Related papers: Algebraic structures generating reaction-diffusion…
The modelling of linear and nonlinear reaction-subdiffusion processes is more subtle than normal diffusion and causes different phenomena. The resulting equations feature a spatial Laplacian with a temporal memory term through a time…
The interplay between structure and dynamics in non-equilibrium steady-state is far from understood. We address this interplay by tracking Brownian Dynamics trajectories of particles in a binary colloid of opposite charges in an external…
Exploiting the quantum integrability condition we construct an ancestor model associated with a new underlying quadratic algebra. This ancestor model represents an exactly integrable quantum lattice inhomogeneous anisotropic model and at…
A new mathematical model for non-equilibrium evaporation/condensation including boiling effect is proposed. A simplified differential-algebraic system of equations is obtained. A code to solve numerically this differential-algebraic system…
A brief review of models to describe nuclear structure and reactions properties is presented, starting from the historical shell model picture and encompassing modern ab initio approaches. A selection of recent theoretical results on…
We consider a model system consisting of two reaction-diffusion equations, where one species diffuses in a volume while the other species diffuses on the surface which surrounds the volume. The two equations are coupled via a nonlinear…
We introduce a nonlinear structure preserving high-order scheme for anisotropic advection-diffusion equations. This scheme, based on Hybrid High-Order methods, can handle general meshes. It also has an entropy structure, and preserves the…
We develop and implement new probabilistic strategy for proving basic results about long time behaviour for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process as…
We describe a basic correspondence between linear algebraic structures within vector embeddings in artificial neural networks and conditional independence constraints on the probability distributions modeled by these networks. Our framework…
In this article we present a construction of a family particle systems that converge after scaling to the solution a non-linear SDE of Reaction-Diffusion type.
In this paper, a class of reaction-diffusion equations for Multiple Sclerosis is presented. These models are derived by means of a diffusive limit starting from a proper kinetic description, taking account of the underlying microscopic…
We show that the nonlinear 2+1--dimensional Three--Wave Resonant Interaction equations, describing several important physical phenomena, can be generated starting from incomplete Lie algebras in the framework of multidimensional…
In this paper, we study the structure of the global attractor for weak and regular solutions of a problem governed by a scalar semilinear reaction-diffusion equation with a non-regular nonlinearity, such that uniquness of solutions can fail…
Given a reaction-advection-diffusion system modelling the sulphation phenomenon, we derive a single regularised non-conservative and path-dependent nonlinear partial differential equation and propose a probabilistic interpretation via a…
Generative machine learning models have revolutionized material discovery by capturing complex structure-property relationships, yet extending these approaches to the inverse design of three-dimensional metamaterials remains limited by…
We study reaction-diffusion equations in cylinders with possibly nonlinear diffusion and possibly nonlinear Neumann boundary conditions. We provide a geometric Poincar\'e-type inequality and classification results for stable solutions, and…
This paper treats the solvability of a semilinear reaction-diffusion system, which incorporates transport (diffusion) and reaction effects emerging from two separated spatial scales: $x$ - macro and $y$ - micro. The system's origin connects…
Analyzing qualitative behaviors of biochemical reactions using its associated network structure has proven useful in diverse branches of biology. As an extension of our previous work, we introduce a graph-based framework to calculate steady…
We investigate the oscillatory dynamics and bifurcation structure of a reaction-diffusion system with bistable nonlinearity and mass conservation, which was proposed by [Otsuji et al, PLoS Comp. Biol. 3 (2007), e108]. The system is a useful…
We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quad-tree of a partitioned…