In this article we consider finite element methods for approximating the solution of partial
differential equations on surfaces. We focus on surface finite elements on triangulated …

We characterize and remedy a failure mode that may arise from multi-scale dynamics with
scale imbalances during training of deep neural networks, such as physics informed neural …

Cells are highly organized objects containing millions of molecules. Each biomolecule has a
specific shape in order to interact with others in the complex machinery. Spatial dynamics …

This essay provides an introduction to the terminology, concepts, methods, and challenges
of image‐based modeling in biology. Image‐based modeling and simulation aims at using …

Mechanochemical processes in thin biological structures, such as the cellular cortex or
epithelial sheets, play a key role during the morphogenesis of cells and tissues. In particular …

Asymmetric cell division plays a crucial role in cell differentiation, unequal replicative
senescence, and stem cell maintenance. In budding yeast, the identities of mother and …

In this paper we present a high-order kernel method for numerically solving diffusion and
reaction-diffusion partial differential equations (PDEs) on smooth, closed surfaces …

We present a computational study of bending models for the curvature elasticity of lipid
bilayer membranes that are relevant for simulations of vesicles and red blood cells. We …

We present and analyze a Virtual Element Method (VEM) for the Laplace-Beltrami equation
on a surface in R3, that we call Surface Virtual Element Method (SVEM). The method …

In this article we present a new implicit numerical scheme for reaction–diffusion–advection
equations on an evolving in time hypersurface Γ (t). The partial differential equations are …