Related papers: A Hybrid Finite-Difference-Particle Method for Che…
In this article, we introduce a new method for discretizing micro-macro models of dilute polymeric fluids by integrating a finite element discretization for the macroscopic fluid dynamic equation with a deterministic variational particle…
The Poisson-Nernst-Planck (PNP) equations are fundamental for modeling ion transport in electrochemical systems, capturing the intricate interplay of concentration gradients, electric fields, and ion fluxes essential for applications such…
Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate…
Optical microscopy provides rich spatio-temporal information characterizing in vivo molecular motion. However, effective forces and other parameters used to summarize molecular motion change over time in live cells due to latent state…
The continuum description of active particle systems is an efficient instrument to analyze a finite size particle dynamics in the limit of a large number of particles. However, it is often the case that such equations appear as nonlinear…
Chemically-active colloids modify the concentration of chemical solutes surrounding them in order to self-propel. In doing so, they generate long-ranged hydrodynamic flows and chemical gradients that modify the trajectories of other…
A novel hybrid spectral difference/embedded finite volume method is introduced in order to apply a discontinuous high-order method for large scale engineering applications involving discontinuities in the flows with complex geometries. In…
We use a deterministic particle method to produce numerical approximations to the solutions of an evolution cross-diffusion problem for two populations. According to the values of the diffusion parameters related to the intra and…
A hyperbolic system approach is proposed for robust computation of anisotropic diffusion equations that appear in quasineutral plasmas. Though the approach exhibits merits of high extensibility and accurate flux computation, the…
The aim of this paper is to analyze a model for chemotaxis based on a local sensing mechanism instead of the gradient sensing mechanism used in the celebrated minimal Keller-Segel model. The model we study has the same entropy as the…
We study existence of solutions in the variational sense for a class of stochastic phase-field models describing moving boundary problems. The models consist of stochastic reaction-diffusion equations with singular diffusion forced by a…
Computational fluid dynamics and discrete element method (CFD-DEM) coupling is an efficient and powerful tool to simulate particle-fluid systems. However, current volume-averaged CFD-DEM relying on direct grid-based mapping between the…
Cells encounter a diverse array of physical and chemical signals as they navigate their natural surroundings. However, their response to the simultaneous presence of multiple cues remains elusive. Particularly, the impact of topography…
We study a chemotaxis system that includes two competitive prey and one predator species in a two-dimensional domain, where the movement of prey (resp. predators) is driven by chemicals secreted by predators (resp. prey), called mutually…
Hybrid particle-field methods are computationally efficient approaches for modelling soft matter systems. So far applications of these methodologies have been limited to constant volume conditions. Here, we reformulate particle-field…
We introduce the multivariate decomposition finite element method (MDFEM) for solving elliptic PDEs with uniform random diffusion coefficients. We show that the MDFEM can be used to reduce the computational complexity of estimating the…
Stochastic reaction-diffusion models are now a popular tool for studying physical systems in which both the explicit diffusion of molecules and noise in the chemical reaction process play important roles. The Smoluchowski diffusion-limited…
Convergence of solutions to a partially diffusive chemotaxis system with indirect signal production and phenotype switching is shown in a two-dimensional setting when the switching rate increases to infinity, thereby providing a rigorous…
We demonstrate that the finite difference grid method (FDM) can be simply modified to satisfy the variational principle and enable calculations of both real and complex poles of the scattering matrix. These complex poles are known as…
We propose numerical simulations of viscoelastic fluids based on a hybrid algorithm combining Lattice-Boltzmann models (LBM) and Finite Differences (FD) schemes, the former used to model the macroscopic hydrodynamic equations, and the…