The Cahn-Hilliard equation is a fundamental model that describes the phase separation
process in multi-component mixtures. It has been successfully extended to many different …

In this paper, we propose and analyze a positivity-preserving, energy stable numerical
scheme for a certain type of reaction-diffusion systems involving the Law of Mass Action with …

In this paper, we summarize some recent advances related to the energetic variational
approach (EnVarA), a general variational framework of building thermodynamically …

We present a detailed convergence analysis for an operator splitting scheme proposed in
[C. Liu, C. Wang, and Y. Wang, J. Comput. Phys., 436 (2021), 110253] for a reaction …

Variational methods have been widely used in soft matter physics for both static and
dynamic problems. These methods are mostly based on two variational principles: the …

We present a structure-preserving Eulerian algorithm for solving-gradient flows and a
structure-preserving Lagrangian algorithm for solving generalized diffusions. Both …

A second-order accurate in time, positivity-preserving, and unconditionally energy stable
operator splitting scheme is proposed and analyzed for reaction-diffusion systems with the …

Simple Summary Since the micro-environment of colonic tumors, including their immune
structure would affect the response to treatments, we study the response of five groups of …

Every colon cancer has its own unique characteristics, and therefore may respond differently
to identical treatments. Here, we develop a data driven mathematical model for the …

We derive a continuum sharp-interface model for moving contact lines with soluble
surfactants in a thermodynamically consistent framework. The model consists of the …