相关论文: Modeling calcium dynamics in neurons with endoplas…
In this paper, we propose a linear and monolithic finite element method for the approximation of an incompressible viscous fluid interacting with an elastic and deforming plate. We use the arbitrary Lagrangian-Eulerian (ALE) approach that…
In the present work, we investigate a model of the invasion of healthy tissue by cancer cells which is described by a system of nonlinear PDEs consisting of a cross-diffusion-reaction equation and two additional nonlinear ordinary…
Neurons encode information about the environment through their activity. As animals explore the environment, neurons rapidly acquire selectivity for distinct features of the external world; characterizing how these selectivity patterns…
We present a robust computational framework for advective-diffusive-reactive systems that satisfies maximum principles, the non-negative constraint, and element-wise species balance property. The proposed methodology is valid on general…
Motivated by recent experiments, the isotropic-nematic phase transition in chromonic liquid crystals is studied. As temperature decreases, nematic nuclei nucleate, grow, and coalesce, giving rise to tactoid microstructures in an isotropic…
We study a mathematical model describing the dynamics of dislocation densities in crystals. This model is expressed as a one-dimensional system of a parabolic equation and a first order Hamilton-Jacobi equation that are coupled together. We…
In vivo calcium imaging through microscopes has enabled deep brain imaging of previously inaccessible neuronal populations within the brains of freely moving subjects. However, microendoscopic data suffer from high levels of background…
We consider a numerical scheme for the approximation of a system that couples the evolution of a two--dimensional hypersurface to a reaction--diffusion equation on the surface. The surfaces are assumed to be graphs and evolve according to…
This paper presents new analytical results for a class of nonlinear parabolic systems of partial different equations with small cross-diffusion which describe the macroscopic dynamics of a variety of large systems of interacting particles.…
Using an exactly soluble one-dimensional atomic model we explore the idea that the recently observed high-order nonlinearity in optical filaments is due to virtual transitions involving the continuum states. We show that the model's…
We present a detailed physiological model of the retina that includes the biochemistry and electrophysiology of phototransduction, neuronal electrical coupling, and the spherical geometry of the eye. The model is a parabolic-elliptic system…
The concentration of intracellular calcium ion (Ca$^{2+}$) exhibits complex oscillations, including bursting and chaos, as observed experimentally. These dynamics are influenced by inherent fluctuations within cells, which serve as crucial…
We consider one-dimensional diffusions, with polynomial drift and diffusion coefficients, so that in particular the motion can be space-inhomogeneous, interacting via one-sided reflections. The prototypical example is the well-known model…
Point polarizable molecules at fixed spatial positions have solvable electrostatic properties in classical approximation, the most familiar being the Clausius-Mossotti (CM) formula. This paper generalizes the model and imagines various…
It is important to understand the coordinated performance of cells in tissue. One possible mechanism in this coordination involves intracellular calcium signaling. The topology of intercellular connections in tissue should also play an…
We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…
A new computational method is presented for study suspensions of charged soft particles undergoing fluctuating hydrodynamic and electrostatic interactions. The proposed model is appropriate for polymers, proteins and porous particles…
We construct a finite element like scheme for fully non-linear integro-partial differential equations arising in optimal control of jump-processes. Special cases of these equations include optimal portfolio and option pricing equations in…
Changes in calcium concentration along the sperm flagellum regulate sperm motility and hyperactivation, characterized by an increased flagellar bend amplitude and beat asymmetry, enabling the sperm to reach and penetrate the ovum (egg). The…
We consider the numerical treatment of one of the most popular finite strain models of the viscoelastic Maxwell body. This model is based on the multiplicative decomposition of the deformation gradient, combined with Neo-Hookean…