Related papers: Exact solutions for diffusive transport on heterog…
Various model problems of ``transport-limited dissolution'' in two dimensions are analyzed using time-dependent conformal maps. For diffusion-limited dissolution (reverse Laplacian growth), several exact solutions are discussed for the…
We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…
Cells and organisms follow aligned structures in their environment, a process that can generate persistent migration paths. Kinetic transport equations are a popular modelling tool for describing biological movements at the mesoscopic…
Spatial extent is a complicating factor in mathematical biology. The possibility that an action at point A cannot immediately affect what happens at point B creates the opportunity for spatial nonuniformity. This nonuniformity must change…
Equations for dislocation evolution bridge the gap between dislocation properties and continuum descriptions of plastic behavior of crystalline materials. Computer simulations can help us verify these evolution equations and find their…
In this article, we consider a species whose population density solves the steady diffusive logistic equation in a heterogeneous environment modeled with the help of a spatially non constant coefficient standing for a resources…
Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The…
For electron transport in parallel-plane semiconducting structures, a model is developed that unifies ballistic and diffusive transport and thus generalizes the Drude model. The unified model is valid for arbitrary magnitude of the mean…
This paper is concerned with a non-homogeneous in space and non-local in time random walk model for anomalous subdiffusive transport of cells. Starting with a Markov model involving a structured probability density function, we derive the…
The prediction of diffusion in solids is necessary to understand the microstructure evolution in materials out of equilibrium. Although one can reasonably predict diffusive transport coefficients using atomistic methods, these approaches…
We consider a family of models having an arbitrary positive amount of mass on each site and randomly exchanging an arbitrary amount of mass with nearest neighbor sites. We restrict to the case of diffusive models. We identify a class of…
Equations of the Loewner class subject to non-constant boundary conditions along the real axis, are formulated and solved giving the geodesic paths of slits growing in the upper half complex plane. The problem is motivated by Laplacian…
Sample-efficient domain adaptation is an open problem in robotics. In this paper, we present affine transport -- a variant of optimal transport, which models the mapping between state transition distributions between the source and target…
This chapter is about Complexity and Spatial Dynamics in Urban Systems. Strong inequalities in the size of cities and the apparent difficulty of limiting their growth raise practical issues for spatial planning. At a time when new…
We experimentally, numerically and analytically explore the diffusive transport of active colloidal particles with sensory delay, navigating motility landscapes in which the self-propulsion speed depends on space. We show how the transport…
We study a reaction-diffusion model posed on two distinct spatial scales that accounts for diffusion, aggregation, fragmentation, and deposition of populations of colloidal particles within a porous material. In this model, the macroscopic…
We consider a model for the dynamics of growing cell populations with heterogeneous mobility and proliferation rate. The cell phenotypic state is described by a continuous structuring variable and the evolution of the local cell population…
Based on a non-equilibrium mechanism for spatial pattern formation we study how position information can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing…
Complex spatial and temporal structures are inherent characteristics of turbulent fluid flows and comprehending them poses a major challenge. This comprehesion necessitates an understanding of the space of turbulent fluid flow…
Moving-habitat models track the density of a population whose suitable habitat shifts as a consequence of climate change. Whereas most previous studies in this area consider 1-dimensional space, we derive and study a spatially 2-dimensional…