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This paper is devoted to the analysis of a numerical scheme for the coagulation and fragmentation equation with diffusion in space. A finite volume scheme is developed, based on a conservative formulation of the space nonhomogeneous…
We present a continuum approach to model segregation of size-bidisperse granular materials in unsteady bounded heap flow as a prototype for modeling segregation in other time varying flows. In experiments, a periodically modulated feed rate…
Drug-Filled Porous Implants (DFPIs) are an innovative solution for delivering drugs in a controlled and sustained manner to target sites. To optimize their performance across various physiological conditions, it is essential to understand…
Drug discovery is a complex process that involves multiple stages and tasks. However, existing molecular generative models can only tackle some of these tasks. We present Generalist Molecular generative model (GenMol), a versatile framework…
Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative…
We focus on the qualitative analysis of a reaction-diffusion with spatial heterogeneity. The system is a generalization of the well known FitzHugh-Nagumo system in which the excitability parameter is space dependent. This heterogeneity…
Dynamic homogenization aims at describing the macroscopic characteristics of wave propagation in microstructured systems. Using a simple method, we derive frequency-dependent homogenized parameters that reproduce the exact dispersion…
We consider a reaction-diffusion system which may serve as a model for a ferment catalytic reaction in chemistry. The model consists of a system of reaction diffusion equations with unbounded time dependent coefficients and different…
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…
In this paper, we study a parabolic reaction diffusion system with constraints that model biofilm growth. Within a unified framework encompassing multiple numerical schemes, we derive the first general convergence rates for approximating…
The reaction-diffusion models have been extensively applied to explain the mechanism of pattern formations in early embryogenesis based on geometrically confined microtissues consisting of human pluripotent stem cells. Recently, mechanical…
Generative AI presents chemists with novel ideas for drug design and facilitates the exploration of vast chemical spaces. Diffusion models (DMs), an emerging tool, have recently attracted great attention in drug R\&D. This paper…
We consider a reaction-diffusion-advection problem in a perforated medium, with nonlinear reactions in the bulk and at the microscopic boundary, and low diffusion scaling. The microstructure changes in time; the microstructural evolution is…
Recent advances in generative modeling with diffusion processes (DPs) enabled breakthroughs in image synthesis. Despite impressive image quality, these models have various prompt compliance problems, including low recall in generating…
Motivated by bacterial chemotaxis and multi-species ecological interactions in heterogeneous environments, we study a general one-dimensional reaction-cross-diffusion system in the presence of spatial heterogeneity in both transport and…
Reaction--diffusion mechanism are a robust paradigm that can be used to represent many biological and physical phenomena over multiple spatial scales. Applications include intracellular dynamics, the migration of cells and the patterns…
The release of hydrophilic solutes from micron scale particulate formulations can be understood as an interfacial transport problem in which diffusion across a heterogeneous amphiphilic coating competes with dissolution and convective…
We investigate diffusion of a peptide drug through Graphene Oxide (GO) membranes that are modeled as a porous layered laminate constructed from aligned flakes of GO. Our experiments using a peptide drug show a tunable non-linear dependence…
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…
Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate…