arXiv subjects

Roman Vetter

Publications and source records attributed to Roman Vetter.

At least 19 recordsLinked to original sources

arXiv2025

Simulating Organogenesis in COMSOL Multiphysics: Tissue Patterning with Directed Cell Migration

We present a COMSOL Multiphysics implementation of a continuum model for directed cell migration, a key mechanism underlying tissue self-organization and morphogenesis. The model is formulated as a partial integro-differential equation (PIDE), combining random motility with non-local, density-dependent guidance cues to capture phenomena such as cell sorting and aggregation. Our framework supports simulations in one, two, and three dimensions, with both zero-flux and periodic boundary conditions, and can be reformulated in a Lagrangian setting to efficiently handle tissue growth and domain deformation. We demonstrate that COMSOL Multiphysics enables a flexible and accessible implementation of PIDEs, providing a generalizable platform for studying collective cell behavior and pattern formation in complex biological contexts.

physics.bio-ph↗

arXiv2025

TinyDEM: Minimal open granular DEM code with sliding, rolling and twisting friction

This article introduces TinyDEM, a lightweight implementation of a full-fledged discrete element method (DEM) solver in 3D. Newton's damped equations of motion are solved explicitly for translations and rotations of a polydisperse ensemble of dry, soft, granular spherical particles, using quaternions to represent their orientation in space without gimbal lock. Particle collisions are modeled as inelastic and frictional, including full exchange of torque. With a general particle-mesh collision routine, complex rigid geometries can be simulated. TinyDEM is designed to be a compact standalone program written in simple C++11, devoid of explicit pointer arithmetics and advanced concepts such as manual memory management or polymorphism. It is parallelized with OpenMP and published freely under the 3-clause BSD license. TinyDEM can serve as an entry point into classical DEM simulations or as a foundation for more complex models of particle dynamics.

physics.comp-ph↗

arXiv2025

PINNverse: Accurate parameter estimation in differential equations from noisy data with constrained physics-informed neural networks

Parameter estimation for differential equations from measured data is an inverse problem prevalent across quantitative sciences. Physics-Informed Neural Networks (PINNs) have emerged as effective tools for solving such problems, especially with sparse measurements and incomplete system information. However, PINNs face convergence issues, stability problems, overfitting, and complex loss function design. Here we introduce PINNverse, a training paradigm that addresses these limitations by reformulating the learning process as a constrained differential optimization problem. This approach achieves a dynamic balance between data loss and differential equation residual loss during training while preventing overfitting. PINNverse combines the advantages of PINNs with the Modified Differential Method of Multipliers to enable convergence on any point on the Pareto front. We demonstrate robust and accurate parameter estimation from noisy data in four classical ODE and PDE models from physics and biology. Our method enables accurate parameter inference also when the forward problem is expensive to solve.

cs.LG↗

arXiv2025

PolyMorph: Extension of PolyHoop for tissue morphogenesis coupled to chemical signaling

We present PolyMorph, a lightweight standalone C++ program that extends its predecessor PolyHoop by a finite-difference solver for multi-component reaction-advection-diffusion equations. PolyMorph simulates two integral parts of tissue morphogenesis in two dimensions: 1) the mechanics of cellular deformation, growth and proliferation, and 2) transport and reaction of an arbitrary number of chemical species. Both of these components are bidirectionally coupled, allowing cells to base their behavior on local information on concentrations and flow, and allowing the chemical transport and reaction kinetics to depend on spatial information such as the local cell type. This bidirectional feedback makes PolyMorph a versatile tool to study a variety of cellular morphogenetic processes such as chemotaxis, cell sorting, tissue patterning with morphogen gradients, Turing patterning, and diffusion- or supply-limited growth with sub-cellular resolution.

cond-mat.soft↗

arXiv2024

Reply to: Assessing the precision of morphogen gradients in neural tube development

In a recent article [Vetter and Iber, Nat. Commun. 13, 1145 (2022)], we demonstrated that single morphogen gradients in the developing mouse neural tube can carry sufficient positional accuracy to explain the patterning precision of progenitor domain boundaries. Zagorski et al. had previously concluded otherwise [Zagorski et al., Science 356, 1379-1383 (2017)], based on methodological inconsistencies that we have revealed. The authors now comment on our work with a Matters Arising letter. We rebut their criticism point by point in the Supplement, and summarize the main aspects here.

physics.bio-ph↗

arXiv2023

A Geometric Mapping from Rectilinear Material Orthotropy to Isotropy: Insights to Plates and Shells

Orthotropic shell structures are ubiquitous in biology and engineering, from bacterial cell walls to reinforced domes. We present a rescaling transformation that maps an orthotropic shallow shell to an isotropic one with a different local geometry. The mapping is applicable to any shell section for which the material orthotropy directions match the principal curvature directions, assuming a commonly used form for the orthotropic shear modulus. Using the rescaling transformation, we derive exact expressions for the buckling pressure as well as the linear indentation response of orthotropic cylinders and general ellipsoids of revolution, which we verify against numerical simulations. Our analysis disentangles the separate contributions of geometric and material anisotropy to shell rigidity. In particular, we identify the geometric mean of orthotropic elastic constants as the key quantifier of material stiffness, playing a role akin to the Gaussian curvature which captures the geometric stiffness contribution. Besides providing insights into the mechanical response of orthotropic shells, our work rigorously establishes the validity of isotropic approximations to orthotropic shells and also identifies situations in which these approximations might fail.

cond-mat.soft↗

arXiv2023

PolyHoop: Soft particle and tissue dynamics with topological transitions

We present PolyHoop, a lightweight standalone C++ implementation of a mechanical model to simulate the dynamics of soft particles and cellular tissues in two dimensions. With only few geometrical and physical parameters, PolyHoop is capable of simulating a wide range of particulate soft matter systems: from biological cells and tissues to vesicles, bubbles, foams, emulsions, and other amorphous materials. The soft particles or cells are represented by continuously remodeling, non-convex, high-resolution polygons that can undergo growth, division, fusion, aggregation, and separation. With PolyHoop, a tissue or foam consisting of a million cells with high spatial resolution can be simulated on conventional laptop computers.

cond-mat.soft↗

arXiv2022

Bacterial biofilms use chiral branches to escape crowded environments by tracking oxygen gradient

Bacterial biofilms collectively develop distinct and ordered structures, including fibers, bundles, and branches. Often, it is unclear how these structural motifs convey specific advantages to bacterial strains under challenging conditions. In oxygen-limited environments, dense bacterial aggregates generally deplete oxygen, which leads to arrest of bacterial growth. However, we observed that biofilm-forming Bacillus subtilis could use branching patterns to escape from these crowded regions by tracking the oxygen gradient. The process depends on the chain-forming ability of the biofilm. As a result of collective branching triggered by bending and mechanical buckling, bacteria can extend from the oxygen-depleted biofilm core to the oxygen available periphery. Remarkably, these bacterial branches are strongly chiral and curve in a clockwise direction. Our analysis revealed that the surface friction and axial rotation of the twisting cell wall break left-right symmetry on solid surfaces and drive chiral bending of bacterial chains. We further observed that the chirality of individual branches could propagate across a large scale and shape the macroscopic morphology of the colony under a limited spatiotemporal growth profile. Taken together, our results provide new insights into how simple physical interactions lead to bacterial collaboration and promote the survival of biofilm-forming strains in challenging environments.

cond-mat.soft↗

arXiv2021

Large-scale orientational order in bacterial colonies during inward growth

During colony growth, complex interactions regulate the bacterial orientation, leading to the formation of large-scale ordered structures, including topological defects and microdomains. These structures may benefit bacterial strains, providing invasive advantages during colonization. Active matter dynamics of growing colonies drives the emergence of these ordered structures. However, additional biomechanical factors also play a significant role during this process. Here we show that the velocity profile of growing colonies creates strong radial orientation during inward growth when crowded populations invade a closed area. During this process, growth geometry sets virtual confinement and dictates the velocity profile. Herein, flow-induced alignment and torque balance on the rod-shaped bacteria significantly differed, resulting in new stable orientational equilibrium in the radial direction. Our analysis revealed that the dynamics of these orientational defects depend on bacterial length and can promote the survival of the longest bacteria around localized nutritional hot spots. The present results indicate a new mechanism underlying structural order and provide mechanistic insights into the dynamics of bacterial growth on complex surfaces.

physics.bio-ph↗

arXiv2020

Modelling the Effects of using Gas Diffusion Layers with Patterned Wettability for Advanced Water Management in Proton Exchange Membrane Fuel Cells

We present a macrohomogeneous two-phase model of a proton exchange membrane fuel cell (PEMFC). The model takes into account the mechanical compression of the gas diffusion layer (GDL), the two-phase flow of water, the transport of the gas species and the electrochemical reaction of the reactant gases. The model was used to simulate the behavior of a PEMFC with a patterned GDL. The results of the reduced model, which considers only the mechanical compression and the two-phase flow, are compared to the experimental ex-situ imbibition data obtained by neutron radiography imaging. The results are in good agreement. Additionally, by using all model features, a simulation of an operating fuel cell has been performed to study the intricate couplings in an operating fuel cell and to examine the patterned GDL effects. The model confirms that the patterned GDL design liberates the pre-defined domains from liquid water and thus locally increases the oxygen diffusivity.

physics.app-ph↗

arXiv2020

Simulating isothermal aging of snow

A Monte Carlo algorithm to simulate the isothermal recrystallization process of snow is presented. The snow metamorphism is approximated by two mass redistribution processes, surface diffusion and sublimation-deposition. The algorithm is justified and its parametrization is determined. The simulation results are compared to experimental data, in particular, the temporal evolution of the specific surface area and the ice thickness. We find that the two effects of surface diffusion and sublimation-deposition can accurately model many aspects of the isothermal metamorphism of snow. Furthermore, it is shown that sublimation-deposition is the dominant contribution for temperatures close to the melting point, whereas surface diffusion dominates at temperatures far below the melting point. A simple approximation of gravitational compaction is implemented to simulate density change.

cond-mat.soft↗

arXiv2019

Collapse of orthotropic spherical shells

We report on the buckling and subsequent collapse of orthotropic elastic spherical shells under volume and pressure control. Going far beyond what is known for isotropic shells, a rich morphological phase space with three distinct regimes emerges upon variation of shell slenderness and degree of orthotropy. Our extensive numerical simulations are in agreement with experiments using fabricated polymer shells. The shell buckling pathways and corresponding strain energy evolution are shown to depend strongly on material orthotropy. We find surprisingly robust orthotropic structures with strong similarities to stomatocytes and tricolpate pollen grains, suggesting that the shape of several of Nature's collapsed shells could be understood from the viewpoint of material orthotropy.

cond-mat.soft↗

arXiv2018

Emergence of active nematics in bacterial biofilms

Growing tissue and bacterial colonies are active matter systems where cell divisions and cellular motion generate active stress. Although they operate in the non-equilibrium regime, these biological systems can form large-scale ordered structures such as nematically aligned cells, topological defects, and fingerings. Mechanical instabilities also play an essential role during growth by generating large structural folding. How active matter dynamics and mechanical instabilities together develop large-scale order in growing tissue is not well understood. Here, we use chain forming Bacillus subtilis, also known as a biofilm, to study the direct relation between active stress and nematic ordering. We find that a bacterial biofilm has intrinsic length scales above which series of mechanical instabilities occur. Localized stress and friction control both linear buckling and edge instabilities. Remarkably, these instabilities develop nematically aligned cellular structures and create pairs of motile and stationary topological defects. We also observe that stress distribution across the biofilm strongly depends on the defect dynamics which can further initiate the formation of sporulation sites by creating three-dimensional structures. By investigating the development of bacterial biofilms and their mechanical instabilities we are proposing a new type of active matter system which provides a unique platform to study the essential roles of nematics in growing biological tissue.

physics.bio-ph↗

arXiv2018

Experimental parameter uncertainty in PEM fuel cell modeling. Part II: Sensitivity analysis and importance ranking

Numerical modeling of proton exchange membrane fuel cells is at the verge of becoming predictive. A crucial requisite for this, though, is that material properties of the membrane-electrode assembly and their functional dependence on the conditions of operation are known with high precision. In this bipartite paper series we determine the most critical transport parameters for which accurate experimental characterization is required in order to enable the simulation of fuel cell operation with sufficient confidence from small to large current densities. In Part II, we employ the two-phase model developed in Part I to carry out extensive forward uncertainty propagation analyses. These include the study of local parameter sensitivity in the vicinity of a baseline parameter set, and a global sensitivity analysis in which a broad range of operating conditions and material properties is covered. A comprehensive ranking list of model parameters is presented, sorted by impact on predicted fuel cell properties such as the current-voltage characteristics and water balance. The top five in this list are, in this order: The membrane hydration isotherm, the electro-osmotic drag coefficient, the membrane thickness, the water diffusivity in the ionomer and its ionic conductivity.

physics.app-ph↗

arXiv2018

Experimental parameter uncertainty in PEM fuel cell modeling. Part I: Scatter in material parameterization

Ever since modeling has become a mature part of proton exchange membrane fuel cell (PEMFC) research and development, it has been plagued by significant uncertainty lying in the detailed knowledge of material properties required. Experimental data published on several transport coefficients are scattered over orders of magnitude, even for the most extensively studied materials such as Nafion membranes, for instance. For PEMFC performance models to become predictive, high-quality input data is essential. In this bipartite paper series, we determine the most critical transport parameters for which accurate experimental characterization is required in order to enable performance prediction with sufficient confidence from small to large current densities. In the first part, a macro-homogeneous two-phase membrane-electrode assembly model is furnished with a comprehensive set of material parameterizations from the experimental and modeling literature. The computational model is applied to demonstrate the large spread in performance prediction resulting from experimentally measured or validated material parameterizations alone. The result of this is a ranking list of material properties, sorted by induced spread in the fuel cell performance curve. The three most influential parameters in this list stem from membrane properties: The Fickean diffusivity of dissolved water, the protonic conductivity and the electro-osmotic drag coefficient.

physics.app-ph↗

arXiv2018

Free open reference implementation of a two-phase PEM fuel cell model

In almost 30 years of PEM fuel cell modeling, countless numerical models have been developed in science and industrial applications, almost none of which have been fully disclosed to the public. There is a large need for standardization and establishing a common ground not only in experimental characterization of fuel cells, but also in the development of simulation codes, to prevent each research group from having to start anew from scratch. Here, we publish the first open standalone implementation of a full-blown, steady-state, non-isothermal two-phase model for low-temperature PEM fuel cells. It is based on macro-homogeneous modeling approaches and implements the most essential through-plane transport processes in a five-layer MEA. The focus is on code simplicity and compactness with only a few hundred lines of clearly readable code, providing a starting point for more complex model development. The model is implemented as a standalone MATLAB function, based on MATLAB's standard boundary value problem solver. The default simulation setup reflects wide-spread commercially available MEA materials. Operating conditions recommended for automotive applications by the European Commission are used to establish new fuel cell simulation base data, making our program a valuable candidate for model comparison, validation and benchmarking.

physics.comp-ph↗

arXiv2015

Packing of elastic wires in flexible shells

The packing problem of long thin filaments that are injected into confined spaces is of fundamental interest for physicists and biologists alike. How linear threads pack and coil is well known only for the ideal case of rigid containers, though. Here, we force long elastic rods into flexible spatial confinement borne by an elastic shell to examine under which conditions recently acquired knowledge on wire packing in rigid spheres breaks down. We find that unlike in rigid cavities, friction plays a key role by giving rise to the emergence of two distinct packing patterns. At low friction, the wire densely coils into an ordered toroidal bundle with semi-ellipsoidal cross-section, while at high friction, it packs into a highly disordered, hierarchic structure. These two morphologies are shown to be separated by a continuous phase transition. Our findings demonstrate the dramatic impact of friction and confinement elasticity on filamentous packing and might drive future research on such systems in physics, biology and even medical technology toward including these mutually interacting effects.

cond-mat.soft↗

arXiv2015

Orthotropic rotation-free thin shell elements

A method to simulate orthotropic behaviour in thin shell finite elements is proposed. The approach is based on the transformation of shape function derivatives, resulting in a new orthogonal basis aligned to a specified preferred direction for all elements. This transformation is carried out solely in the undeformed state leaving minimal additional impact on the computational effort expended to simulate orthotropic materials compared to isotropic, resulting in a straightforward and highly efficient implementation. This method is implemented for rotation-free triangular shells using the finite element framework built on the Kirchhoff--Love theory employing subdivision surfaces. The accuracy of this approach is demonstrated using the deformation of a pinched hemispherical shell (with a 18° hole) standard benchmark. To showcase the efficiency of this implementation, the wrinkling of orthotropic sheets under shear displacement is analyzed. It is found that orthotropic subdivision shells are able to capture the wrinkling behavior of sheets accurately for coarse meshes without the use of an additional wrinkling model.

math.NA↗