Related papers: Exact solutions for diffusive transport on heterog…
We present a domain decomposition approach for the simulation of charge transport in heterojunction semiconductors. The problem is characterized by a large variation of primary variables across an interface region of a size much smaller…
We model two time and space scales discrete observations by using a unique continuous diffusion process with time dependent coefficient. We define new parameters for the large scale model as functions of the small scale distribution…
We propose a novel multiple-scale spatial marching method for flows with slow streamwise variation. The key idea is to couple the boundary region equations, which govern large-scale flow evolution, with local exact coherent structures that…
A living cell's interior is one of the most complex and intrinsically dynamic systems, providing an elaborate interplay between cytosolic crowding and ATP-driven motion, which controls cellular functionality. Here, we investigated two…
High-fidelity numerical simulations of chaotic, high dimensional nonlinear dynamical systems are computationally expensive, necessitating the development of efficient surrogate models. Most surrogate models for such systems are…
This work concerns efficient and reliable numerical simulations of the dynamic behaviour of a moving-boundary model for tubulin-driven axonal growth. The model is nonlinear and consists of a coupled set of a partial differential equation…
This paper studies spatial patterns formed by proximate population migration driven by real wage gradients and other idiosyncratic factors. The model consists of a tractable core-periphery model incorporating a quasi-linear log utility…
Mathematical models of diffusive transport underpin our understanding of chemical, biochemical and biological transport phenomena. Analysis of such models often focusses on relatively simple geometries and deals with diffusion through…
Recently a Dynamic-Monge-Kantorovich formulation of the PDE-based $L^1$-optimal transport problem was presented. The model considers a diffusion equation enforcing the balance of the transported masses with a time-varying conductivity that…
In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic…
Transport of rodlike particles in confinement environments of macromolecular networks plays crucial roles in many important biological processes and technological applications. The relevant understanding has been limited to thin rods with…
This paper deals with the unsupervised domain adaptation problem, where one wants to estimate a prediction function $f$ in a given target domain without any labeled sample by exploiting the knowledge available from a source domain where…
Spatial self-organization emerges in distributed systems exhibiting local interactions when nonlinearities and the appropriate propagation of signals are at work. These kinds of phenomena can be modeled with different frameworks, typically…
We study the effect of disorder on the particle density evolution in a classical Hamiltonian driven lattice setup. If the disorder is localized within a finite sub-domain of the lattice, the emergence of strong tails in the density…
We consider Markov models of large-scale networks where nodes are characterized by their local behavior and by a mobility model over a two-dimensional lattice. By assuming random walk, we prove convergence to a system of partial…
Adaptive transport networks in biological and physical systems exhibit hierarchical organization, characteristic channel spacing, and robust scaling relations. Existing adaptive network models, formulated on a lattice, successfully…
Diffusion generative models have demonstrated remarkable success in visual domains such as image and video generation. They have also recently emerged as a promising approach in robotics, especially in robot manipulations. Diffusion models…
Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…
A ubiquitous observation in cell biology is that diffusion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This…
The basic conceptual picture and theoretical basis for development of transport equations in porous media are examined. The general form of the governing equations is derived for conservative chemical transport in heterogeneous geological…