Related papers: Splitting Schemes & Segregation In Reaction-(Cross…
We consider reaction diffusion systems where components diffuse inside the domain and react on the surface through mass transport type boundary conditions. Under reasonable hypotheses, we establish the existence of component wise…
As language models become more general purpose, increased attention needs to be paid to detecting out-of-distribution (OOD) instances, i.e., those not belonging to any of the distributions seen during training. Existing methods for…
Flowing granular materials segregate due to differences in particle size (driven by percolation) and density (driven by buoyancy). Modelling the segregation of mixtures of large/heavy particles and small/light particles is challenging due…
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or…
We establish certain maximum principles for a class of strongly coupled elliptic (or cross diffusion) systems of $m\ge2$ equations. The reaction parts can be non cooperative. These new results will be crucial in obtaining coexistence and…
A finite-volume scheme for a cross-diffusion model arising from the mean-field limit of an interacting particle system for multiple population species is studied. The existence of discrete solutions and a discrete entropy production…
Density-based Out-of-distribution (OOD) detection has recently been shown unreliable for the task of detecting OOD images. Various density ratio based approaches achieve good empirical performance, however methods typically lack a…
Strang splitting is a widely used second-order method for solving diffusion-reaction problems. However, its convergence order is often reduced to order $1$ for Dirichlet boundary conditions and to order $1.5$ for Neumann and Robin boundary…
We consider a distributed source coding system in which several observations are communicated to the decoder using limited transmission rate. The observations must be separately coded. We introduce a robust distributed coding scheme which…
We show that the Turing patterns in reaction systems with subdiffusion can be replicated in an effective system with Markovian cross-diffusion. The effective system has the same Turing instability as the original system, and the same…
This paper deals with the existence of global weak solutions for a wide class of (multiple species) cross-diffusions systems. The existence is based on two different ingredients: an entropy estimate giving some gradient control and a…
In this work, we study the existence and nonexistence of nonnegative solutions to a class of nonlocal elliptic systems set in a bounded open subset of $\mathbb{R}^N$. The diffusion operators are of type $u_i\mapsto d_i(-\Delta)^{s_i}u_i$…
Predicting particle segregation has remained challenging due to the lack of a general model for the segregation velocity that is applicable across a range of granular flow geometries. Here, a segregation velocity model for dense granular…
A new upscaling procedure that provides 1D representations of 2D mixing-limited reactive transport systems is developed and applied. A key complication with upscaled models in this setting is that the procedure must differentiate between…
We introduce the notion of corresponding a chemical reaction network to a split network translation, and use this novel process to extend the scope of existing network-based theory for characterizing the steady state set of mass-action…
A wide range of new Q-conditional symmetries for reaction-diffusion systems with power diffusivities are constructed. The relevant non-Lie ansatze to reduce the reaction-diffusion systems to ODE systems and examples of exact solutions are…
We consider a reaction-diffusion equation on a network subjected to dynamic boundary conditions, with time delayed behaviour, also allowing for multiplicative Gaussian noise perturbations. Exploiting semigroup theory, we rewrite the…
By means of analytical calculations and numerical simulations we study the diffusion properties in quasi-two-dimensional structures with two exciton subsystems with an exchange between them. The experimental realisation is possible in…
The replication and differentiation of spots in reaction diffusion equations are studied by extending the Gray-Scott model with self-replicating spots to include many degrees of freedom needed to model systems with many chemicals. By…
Streamer electrical discharges are often investigated with computer simulations of density models (also called drift-diffusion-reaction models). We review these models, detailing their physical foundations, their range of validity and the…