Related papers: Renormalisation for Reaction-Diffusion Systems wit…
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…
The importance and usefulness of renormalization are emphasized in nonrelativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin…
The real-space renormalization group technique is introduced to evaluate the effective diffusion constant for diffusion in inhomogeneous media, which has been obtained by singular perturbation methods. Our method is formulated on a…
The dispersive optical-model is applied to transfer reactions. A systematic study of $(d,p)$ reactions on closed-shell nuclei using the finite-range adiabatic reaction model is performed at several beam energies and results are compared to…
We consider interacting particle dynamics with Vicsek type interactions, and their macroscopic PDE limit, in the non-mean-field regime; that is, we consider the case in which each particle/agent in the system interacts only with a…
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…
We propose a modification of the non-perturbative renormalization-group (NPRG) which applies to lattice models. Contrary to the usual NPRG approach where the initial condition of the RG flow is the mean-field solution, the lattice NPRG uses…
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…
Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories, and to gain insight into the interplay between continuous and discrete rescaling. With minimal assumptions, the methods…
Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic…
We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena…
Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations. Some of them resemble the steady irregular…
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…
Originating from the pioneering study of Alan Turing, the bifurcation analysis predicting spatial pattern formation from a spatially uniform state for diffusing morphogens or chemical species that interact through nonlinear reactions is a…
We write exact renormalization-group recursion relations for a ferromagnetic Ising model on the diamond hierarchical lattice with an aperiodic distribution of exchange interactions according to a class of generalized two-letter Fibonacci…
A large class of evolutionary processes can be modeled by a rule which involves self-replication of some physical quantity with a non local rescaling. I show that a class of such models are exactly solvable -- in the discrete as well as…
Motivated by bacterial chemotaxis and multi-species ecological interactions in heterogeneous environments, we study a general one-dimensional reaction-cross-diffusion system in the presence of spatial heterogeneity in both transport and…
We investigate the renormalization group flows and fixed point structure of many coupled minimal models. The models are coupled two by two by energy-energy couplings. We take the general approach where the bare couplings are all taken to be…
A stochastic reaction-diffusion model is studied on a networked support. In each patch of the network two species are assumed to interact following a non-normal reaction scheme. When the interaction unit is replicated on a directed linear…
We study diffusion-controlled processes in nonequilibrium steady states, where standard rate theory assumptions break down. Using transition path theory, we generalize the relations between reactive probability fluxes and measures of the…