Related papers: Reaction-diffusion processes in zero transverse di…
The Reggeon field theory in zero transverse dimensions is investigated. Two versions of the theory are considered: one that allows at most triple pomeron interactions and the other that embodies an additional 2-->2 quartic Reggeon coupling.…
The Reggeon field theory with zero transverse dimensions is studied in the Hamiltonian formulation for both sub-and supercritical pomeron. Mathematical aspects of the model, in particular the scalar products in the space of quantum states,…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
Pattern formation has been extensively studied in the context of evolving (time-dependent) domains in recent years, with domain growth implicated in ameliorating problems of pattern robustness and selection, in addition to more realistic…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
Understanding the asymptotic behavior of reaction-diffusion (RD) systems is crucial for modeling processes ranging from species coexistence in ecology to biochemical interactions within cells. In this work, we analyze RD systems in which…
We look for similarity transformations which yield mappings between different one-dimensional reaction-diffusion processes. In this way results obtained for special systems can be generalized to equivalent reaction-diffusion models. The…
We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…
While the mathematical foundations of score-based generative models are increasingly well understood for unconstrained Euclidean spaces, many practical applications involve data restricted to bounded domains. This paper provides a…
Reaction-diffusion systems with reversible reactions generically display power-law relaxation towards chemical equilibrium. In this work we investigate through numerical simulations aging processes that characterize the non-equilibrium…
Many non-equilibrium systems display dynamic phase transitions from active to absorbing states, where fluctuations cease entirely. Based on a field theory representation of the master equation, the critical behavior can be analyzed by means…
It is usually assumed that the high-energy evolution of partons in QCD remains local in coordinate space. In particular, fixed impact-parameter scattering is thought to be in the universality class of one-dimensional reaction-diffusion…
Toy models of interacting Pomerons with triple and quaternary Pomeron vertices in zero transverse dimension are investigated. Numerical solutions for eigenvalues and eigenfunctions of the corresponding Hamiltonians are obtained, providing…
In this paper we consider the mathematical relationship between nonlocal interactions of convolution type and multiple diffusive substances in high dimensions. Motivated by that the nonlocal evolution equations reproduce similar patterns to…
Morphogenesis is central to biology but remains largely unexplored in chemistry. Reaction-diffusion (RD) mechanisms are, however, essential to understand how shape emerges in the living world. While numerical methods confirm the incredible…
We consider general multi-species models of reaction diffusion processes and obtain a set of constraints on the rates which give rise to closed systems of equations for correlation functions. Our results are valid in any dimension and on…
I discuss recent progress in understanding the high-energy evolution in QCD, which points towards a remarkable correspondence with the reaction-diffusion problem of statistical physics. This enables us to determine the asymptotic behaviour…
We propose a mathematical model, namely a reaction-diffusion system, to describe social behaviour of cockroaches. An essential new aspect in our model is that the dispersion behaviour due to overcrowding effect is taken into account {as a…
In a recent article the most general non-uniform reaction-diffusion models on a one-dimensional lattice with boundaries were considered, for which the time evolution equations of correlation functions are closed and the stationary profile…
High energy scattering was recently shown to be similar to a reaction-diffusion process. The latter defines a wide universality class that also contains e.g. some specific population evolution models. The common point of all these models is…