Related papers: Effective transient behaviour of heterogeneous med…
We investigate a two-component reaction-diffusion system with a slow-fast structure and spatially varying coefficients $f_1$ and $f_2$ appearing in the slow equation. Under mild boundedness and regularity conditions on $f_1$ and $f_2$ the…
In this note, we demonstrated for the first time that one can derive an expression for the effective diffusion coefficient, equal to the Lifson-Jackson formula, using a subsequent homogenization of the 1D reaction-diffusion-advection…
Real-world datasets are inherently heterogeneous, yet how per-class structural differences and sampling imbalance shape the training dynamics of diffusion models-and potentially exacerbate disparities-remains poorly understood. While models…
The final stage of latex film formation was simulated by introducing donors and acceptors into the adjacent compartments of a cube. Homogenous and/or heterogeneous donor-acceptor distributions were chosen for different types of simulations.…
We introduce a class of discrete random walk model driven by global memory effects. At any time the right-left transitions depend on the whole previous history of the walker, being defined by an urn-like memory mechanism. The characteristic…
The reaction-diffusion processes in a growing domain involves a dilution term that modifies the properties of the homogeneous state that, in contrast to a fixed domain, depends on time. We study how the dilution term changes the steady…
It is well known that the classical energetically consistent micropolar model has limits in simulating the frequency band structure of packed granular materials (see Merkel et al., 2011). It is here shown that if a standard continualization…
Understanding the structure of real data is paramount in advancing modern deep-learning methodologies. Natural data such as images are believed to be composed of features organized in a hierarchical and combinatorial manner, which neural…
The aim of the present study is to derive the effective quasi-static behaviour of a composite medium, made of a poroelastic matrix containing elastic impervious inclusions. For this purpose, the asymptotic homogenisation method is used. On…
We consider a system of differential equations in a fast long range dependent random environment and prove a homogenization theorem involving multiple scaling constants. The effective dynamics solves a rough differential equation, which is…
The application of diffusion transformers is suffering from their significant inference costs. Recently, feature caching has been proposed to solve this problem by reusing features from previous timesteps, thereby skipping computation in…
We investigate a reaction-diffusion problem in a two-component porous medium with a nonlinear interface condition between the different components. One component is connected and the other one is disconnected. The ratio between the…
We propose an efficient numerical strategy for simulating fluid flow through porous media with highly oscillatory characteristics. Specifically, we consider non-linear diffusion models. This scheme is based on the classical homogenization…
Understanding how species persist under interacting stressors is a central challenge in ecology. We develop a spatially explicit reaction-diffusion framework to investigate competing species in landscapes shaped by climate variability,…
We study the problem of homogenization for inertial particles moving in a time dependent random velocity field and subject to molecular diffusion. We show that, under appropriate assumptions on the velocity field, the large--scale,…
Long-range human movement generation remains a central challenge in computer vision and graphics. Generating coherent transitions across semantically distinct motion domains remains largely unexplored. This capability is particularly…
This work presents a rigorous prediction of the effective equations governing the paramagnetic-ferromagnetic phase transition in a perforated three-dimensional body. Assuming a periodic distribution of perforations, we investigate the…
Flows enabled by phoretic mechanisms are of significant interest in several biological and biomedical processes, such as bacterial motion and targeted drug delivery. Here, we develop a homogenization-based macroscopic boundary condition…
Diffusion generative models unlock new possibilities for inverse problems as they allow for the incorporation of strong empirical priors in scientific inference. Recently, diffusion models are repurposed for solving inverse problems using…
We introduce a homogenization approach to characterize the dynamical response of a generic dispersive spacetime crystal in the long-wavelength limit. The theory is applied to dispersive spacetime platforms with a travelling-wave modulation.…