Related papers: Models solvable through the empty-interval method
We find analytical solutions to the evolution of interacting two-level atoms when the master equation is symmetric under the permutation of atomic labels. The master equation includes atomic independent dissipation. The method to obtain the…
We present the exact solution for the full dynamics of a nonequilibrium spin chain and its dual reaction-diffusion model, for arbitrary initial conditions. The spin chain is driven out of equilibrium by coupling alternating spins to two…
A class of $d$-dimensional reaction-diffusion models interpolating continuously between the diffusion-coagulation and the diffusion-annihilation models is introduced. Exact relations among the observables of different models are…
The exchange-driven growth model describes the mean field kinetics of a population of composite particles (clusters) subject to pairwise exchange interactions. Exchange in this context means that upon interaction of two clusters, one loses…
Non-reciprocal interactions are present in many systems out of equilibrium. The rate of entropy production is a measure that quantifies the time irreversibility of a system, and thus how far it is from equilibrium. In this work, we…
The time-global existence of unique smooth positive solutions to the reaction diffusion equations of the Keener-Tyson model for the Belousov-Zhabotinsky reaction in the whole space is established with bounded non-negative initial data.…
Diffusion models are state-of-the-art generative models, yet their samples often fail to satisfy application objectives such as safety constraints or domain-specific validity. Existing techniques for alignment require gradients, internal…
We have studied $A+A \rightarrow \emptyset$ reaction-diffusion model on a ring, with a bias $\epsilon$ $(0 \leq \epsilon \leq 0.5)$ of the random walkers $A$ to hop towards their nearest neighbor. Though the bias is local in space and time,…
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…
This work is part of a general study on the long-term safety of the geological repository of nuclear wastes. A diffusion equation with a moving free boundary in one dimension is introduced and studied. The model describes some mechanisms…
We study the dynamics of an asymmetric simple exclusion process with open boundaries and local interactions using a pair approximation which generalizes the 2-node cluster mean field theory and the Markov chain approach to kinetics and…
In this paper, the applicability of the entropy method for the trend towards equilibrium for reaction-diffusion systems arising from first order chemical reaction networks is studied. In particular, we present a suitable entropy structure…
This paper delves into a nonparametric estimation approach for the interaction function within diffusion-type particle system models. We introduce two estimation methods based upon an empirical risk minimization. Our study encompasses an…
We consider a reaction-diffusion equation with a half-Laplacian. In the case where the solution is independent on time, the model reduces to the Peierls-Nabarro model describing dislocations as transition layers in a phase field setting. We…
This work explores the influence of domain size of a non-compact two dimensional annular domain on the evolution of pattern formation that is modelled by an \textit{activator-depleted} reaction-diffusion system. A closed form expression is…
A formalism using a double Laplace Fourier transform of the transport equation yields the return probabilities of the vacancy in the vicinity of the tracer atom in the presence of solute-vacancy interactions of arbitrary extension. Studying…
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…
A one-dimensional reaction-diffusion model consisting of two species of particles and vacancies on a ring is introduced. The number of particles in one species is conserved while in the other species it can fluctuate because of creation and…
We consider a diffusion-limited reaction in case the reacting entities are not available simultaneously. Due to the fact that the reaction takes place after a spatiotemporal accumulation of reactants, the underlying rate equation has to be…
We study the discrete Gierer-Meinhardt model of reaction-diffusion on three different types of networks: regular, random and scale-free. The model dynamics lead to the formation of stationary Turing patterns in the steady state in certain…