In this paper, we propose a mesh-free method to solve interface problems using the deep
learning approach. Two types of PDEs are considered. The first one is an elliptic PDE with a …

In this paper, we propose a novel mesh-free method for solving nonconvex energy
minimization problems for martensitic phase transitions and twinning in crystals using the …

A cell's ability to change shape is one of the most fundamental biological processes and is
essential for maintaining healthy organisms. When the ability to control shape goes awry, it …

A living cell actively generates traction forces on its environment with its actin cytoskeleton.
These forces deform the cell elastic substrate which, in turn, affects the traction forces …

The aim of this paper is to place the cell locomotion problem within the general framework of
classical continuum mechanics, and while doing so, to account for the deformation of the …

Many practical problems, including modeling composite materials, nuclear waste disposal,
oil reservoir simulations, and flows in porous medium, commonly involve interface problems …

Actin growth is a fundamental biophysical process and it is, at the same time, a prototypical
example of diffusion-mediated surface growth. We formulate a coupled chemo-mechanical …

The conditions under which biological cells switch from a static to a motile state are
fundamental to the understanding of many healthy and pathological processes. In this …

We propose a mesh-free method to solve nonconvex energy minimization problems for
martensitic phase transitions and twinning in crystals, using the deep learning approach …

Cell migration is one of the most studied phenomena in biology since it plays a fundamental
role in many physiological and pathological processes such as morphogenesis, wound …