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A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for…
Discriminative classifiers have become a foundational tool in deep learning for medical imaging, excelling at learning separable features of complex data distributions. However, these models often need careful design, augmentation, and…
Sparse-view sampling in dual-energy computed tomography (DECT) significantly reduces radiation dose and increases imaging speed, yet is highly prone to artifacts. Although diffusion models have demonstrated potential in effectively handling…
This paper considers a time-fractional diffusion-wave equation with a high-contrast heterogeneous diffusion coefficient. A numerical solution to this problem can present great computational challenges due to its multiscale nature.…
We consider a situation commonly encountered in microfluidics: two streams of miscible liquids are brought at a junction to flow side by side within a microchannel, allowing solutes to diffuse from one stream to the other and possibly…
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…
We report an approach to fully visualize the flow of two immiscible fluids through a model three-dimensional (3D) porous medium at pore-scale resolution. Using confocal microscopy, we directly image the drainage of the medium by the…
The analysis and design of advection-diffusion based molecular communication (MC) systems in cylindrical environments is of particular interest for applications such as micro-fluidics and targeted drug delivery in blood vessels. Therefore,…
There are many processes in cell biology that can be modeled in terms of particles diffusing in a two-dimensional (2D) or three-dimensional (3D) bounded domain $\Omega \subset \R^d$ containing a set of small subdomains or interior…
We study the diffusion-reaction-advection model for mobile chemical species together with the dissolution and precipitation of immobile species in a porous medium at the micro-scale. This leads to a system of semilinear parabolic partial…
Droplet patterns condensing on solid substrates (breath figures) tend to evolve into a self-similar regime, characterized by a bimodal droplet size distribution. The distributions comprise a bell-shaped peak of monodisperse large droplets,…
In this work we present a mathematical framework that quantifies the gas-exchange processes in the lung. The theory is based on the solution of the one-dimensional diffusion equation on a simplified model of lung septum. Gases dissolved…
In this paper, we investigate the use of diffusion models which are pre-trained on large-scale image-caption pairs for open-vocabulary 3D semantic understanding. We propose a novel method, namely Diff2Scene, which leverages frozen…
We present a general mechanistic model of mass diffusion for a composite sphere placed in a large ambient medium. The multi-layer problem is described by a system of diffusion equations coupled via interlayer boundary conditions such as…
The diffusion coefficient of a circular shaped inclusion in a liquid membrane is investigated by taking into account the interaction between membranes and bulk solvents of arbitrary thickness. As illustrative examples, the diffusion…
In this paper, we study the viscous fluid cosmological model that when certain conditions are invoked mimics the $\Lambda$CDM model. The background equations governing the evolution of viscous interacting fluids in a multifluid system are…
We introduce a \textit{non-modal} analysis technique that characterizes the diffusion properties of spectral element methods for linear convection-diffusion systems. While strictly speaking only valid for linear problems, the analysis is…
We propose a diffuse interface model to describe tumor as a multicomponent deformable porous medium. We include mechanical effects in the model by coupling the mass balance equations for the tumor species and the nutrient dynamics to a…
We investigate a single particle on a 3-dimensional, cubic lattice with a random on-site potential (3D Anderson model). We concretely address the question whether or not the dynamics of the particle is in full accord with the diffusion…
Denoising diffusion models have demonstrated outstanding results in 2D image generation, yet it remains a challenge to replicate its success in 3D shape generation. In this paper, we propose leveraging multi-view depth, which represents…