Related papers: Reaction Diffusion Models in One Dimension with Di…
A method for classifying $n$-species reaction-diffusion models, admitting shock solutions is presented. The most general one-dimensional two-species reaction-diffusion model with nearest neighbor interactions admitting uniform product…
Mass-conserving reaction-diffusion (MCRD) systems are widely used to model phase separation and pattern formation in cell polarity, biomolecular condensates, and ecological systems. Numerical simulations and formal asymptotic analysis…
Reaction-diffusion systems, which consist of the reacting particles subject to diffusion process, constitute one of the common examples of non-linear statistical systems. In low space dimensions $d \leq 2$ the usual description by means of…
The kinetics of bimolecular reactions in solution depends, among other factors, on intermolecular forces such as steric repulsion or electrostatic interaction. Microscopically, a pair of molecules first has to meet by diffusion before the…
We establish the boundedness of solutions of reaction-diffusion systems with quadratic (in fact slightly super-quadratic) reaction terms that satisfy a natural entropy dissipation property, in any space dimension N>2. This bound imply the…
We analytically investigate a 1d branching-coalescing model with reflecting boundaries in a canonical ensemble where the total number of particles on the chain is conserved. Exact analytical calculations show that the model has two…
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…
Selected theoretical developments in modeling of deposition of submicrometer size (submicron) particles on solid surfaces, with and without surface diffusion, of interest in colloid, polymer, and certain biological systems, are surveyed. We…
Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by…
We develop a class of nonlocal delay Reaction-Diffusion (RD) models in a circular domain. Previous modeling efforts include RD population models with respect to one-dimensional unbounded domain, unbounded strip and rectangular spatial…
Abridged abstract: Inert interactions between randomly moving entities and spatial disorder play a crucial role in quantifying the diffusive properties of a system. These interactions affect only the movement of the entities, and examples…
The diffusion-controlled reaction $kA\rightarrow\emptyset$ is known to be strongly dependent on fluctuations in dimensions $d\le d_c=2/(k-1)$. We develop a field theoretic renormalization group approach to this system which allows explicit…
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…
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 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…
We examine the dynamic spreading of a dense overdamped suspension of particles under power law repulsive potentials, often called Riesz gases. That is, potentials that decay with distance as 1/r^k where k\in (-2,\infty]. Depending on the…
We apply the Nozieres-Gallet dynamic renormalization group (RG) scheme to a continuum equilibrium model of a d-dimensional surface relaxing by linear surface tension and linear surface diffusion, and which is subject to a lattice potential…
We study the two dimensional XY model with quenched random phases and its Coulomb gas formulation. A novel renormalization group (RG) method is developed which allows to study perturbatively the glassy low temperature XY phase and the…
A growth model which describes the deposition of particles (or the growth of a rigid crystal) on a disordered substrate is investigated. The dynamic renormalization group is applied to the stochastic growth equation using the Martin, Sigga,…
We study critical spreading dynamics in the two-dimensional contact process (CP) with quenched disorder in the form of random dilution. In the pure model, spreading from a single particle at the critical point $\lambda_c$ is characterized…