Related papers: Renormalization Group Calculation for the Reaction…
The $A + B\to 0$ diffusion-limited reaction, with equal initial densities $a(0) = b(0) = n_0$, is studied by means of a field-theoretic renormalization group formulation of the problem. For dimension $d > 2$ an effective theory is derived,…
We study a class of reaction-diffusion model extrapolating continuously between the pure coagulation-diffusion case ($A+A\to A$) and the pure annihilation-diffusion one ($A+A\to\emptyset$) with particles input ($\emptyset\to A$) at a rate…
Renormalization group calculations for fluctuation-dominated reaction-diffusion systems are generally in agreement with simulations and exact solutions. However, simulations of the single-species reactions 3A->(0,A,2A) at their upper…
A recent argument of Oerding shows that our calculation of the quantity Delta, which determines the amplitude of the asymptotic decay of the particle density in d < 2 < 4, was in error. Instead it is simply given by Delta = n_0, the initial…
We review the application of field-theoretic renormalization group (RG) methods to the study of fluctuations in reaction-diffusion problems. We first investigate the physical origin of universality in these systems, before comparing RG…
An analytical renormalization group treatment is presented of a model which, for one value of parameters, is equivalent to diffusion limited aggregation. The fractal dimension of DLA is computed to be 2-1/2+1/5=1.7. Higher multifractal…
A simple example of a non-equilibrium system for which fluctuations are important is a system of particles which diffuse and may annihilate in pairs on contact. The renormalization group can be used to calculate the time dependence of the…
The field theoretic renormalization group is applied to the stochastic Navier-Stokes equation with the stirring force correlator of the form k^(4-d-2\epsilon) in the d-dimensional space, in connection with the problem of construction of the…
We present a detailed investigation of the momentum-dependent self-energy Sigma(k) at zero frequency of weakly interacting bosons at the critical temperature T_c of Bose-Einstein condensation in dimensions 3<=D<4. Applying the functional…
We study the relationship between the renormalization group and the diffusion equation. We consider the exact renormalization group equation for a scalar field that includes an arbitrary cutoff function and an arbitrary quadratic seed…
We study a large class of 1D reaction diffusion models with quenched disorder using a real space renormalization group method (RSRG) which yields exact results at large time. Particles (e.g. of several species) undergo diffusion with random…
The exact renormalization group is applied to a nonlinear diffusion equation with a discontinuous diffusion coefficient. The generating functional of the solution for the initial-value problem of nonlinear diffusion equations is first…
Functional renormalisation group approach is applied to a system of kaons with finite chemical potential. A set of approximate flow equations for the effective couplings is derived and solved. At high scale the system is found to be at the…
We consider the properties of the diffusion controlled reaction A+B->0 in the steady state, where fixed currents of A and B particles are maintained at opposite edges of the system. Using renormalisation group methods, we explicitly…
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…
An exact renormalization group equation describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. It interpolates between the microphysical laws and the complex macroscopic phenomena. We…
We study a two-species reaction-diffusion system with the reactions $A+A\to (0, A)$ and $A+B\to A$, with general diffusion constants $D_A$ and $D_B$. Previous studies showed that for dimensions $d\leq 2$ the $B$ particle density decays with…
Through appropriate projections of an exact renormalization group equation, we study fixed points, critical exponents and nontrivial renormalization group flows in scalar field theories in $2<d<4$. The standard upper critical dimensions…
We study elastic systems such as interfaces or lattices, pinned by quenched disorder. To escape triviality as a result of ``dimensional reduction'', we use the functional renormalization group. Difficulties arise in the calculation of the…
We address via numerical simulation the two-dimensional bimolecular annihilation reaction $A + A \to \emptyset$ in the presence of quenched, random impurities. Renormalization group calculations have suggested that this reaction displays…