frequency hair structures. These decomposed textures are later parameterized with different generative models, emulating common stages in the hair modeling process. We conduct extensive experiments to validate the architecture design of Perm, and finally deploy the trained model as a generic prior to solve task-agnostic problems, further showcasing its flexibility and superiority in tasks such as 3D hair parameterization, hairstyle interpolation, single-view hair reconstruction, and hair-conditioned image generation.

arXiv Supplementary Material Code

DeepHadad: Enhancing Readability of Damaged Inscriptions with Synthetic Data

A. C. Aioanei, J. Klein, K. M. Klein, R. Hunziker-Rodewald, and D. L. Michels.

Journal on Computing and Cultural Heritage, ACM (2025).

The deterioration of ancient inscriptions over centuries has resulted in irrevocable loss of vital written records, hampering epigraphic analysis, and creating significant gaps in historical knowledge. Factors such as eroded letters and physical damage often compromise the readability of these inscriptions. We present DeepHadad, a neural network trained on procedurally generated synthetic data that uses displacement maps and image-to-image translation to digitally restore severely damaged ancient inscriptions to a more readable state. The network’s name is derived from the famous Panamuwa (I) inscription on the mid-8th century BCE Hadad statue, where, at certain places, only faint traces of letters remain on the damaged basalt statue. A key challenge in this work is the lack of well-preserved and damaged glyph pairs for training, as each glyph instance is unique and therefore not found in different states of erosion. We address this by generating synthetic training data through simulated erosion processes, enabling our neural network to successfully generalize to real data. By extracting and overlaying completion maps onto the 3D model, we significantly enhance the legibility of the barely recognizable Aramaic inscription on the Hadad statue. Quantitative and qualitative experiments confirm that our approach can recover textual content that would otherwise be lost or recoverable only through time-consuming manual work. This research opens a pioneering avenue for employing state-of-the-art artificial intelligence (AI) to enrich the readability of ancient textual heritage. Our methodology facilitates a more comprehensive analysis of significant inscriptions and demonstrates the potential of AI-assistive technologies to advance the field of ancient restoration and epigraphic studies.

Journal Paper Conference Version

A Flexible Mold for Facade Panel Fabrication

F. Rist, Z. Wang, D. Pellis, M. Palma, D. Liu, E. Grinspun, and D. L. Michels.

ACM Transactions on Graphics (SIGGRAPH Asia 2024), ACM (2024).

Architectural surface panelling often requires fabricating molds for panels, a process that can be cost-inefficient and material-wasteful when using traditional methods such as CNC milling. In this paper, we introduce a novel solution to generating molds for efficiently fabricating architectural panels. At the core of our method is a machine that utilizes a deflatable membrane as a flexible mold. By adjusting the deflation level and boundary element positions, the membrane can be reconfigured into various shapes, allowing for mass customization with significantly lower overhead costs. We devise an efficient algorithm that works in sync with our flexible mold machine that optimizes the placement of customizable boundary element positions, ensuring the fabricated panel matches the geometry of a given input shape: (1) Using a quadratic Weingarten surface arising from a natural assumption on the membrane's stress, we can approximate the initial placement of the boundary element from the input shape's geometry; (2) we solve the inverse problem with a simulator-in-the-loop optimizer by searching for the optimal placement of boundary curves with sensitivity analysis. We validate our approach by fabricating baseline panels and a facade with a wide range of curvature profiles, providing a detailed numerical analysis on simulation and fabrication, demonstrating significant advantages in cost and flexibility.

Project Page

End-to-end Optimization of Fluidic Lenses

M. Na, H. A. Jiménez Romero, X. Yang, J. Klein, D. L. Michels, and W. Heidrich.

SIGGRAPH Asia 2024 Technical Paper, ACM (2024).

Prototyping and small volume production of custom imaging-grade lenses is difficult and expensive, especially for more complex aspherical shapes. Fluidic shaping has recently been proposed as a potential solution: It makes use of the atomic level smoothness of interfaces between liquids, where the shape of the interface can be carefully controlled by boundary conditions, buoyancy control and other physical parameters. If one of the liquids is a resin, its shape can be "frozen" by curing, thus creating a solid optical element. While fluidic shaping is a promising avenue, the shape space generated by this method is currently only described in the form of partial differential equations, which are incompatible with existing lens design processes. Moreover, we show that the existing PDEs are inaccurate for larger curvatures. In this work, we develop a new formulation of the shape space lenses generated by the fluidic shaping technique. It overcomes the inaccuracies of previous models, and, through a differentiable implementation, can be integrated into recent end-to-end optical design pipelines based on differentiable ray tracing. We extensively evaluate the model and the design pipeline with simulations, as well as initial physical prototypes.

Project Page

Digital Salon: An AI and Physics-Driven Tool for 3D Hair Grooming and Simulation

C. He, J. A. Amador Herrera, Y. Zhou, Z. Shu, X. Sun, Y. Feng, S. Pirk, D. L. Michels, M. Zhang, Y. Wang, and H. Rushmeier.

SIGGRAPH Asia 2024 Real-Time Live!, ACM (2024).

Digital Salon is a revolutionary tool for 3D hair grooming and simulation, integrating AI and physics-based algorithms to simplify hair modeling, animation, and rendering. It enables users to generate detailed hairstyles through natural language descriptions. This tool combines text-based hair creation, interactive editing, and high-quality rendering into a unified pipeline. Digital Salon’s innovative real-time simulation and versatile capabilities allow for the dynamic representation of various hair types and interactions with support for 10,000 to 80,000 strands, making advanced hair design accessible to users of all skill levels and dramatically streamlining the creative process in digital media.

Project Page

A Lennard-Jones Layer for Distribution Normalization

M. Na, J. Klein, B. Zhang, W. Pałubicki, S. Pirk, and D. L. Michels.

Transactions on Machine Learning Research, JMLR (2024).

We introduce the Lennard-Jones layer (LJL) for the equalization of the density of 2D and 3D point clouds through systematically rearranging points without destroying their overall structure (distribution normalization). LJL simulates a dissipative process of repulsive and weakly attractive interactions between individual points by considering the nearest neighbor of each point at a given moment in time. This pushes the particles into a potential valley, reaching a well-defined stable configuration that approximates an equidistant sampling after the stabilization process. We apply LJLs to redistribute randomly generated point clouds into a randomized uniform distribution. Moreover, LJLs are embedded in the generation process of point cloud networks by adding them at later stages of the inference process. The improvements in 3D point cloud generation utilizing LJLs are evaluated qualitatively and quantitatively. Finally, we apply LJLs to improve the point distribution of a score-based 3D point cloud denoising network. In general, we demonstrate that LJLs are effective for distribution normalization which can be applied at negligible cost without retraining the given neural network.

Project Page

Synthetic Data at Scale: A Development Model to Efficiently Leverage Machine Learning in Agriculture

J. Klein, R. E. Waller, S. Pirk, W. Pałubicki, M. Tester, and D. L. Michels.

Frontiers in Plant Science, Frontiers Media (2024).

The rise of artificial intelligence (AI) and in particular modern machine learning (ML) algorithms during the last decade has been met with great interest in the agricultural industry. While undisputedly powerful, their main drawback remains the need for sufficient and diverse training data. The collection of real datasets and their annotation are the main cost drivers of ML developments, and while promising results on synthetically generated training data have been shown, their generation is not without difficulties on their own. In this paper, we present a development model for the iterative, cost-efficient generation of synthetic training data. Its application is demonstrated by developing a low-cost early disease detector for tomato plants (Solanum lycopersicum) using synthetic training data. A neural classifier is trained by exclusively using synthetic images, whose generation process is iteratively refined to obtain optimal performance. In contrast to other approaches that rely on a human assessment of similarity between real and synthetic data, we instead introduce a structured, quantitative approach. Our evaluation shows superior generalization results when compared to using non-task-specific real training data and a higher cost efficiency of development compared to traditional synthetic training data.

Front. Plant Sci.

Computationally Effective Approach for Studies of Mechanism and Thermodynamics of Heterogeneous Catalytic Processes on Metal Oxides

E. G. Ragoyja, V. E. Matulis, O. A. Ivashkevich, D. A. Lyakhov, and D. L. Michels.

International Journal of Quantum Chemistry, Wiley (2024).

To understand the nature of heterogeneous catalytic processes and improve their efficiency, it is necessary to conduct both experimental and theoretical studies. At the same time, there is no unified approach to obtaining the necessary data using quantum chemistry methods. In this work, problems of the existing calculational approaches are analyzed. The obtained information is used to develop the original three-layer embedded cluster model approach, which is shown to be the most effective. The general algorithm for obtaining such models for various oxides is formulated. The sufficient accuracy of the proposed models in predicting geometric and energy characteristics, vibrational frequencies, activation barriers, and thermodynamic characteristics is verified. The specifics of calculating the thermodynamic characteristics of heterogeneous processes using the proposed cluster models is studied in detail. The developed approach is an effective tool for studying the mechanism of heterogeneous catalytic processes both by itself and in combination with experiment.

Int. J. Quantum Chem.

Higher Validity, Lower Radiation: A New Ictal Single-Photon Emission Computed Tomography Framework

F. Bitzer, L. Walger, T. Bauer, F. Schulte, F. C. Gaertner, M. Schmitz, M. Schidlowski, R. von Wrede, A. Rácz, T. Baumgartner, V. Gnatkovsky, D. Paech, V. Borger, H. Vatter, B. Weber, D. L. Michels, T. Stöcker, M. Essler, J. W. Sander, A. Radbruch, R. Surges, and T. Rüber.

Annals of Neurology, Wiley (2024).

Objective: To assess whether arterial spin labeling perfusion images of healthy controls can enhance ictal single-photon emission computed tomography analysis and whether the acquisition of the interictal image can be omitted.
Methods: We developed 2 pipelines: The first uses ictal and interictal images and compares these to single-photon emission computed tomography and arterial spin labeling of healthy controls. The second pipeline uses only the ictal image and the analogous healthy controls. Both pipelines were compared to the gold standard analysis and evaluated on data of individuals with epilepsy who underwent ictal single-photon emission computed tomography imaging during presurgical evaluation between 2010 and 2022. Fifty healthy controls prospectively underwent arterial spin labeling imaging. The correspondence between the detected hyperperfusion and the postoperative resection cavity or the presumably affected lobe was assessed using Dice score and mean Euclidean distance. Additionally, the outcomes of the pipelines were automatically assigned to 1 of 5 concordance categories.
Results: Inclusion criteria were met by 43 individuals who underwent epilepsy surgery and by 73 non-surgical individuals with epilepsy. Compared to the gold standard analysis, both pipelines resulted in significantly higher Dice scores and lower mean distances (p<0.05). The combination of both provided localizing results in 85/116 cases, compared to 54/116 generated by the current gold standard analysis and the ictal image alone produced localizing results in 60/116 (52%) cases.
Interpretation: We propose a new ictal single-photon emission computed tomography protocol; it finds relevantly more ictal hyperperfusion, and halves the radiation dose in about half of the individuals.

Ann. Neurol.

Comparative Analysis of Absorption Resonances between Carbynes and Cyclo[n]carbons

R. B. Payod, A. L. Pushkarchuk, D. L. Michels, D. A. Lyakhov, and V. A. Saroka.

Journal of Physics: Condensed Matter, IOP (2024).

Two approaches are presented here to analyze the absorption resonances between carbynes and cyclo[n]carbons, namely the analytical tight-binding model to calculate the optical selection rules of cumulenic atomic rings and chains and the ab initio time-dependent density functional theory for the optical investigation of polyynic carbon ring and chains. The optical absorption spectra of the carbon ring match that of the finite chain when their eigen energies align following the N_ring=2N_chain+2 rule, which states that the number of atoms in an atomic ring N_ring is twice the number of atoms on a finite chain N_chain with two additional atoms. Two representative atomic chains are chosen for our numerical calculations, specifically carbynes with N=7 and 8 carbon atoms as optical resonance spectra match to a recently synthesized carbon ring called cyclo[18]carbon. Despite the mismatch in resonance peaks, molecular orbital transitions of both carbynes N=7 and 8 and cyclo[18]carbon reveal a wave function symmetry change from inversion to reflection and vice versa for allowed molecular orbital transitions, which results in electron density redistribution along the polyynic carbyne axis or the cyclo[18]carbon circumference. Our investigation of the correlation of optical absorption peaks between carbynes and cyclo[n]carbons is a step towards enhancing the reliability of allotrope identification in advanced molecular device spectroscopy. Moreover, this work could facilitate the non-invasive, rapid and crucial assessment of these sensitive 1D allotropes by providing accurate descriptions of their electronic and optical properties, particularly in controlled synthesis environments.

J. Phys. Condens. Matter

Cyclogenesis: Simulating Hurricanes and Tornadoes

J. A. Amador Herrera, J. Klein, D. Liu, W. Pałubicki, S. Pirk, and D. L. Michels.

ACM Transactions on Graphics (SIGGRAPH 2024), ACM (2024).

Cyclones are large-scale phenomena that result from complex heat and water transfer processes in the atmosphere, as well as from the interaction of multiple hydrometeors, i.e., water and ice particles. When cyclones make landfall, they are considered natural disasters and spawn dread and awe alike. We propose a physically-based approach to describe the 3D development of cyclones in a visually convincing and physically plausible manner. Our approach allows us to capture large-scale heat and water continuity, turbulent microphysical dynamics of hydrometeors, and mesoscale cyclonic processes within the planetary boundary layer. Modeling these processes enables us to simulate multiple hurricane and tornado phenomena. We evaluate our simulations quantitatively by comparing to real data from storm soundings and observations of hurricane landfall from climatology research. Additionally, qualitative comparisons to previous methods are performed to validate the different parts of our scheme. In summary, our model simulates cyclogenesis in a comprehensive way that allows us to interactively render animations of some of the most complex weather events.

Project Page

Scintilla: Simulating Combustible Vegetation for Wildfires

A. Kokosza, H. Wrede, D. González Esparza, M. Makowski, D. Liu, D. L. Michels, S. Pirk, and W. Pałubicki.

ACM Transactions on Graphics (SIGGRAPH 2024), ACM (2024).

Wildfires are a complex physical phenomenon that involves the combustion of a variety of flammable materials ranging from fallen leaves and dried twigs to decomposing organic material and living flora. All these materials can potentially act as fuel with different properties that determine the progress and severity of a wildfire. In this paper, we propose a novel approach for simulating the dynamic interaction between the varying components of a wildfire, including processes of convection, combustion and heat transfer between vegetation, soil and atmosphere. We propose a novel representation of vegetation that includes detailed branch geometry, fuel moisture, and distribution of grass, fine fuel, and duff. Furthermore, we model the ignition, generation, and transport of fire by firebrands and embers. This allows simulating and rendering virtual 3D wildfires that realistically capture key aspects of the process, such as progressions from ground to crown fires, the impact of embers carried by wind, and the effects of fire barriers and other human intervention methods. We evaluate our approach through numerous experiments and based on comparisons to real-world wildfire data.

Project Page

LAESI: Leaf Area Estimation with Synthetic Imagery

J. Kałużny, Y. Schreckenberg, K. Cyganik, P. Annighöfer, S. Pirk, D. L. Michels, M. Cieslak, F. Assaad-Gerbert, B. Benes, and W. Pałubicki.

Synthetic Data for Computer Vision (SynData4CV 2024), IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2024).

We introduce LAESI, a Synthetic Leaf Dataset of 100,000 synthetic leaf images on millimeter paper, each with semantic masks and surface area labels. This dataset provides a resource for leaf morphology analysis primarily aimed at beech and oak leaves. We evaluate the applicability of the dataset by training machine learning models for leaf surface area prediction and semantic segmentation, using real images for validation. Our validation shows that these models can be trained to predict leaf surface area with a relative error not greater than an average human annotator. LAESI also provides an efficient framework based on 3D procedural models and generative AI for the large-scale, controllable generation of data with potential further applications in agriculture and biology. We evaluate the inclusion of generative AI in our procedural data generation pipeline and show how data filtering based on annotation consistency results in datasets which allow training the highest performing vision models.

arXiv

Generating Diverse Agricultural Data for Vision-Based Farming Applications

M. Cieslak, U. Govindarajan, A. Garcia, A. Chandrashekar, T. Hädrich, A. Mendoza-Drosik, D. L. Michels, S. Pirk, C.-C. Fu, and W. Pałubicki.

Challenges & Opportunities for Computer Vision in Agriculture (Agriculture-Vision 2024), IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2024).

We present a specialized procedural model for generating synthetic agricultural scenes, focusing on soybean crops, along with various weeds. This model is capable of simulating distinct growth stages of these plants, diverse soil conditions, and randomized field arrangements under varying lighting conditions. The integration of real-world textures and environmental factors into the procedural generation process enhances the photorealism and applicability of the synthetic data. Our dataset includes 12,000 images with semantic labels, offering a comprehensive resource for computer vision tasks in precision agriculture, such as semantic segmentation for autonomous weed control. We validate our model's effectiveness by comparing the synthetic data against real agricultural images, demonstrating its potential to significantly augment training data for machine learning models in agriculture. This approach not only provides a cost-effective solution for generating high-quality, diverse data but also addresses specific needs in agricultural vision tasks that are not fully covered by general-purpose models.

arXiv

Gazebo Plants: Simulating Plant-Robot Interaction with Cosserat Rods

J. Deng, S. Marri, J. Klein, W. Pałubicki, S. Pirk, G. Chowdhary, and D. L. Michels.

Robotics and Sustainability, IEEE International Conference on Robotics and Automation (ICRA 2024).

Robotic harvesting has the potential to positively impact agricultural productivity, reduce costs, improve food quality, enhance sustainability, and to address labor shortage. In the rapidly advancing field of agricultural robotics, the necessity of training robots in a virtual environment has become essential. Generating training data to automatize the underlying computer vision tasks such as image segmentation, object detection and classification, also heavily relies on such virtual environments as synthetic data is often required to overcome the shortage and lack of variety of real data sets. However, physics engines commonly employed within the robotics community, such as ODE, Simbody, Bullet, and DART, primarily support motion and collision interaction of rigid bodies. This inherent limitation hinders experimentation and progress in handling non-rigid objects such as plants and crops. In this contribution, we present a plugin for the Gazebo simulation platform based on Cosserat rods to model plant motion. It enables the simulation of plants and their interaction with the environment. We demonstrate that, using our plugin, users can conduct harvesting simulations in Gazebo by simulating a robotic arm picking fruits and achieve results comparable to real-world experiments.

arXiv

DigitalSalon: A Fast Simulator for Dense Hair via Augmented Mass-Spring Model

J. A. Amador Herrera, Y. Zhou, X. Sun, Z. Su, C. He, S. Pirk, and D. L. Michels.

Preprint (10754/697970), KAUST Repository (2024).

We propose a novel Augmented Mass-Spring (AMS) model for real-time simulation of hair at strand level. Our approach considers the traditional edge, bending, and torsional degrees of freedom in mass-spring systems, but incorporates an additional one-way biphasic coupling with a ghost rest-shape configuration. Trough multiple evaluation experiments with varied hairstyles and dynamical settings, we show that AMS improves the stability of the system, and provides an emergent pseudo-stiffness which, in turn, alleviates sagging effects, helps preserving the global hair geometry, and enables the simulation of non-Hookean effects during intense hair motion. Using an heptadiagonal decomposition of the resulting matrix, our approach provides the efficiency advantages of mass-spring systems over more complex constitutive hair models, while enabling a more robust simulation of multiple hair configurations, including facial hair. Finally, our results demonstrate that our framework enables the generation and editing of simulation-ready hair assets in real-time.

KAUST Repository Video

On the Algorithmic Recovering of Coefficients in Linearizable Differential Equations

D. A. Lyakhov and D. L. Michels.

arXiv:2404.01798, Cornell University Library (2024).

We investigate the problem of recovering coefficients in scalar nonlinear ordinary differential equations that can be exactly linearized. This contribution builds upon prior work by Lyakhov, Gerdt, and Michels, which focused on obtaining a linearizability certificate through point transformations. Our focus is on quasi-linear equations, specifically those solved for the highest derivative with a rational dependence on the variables involved. Our novel algorithm for coefficient recovery relies on basic operations on Lie algebras, such as computing the derived algebra and the dimension of the symmetry algebra. This algorithmic approach is efficient, although finding the linearization transformation necessitates computing at least one solution of the corresponding Bluman-Kumei equation system.

arXiv

On Classification Problems of Helical Surfaces and Flexible Polyhedra

Dissertation of Y. Liu. Doctoral Advisor: D. L. Michels.
Committee Members: H. Pottmann, M. Hadwiger, J. Schicho.

Applied Mathematics and Computational Sciences Program,
CEMSE Division, KAUST (2024).

Mathematics perennially explores classification problems, with a focus on the intriguing task of categorizing geometric structures. This type of classification can take a straightforward approach, relying on simple descriptions of shapes, or with an in-depth consideration of their determining well-hidden algebraic structures. This dissertation is dedicated to the classification of two specific geometric structures. First, helical surfaces with a constant ratio of principal curvatures (CRPC) are studied. A proper generating curve of such a surface is expected so that the surface can be parameterized as simply as possible. The analysis of the smoothness and the singularity of the surface allows us to glue pieces of locally parameterized surfaces to a global one. This results in a shape classification of helical CRPC surfaces. The second part tackles the famous classification problem of flexible Kokotsakis polyhedra given by discrete 3×3 meshes. During the flexion of such a mesh, the relations among its rotating angles are transformed into polynomials. Therefore, concepts arising from the theory of polynomials are utilized such as field extension and factorization in order to classify the flexible meshes by their corresponding polynomials. Conversely, by setting up the polynomials, we can recover the shape information in angles and construct a flexible mesh of each class.

KAUST Repository

Flexible Kokotsakis Meshes with Skew Faces: Generalization of the Orthodiagonal Involutive Type

A. Aikyn, Y. Liu, D. A. Lyakhov, F. Rist, H. Pottmann, and D. L. Michels.

Computer-Aided Design, Elsevier (2024).

In this paper, we introduce and study a remarkable class of mechanisms formed by a 3×3 arrangement of rigid quadrilateral faces with revolute joints at the common edges. In contrast to the well-studied Kokotsakis meshes with a quadrangular base, we do not assume the planarity of the quadrilateral faces. Our mechanisms are a generalization of Izmestiev's orthodiagonal involutive type of Kokotsakis meshes formed by planar quadrilateral faces. The importance of this Izmestiev class is undisputed as it represents the first known flexible discrete surface – T-nets – which has been constructed by Graf and Sauer. Our algebraic approach yields a complete characterization of all flexible 3×3 quad meshes of the orthodiagonal involutive type up to some degenerated cases. It is shown that one has a maximum of 8 degrees of freedom to construct such mechanisms. This is illustrated by several examples, including cases which could not be realized using planar faces. We demonstrate the practical realization of the proposed mechanisms by building a physical prototype using stainless steel. In contrast to plastic prototype fabrication, we avoid large tolerances and inherent flexibility.

Project Page

Deep Aramaic: Towards a Synthetic Data Paradigm Enabling Machine Learning in Epigraphy

A. C. Aioanei, R. Hunziker-Rodewald, K. M. Klein, and D. L. Michels.

PLOS ONE, Public Library of Science (2024).

Epigraphy is witnessing a growing integration of artificial intelligence, notably through its subfield of machine learning (ML), especially in tasks like extracting insights from ancient inscriptions. However, scarce labeled data for training ML algorithms severely limits current techniques, especially for ancient scripts like Old Aramaic. Our research pioneers an innovative methodology for generating synthetic training data tailored to Old Aramaic letters. Our pipeline synthesizes photo-realistic Aramaic letter datasets, incorporating textural features, lighting, damage, and augmentations to mimic real-world inscription diversity. Despite minimal real examples, we engineer a dataset of 250000 training and 25000 validation images covering the 22 letter classes in the Aramaic alphabet. This comprehensive corpus provides a robust volume of data for training a residual neural network (ResNet) to classify highly degraded Aramaic letters. The ResNet model demonstrates 95% accuracy in classifying real images from the 8th century BCE Hadad statue inscription (KAI 214). Additional experiments validate performance on varying materials and styles, proving effective generalization. Our results validate the model's capabilities in handling diverse real-world scenarios, proving the viability of our synthetic data approach and avoiding the dependence on scarce training data that has constrained epigraphic analysis. Our innovative framework elevates interpretation accuracy on damaged inscriptions, thus enhancing knowledge extraction from these historical resources.

PLOS ONE

Zero-Level-Set Encoder for Neural Distance Fields

S. R. Jeske, J. Klein, D. L. Michels, and J. Bender.

arXiv:2310.06644, Cornell University Library (2024).

Neural shape representation generally refers to representing 3D geometry using neural networks, e.g., to compute a signed distance or occupancy value at a specific spatial position. In this paper, we present a novel encoder-decoder neural network for embedding 3D shapes in a single forward pass. Our architecture is based on a multi-scale hybrid system incorporating graph-based and voxel-based components, as well as a continuously differentiable decoder. Furthermore, the network is trained to solve the Eikonal equation and only requires knowledge of the zero-level set for training and inference. This means that in contrast to most previous work, our network is able to output valid signed distance fields without explicit prior knowledge of non-zero distance values or shape occupancy. We further propose a modification of the loss function in case that surface normals are not well defined, e.g., in the context of non-watertight surfaces and non-manifold geometry. Overall, this can help reduce the computational overhead of training and evaluating neural distance fields, as well as enabling the application to difficult shapes. We finally demonstrate the efficacy, generalizability and scalability of our method on datasets consisting of deforming shapes, both based on simulated data and raw 3D scans. We further show single-class and multi-class encoding, on both fixed and variable vertex-count inputs, showcasing a wide range of possible applications.

arXiv

On the Algorithmic Verification of Nonlinear Superposition for Systems of First Order Ordinary Differential Equations

V. Treumova, D. A. Lyakhov, and D. L. Michels.

arXiv:2401.17012, Cornell University Library (2024).

This paper belongs to a group of work in the intersection of symbolic computation and group analysis aiming for the symbolic analysis of differential equations. The goal is to extract important properties without finding the explicit general solution. In this contribution, we introduce the algorithmic verification of nonlinear superposition properties and its implementation. More exactly, for a system of nonlinear ordinary differential equations of first order with a polynomial right-hand side, we check if the differential system admits a general solution by means of a superposition rule and a certain number of particular solutions. It is based on the theory of Newton polytopes and associated symbolic computation. The developed method provides the basis for the identification of nonlinear superpositions within a given system and for the construction of numerical methods which preserve important algebraic properties at the numerical level.

arXiv

Indirect Interaction of ¹³C Nuclear Spins in Diamond with NV Centers: Simulation of the Full J-coupling Tensorse

A. Nizovtsev, A. Pushkarchuk, S. Kuten, D. L. Michels, D. A. Lyakhov, N. Kargin, and S. Kilin.

Frontiers in Quantum Science and Technology, Frontiers Media (2024).

Recent experiments on the detection, imaging, characterization and control of multiple ¹³C nuclear spins, as well as of individual ¹³C-¹³C dimers in diamond using a single nitrogen-vacancy (NV) center as a sensor, along with the impressive progress in increasing the spectral resolution of such sensor (up to sub-Hertz), have created a request for detailed knowledge of all possible spin interactions in the studied systems. Here, we focus on the indirect interaction (J-coupling) of ¹³C nuclear spins in diamond, which was not previously taken into account in studies of NV centers. Using two different levels of the density functional theory (DFT), we simulated the full tensors ⁿJ_KL (K, L = X, Y, Z), describing n-bond J-coupling of nuclear spins ¹³C in H-terminated diamond-like clusters C₁₀H₁₆ (adamantane) and C₃₅H₃₆, as well as in the cluster C₃₃[NV^-]H₃₆ hosting the negatively charged NV^- center. We found that, in addition to the usually considered isotropic scalar ⁿJ-coupling constant, the anisotropic contributions to the ⁿJ-coupling tensor are essential. We also showed that the presence of the NV center affects the J-coupling characteristics, especially in the case of ¹³C–¹³C pairs located near the vacancy of the NV center.

Front. Quantum Sci. Technol.

Effects of the Nature of Donor Substituents on the Photophysical and Electroluminescent Properties of Derivatives of Perfluorobiphenyl: Donor-Acceptor versus Donor-Acceptor-Donor Types of AIEE/TADF Emitters

I. Hladka, Y. Danyliv, M. Stanitska, O. Bezvikonnyi, D. Y. Volyniuk, R. Lytvyn, Y. Horak, V. Matulis, D. A. Lyakhov, D. L. Michels, P. Y. Stakhira, and J. V. Grazulevicius.

Journal of Materials Chemistry C, Royal Society of Chemistry (2024).

The synthesis and properties of the group of organic electroactive compounds based on electron-deficient perfluorobiphenyl (PFBP) are described. The influence of electron-donating substituents on the properties of PFBF is analyzed. A comparative study of the derivatives with donor-acceptor versus donor-acceptor-donor molecular architectures is reported. The geometry and electronic characteristics of compounds in the ground and the excited states were studied within density functional theory. It is shown that for all the studied compounds S0→S1 excitations are characterized by intramolecular charge transfer from electron-donating phenothiazine, phenoxazine or furoindole moieties to electron-accepting PFBP moiety. The differences and similarities of the absorption and emission spectra of the compounds and aggregation-induced emission enhancement are explained in terms of their geometrical and electronic structure. The compounds are characterized by the relatively high values of temperature of 5% weight loss reaching 333°C. The synthesized perfluorobiphenyl derivatives exhibit photoluminescence in the full visible spectrum covering from deep-blue to red colors. The compounds containing phenothiazine or phenoxazine fragments are characterised by the combination of thermally activated delayed fluorescence and aggregation induced emission enhancement. The ionization potentials of the solid films of the compounds estimated by photoelectron emission spectrometry range from 5.67 to 5.95 eV. Phenoxazine-based compound exhibit time-of-flight hole mobility of 8.78×10^-5 cm²/V·s at the electric field of 7.22×10⁵ V/cm. Green organic light emitting diode based on the derivative with two phenoxazine donor units shows external quantum efficiency of 11.5%.

J. Mater. Chem. C.

On the Algebraic Classification of Non-singular Flexible Kokotsakis Polyhedra

Y. Liu, Y. Ouyang, and D. L. Michels.

arXiv:2401.14291, Cornell University Library (2024).

Across various scientific and engineering domains, a growing interest in flexible and deployable structures is becoming evident. These structures facilitate seamless transitions between distinct states of shape and find broad applicability ranging from robotics and solar cells to meta-materials and architecture. In this contribution, we study a class of mechanisms known as Kokotsakis polyhedra with a quadrangular base. These are 3×3 quadrilateral meshes whose faces are rigid bodies and joined by hinges at the common edges. Compared to prior work, the quadrilateral faces do not have to be planar. In general, such meshes are not flexible, and the problem of finding and classifying the flexible ones is old, but until now largely unsolved. It appears that the tangent values of the dihedral angles between different faces are algebraically related through polynomials. Specifically, by fixing one angle as a parameter, the others can be parameterized algebraically and hence belong to an extended rational function field of the parameter. We use this approach to characterize shape restrictions resulting in flexible polyhedra.

arXiv

A Physically-inspired Approach to the Simulation of Plant Wilting

F. Maggioli, J. Klein, T. Hädrich, E. Rodolà, W. Pałubicki, S. Pirk, and D. L. Michels.

SIGGRAPH Asia 2023 Technical Paper, ACM (2023).

Plants are among the most complex objects to be modeled in computer graphics. While a large body of work is concerned with structural modeling and the dynamic reaction to external forces, our work focuses on the dynamic deformation caused by plant internal wilting processes. To this end, we motivate the simulation of water transport inside the plant which is a key driver of the wilting process. We then map the change of water content in individual plant parts to branch stiffness values and obtain the wilted plant shape through a position based dynamics simulation. We show, that our approach can recreated measured wilting processes and does so with a higher fidelity than approaches ignoring the internal water flow. Realistic plant wilting is not only important in a computer graphics context but can also aid the development of machine learning algorithms in agricultural applications through the generation of synthetic training data.

Project Page

Comparative DFT Study of Small Anionic Silver and Copper Clusters. Evolution of Structure and Physicochemical Properties

V. Matulis, O. Ivashkevich, D. Lappo, D. A. Lyakhov, and D. L. Michels.

The Journal of Physical Chemistry C, American Chemical Society (2023).

Based on both total energy calculations and comparison of experimental and calculated characteristics of photoelectron spectrum (PHES), the structural assignment of clusters Ag_n^- (n=13–16) and Cu_m^- (m=14–17) has been made using the density functional theory (DFT) model with our previously developed S2LYP functional. A comparative study of size dependence of geometry, electronic structure and physicochemical properties has been carried out for series of anionic silver and copper clusters containing up to 20 atoms. For the cases when two isomers contribute to the experimental PHES, the isomerization barriers and molar ratio of isomers were estimated. It has been shown that the geometry and the properties that are determined mainly by ns-derived electronic states are similar for copper and silver clusters. However, due to larger contribution of (n-1)d-electrons to the chemical bond, the potential energy surface of copper clusters is less smooth, and these clusters are characterized by higher isomerization energies compared to silver clusters. The isomerization energies of clusters and the number of isomers with similar energies increase with enlarging cluster size. Thus, clusters containing less than 20 atoms easily overcome the barriers of intramolecular isomerization (i.e., behave like liquids). However, it is expected that cooled clusters containing several tens of atoms will have a rigid geometry due to high intramolecular isomerization energies.

ACS J. Phys. Chem. C

Effect of the Isotiazole Adjuvants in Combination with Cisplatin in Chemotherapy of Neuroepithelial Tumors: Experimental Results and Modeling

V. Potkin, A. Pushkarchuk, A. Zamaro, H. Zhou, S. Kilin, S. Petkevich, I. Kolesnik, D. L. Michels, D. A. Lyakhov, and V. A. Kulchitsky.

Scientific Reports, Nature Research (2023).

Chemotherapy is one of the main treatment options for cancer, but it is usually accompanied with negative side effects. The classical drugs combination with synergistic adjuvants can be the solution to this problem, allowing reducing therapeutic dose. Elucidating the mechanism of adjuvant action is of key importance for the selection of the optimal agent. Here we examine the system drug-adjuvant to explain the observed effect in practice. We used the first line drug cisplatin. Morpholinium and 4-methylpiperazinium 4,5-dichloro isothiazol-3-carboxylates were selected as adjuvants. The study of the cisplatin-adjuvant system was carried out by quantum chemical modeling using DFT. It turned out that adjuvants form conjugates with cisplatin that lead to the relocation of frontier molecular orbitals as well as increase of conjugate’s dipole moment. It resulted in change of the interaction character with DNA and increase of the bioactivity of the system. The data obtained are the basis for expanding the studies to include other drugs and adjuvants. Oncologists will have opportunity to use “classical” chemotherapy drugs in combination with synergists for those patients who have not been previously recommended to such a treatment because of pronounced toxic side effects.

Nature Scientific Reports

Rhizomorph: The Coordinated Function of Shoots and Roots

B. Li, J. Klein, D. L. Michels, B. Benes, S. Pirk, and W. Pałubicki.

ACM Transactions on Graphics (SIGGRAPH 2023), ACM (2023).

Computer graphics has dedicated a considerable amount of effort to generating realistic models of trees and plants. Many existing methods leverage procedural modeling algorithms – that often consider biological findings – to generate branching structures of individual trees. While the realism of tree models generated by these algorithms steadily increases, most approaches neglect to model the root system of trees. However, the root system not only adds to the visual realism of tree models but also plays an important role in the development of trees. In this paper, we advance tree modeling in the following ways: First, we define a physically-plausible soil model to simulate resource gradients, such as water and nutrients. Second, we propose a novel developmental procedural model for tree roots that enables us to emergently develop root systems that adapt to various soil types. Third, we define long-distance signaling to coordinate the development of shoots and roots. We show that our advanced procedural model of tree development enables – for the first time – the generation of trees with their root systems.

Project Page

UrbanFlow: Designing Comfortable Outdoor Areas

D. Liu, F. Rist, and D. L. Michels.

Symposium on Simulation for Architecture and Urban Design (SimAUD 2023), ANNSIM (2023).

Design decisions in urban planning have to be made with particular carefulness as the resulting constraints are binding for the whole architectural design that follows. In this context, investigating and optimizing the airflow in urban environments is critical to design comfortable outdoor areas as unwanted effects such as windy areas and the formation of heat pockets have to be avoided. Our UrbanFlow framework enables interactive architectural design allowing for decision making based on simulating urban flow. Compared to real-time fluid flow simulation, enabling interactive architecture design poses an even higher computational efficiency challenge as evaluating a design by simulation usually requires hundreds of time steps. This is addressed based on a highly efficient Eulerian fluid simulator in which we incorporate a unified porosity model which is devised to encode digital urban models containing objects such as buildings and trees. UrbanFlow is equipped with an optimization routine enabling the direct computation of design adaptations improving livability and comfort for given parameterized architectural designs. To ensure convergence of the optimization process, instead of the classical Navier-Stokes equations, the Reynolds-averaged Navier-Stokes equations are solved as this can be done on a relatively coarse grid and allows for the decoupling of the effects of turbulent eddies which are taken into account using a separate turbulence model. As we demonstrate on a real-world example taken from an ongoing architectural competition, this results in a fast convergence of the optimization process which computes a design adaptation avoiding heat pockets as well as uncomfortable windy areas. UrbanFlow exploits the power of the graphics processing unit running on a single desktop computer as it is widely available in most architectural and urban planning firms. We also provide a plugin which enable its use with the Rhinoceros 3D software widely used in computational design and architecture.

Project Page

DFT Study of the NO Reduction Mechanism on Ag/γ-Al₂O₃

E. G. Ragoyja, V. E. Matulis, O. A. Ivashkevich, D. A. Lyakhov, and D. L. Michels.

The Journal of Physical Chemistry C, American Chemical Society (2023).

NO catalytic reduction on Ag/γ-Al₂O₃ catalysts is a very promising process from the industrial and ecological perspective. Details of its mechanism, which are still not fully clear, have great importance for a deep understanding of various heterogeneous NO reduction processes. In this work, a thorough theoretical study of the mechanism of NO reduction on the Ag/γ-Al₂O₃ catalyst is carried out. Two schemes of the mechanism for catalysts with different silver concentrations and, subsequently, with different reaction centers, are proposed. For the catalyst with a low silver content, a mechanism based on isocyanate species is proposed, while for catalysts with a high silver content, key intermediates are adsorbed NO dimers. The thermodynamic and kinetic feasibility of the proposed schemes is confirmed by density functional theory calculations of the reaction pathways both on isolated silver clusters and on the catalyst surface. These schemes explain the experimentally observed N₂O or N₂ prevalence in the reaction products. Calculations of the catalyst surface are carried out within the original three-layer embedded cluster model, which provides accurate results of calculations of vibrational frequencies, geometries, and energy characteristics. The process of silver particle migration along the catalyst surface is studied. Energy barriers of migration are estimated. The influence of the catalytic center nature and presence of the aluminum oxide support on NO, N₂, and N₂O adsorption processes are studied, and the corresponding adsorption energies are calculated.

ACS J. Phys. Chem. C

Mechanism of Bubbles Formation and Anomalous Phase Separation in the CoNiP System

M. I. Panasyuk, T. I. Zubar, T. I. Usovich, D. I. Tishkevich, O. D. Kanafyev, V. A. Fedkin, A. N. Kotelnikova, S. V. Trukhanov, D. L. Michels, D. A. Lyakhov, T. N. Vershinina, V. M. Fedosyuk, and A. V. Trukhanov.

Scientific Reports, Nature Research (2023).

This study announces the anomalous phase separation in CoNiP alloy electroplating. The observed phenomenon of the formation of magnetic bubbles was described for the first time for this triple CoNiP system. This study briefly covers all stages of magnetic bubble formation, starting from the formation of an amorphous phosphor-rich sublayer, followed by nucleation centers, and finally cobalt-rich bubbles. An explanation for the anomalous mechanism of bubble formation was found in the effects of additives and the phenomena of depolarization and superpolarization.

Nature Scientific Reports

Recognizing the Shape and Size of Tundra Lakes in Synthetic Aperture Radar (SAR) Images Using Deep Learning Segmentation

D. Demchev, I. Sudakow, A. Khodos, I. Abramova, D. A. Lyakhov, and D. L. Michels.

Remote Sensing, MDPI (2023).

Permafrost tundra contains more than twice as much carbon as is currently in the atmosphere, and it is warming six times as fast as the global mean. Tundra lakes dynamics is a robust indicator of global climate processes, and is still not well understood. Satellite data, particularly, from synthetic aperture radar (SAR) is a suitable tool for tundra lakes recognition and monitoring of their changes. However, manual analysis of lake boundaries can be slow and inefficient; therefore, reliable automated algorithms are required. To address this issue, we propose a two-stage approach, comprising instance deep-learning-based segmentation by U-Net, followed by semantic segmentation based on a watershed algorithm for separating touching and overlapping lakes. Implementation of this concept is essential for accurate sizes and shapes estimation of an individual lake. Here, we evaluated the performance of the proposed approach on lakes, manually extracted from tens of C-band SAR images from Sentinel-1, which were collected in the Yamal Peninsula and Alaska areas in the summer months of 2015–2022. An accuracy of 0.73, in terms of the Jaccard similarity index, was achieved. The lake’s perimeter, area and fractal sizes were estimated, based on the algorithm framework output from hundreds of SAR images. It was recognized as lognormal distributed. The evaluation of the results indicated the efficiency of the proposed approach for accurate automatic estimation of tundra lake shapes and sizes, and its potential to be used for further studies on tundra lake dynamics, in the context of global climate change, aimed at revealing new factors that could cause the planet to warm or cool.

Remote Sensing

Helical Surfaces with a Constant Ratio of Principal Curvatures

Y. Liu, O. Pirahmad, H. Wang, D. L. Michels, and H. Pottmann.

Contributions to Algebra and Geometry, Springer (2022).

We determine all helical surfaces in three-dimensional Euclidean space which possess a constant ratio a:=κ₁/κ₂ of principal curvatures (CRPC surfaces), thus providing the first explicit CRPC surfaces beyond the known rotational ones. Our approach is based on the involution of conjugate surface tangents and on well chosen generating profiles such that the characterizing differential equation is sufficiently simple to be solved explicitly. We analyze the resulting surfaces, their behavior at singularities that occur for a>0, and provide an overview of the possible shapes.

Project Page

A Current Loop Model for the Fast Simulation of Ferrofluids

H. Shao, L. Huang, and D. L. Michels.

IEEE Transactions on Visualization and Computer Graphics (TVCG 2022), IEEE (2022).

Ferrofluids are oil-based liquids containing magnetic particles that interact with magnetic fields without solidifying. Leveraging the exploration of new applications of these promising materials (such as in optics, medicine and engineering) requires high fidelity modeling and simulation capabilities in order to accurately explore ferrofluids in silico. While recent work addressed the macroscopic simulation of large-scale ferrofluids using smoothed-particle hydrodynamics (SPH), such simulations are computationally expensive. In their work, the Kelvin force model has been used to calculate interactions between different SPH particles. The application of this model results in a force pointing outwards with respect to the fluid surface causing significant levitation problems. This drawback limits the application of more advanced and efficient SPH frameworks such as divergence-free SPH (DFSPH) or implicit incompressible SPH (IISPH). In this contribution, we propose a current loop magnetic force model which enables the fast macroscopic simulation of ferrofluids. Our new force model results in a force term pointing inwards allowing for more stable and fast simulations of ferrofluids using DFSPH and IISPH.

Project Page

ACM SIGGRAPH / Eurographics Symposium of Computer Animation 2022

D. L. Michels and S. Pirk (Eds.).

Computer Graphics Forum (SCA 2022), Wiley (2022).

The origin of computer animation dates back at least to the early 20th century when pioneers such as the cartoonist Winsor McCay started to generate sequences of animated images. McCay's 1914 work Gertie the Dinosaur – widely considered as a breakthrough establishing the new genre of animated film – has been the first to use animation loops, keyframes, and registration marks. With the advent of the digital era and the attendant increase of digital computers, animation techniques developed rapidly and became more sophisticated. In the 1990s, the first feature-length film made entirely on computers, Toy Story, has been produced by Pixar on behalf of Disney for the cinema.
Today, the creation of impressive three-dimensional scenes and deceptively real special effects are state-of-the-art. These developments would not have been possible without dedicated research in this area, and therefore it is not surprising that computer animation has always been at the core of the computer graphics community and advances have been primarily presented at the main North American graphics conference SIGGRAPH and at its European counterpart Eurographics.
In 2002, the community established an animation-focused academic venue next to the flagship SIGGRAPH and Eurographics conferences: This year, we celebrate the 20th anniversary of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA) and its 21st edition. SCA 2022 takes place as a hybrid symposium hosted at Durham University with the support of its chairs and a diverse team of 55 experts from leading institutions serving on the international program committee. Moreover, the list of SCA's sponsors comprising Adobe, Disney Research Studios, KAUST Visual Computing Center, and Google reflects the industrial need of the presented topics which have to be understood as animation and simulation in a broad sense, defined as computation dealing with time-varying phenomena. While at the beginning of computer animation, the focus has almost exclusively been on movies and later on games, today the spectrum ranges from controlling smart agents in robotics over complex autonomous driving simulators to cloth animation for virtual try-on applications in e-commerce. Computer animation has truly become a key enabling technology for a diverse set of applications spanning digital services, medicine, robotics, consumer electronics and entertainment, as well as scientific discovery, to name just a few. Ongoing developments in virtual and augmented reality as well as in the context of the so-called metaverse reinforce this trend.
The SCA community has been and will be at the forefront of these developments and the conference will continue to be the premier forum for innovations in computer animation and simulation. This is reflected by this year's 78 submitted and 30 accepted academic papers corresponding to the highest number of submissions as well as the most accepted papers since ten years. With an acceptance rate of 38.5%, we are slightly below the average acceptance rate of the previous ten SCA conferences indicating that the increase of papers did not compromise quality. We are more than happy to present this year's papers included in this issue of Eurographics' flagship journal Computer Graphics Forum to the community.

CGF

A Fast Unsmoothed Aggregation Algebraic Multigrid Framework for the Large-Scale Simulation of Incompressible Flow

H. Shao, L. Huang, and D. L. Michels.

ACM Transactions on Graphics (SIGGRAPH 2022), ACM (2022).

Multigrid methods are quite efficient for solving the pressure Poisson equation in simulations of incompressible flow. However, for viscous liquids, geometric multigrid turned out to be less efficient for solving the variational viscosity equation. In this contribution, we develop an Unsmoothed Aggregation Algebraic MultiGrid (UAAMG) method with a multi-color Gauss-Seidel smoother, which consistently solves the variational viscosity equation in a few iterations for various material parameters. Moreover, we augment the OpenVDB data structure with Intel SIMD intrinsic functions to perform the sparse matrix-vector multiplication efficiently on all multigrid levels. With the above contributions, our framework is 2.0 to 14.6 times faster compared to the state-of-the-art adaptive octree solver in commercial software for the large-scale simulation of both non-viscous and viscous flow.

Project Page

Ecoclimates: Climate-response Modeling of Vegetation

W. Pałubicki, M. Makowski, W. Gajda, T. Hädrich, D. L. Michels, and S. Pirk.

ACM Transactions on Graphics (SIGGRAPH 2022), ACM (2022).

One of the greatest challenges to mankind is understanding the underlying principles of climate change. Over the last years, the role of forests in climate change has received increased attention. This is due to the observation that not only the atmosphere has a principal impact on vegetation growth but also that vegetation is contributing to local variations of weather resulting in diverse microclimates. The interconnection of plant ecosystems and weather is described and studied as ecoclimates. In this work we take steps towards simulating ecoclimates by modeling the feedback loops between vegetation, soil, and atmosphere. This allows us to realistically capture vegetation response to climate change. In contrast to existing methods that only describe the climate at a global scale, our model aims at simulating local variations of climate. Specifically, we model tree growth interactively in response to gradients of water, temperature and light. As a result, we are able to capture a range of ecoclimate phenomena that have not been modeled before, including geomorphic controls, forest edge effects, the Foehn effect and spatial vegetation patterning. To validate the plausibility of our method we conduct a comparative analysis to studies from ecology and climatology. Consequently, our method advances the state-of-the-art of generating highly realistic outdoor landscapes of vegetation.

Project Page

Fluids, Threads and Fibers: Towards High Performance Physics-based Modeling and Simulation

Dissertation of H. Shao. Doctoral Advisor: D. L. Michels.
Committee Members: D. E. Keyes, H. Pottmann, N. Thuerey.

Applied Mathematics and Computational Sciences Program,
CEMSE Division, KAUST (2022).

Accelerating physics-based simulations has been an evergreen topic across different scientific communities. This dissertation is devoted to this subject addressing bottlenecks in state-of-the-art approaches to the simulation of fluids of large-scale scenes, viscous threads, magnetic fluids, and the simulation of fibers and thin structures. The contributions within the thesis are rooted in mathematical modeling and numerical simulation as well as in machine learning.
The first part deals with the simulation of incompressible flow in a multigrid fashion. For the variational viscous equation, geometric multigrid is inefficient. An Unsmoothed Aggregation Algebraic Multigrid method is devised with a multi-color Gauss-Seidel smoother, which consistently solves this equation in a few iterations for various material parameters. This framework is 2.0 to 14.6 times faster compared to the state-of-the-art adaptive octree solver in commercial software for the large-scale simulation of both non-viscous and viscous flow.
In the second part, a new physical model is devised to accelerate the macroscopic simulation of magnetic fluids. Previous work is based on the classical Smoothed-Particle Hydrodynamics (SPH) method and a Kelvin force model. Unfortunately, this model results in a force pointing outwards causing significant levitation problems limiting the application of more advanced SPH frameworks such as Divergence-Free SPH (DFSPH) or Implicit Incompressible SPH (IISPH). This shortcoming has been addressed with this new current loop magnetic force model resulting in more stable and fast simulations of magnetic fluids using DFSPH and IISPH.
Following a different trajectory, the third part of this thesis aims for the acceleration of iterative solvers widely used to accurately simulate physical systems. We speedup the simulation for rod dynamics with Graph Networks by predicting the initial guesses to reduce the number of iterations for the constraint projection part of a Position-based Dynamics solver. Compared to existing methods, this approach guarantees long-term stability and therefore leads to more accurate solutions.

KAUST Repository

DCGrid: An Adaptive Grid Structure for Memory-Constrained Fluid Simulation on the GPU

W. Raateland, T. Hädrich, J. A. Amador Herrera, D. T. Banuti, W. Pałubicki, S. Pirk, K. Hildebrandt, and D. L. Michels.

Proceedings of the ACM on Computer Graphics and Interactive Techniques (I3D), ACM (2022).

We introduce Dynamic Constrained Grid (DCGrid), a hierarchical and adaptive grid structure for fluid simulation combined with a scheme for effectively managing the grid adaptations. DCGrid is designed to be implemented on the GPU and used in high-performance simulations. Specifically, it allows us to efficiently vary and adjust the grid resolution across the spatial domain and to rapidly evaluate local stencils and individual cells in a GPU implementation. A special feature of DCGrid is that the control of the grid adaption is modeled as an optimization under a constraint on the maximum available memory, which addresses the memory limitations in GPU-based simulation. To further advance the use of DCGrid in high-performance simulations, we complement DCGrid with an efficient scheme for approximating collisions between fluids and static solids on cells with different resolutions. We demonstrate the effectiveness of DCGrid for smoke flows and complex cloud simulations in which terrain-atmosphere interaction requires working with cells of varying resolution and rapidly changing conditions. Finally, we compare the performance of DCGrid to that of alternative adaptive grid structures.

Project Page

Mechanisms of Elastoplastic Deformation and their Effect on Hardness of Nanogranular Ni-Fe Coatings

T. I. Zubar, V. M. Fedosyuk, D. I. Tishkevich, M. I. Panasyuk, O. D. Kanafyev, A. Kozlovskiy, M. Zdorovets, D. L. Michels, D. A. Lyakhov, and A. V. Trukhanov.

International Journal of Mechanical Sciences, Elsevier (2022).

This article contains the study of correlation between the microstructure, mechanical properties and mechanisms of elastoplastic deformation of Ni-Fe coatings that were grown in five electrodeposition modes and had fundamentally different microstructures. A nonlinear change in hardness was detected using nanoindentation. Explanation of the abnormal change in hardness was found in the nature of the relaxation method of elastoplastic energy under load. It is shown that the deformation of coatings with a grain size of 100 nm or more occurs due to dislocation slip. A decrease in grain size leads to the predominance of deformation due to rotations and sliding of grains, as well as surface and grain boundary diffusion. The effect of deformation mechanisms on the nanoscale hardness of Ni-Fe coatings was established. Full hardening of the coatings (both in the bulk and on the surface) was achieved while maintaining the balance of three mechanisms of elastoplastic deformation in the sample. Unique coatings consisting of two fractions of grains (70% of nano-grains and 30% of their agglomerates) demonstrate high crack resistance and full-depth hardening up to H = 7.4 GPa due to the release of deformation energy for amorphization and agglomeration of nanograins.

IJMS

RLSS: A Deep Reinforcement Learning Algorithm for Sequential Scene Generation

A. Ostonov, P. Wonka, and D. L. Michels.

IEEE Winter Conference on Applications of Computer Vision (WACV 2022), IEEE (2022).

We present RLSS: a reinforcement learning algorithm for sequential scene generation. This is based on employing the proximal policy optimization (PPO) algorithm for generative problems. In particular, we consider how to effectively reduce the action space by including a greedy search algorithm in the learning process. Our experiments demonstrate that our method converges for a relatively large number of actions and learns to generate scenes with predefined design objectives. This approach is placing objects iteratively in the virtual scene. In each step, the network chooses which objects to place and selects positions which result in maximal reward. A high reward is assigned if the last action resulted in desired properties whereas the violation of constraints is penalized. We demonstrate the capability of our method to generate plausible and diverse scenes efficiently by solving indoor planning problems and generating Angry Birds levels.

WACV

Weatherscapes: Nowcasting Heat Transfer and Water Continuity

J. A. Amador Herrera, T. Hädrich, W. Pałubicki, D. T. Banuti, S. Pirk, and D. L. Michels.

ACM Transactions on Graphics (SIGGRAPH Asia 2021), ACM (2021).

Due to the complex interplay of various meteorological phenomena, simulating weather is a challenging and open research problem. In this contribution, we propose a novel physics-based model that enables simulating weather at interactive rates. By considering atmosphere and pedosphere we can define the hydrologic cycle – and consequently weather – in unprecedented detail. Specifically, our model captures different warm and cold clouds, such as mammatus, hole-punch, multi-layer, and cumulonimbus clouds as well as their dynamic transitions. We also model different precipitation types, such as rain, snow, and graupel by introducing a comprehensive microphysics scheme. The Wegener-Bergeron-Findeisen process is incorporated into our Kessler-type microphysics formulation covering ice crystal growth occurring in mixed-phase clouds. Moreover, we model the water run-off from the ground surface, the infiltration into the soil, and its subsequent evaporation back to the atmosphere. We account for daily temperature changes, as well as heat transfer between pedosphere and atmosphere leading to a complex feedback loop. Our framework enables us to interactively explore various complex weather phenomena. Our results are assessed visually and validated by simulating weatherscapes for various setups covering different precipitation events and environments, by showcasing the hydrologic cycle, and by reproducing common effects such as Foehn winds. We also provide quantitative evaluations creating high-precipitation cumulonimbus clouds by prescribing atmospheric conditions based on infrared satellite observations. With our model we can generate dynamic 3D scenes of weatherscapes with high visual fidelity and even nowcast real weather conditions as simulations by streaming weather data into our framework.

Project Page

Ships, Splashes, and Waves on a Vast Ocean

L. Huang, Z. Qu, X. Tan, X. Zhang, D. L. Michels, and C. Jiang.

ACM Transactions on Graphics (SIGGRAPH Asia 2021), ACM (2021).

The simulation of large open water surface is challenging using a uniform volumetric discretization of the Navier-Stokes equations. Simulating water splashes near moving objects, which height field methods for water waves cannot capture, necessitates high resolutions. Such simulations can be carried out using the Fluid-Implicit-Particle (FLIP) method. However, the FLIP method is not efficient for the long-lasting water waves that propagate to long distances, which require sufficient depth for a correct dispersion relationship. This paper presents a new method to tackle this dilemma through an efficient hybridization of volumetric and surface-based advection-projection discretizations. We design a hybrid time-stepping algorithm that combines a FLIP domain and an adaptively remeshed Boundary Element Method (BEM) domain for the incompressible Euler equations. The resulting framework captures the detailed water splashes near moving objects with the FLIP method, and produces convincing water waves with correct dispersion relationships at modest additional costs.

Project Page

Learning to Reconstruct Botanical Trees from Single Images

B. Li, J. Kałużny, J. Klein, D. L. Michels, W. Pałubicki, B. Benes, and S. Pirk.

ACM Transactions on Graphics (SIGGRAPH Asia 2021), ACM (2021).

We introduce a novel method for reconstructing the 3D geometry of botanical trees from single photographs. Faithfully reconstructing a tree from single-view sensor data is a challenging and open problem because many possible 3D trees exist that fit the tree's shape observed from a single view. We address this challenge by defining a reconstruction pipeline based on three neural networks. The networks simultaneously mask out trees in input photographs, identify a tree's species, and obtain its 3D radial bounding volume – our novel 3D representation for botanical trees. Radial bounding volumes (RBV) are used to orchestrate a procedural model primed on learned parameters to grow a tree that matches the main branching structure and the overall shape of the captured tree. While the RBV allows us to faithfully reconstruct the main branching structure, we use the procedural model's morphological constraints to generate realistic branching for the tree crown. This constraints the number of solutions of tree models for a given photograph of a tree. We show that our method reconstructs various tree species even when the trees are captured in front of complex backgrounds. Moreover, although our neural networks have been trained on synthetic data with data augmentation, we show that our pipeline performs well for real tree photographs. We evaluate the reconstructed geometries with several metrics, including leaf area index and maximum radial tree distances.

Project Page

Accurately Solving Rod Dynamics with Graph Learning

H. Shao, T. Kugelstadt, T. Hädrich, W. Pałubicki, J. Bender, S. Pirk, and D. L. Michels.

Advances in Neural Information Processing Systems, NeurIPS (2021).

Iterative solvers are widely used to accurately simulate physical systems. These solvers require initial guesses to generate a sequence of improving approximate solutions. In this contribution, we introduce a novel method to accelerate iterative solvers for rod dynamics with graph networks (GNs) by predicting the initial guesses to reduce the number of iterations. Unlike existing methods that aim to learn physical systems in an end-to-end manner, our approach guarantees long-term stability and therefore leads to more accurate solutions. Furthermore, our method improves the run time performance of traditional iterative solvers for rod dynamics. To explore our method we make use of position-based dynamics (PBD) as a common solver for physical systems and evaluate it by simulating the dynamics of elastic rods. Our approach is able to generalize across different initial conditions, discretizations, and realistic material properties. We demonstrate that it also performs well when taking discontinuous effects into account such as collisions between individual rods. Finally, to illustrate the scalability of our approach, we simulate complex 3D tree models composed of over a thousand individual branch segments swaying in wind fields.

Project Page

Integral Methods for Versatile Fluid Simulation

Dissertation of L. Huang. Doctoral Advisor: D. L. Michels.
Committee Members: C. Batty, W. Heidrich, H. Pottmann.

Applied Mathematics and Computational Sciences Program,
CEMSE Division, KAUST (2021).

Physical simulations of natural phenomena usually boil down to solving an ordinary or partial differential equation system. Partial differential equation systems can be formulated either in differential form or in integral form. This dissertation explores integral methods for the simulation of magnetic fluids, so-called ferrofluids, and the surface of the vast ocean. The first two parts of this dissertation aim to contribute to the development of accurate and efficient methods for simulating ferrofluids on the macroscopic (in the order of millimeters) scale. The magnetic nature of these fluids imposes challenges for the simulation. The two most important challenges are to first model the influence of ferrofluids on their surrounding magnetic fields and second the influence of magnetic forces on the fluids' dynamics. To tackle these challenges, two Lagrangian simulation methods have been proposed. The first method discretizes the magnetic substance as clusters of particles carrying radial basis functions and applies magnetic forces between these particles. This is a mesh-free method suitable for particle-based fluid simulation frameworks such as smoothed-particle hydrodynamics. The second method follows another direction, only discretizing the fluid's surface as triangles and vertices. A surface-based simulation for the fluid part is employed, and a boundary element method is utilized for the magnetic part. The magnetic forces are added as gradients of the magnetic energy defined on the fluid's surface. The second approach has to solve significantly fewer unknowns in the underlying equations, and uses a more accurate surface tension model compared to the radial basis function approach. The proposed methods are able to reproduce a series of characteristic phenomena of magnetic fluids, both qualitatively and in some cases even quantitatively which leads to a better understanding of such kind of materials. The boundary element method employed in the second part shows advantages beyond ferrofluids. In the third part of this thesis, a boundary element method is coupled with a particle-based fluid simulator for ocean simulation. The wavy motion of the ocean is simulated using large triangle meshes, while water splashes are simulated using particles. This approach is much more efficient in terms of computation time and memory consumption.

KAUST Repository

Lunar Terrain Coverage Analysis Data Delivery Workflow

C.-A. Lee, M. A. Shaikh, C. H. Lee, and D. L. Michels.

ASCEND 2021, AIAA (2021).

In this work, we are developing a lunar terrain database to enable fast rendering of sun illumination and earth visibility for a proposed coverage analysis tool. This development will advance lunar mission design and formulation for current and future communications architectures, and will will aid in lunar surface mission planning and communications/navigation operations. An additional objective in this work enables characterizing multi-path fading losses between lunar surface assets and earth based on the computed local terrain masks. Our effort can be described in three steps: (1) we parallelize a brute force algorithm, which computes elevation masks from laser altimetry data acquired by the Lunar Reconnaissance Orbiter’s (LRO) Lunar Orbiter Laser Altimeter (LOLA); (2) we investigate parallel I/O methods to store terrain mask information from step (1) into a parallel file system; and (3) we finally deliver data to the terrain coverage analysis tool.

AIAA Aerospace Research Central

From Stormscapes to Wildfires: On the Physically-based Modeling and Simulation of Complex Natural Phenomena

Dissertation of T. Hädrich. Doctoral Advisor: D. L. Michels.
Committee Members: D. L. James, H. Pottmann, P. Wonka.

Computer Science Program,
CEMSE Division, KAUST (2021).

We propose a new atmospheric model based on first-principles for the simulation of clouds. Our approach is able to simulate the realistic formation of various cloud types, such as cumulus, stratus, stratocumulus, their temporal evolution, and transitions between cloud types. Moreover, we are able to model strongly rotating thunderstorms known as supercells. Our method allows us to simulate cloud formations of up to about 20km×20km at interactive rates. For the intuitive exploration, we identified a light-weight parameter set to interactively explore cloud formations. We demonstrate that our model can be coupled with data from real-time weather services to simulate cloud formations in the now.
Moreover, we present a novel approach for the simulation of wildfires. Our model is able to realistically capture the combustion process of trees, heat transfer with the environment and fire propagation between trees. We demonstrate that our approach is capable of realistically simulating the propagation of fire through entire ecosystems with varying vegetation occupancy. We integrated our atmospheric model which allows us to simulated clouds emerging from the evaporation of water from burning trees leading to complex so called flammagenitus patterns which are usually observed over wildfires. Our system runs at interactive rates which enables the exploration of wildfires in different environments.

KAUST Repository

Features of Structure, Magnetic State and Electrodynamic Performance of SrFe_12−xIn_xO₁₉

V. A. Turchenko, S. V. Trukhanov, V. G. Kostishin, F. Damay, F. Porcher, D. S. Klygach, M. G. Vakhitov, D. A. Lyakhov, D. L. Michels, B. Bozzo, I. Fina, M. A. Almessiere, Y. Slimani, A. Baykal, D. Zhou, and A. V. Trukhanov.

Scientific Reports, Nature Research (2021).

Indium-substituted strontium hexaferrites were prepared by the conventional solid-phase reaction method. Neutron diffraction patterns were obtained at room temperature and analyzed using the Rietveld methods. A linear dependence of the unit cell parameters is found. In³⁺ cations are located mainly in octahedral positions of 4f_VI and 12 k. The average crystallite size varies within 0.84-0.65 μm. With increasing substitution, the T_C Curie temperature decreases monotonically down to ~ 520 K. ZFC and FC measurements showed a frustrated state. Upon substitution, the average and maximum sizes of ferrimagnetic clusters change in the opposite direction. The M_r remanent magnetization decreases down to ~ 20.2 emu/g at room temperature. The M_s spontaneous magnetization and the k_eff effective magnetocrystalline anisotropy constant are determined. With increasing substitution, the maximum of the ε^/ real part of permittivity decreases in magnitude from ~ 3.3 to ~ 1.9 and shifts towards low frequencies from ~ 45.5 GHz to ~ 37.4 GHz. The maximum of the tg(α) dielectric loss tangent decreases from ~ 1.0 to ~ 0.7 and shifts towards low frequencies from ~ 40.6 GHz to ~ 37.3 GHz. The low-frequency maximum of the μ^/ real part of permeability decreases from ~ 1.8 to ~ 0.9 and slightly shifts towards high frequencies up to ~ 34.7 GHz. The maximum of the tg(δ) magnetic loss tangent decreases from ~ 0.7 to ~ 0.5 and shifts slightly towards low frequencies from ~ 40.5 GHz to ~ 37.7 GHz. The discussion of microwave properties is based on the saturation magnetization, natural ferromagnetic resonance and dielectric polarization types.

Nature Scientific Reports

Fire in Paradise: Mesoscale Simulation of Wildfires

T. Hädrich, D. T. Banuti, W. Pałubicki, S. Pirk, and D. L. Michels.

ACM Transactions on Graphics (SIGGRAPH 2021), ACM (2021).

Resulting from changing climatic conditions, wildfires have become an existential threat across various countries around the world. The complex dynamics paired with their often rapid progression renders wildfires an often disastrous natural phenomenon that is difficult to predict and to counteract. In this paper we present a novel method for simulating wildfires with the goal to realistically capture the combustion process of individual trees and the resulting propagation of fires at the scale of forests. We rely on a state-of-the-art modeling approach for large-scale ecosystems that enables us to represent each plant as a detailed 3D geometric model. We introduce a novel mathematical formulation for the combustion process of plants – also considering effects such as heat transfer, char insulation, and mass loss – as well as for the propagation of fire through the entire ecosystem. Compared to other wildfire simulations which employ geometric representations of plants such as cones or cylinders, our detailed 3D tree models enable us to simulate the interplay of geometric variations of branching structures and the dynamics of fire and wood combustion. Our simulation runs at interactive rates and thereby provides a convenient way to explore different conditions that affect wildfires, ranging from terrain elevation profiles and ecosystem compositions to various measures against wildfires, such as cutting down trees as firebreaks, the application of fire retardant, or the simulation of rain.

Project Page

Lost Photon Enhances Superresolution

A. B. Mikhalychev, P. I. Novik, I. L. Karuseichyk, D. A. Lyakhov, D. L. Michels, and D. Mogilevtsev.

npj Quantum Information, Nature Publishing Group (2021).

Quantum imaging can beat classical resolution limits, imposed by diffraction of light. In particular, it is known that one can reduce the image blurring and increase the achievable resolution by illuminating an object by entangled light and measuring coincidences of photons. If an n-photon entangled state is used and the nth-order correlation function is measured, the point-spread function (PSF) efficiently becomes √n times narrower relatively to classical coherent imaging. Quite surprisingly, measuring n-photon correlations is not the best choice if an n-photon entangled state is available. We show that for measuring (n-1)-photon coincidences (thus, ignoring one of the available photons), PSF can be made even narrower. This observation paves a way for a strong conditional resolution enhancement by registering one of the photons outside the imaging area. We analyze the conditions necessary for the resolution increase and propose a practical scheme, suitable for observation and exploitation of the effect.

npj Quantum Information

Exponential Rosenbrock Methods and Their Application in Visual Computing

V. T. Luan and D. L. Michels.

Rosenbrock–Wanner-Type Methods, Springer (2021).

We introduce a class of explicit exponential Rosenbrock methods for the time integration of large systems of stiff differential equations. Their application with respect to simulation tasks in the field of visual computing is discussed where these time integrators have shown to be very competitive compared to standard techniques. In particular, we address the simulation of elastic and nonelastic deformations as well as collision scenarios focusing on relevant aspects like stability and energy conservation, large stiffnesses, high fidelity and visual accuracy.

Springer Link

Domain Adaptation with Morphologic Segmentation

J. Klein, S. Pirk, and D. L. Michels.

Workshop Autonomous Driving: Perception, Prediction and Planning (ADP3), IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2021).

We present a novel domain adaptation framework that uses morphologic segmentation to translate images from arbitrary input domains (real and synthetic) into a uniform output domain. Our framework is based on an established image-to-image translation pipeline that allows us to first transform the input image into a generalized representation that encodes morphology and semantics – the edge-plus-segmentation map (EPS) – which is then transformed into an output domain. Images transformed into the output domain are photo-realistic and free of artifacts that are commonly present across different real (e.g. lens flare, motion blur, etc.) and synthetic (e.g. unrealistic textures, simplified geometry, etc.) data sets. Our goal is to establish a preprocessing step that unifies data from multiple sources into a common representation that facilitates training downstream tasks in computer vision. This way, neural networks for existing tasks can be trained on a larger variety of training data, while they are also less affected by overfitting to specific data sets. We showcase the effectiveness of our approach by qualitatively and quantitatively evaluating our method on four data sets of simulated and real data of urban scenes.

arXiv Project Page Video

Controlling Wave-front Shape and Propagation Time with Tunable Disordered Non-Hermitian Multilayers

D. Novitsky, D. A. Lyakhov, D. L. Michels, D. Redka, A. Pavlov, and A. Shalin.

Scientific Reports, Nature Research (2021).

Unique and flexible properties of non-Hermitian photonic systems attract ever-increasing attention via delivering a whole bunch of novel optical effects and allowing for efficient tuning light-matter interactions on nano- and microscales. Together with an increasing demand for the fast and spatially compact methods of light governing, this peculiar approach paves a broad avenue to novel optical applications. Here, unifying the approaches of disordered metamaterials and non-Hermitian photonics, we propose a conceptually new and simple architecture driven by disordered loss-gain multilayers and, therefore, providing a powerful tool to control both the passage time and the wave-front shape of incident light with different switching times. For the first time we show the possibility to switch on and off kink formation by changing the level of disorder in the case of adiabatically raising wave fronts. At the same time, we deliver flexible tuning of the output intensity by using the nonlinear effect of loss and gain saturation. Since the disorder strength in our system can be conveniently controlled with the power of the external pump, our approach can be considered as a basis for different active photonic devices.

Nature Scientific Reports

Efficient Exponential Time Integration for Simulating Nonlinear Coupled Oscillators

V. T. Luan and D. L. Michels.

Journal of Computational and Applied Mathematics, Elsevier (2021).

In this paper, we propose an advanced time integration technique associated with explicit exponential Rosenbrock-based methods for the simulation of large stiff systems of nonlinear coupled oscillators. In particular, a novel reformulation of these systems is introduced and a general family of efficient exponential Rosenbrock schemes for simulating the reformulated system is derived. Moreover, we show the required regularity conditions and prove the convergence of these schemes for the system of coupled oscillators. We present an efficient implementation of this new approach and discuss several applications in scientific and visual computing. The accuracy and efficiency of our approach are demonstrated through a broad spectrum of numerical examples, including a nonlinear Fermi–Pasta–Ulam–Tsingou model, elastic and nonelastic deformations as well as collision scenarios focusing on relevant aspects such as stability and energy conservation, large numerical stiffness, high fidelity, and visual accuracy.

J. Comput. Appl. Math.

The Influence of the Synthesis Conditions on the Magnetic Behaviour of the Densely Packed Arrays of Ni Nanowires in Porous Anodic Alumina Membrane

A. Vorobjova, D. Tishkevich, D. Shimanovich, T. Zubar, K. Astapovich, A. Kozlovskiy, M. Zdorovets, A. Zhaludkevich, D. A. Lyakhov, D. L. Michels, D. Vinnik, V. Fedosyuk, and A. Trukhanov.

RSC Advances, Royal Society of Chemistry (2021).

The densely packed arrays of Ni nanowires of 70 nm diameter and 6-12 μm length were obtained via electrodeposition into porous alumina membranes (PAAMs) of 55–75 μm thickness. The morphology, microstructure and magnetic properties between the room and liquid-helium temperature of Ni nanowires in PAAMs have been investigated using scanning electron microscopy, X-ray diffraction and vibrating sample magnetometry. The crystal structure of the Ni nanowires is fcc with (220) preferred orientation. The magnetic characteristics of the Ni nanowires in PAAMs were compared with the same characteristics of bulk Ni and with other researchers' data. The effect of the porous alumina membrane and the Ni nanowires synthesis conditions on the magnetic characteristics of Ni nanowire arrays has been studied. The coercivity reached more than 750 kOe and the squareness ratio up to 0.65 under the proposed optimal synthesis conditions for Ni nanowires. Magnetic parameters of the densely packed arrays of Ni nanowires allow using them in magnetic recording media, hard disk drives, storage systems and sensors. In addition, such structures are of considerable interest for basic research on nanomagnetism which is significantly different from the magnetic properties of bulk and thin films materials.

RSC Adv.

DFT Study of NO Reduction Process on Ag/γ-Al₂O₃ Catalyst: Some Aspects of Mechanism and Catalyst Structure

V. E. Matulis, E. G. Ragoyja, O. A. Ivashkevich, D. A. Lyakhov, and D. L. Michels.

The Journal of Physical Chemistry C, American Chemical Society (2020).

Catalysts based on Ag/γ-Al₂O₃ are perspective systems for practical implementation of catalytic NO reduction. Nevertheless, the mechanism and regularities of this process have still not been fully investigated. Herein, we present the results of quantum-chemical research of the Ag/γ-Al₂O₃ catalyst surface and some aspects of the NO reduction mechanism on it. Proposed calculation methods using DFT and cluster models of the catalyst surface are compared and verified. The possibility of existence of small adsorbed neutral and cationic silver clusters on the surface of the catalyst is shown. It is demonstrated that NO adsorption on these clusters is energetically favorable, in the form of both monomers and dimers. The scheme of NO selective catalytic reduction (SCR) that explains increasing of N₂O side-product amount on catalysts with silver fraction more than 2 wt % is proposed. The feasibility of this scheme is justified with calculated data. Some recommendations that allow decreasing amounts of N₂O are developed.

ACS J. Phys. Chem. C

Surface-Only Ferrofluids

L. Huang and D. L. Michels.

ACM Transactions on Graphics (SIGGRAPH Asia 2020), ACM (2020).

We devise a novel surface-only approach for simulating the three dimensional free-surface flow of incompressible, inviscid, and linearly magnetizable ferrofluids. A Lagrangian velocity field is stored on a triangle mesh capturing the fluid's surface. The two key problems associated with the dynamic simulation of the fluid's interesting geometry are the magnetization process transitioning the fluid from a non-magnetic into a magnetic material, and the evaluation of magnetic forces. In this regard, our key observation is that for linearly incompressible ferrofluids, their magnetization and application of magnetic forces only require knowledge about the position of the fluids' boundary. Consequently, our approach employs a boundary element method solving the magnetization problem and evaluating the so-called magnetic pressure required for the force evaluation. The magnetic pressure is added to the Dirichlet boundary condition of a surface-only liquids solver carrying out the dynamical simulation. By only considering the fluid's surface in contrast to its whole volume, we end up with an efficient approach enabling more complex and realistic ferrofluids to be explored in the digital domain without compromising efficiency. Our approach allows for the use of physical parameters leading to accurate simulations as demonstrated in qualitative and quantitative evaluations.

Project Page

Stormscapes: Simulating Cloud Dynamics in the Now

T. Hädrich, M. Makowski, W. Pałubicki, D. T. Banuti, S. Pirk, and D. L. Michels.

ACM Transactions on Graphics (SIGGRAPH Asia 2020), ACM (2020).

The complex interplay of a number of physical and meteorological phenomena makes simulating clouds a challenging and open research problem. We explore a physically accurate model for simulating clouds and the dynamics of their transitions. We propose first-principle formulations for computing buoyancy and air pressure that allow us to simulate the variations of atmospheric density and varying temperature gradients. Our simulation allows us to model various cloud types, such as cumulus, stratus, and stratoscumulus, and their realistic formations caused by changes in the atmosphere. Moreover, we are able to simulate large-scale cloud super cells – clusters of cumulonimbus formations – that are commonly present during thunderstorms. To enable the efficient exploration of these stormscapes, we propose a lightweight set of high-level parameters that allow us to intuitively explore cloud formations and dynamics. Our method allows us to simulate cloud formations of up to about 20km×20km extents at interactive rates. We explore the capabilities of physically accurate and yet interactive cloud simulations by showing numerous examples and by coupling our model with atmosphere measurements of real-time weather services to simulate cloud formations in the now. Finally, we quantitatively assess our model with cloud fraction profiles, a common measure for comparing cloud types.

Project Page

Optimal Correlation Order in Superresolution Optical Fluctuation Microscopy

S. Vlasenko, A. B. Mikhalychev, I. L. Karuseichyk, D. A. Lyakhov, D. L. Michels, and D. Mogilevtsev.

Physical Review A, American Physical Society (2020).

Here, we show that superresolution optical fluctuation microscopy might not lead to ideally infinite superresolution enhancement with increasing of the order of measured cumulants. Using information analysis for estimating error bounds on the determination of point-source positions, we show that reachable precision per measurement might be saturated with increasing of the order of the measured cumulants in the superresolution regime. In fact, there is an optimal correlation order beyond which there is practically no improvement for objects of three and more point sources. However, for objects of just two sources, one still has an intuitively expected resolution increase with the cumulant order.

Physical Review A

In Silico Design of Deep Space Optical Links

C.-A. Lee, H. Xie, C. H. Lee, D. A. Lyakhov, and D. L. Michels.

ASCEND 2020, AIAA (2020).

As deep space links migrate toward higher frequency bands like K_a and optical, thorough trade-space exploration becomes increasingly valuable for designing reliable and efficient communications systems. In this contribution, we leveraged high-performance, concurrent simulations when the run-time complexity of simulation software overwhelms capabilities of ordinary desktop machines. The first part of this manuscript describes how to run error correcting code simulations concurrently on a high-performance supercomputer. The second part of this study describes a framework to produce azimuth and elevation terrain masks from imagery of the Lunar South Pole.

AIAA Aerospace Research Central

Surface-Enhanced Raman Spectroscopy of Organic Molecules and Living Cells with Gold-Plated Black Silicon

L. Golubewa, R. Karpicz, I. Matulaitiene, A. Selskis, D. Rutkauskas, A. Pushkarchuk, T. Khlopina, D. L. Michels, D. A. Lyakhov, T. Kulahava, A. Shah, Y. Svirko, and P. Kuzhir.

ACS Applied Materials & Interfaces, American Chemical Society (2020).

Black silicon (bSi) refers to an etched silicon surface comprising arrays of microcones that effectively suppress reflection from UV to near-infrared (NIR) while simultaneously enhancing the scattering and absorption of light. This makes bSi covered with a nm-thin layer of plasmonic metal, i.e., gold, an attractive substrate material for sensing of bio-macromolecules and living cells using surface-enhanced Raman spectroscopy (SERS). The performed Raman measurements accompanied with finite element numerical simulation and density functional theory analysis revealed that at the 785nm excitation wavelength, the SERS enhancement factor of the bSi/Au substrate is as high as 10⁸ due to a combination of electromagnetic and chemical mechanisms. This finding makes the SERS-active bSi/Au substrate suitable for detecting trace amounts of organic molecules. We demonstrate the outstanding performance of this substrate by highly sensitive and specific detection of a small organic molecule of 4-mercaptobenzoic acid and living C6 rat glioma cell nucleic acids/proteins/lipids. Specifically, the bSi/Au SERS-active substrate offers a unique opportunity to investigate the living cells’ malignant transformation using characteristic protein disulfide Raman bands as a marker. Our findings evidence that bSi/Au provides a pathway to the highly sensitive and selective, scalable, and low-cost substrate for lab-on-a-chip SERS biosensors that can be integrated into silicon-based photonics devices.

ACS Appl. Mater. Interfaces

Interactive Wood Fracture

T. Hädrich, J. Scheffczyk, W. Pałubicki, S. Pirk, and D. L. Michels.

ACM SIGGRAPH/Eurographics Symposium on Computer Animation (Poster), Eurographics Digital Library (2020).

We propose a new approach for the simulation of wood as anisotropic material that takes its inherent fiber structure into account. Our approach is based on the Position-based Dynamics framework. We use the Shape Matching approach as the basis for modeling the isotropic attribute of wood. For simulating anisotropic behavior we employ a fiber model based on the Cosserat rod theory. Our approach supports dynamic fracturing and captures typical breaking patterns of wood.

Eurographics Digital Library Abstract (PDF) Video

Wind Erosion: Shape Modifications by Interactive Particle-based Erosion and Deposition

V. Krs, T. Hädrich, D. L. Michels, O. Deussen, S. Pirk, and B. Benes.

ACM SIGGRAPH/Eurographics Symposium on Computer Animation (Poster), Eurographics Digital Library (2020).

We present a novel user-assisted method for physics-inspired modeling of geomorphological features on polygonal meshes using material erosion and deposition as the driving mechanisms. Polygonal meshes defining an input scene are converted into a volumetric data structure that efficiently tracks the mass and boundary of the resulting morphological changes. We use Smoothed Particle Hydrodynamics to simulate fluids and to track eroded material. Eroded material is converted to material particles and naturally deposits in locations such as sinks and corners. Once deposited, we convert material particles back into the volumetric representation.

Eurographics Digital Library Abstract (PDF) Video

Rise of Nations: Why do empires expand and fall?

S. Vakulenko, D. A. Lyakhov, A. G. Weber, D. Lukichev, and D. L. Michels.

Chaos: An Interdisciplinary Journal of Nonlinear Science, AIP (2020).

We consider centralized networks composed of multiple satellites arranged around a few dominating super-egoistic centers. These so-called empires are organized using a divide and rule framework enforcing strong center-satellite interactions while keeping the pairwise interactions between the satellites sufficiently weak. We present a stochastic stability analysis, in which we consider these dynamical systems as stable if the centers have sufficient resources while the satellites have no value. Our model is based on a Hopfield type network which proved its significance in the field of artificial intelligence. Using this model, it is shown that the divide and rule framework provides important advantages: it allows for completely controlling the dynamics in a straight-forward way by adjusting center-satellite interactions. Moreover, it is shown that such empires should only have a single ruling center to provide sufficient stability. To survive, empires should have switching mechanisms implementing adequate behavior models by choosing appropriate local attractors in order to correctly respond to internal and external challenges. By an analogy with Bose-Einstein condensation, we show that if the noise correlations are negative for each pair of nodes, then the most stable structure with respect to noise is a globally connected network. For social systems, we show that controllability by their centers is only possible if the centers evolve slowly. Except for short periods when the state approaches a certain stable state, the development of such structures is very slow and negatively correlated with the size of the system's structure. Hence, increasing size eventually end up in the "control trap".

AIP Chaos

Method of Surface Energy Investigation by Lateral AFM: Application to Control Growth Mechanism of Nanostructured NiFe Films

T. I. Zubar, V. M. Fedosyuk, S. V. Trukhanov, D. I. Tishkevich, D. L. Michels, D. A. Lyakhov, and A. V. Trukhanov.

Scientific Reports, Nature Research (2020).

A new method for the specific surface energy investigation based on a combination of the force spectroscopy and the method of nanofriction study using atomic force microscopy was proposed. It was shown that air humidity does not affect the results of investigation by the proposed method as opposed to the previously used methods. Therefore, the method has high accuracy and repeatability in air without use of climate chambers and liquid cells. The proposed method has a high local resolution and is suitable for investigation of the specific surface energy of individual nanograins or fixed nanoparticles. The achievements described in the paper demonstrate one of the method capabilities, which is to control the growth mechanism of thin magnetic films. The conditions for the transition of the growth mechanism of thin Ni80Fe20 films from island to layer-by-layer obtained via electrolyte deposition have been determined using the proposed method and the purpose made probes with Ni coating.

Nature Scientific Reports

Contact Linearizability of Scalar Ordinary Differential Equations of Arbitrary Order

Y. Liu, D. A. Lyakhov, and D. L. Michels.

Computer Algebra in Scientific Computing (CASC 2020), Springer (2020).

We consider the problem of the exact linearization of scalar nonlinear ordinary differential equations by contact transformations. This contribution is extending previous work by Lyakhov, Gerdt, and Michels addressing linearizability by means of point transformations. We have restricted ourselves to quasi-linear equations solved for the highest derivative with a rational dependence on the occurring variables. As in the case of point transformations, our algorithm is based on simple operations on Lie algebras such as computing the derived algebra and the dimension of the symmetry algebra. The linearization test is an efficient algorithmic procedure while finding the linearization transformation requires the computation of at least one solution of the corresponding system of the Bluman-Kumei equation.

Springer Link

On Ambarzumyan-type Inverse Problems of Vibrating String Equations

Y. Ashrafyan and D. L. Michels.

arXiv:2008.13035, Cornell University Library (2020).

We consider the inverse spectral theory of vibrating string equations. In this regard, first eigenvalue Ambarzumyan-type uniqueness theorems are stated and proved subject to separated, self-adjoint boundary conditions. More precisely, it is shown that there is a curve in the boundary parameters' domain on which no analog of it is possible. Necessary conditions of the n-th eigenvalue are identified, which allows to state the theorems. In addition, several properties of the first eigenvalue are examined. Lower and upper bounds are identified, and the areas are described in the boundary parameters' domain on which the sign of the first eigenvalue remains unchanged. This paper contributes to inverse spectral theory as well as to direct spectral theory.

arXiv

Early-Stage Growth Mechanism and Synthesis Conditions-Dependent Morphology of Nanocrystalline Bi Films Electrodeposited from Perchlorate Electrolyte

D. Tishkevich, S. Grabchikov, T. Zubar, D. Vasin, S. Trukhanov, A. Vorobjova, D. Yakimchuk, A. Kozlovskiy, M. Zdorovets, S. Giniyatova, D. Shimanovich, D. A. Lyakhov, D. L. Michels, M. Dong, S. Gudkova, and A. Trukhanov.

Nanomaterials, MDPI (2020).

Bi nanocrystalline films were formed from perchlorate electrolyte (PE) on Cu substrate via electrochemical deposition with different duration and current densities. The microstructural, morphological properties, and elemental composition were studied using scanning electron microscopy (SEM), atomic force microscopy (AFM), and energy-dispersive X-ray microanalysis (EDX). The optimal range of current densities for Bi electrodeposition in PE using polarization measurements was demonstrated. For the first time, it was shown and explained why, with a deposition duration of 1s, co-deposition of Pb and Bi occurs. The correlation between synthesis conditions and chemical composition and microstructure for Bi films was discussed. The analysis of the microstructure evolution revealed the changing mechanism of the films' growth from pillar-like (for Pb-rich phase) to layered granular form (for Bi) with deposition duration rising. This abnormal behavior is explained by the appearance of a strong Bi growth texture and coalescence effects. The investigations of porosity showed that Bi films have a closely-packed microstructure. The main stages and the growth mechanism of Bi films in the galvanostatic regime in PE with a deposition duration of 1-30s are proposed.

Nanomaterials

Unambiguous Scattering Matrix for Non-Hermitian Systems

A. Novitsky, D. A. Lyakhov, D. L. Michels, A. A. Pavlov, A. Shalin, and D. V. Novitsky.

Physical Review A, American Physical Society (2020).

PT symmetry is a unique platform for light manipulation and versatile use in unidirectional invisibility, lasing, sensing, etc. Broken and unbroken PT-symmetric states in non-Hermitian open systems are described by scattering matrices. A multilayer structure, as a simplest example of the open system, has no certain definition of the scattering matrix, since the output ports can be permuted. The uncertainty in definition of the exceptional points bordering PT-symmetric and PT-symmetry-broken states poses an important problem, because the exceptional points are indispensable in applications as sensing and mode discrimination. Here we derive the proper scattering matrix from the unambiguous relation between the PT-symmetric Hamiltonian and scattering matrix. We reveal that the exceptional points of the scattering matrix with permuted output ports are not related to the PT symmetry breaking. Nevertheless, they can be employed for finding a lasing onset as demonstrated in our time-domain calculations and scattering-matrix pole analysis. Our results are important for various applications of the non-Hermitian systems including encircling exceptional points, coherent perfect absorption, PT-symmetric plasmonics, etc.

Physical Review A

Percolation and Transport Properties in the Mechanically Deformed Composites Filled with Carbon Nanotubes

A. Plyushch, D. A. Lyakhov, M. Šimėnas, D. Bychanok, J. Macutkevič, D. L. Michels, J. Banys, P. Lamberti, and P. Kuzhir.

Applied Sciences, Special Issue Numerical and Analytical Methods in Electromagnetics, MDPI (2020).

The conductivity and percolation concentration of the composite material filled with randomly distributed carbon nanotubes were simulated as a function of the mechanical deformation. Nanotubes were modelled as the hard-core ellipsoids of revolution with high aspect ratio. The evident anisotropy was observed in the percolation threshold and conductivity. The minimal mean values of the percolation of 4.6 vol. % and maximal conductivity of 0.74 S/m were found for the isotropic composite. Being slightly aligned, the composite demonstrates lower percolation concentration and conductivity along the orientation of the nanotubes compared to the perpendicular arrangement.

Applied Sciences

Reconstructing Compound Objects by Quantum Imaging with Higher-order Correlation Functions

A. B. Mikhalychev, B. Bessire, I. L. Karuseichyk, A. A. Sakovich, M. Unternährer, D. A. Lyakhov, D. L. Michels, A. Stefanov, and D. Mogilevtsev.

Communications Physics, Nature Research (2019).

Quantum imaging has a potential of enhancing precision of the object reconstruction by using quantum correlations of the imaging field. This is especially important for imaging requiring low-intensity fields up to the level of few-photons. However, quantum imaging generally leads to nonlinear estimation problems. The complexity of these problems rapidly increases with the number of parameters describing the object. We suggest a way to drastically reduce the complexity for a wide class of problems. The key point of our approach is connecting the features of the Fisher information with the parametric locality of the problem, and building the efficient iterative inference scheme reconstructing only a subset of the whole set of parameters in each step. This iterative scheme is linear on the total number of parameters. This scheme is applied to quantum near-field imaging, the inference procedure is developed resulting in super-resolving reconstruction of grey compound transmission objects. The functionality of the method is demonstrated with experimental data obtained by measurements of higher-order correlation functions for imaging with entangled twin-photons and pseudo-thermal light sources. By analyzing the informational content of the measurement, it becomes possible to predict the existence of optimal photon correlations providing for the best image resolution in the super-resolution regime. This prediction is experimentally confirmed. It is also shown how an estimation bias stemming from image features may drastically improve the resolution.

Nature Communications Physics

On the Accurate Large-scale Simulation of Ferrofluids

L. Huang, T. Hädrich, and D. L. Michels.

ACM Transactions on Graphics (SIGGRAPH 2019), ACM (2019).

We present an approach to the accurate and efficient large-scale simulation of the complex dynamics of ferrofluids based on physical principles. Ferrofluids are liquids containing magnetic particles that react to an external magnetic field without solidifying. In this contribution, we employ smooth magnets to simulate ferrofluids in contrast to previous methods based on the finite element method or point magnets. We solve the magnetization using the analytical solution of the smooth magnets' field, and derive the bounded magnetic force formulas addressing particle penetration. We integrate the magnetic field and force evaluations into the fast multipole method allowing for efficient large-scale simulations of ferrofluids. The presented simulations are well reproducible since our approach can be easily incorporated into a framework implementing a Fast Multipole Method and a Smoothed Particle Hydrodynamics fluid solver with surface tension. We provide a detailed analysis of our approach and validate our results against real wet lab experiments. This work can potentially open the door for a deeper understanding of ferrofluids and for the identification of new areas of applications of these materials.

Selected as the front cover of the ACM Transactions on Graphics, Proceedings of SIGGRAPH 2019.

Featured in the conference's Technical Papers Trailer, KAUST's Discovery, and Two Minute Papers.

ACM Library Project Page Trailer Front Cover Discovery Phys.org EurekAlert! 80 LEVEL Two Minute Papers

Synthetic Silviculture: Multi-scale Modeling of Plant Ecosystems

M. Makowski, T. Hädrich, J. Scheffczyk, D. L. Michels, S. Pirk, and W. Pałubicki.

ACM Transactions on Graphics (SIGGRAPH 2019), ACM (2019).

Due to the enormous amount of detail and the interplay of various biological phenomena, modeling realistic ecosystems of trees and other plants is a challenging and open problem. Previous research on modeling plant ecologies has focused on representations to handle this complexity, mostly through geometric simplifications, such as points or billboards. In this paper we describe a multi-scale method to design large-scale ecosystems with individual plants that are realistically modeled and faithfully capture biological features, such as growth, plant interactions, different types of tropism, and the competition for resources. Our approach is based on leveraging inter- and intra-plant self-similarities for efficiently modeling plant geometry. We focus on the interactive design of plant ecosystems of up to 500K plants, while adhering to biological priors known in forestry and botany research. The introduced parameter space supports modeling properties of nine distinct plant ecologies (e.g. deciduous forest, boreal forest, tundra, etc.) while each plant is represented as a 3D surface mesh as required by commodity rendering systems. The capabilities and usefulness of our framework are illustrated through numerous models of forests, individual plants, and validations.

Featured in the conference's Technical Papers Trailer and 80 LEVEL.

ACM Library Project Page Trailer 80 LEVEL Two Minute Papers

On the Consistency Analysis of Finite Difference Approximations

D. L. Michels, V. P. Gerdt, Y. A. Blinkov, and D. A. Lyakhov.

Journal of Mathematical Sciences, Springer (2019).

Finite difference schemes are widely used in applied mathematics to numerically solve partial differential equations. However, for a given solution scheme, it is usually difficult to evaluate the quality of the underlying finite difference approximation with respect to the inheritance of algebraic properties of the differential problem under consideration. In this paper, we present an appropriate quality criterion of strong consistency for finite difference approximations to systems of nonlinear partial differential equations. This property strengthens the standard requirement of consistency of difference equations with differential ones. We use a verification algorithm for strong consistency, which is based on the computation of difference Gröbner bases. This allows for the evaluation and construction of solution schemes that preserve some fundamental algebraic properties of the system at the discrete level. We demonstrate the suggested approach by simulating a Kármán vortex street for the two-dimensional incompressible viscous flow described by the Navier–Stokes equations.

Springer Link

On the Algorithmic Linearizability of Nonlinear Ordinary Differential Equations

D. A. Lyakhov, V. P. Gerdt, and D. L. Michels.

Journal of Symbolic Computation, Elsevier (2019).

Solving nonlinear ordinary differential equations is one of the fundamental and practically important research challenges in mathematics. However, the problem of their algorithmic linearizability so far remained unsolved. In this contribution, we propose a solution of this problem for a wide class of nonlinear ordinary differential equation of arbitrary order. We develop two algorithms to check if a nonlinear differential equation can be reduced to a linear one by a point transformation of the dependent and independent variables. In this regard, we have restricted ourselves to quasi-linear equations with a rational dependence on the occurring variables and to point transformations. While the first algorithm is based on a construction of the Lie point symmetry algebra and on the computation of its derived algebra, the second algorithm exploits the differential Thomas decomposition and allows not only to test the linearizability, but also to generate a system of nonlinear partial differential equations that determines the point transformation and the coefficients of the linearized equation. The implementation of our algorithms is discussed and evaluated using several examples.

Elsevier Link

OIL: Observational Imitation Learning

G. Li, M. Mueller, V. Casser, N. Smith, D. L. Michels, and B. Ghanem.

Robotics: Science and Systems (RSS 2019).

Recent work has explored the problem of autonomous navigation by imitating a teacher and learning an end-to-end policy, which directly predicts controls from raw images. However, these approaches tend to be sensitive to mistakes by the teacher and do not scale well to other environments or vehicles. To this end, we propose Observational Imitation Learning (OIL), a novel imitation learning variant that supports online training and automatic selection of optimal behavior by observing multiple imperfect teachers. We apply our proposed methodology to the challenging problems of autonomous driving and UAV racing. For both tasks, we utilize the Sim4CV simulator that enables the generation of large amounts of synthetic training data and also allows for online learning and evaluation. We train a perception network to predict waypoints from raw image data and use OIL to train another network to predict controls from these waypoints. Extensive experiments demonstrate that our trained network outperforms its teachers, conventional imitation learning (IL) and reinforcement learning (RL) baselines and even humans in simulation.

arXiv Project Page

Learning a Controller Fusion Network by Online Trajectory Filtering for Vision-based UAV Racing

M. Mueller, G. Li, V. Casser, N. Smith, D. L. Michels, and B. Ghanem.

Third International Workshop on Computer Vision for UAVs (UAVision 2019), IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2019).

Autonomous UAV racing has recently emerged as an interesting research problem. The dream is to beat humans in this new fast-paced sport. A common approach is to learn an end-to-end policy that directly predicts controls from raw images by imitating an expert. However, such a policy is limited by the expert it imitates and scaling to other environments and vehicle dynamics is difficult. One approach to overcome the drawbacks of an end-to-end policy is to train a network only on the perception task and handle control with a PID or MPC controller. However, a single controller must be extensively tuned and cannot usually cover the whole state space. In this paper, we propose learning an optimized controller using a DNN that fuses multiple controllers. The network learns a robust controller with online trajectory filtering, which suppresses noisy trajectories and imperfections of individual controllers. The result is a network that is able to learn a good fusion of filtered trajectories from different controllers leading to significant improvements in overall performance. We compare our trained network to controllers it has learned from, end-to-end baselines and human pilots in a realistic simulation; our network beats all baselines in extensive experiments and approaches the performance of a professional human pilot.

arXiv Video

Über Konzeption und Methodik computergestützter Simulationen

D. L. Michels.

Human and Technology in the Digital Age, Springer (2019).

Die computergestützte Simulation hat sich im Zuge steigender konzeptioneller und technischer Möglichkeiten zu einer zentralen Kulturtechnik herausgebildet. Neben klassischer Theorie und Experiment stellt sie nunmehr einen gleichberechtigten digitalen Methodenapparat zu Analyse und Vorhersage und schließlich zur Schaffung wissenschaftlicher Erkenntnisse dar. Die Auslagerung schwieriger Problemstellungen in die digitale Welt ermöglicht in vielen Fällen deren effiziente Lösung und läßt in ihrer inversen Formulierung die Bewältigung komplexer Optimierungsprobleme zu. Umgekehrt erlaubt sie die Steuerung digitaler Systeme sowie deren Reaktion im Hinblick auf sensorische Dateneingaben und läßt dadurch eine adäquate Interaktion dieser Systeme mit ihrer realen Umwelt zu. Dieser Beitrag führt unter konzeptionellen Gesichtspunkten in die Grundlagen computergestützter Simulationen ein und diskutiert Möglichkeiten und Grenzen des resultierenden technischen Methodenapparats.

Springer Link

A Strongly Consistent Finite Difference Scheme for Steady Stokes Flow and its Modified Equations

Y. A. Blinkov, V. P. Gerdt, D. A. Lyakhov, and D. L. Michels.

Computer Algebra in Scientific Computing (CASC 2018), Springer (2018).

We construct and analyze a strongly consistent second-order finite difference scheme for the steady two-dimensional Stokes flow. The pressure Poisson equation is explicitly incorporated into the scheme. Our approach suggested by the first two authors is based on a combination of the finite volume method, difference elimination, and numerical integration. We make use of the techniques of the differential and difference Janet/Gröbner bases. In order to prove strong consistency of the generated scheme we correlate the differential ideal generated by the polynomials in the Stokes equations with the difference ideal generated by the polynomials in the constructed difference scheme. Additionally, we compute the modified differential system of the obtained scheme and analyze the scheme's accuracy and strong consistency by considering this system. An evaluation of our scheme against the established marker-and-cell method is carried out.

arXiv

Teaching UAVs to Race: End-to-End Regression of Agile Controls in Simulation

M. Mueller, V. Casser, N. Smith, D. L. Michels, and B. Ghanem.

Second International Workshop on Computer Vision for UAVs (UAVision 2018), European Conference on Computer Vision (ECCV 2018).

Automating the navigation of unmanned aerial vehicles (UAVs) in diverse scenarios has gained much attention in recent years. However, teaching UAVs to fly in challenging environments remains an unsolved problem, mainly due to the lack of training data. In this paper, we train a deep neural network to predict UAV controls from raw image data for the task of autonomous UAV racing in a photo-realistic simulation. Training is done through imitation learning with data augmentation to allow for the correction of navigation mistakes. Extensive experiments demonstrate that our trained network (when sufficient data augmentation is used) outperforms state-of-the-art methods and flies more consistently than many human pilots. Additionally, we show that our optimized network architecture can run in real-time on embedded hardware, allowing for efficient on- board processing critical for real-world deployment.

Best Paper/Presentation Award.

Springer Link Paper (PDF) KAUST News

A Quantitative Platform for Non-Line-of-Sight Imaging Problems

J. Klein, M. Laurenzis, D. L. Michels, and M. B. Hullin.

British Machine Vision Conference (BMVC 2018), British Machine Vision Association (2018).

The computational sensing community has recently seen a surge of works on imaging beyond the direct line of sight. However, most of the reported results rely on drastically different measurement setups and algorithms, and are therefore hard to impossible to compare quantitatively. Here, we focus on an important class of approaches, namely those that that aim to reconstruct scene properties from time-resolved optical impulse responses. In this paper, we introduce a collection of reference data and quality metrics that are tailored to the most common use cases, and we define reconstruction challenges that we hope will aid the development and assessment of future methods.

Project Page Paper (PDF) Supplementary Material (PDF)

Conjugated Polymers as a New Class of Dual-Mode Matrices for MALDI Mass Spectrometry and Imaging

K. Horatz, M. Giampà, Y. Karpov, K. Sahre, H. Bednarz, A. Kiriy, B. Voit, K. Niehaus, N. Hadjichristidis, D. L. Michels, and F. Lissel.

Journal of the American Chemical Society, American Chemical Society (2018).

Matrix-Assisted Laser Desorption/Ionization Mass Spectrometry MALDI MS and MALDI MS Imaging are ubiquitous analytical methods in medical, pharmaceutical, biological and environmental research. Currently, there is a strong interest in the investigation of low molecular weight compounds (LMWCs), especially to trace and understand metabolic pathways, requiring the development of new matrix systems which have favorable optical properties, a high ionization efficiency, and are MALDI silent in the LMWC area. In this paper, five conjugated polymers, poly[naphthalene-diimide-bithiophene] (PNDI(T2)), poly[3-dodecylthiophene] (P3DDT), poly[2,3-bis-(3-octyloxyphenyl)quinoxaline-5,8-diyl-alt-thiophene-2,5-diyl] (PTQ1), poly[isoindigo-bithiophene] (PII(T2)), and poly[9,9-octylfluorene] (P9OFl) are investigated as matrices. The polymers have a strong optical absorption, are solution-processable, and can be coated into thin films, allowing to vastly reduce the amount of matrix used. All investigated polymers function as matrices in both positive and negative mode MALDI, classifying them as rare dual-mode matrices, and show a very good analyte ionization ability in both modes. PNDI(T2), P3DDT, PTQ1, and PII(T2) are MALDI silent in the full measurement range (> m/z = 150k), except at high laser intensities. In MALDI MS experiments of single analytes and a complex biological sample, the performance of the polymers was found to be as good as two commonly used matrices (2,5-DHB for positive, and 9AA for negative mode measurements). The detection limit of two standard analytes was determined being below 164 pmol for reserpine (RP) and below 245 pmol for cholic acid (ChA). Additionally P3DDT was used successfully in first MALDI MS Imaging experiments allowing to visualize the tissue morphology of rat brain sections.

Selected for ACS Editors' Choice, JACS Spotlight, and supplementary journal cover (open access).

Featured by KAUST's Discovery, Phys.org, AAAS's EurekAlert!, and the COMPAMED Magazine.

ACS JACS Discovery Phys.org EurekAlert! COMPAMED

Concentrated Mixed Cation Acetate "Water-in-Salt" Solutions as Green and Low Cost High Voltage Electrolytes for Aqueous Batteries

M. R. Lukatskaya, J. Feldblyum, D. G. Mackanic, F. Lissel, D. L. Michels, Y. Cui, and Z. Bao.

Energy & Environmental Science, Royal Society of Chemistry (2018).

Electrolyte solutions are a key component of energy storage devices that significantly impact capacity, safety, and cost. Recent developments in "water-in-salt" (WIS) aqueous electrolyte research have enabled the demonstration of aqueous Li-ion batteries that operate with capacities and cyclabilities comparable with those of commercial non-aqueous Li-ion batteries. Critically, the use of aqueous electrolyte mitigates safety risks associated with non-aqueous electrolytes. However, the high cost and potential toxicity of imide-based WIS electrolytes limit their practical deployment. In this report, we disclose the efficacy of inexpensive, non-toxic mixed cation electrolyte systems for Li-ion batteries that otherwise provide the same benefits as current WIS electrolytes: extended electrochemical stability window and compatibility with traditional intercalation Li-ion battery electrode materials. We take advantage of the high solubility of potassium acetate to achieve the WIS condition in a eutectic mixture of lithium and potassium acetate; with water-to-cation ratio as low as 1.3. Our work suggests an important direction for the practical realization of safe, low-cost, and high-performance Li-ion batteries.

Selected as an outstanding "hot article" by the editors (open access).

Royal Society of Chemistry

Geometric-Integration Tools for the Simulation of Musical Sounds

A. Ishikawa, D. L. Michels, and T. Yaguchi.

Japan Journal of Industrial and Applied Mathematics, Springer (2018).

During the last decade, much attention has been given to sound rendering and the simulation of acoustic phenomena by solving appropriate models described by Hamiltonian partial differential equations. In this contribution, we introduce a procedure to develop appropriate tools inspired from geometric integration in order to simulate musical sounds. Geometric integrators are numerical integrators of excellent quality that are designed exclusively for Hamiltonian ordinary differential equations. The introduced procedure is a combination of two techniques in geometric integration: the semi-discretization method by Celledoni et al. (J Comput Phys 231:6770–6789, 2012) and symplectic partitioned Runge–Kutta methods. This combination turns out to be a right procedure that derives numerical schemes that are effective and suitable for computation of musical sounds. By using this procedure we derive a series of explicit integration algorithms for a simple model describing piano sounds as a representative example for virtual instruments. We demonstrate the advantage of the numerical methods by evaluating a variety of numerical test cases.

Springer Link Paper (PDF) BibTeX

Multi-Scale Terrain Texturing using Generative Adversarial Networks

J. Klein, S. Hartmann, M. Weinmann, and D. L. Michels.

Image and Vision Computing New Zealand (IVCNZ 2017), IEEE Xplore Digital Library (2017).

We propose a novel, automatic generation process for detail maps that allows the reduction of tiling artifacts in real-time terrain rendering. This is achieved by training a generative adversarial network (GAN) with a single input texture and subsequently using it to synthesize a huge texture spanning the whole terrain. The low-frequency components of the GAN output are extracted, down-scaled and combined with the high-frequency components of the input texture during rendering. This results in a terrain texture that is both highly detailed and non-repetitive, which eliminates the tiling artifacts without decreasing overall image quality. The rendering is efficient regarding both memory consumption and computational costs. Furthermore, it is orthogonal to other techniques for terrain texture improvements such as texture splatting and can directly be combined with them.

IEEE Xplore Digital Library

Interactive Wood Combustion for Botanical Tree Models

S. Pirk, M. Jarząbek, T. Hädrich, D. L. Michels, and W. Pałubicki.

ACM Transactions on Graphics (SIGGRAPH Asia 2017), ACM (2017).

We present a novel method for the combustion of botanical tree models. Tree models are represented as connected particles for the branching structure and a polygonal surface mesh for the combustion. Each particle stores biological and physical attributes that drive the kinetic behavior of a plant and the exothermic reaction of the combustion. Coupled with realistic physics for rods, the particles enable dynamic branch motions. We model material properties, such as moisture and charring behavior, and associate them with individual particles. The combustion is efficiently processed in the surface domain of the tree model on a polygonal mesh. A user can dynamically interact with the model by initiating fires and by inducing stress on branches. The flames realistically propagate through the tree model by consuming the available resources. Our method runs at interactive rates and supports multiple tree instances in parallel. We demonstrate the effectiveness of our approach through numerous examples and evaluate its plausibility against the combustion of real wood samples.

Featured in the conference's Technical Papers Trailer and by AAAS's EurekAlert!.

ACM Library Project Page Trailer EurekAlert! Two Minute Papers

Symbolic-Numeric Integration of the Dynamical Cosserat Equations

D. A. Lyakhov, V. P. Gerdt, A. G. Weber, and D. L. Michels.

Computer Algebra in Scientific Computing (CASC 2017), Springer (2017).

We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized α-method illustrating the computational efficiency of our approach for problems in structural mechanics.

Springer Link arXiv

A Stiffly Accurate Integrator for Elastodynamic Problems

D. L. Michels, V. T. Luan, and M. Tokman.

ACM Transactions on Graphics (SIGGRAPH 2017), ACM (2017).

We present a new integration algorithm for the accurate and efficient solution of stiff elastodynamic problems governed by the second-order ordinary differential equations of structural mechanics. Current methods have the shortcoming that their performance is highly dependent on the numerical stiffness of the underlying system that often leads to unrealistic behavior or a significant loss of efficiency. To overcome these limitations, we present a new integration method which is based on a mathematical reformulation of the underlying differential equations, an exponential treatment of the full nonlinear forcing operator as opposed to more standard partially implicit or exponential approaches, and the utilization of the concept of stiff accuracy which ensures that the efficiency of the simulations is significantly less sensitive to increased stiffness. As a consequence, we are able to tremendously accelerate the simulation of stiff systems compared to established integrators and significantly increase the overall accuracy. The advantageous behavior of this approach is demonstrated on a broad spectrum of complex examples like deformable bodies, textiles, bristles, and human hair. Our easily parallelizable integrator enables more complex and realistic models to be explored in visual computing without compromising efficiency.

Featured in the conference's Technical Papers Trailer and by UC News.

ACM Library Project Page Trailer UC News

Algorithmic Verification of Linearizability for Ordinary Differential Equations

D. A. Lyakhov, V. P. Gerdt, and D. L. Michels.

ACM International Symposium on Symbolic and Algebraic Computation (ISSAC 2017), ACM 2017.

For a nonlinear ordinary differential equation solved with respect to the highest order derivative and rational in the other derivatives and in the independent variable, we devise two algorithms to check if the equation can be reduced to a linear one by a point transformation of the dependent and independent variables. The first algorithm is based on a construction of the Lie point symmetry algebra and on the computation of its derived algebra. The second algorithm exploits the differential Thomas decomposition and allows not only to test the linearizability, but also to generate a system of nonlinear partial differential equations that determines the point transformation and the coefficients of the linearized equation. The implementation of both algorithms is discussed and their application is illustrated using several examples.

ACM SIGSAM Distinguished Paper Award.

ACM Library arXiv SIGSAM Awards

On Strongly Consistent Finite Difference Approximations to the Navier-Stokes Equations

D. A. Lyakhov, V. P. Gerdt, and D. L. Michels.

Foundations of Computational Mathematics (FoCM 2017), Symbolic Analysis Workshop (Poster), FoCM 2017.

The finite difference method is widely used for solving partial differential equations in the computational sciences. The decisive factor for its successful application is the quality of the underlying finite difference approximations. In this contribution, we present a computer algebra assisted approach to generate appropriate finite difference approximations to systems of polynomially nonlinear partial differential equations on regular Cartesian grids. The generated approximations satisfy the major quality criterion – strong consistency – which implies the preservation of fundamental algebraic properties of the system at the discrete level. This criterion admits a verification algorithm. We apply our approach to the Navier-Stokes equations and construct strongly consistent approximations. Moreover, we construct two approximations which are not only strongly consistent but also fully conservative.

Symbolic Analysis Workshop

Discrete Computational Mechanics for Stiff Phenomena

D. L. Michels and J. P. T. Mueller.

ACM SIGGRAPH Asia 2016, Course Notes, ACM (2016).

Many natural phenomena which occur in the realm of visual computing and computational physics, like the dynamics of cloth, fibers, fluids, and solids as well as collision scenarios are described by stiff Hamiltonian equations of motion, i.e. differential equations whose solution spectra simultaneously contain extremely high and low frequencies. This usually impedes the development of physically accurate and at the same time efficient integration algorithms. We present a straightforward computationally oriented introduction to advanced concepts from classical mechanics. We provide an easy to understand step-by-step introduction from variational principles over the Euler-Lagrange formalism and the Legendre transformation to Hamiltonian mechanics. Based on such solid theoretical foundations, we study the underlying geometric structure of Hamiltonian systems as well as their discrete counterparts in order to develop sophisticated structure preserving integration algorithms to efficiently perform high fidelity simulations.

ACM Library WWW

On the General Analytical Solution of the Kinematic Cosserat Equations

D. L. Michels, D. A. Lyakhov, V. P. Gerdt, Z. Hossain, I. H. Riedel-Kruse, and A. G. Weber.

Computer Algebra in Scientific Computing (CASC 2016), Springer (2016).

Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies a simple explicitly given algebraic relation. As our main theoretical result, in addition to the construction of the solution, we proof its generality. Based on this observation, a hybrid semi-analytical solver for highly viscous two-way coupled fluid-rod problems is developed which allows for the interactive high-fidelity simulations of flagellated microswimmers as a result of a substantial reduction of the numerical stiffness.

Springer Link Paper (PDF)