Related papers: Effective transient behaviour of heterogeneous med…
Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong…
In this work we examine the dispersion of conservative tracers (bromide and fluorescein) in an experimentally-constructed three-dimensional dual-porosity porous medium. The medium is highly heterogeneous ($\sigma_Y^2=5.7$), and consists of…
We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective…
Characterization of composite materials, whose properties vary in space over microscopic scales, has become a problem of broad interdisciplinary interest. In particular, estimation of the inhomogeneous transport coefficients, e.g. the…
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…
The goal of the paper is to describe the large time behaviour of a Markov process associated with a symmetric diffusion in a high-contrast random environment and to characterize the limit semigroup and the limit process under the diffusive…
Background and Objective: This proof of concept study investigates mathematical modelling of blood flow and oxygen transport in cerebral microcirculation, focusing on understanding hemodynamic responses. By coupling oxygen transport models…
In this work we use tempered fractional advection-diffusion equations to model the dispersive transport in disordered materials. A numerical method is derived to approximate the solution of such differential models and we prove that it is…
This paper presents a simple tool for characterising the timescale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in…
We study mean-field inclusion processes with an additional slow phase, in which particle interactions occur at a vanishing rate proportional to the inverse system size. In the thermodynamic limit, such systems exhibit condensation at high…
The phenomenon of macroscopic homogenization is illustrated with a simple example of diffusion. We examine the conditions under which a $d$--dimensional simple random walk in a symmetric random media converges to a Brownian motion. For…
We study memory based random walk models to understand diffusive motion in crowded heterogeneous environment. The models considered are non-Markovian as the current move of the random walk models is determined by randomly selecting a move…
A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
This article considers the computational (acoustic) wave propagation in strongly heterogeneous structures beyond the assumption of periodicity. A high contrast between the constituents of microstructured multiphase materials can lead to…
We introduce the concept of Randomly Modulated Gaussian Processes as a unifying framework for modeling, analyzing and classifying anomalous diffusion models in heterogeneous media. This formulation incorporates correlations in the…
Aggregations are emergent features common to many biological systems. Mathematical models to understand their emergence are consequently widespread, with the aggregation-diffusion equation being a prime example. Here we study the…
We present first elements of kinetic theory appropriate to the inhomogeneous phase of the HMF model. In particular, we investigate the case of strongly inhomogeneous distributions for $T\to 0$ and exhibit curious behaviour of the force…
We consider the homogenisation of a coupled reaction-diffusion process in a porous medium with evolving microstructure. A concentration-dependent reaction rate at the interface of the pores with the solid matrix induces a…
Direct numerical simulation of diffusion through heterogeneous media can be difficult due to the computational cost of resolving fine-scale heterogeneities. One method to overcome this difficulty is to homogenize the model by replacing the…