Related papers: On pattern formation in reaction-diffusion systems…
We study a two-species cross-diffusion model that is inspired by a system of convection-diffusion equations derived from an agent-based model on a two-dimensional discrete lattice. The latter model has been proposed to simulate gang…
We explain how to use diffusion models to learn inverse renormalization group flows of statistical and quantum field theories. Diffusion models are a class of machine learning models which have been used to generate samples from complex…
Cross-diffusion systems arise as hydrodynamic limits of lattice multi-species interacting particle models. The objective of this work is to provide a numerical scheme for the simulation of the cross-diffusion system identified in [J.…
We derive a model for the non-isothermal reaction-diffusion equation. Combining ideas from non-equilibrium thermodynamics with the energetic variational approach we obtain a general system modeling the evolution of a non-isothermal chemical…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
This paper presents a nonlinear reaction-diffusion-fluid system that simulates radiofrequency ablation within cardiac tissue. The model conveys the dynamic evolution of temperature and electric potential in both the fluid and solid regions,…
Spatial and temporal pattern formation in reaction-diffusion systems is typically studied with two or more equations, as scalar reaction-diffusion equations confined to convex domains do not admit stable inhomogeneous states in time or…
This paper proposes the Ricci-flow equation from Riemannian geometry as a general geometric framework for various nonlinear reaction-diffusion systems (and related dissipative solitons) in mathematical biology. More precisely, we propose a…
The non-equilibrium dynamic fluctuations of a stochastic version of the Gray-Scott (GS) model are studied analytically in leading order in perturbation theory by means of the dynamic renormalization group. There is an attracting stable…
A novel global energy model for multi-class semantic image segmentation is proposed that admits very efficient exact inference and derivative calculations for learning. Inference in this model is equivalent to MAP inference in a particular…
We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles. The resulting…
For a given thermodynamic system, and a given choice of coarse-grained state variables, the knowledge of a force-flux constitutive law is the basis for any nonequilibrium modeling. In the first paper of this series we established how, by a…
We develop a linear fully discrete structure-preserving finite element method for a diffuse-interface model of tumour growth. The system couples a Cahn--Hilliard type equation with a nonlinear reaction-diffusion equation for nutrient…
The dynamics of cross-diffusion models leads to a high computational complexity for implicit difference schemes, turning them unsuitable for tasks that require results in real-time. We propose the use of two operator splitting schemes for…
We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…
In this paper, we provide a graphic formulation of non-isothermal reaction systems and show that a non-isothermal detailed balanced network system converges (locally) asymptotically to the unique equilibrium within the invariant manifold…
In this paper we investigate the reaction--diffusion system corresponding to the Newton--Leipnik chaotic system originally developed to model the rigid body motion through linear feedback (LFRBM). We develop a nonlinear synchronization…
This paper presents a matrix formulation of the scalar laws of radiative transfer. The method applies to coupled mixed boundary condition problems on general domains. Participating media can range from transparent to absorbing, emitting,…
We present an investigation into diffusion models for molecular generation, with the aim of better understanding how their predictions compare to the results of physics-based calculations. The investigation into these models is driven by…
Predicting protein functional characteristics from structure remains a central problem in protein science, with broad implications from understanding the mechanisms of disease to designing novel therapeutics. Unfortunately, current machine…