​​

​​​​Selected Publications

ACM SIGGRAPH 2021

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

npj Quantum Information

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.

arXiv

CVPR

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

Scientific Reports

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

Elsevier

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.

Royal Society of Chemistry

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.

arXiv

Accurately Solving Physical Systems with Graph Learning

H. Shao, T. Kugelstadt, T. Hädrich, W. Pałubicki, J. Bender, S. Pirk, and D. L. Michels.
arXiv:2006.03897, Cornell University Library (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 physical systems 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. 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. Finally, we demonstrate that our method 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.

arXiv Project Page

American Chemical Society

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

ACM SIGGRAPH Asia 2020

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

ACM SIGGRAPH Asia 2020

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

Physical Review A

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

American Institute of Aeronautics and Astronautics

In Silico Design of Deep Space Optical Links

C. 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 Ka 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

American Chemical Society

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

SCA 2020

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

SCA 2020

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

American Institute of Physics

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

Scientific Reports

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

Springer Nature

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

arXiv

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

Nanomaterials

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

Physical Review A

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

Applied Sciences

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

Communications Physics

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

ACM SIGGRAPH 2019

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

ACM SIGGRAPH 2019

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

Springer Nature

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

Elsevier

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

RSS

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

CVPR

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

Springer Nature

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

Springer Nature

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

ECCV

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

BMVC

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)

American Chemical Society

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

Royal Society of Chemistry

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

Springer Nature

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

IEEE

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

ACM SIGGRAPH Asia 2017

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

Springer Nature

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

ACM SIGGRAPH 2017

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

ACM

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

FoCM

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

ACM SIGGRAPH Asia 2016

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

Springer Nature

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)