TITLE

Renormalization group approach to reaction-diffusion systems with input in disordered media

AUTHOR(S)
Park, Jeong-Man
PUB. DATE
February 2000
SOURCE
AIP Conference Proceedings;2000, Vol. 501 Issue 1, p324
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We consider reaction-diffusion systems of a single species (A+A→0\) with a particle input in the presence of weak potential disorders in media. Random potential disorders with sufficiently long-ranged interactions are known to lead to anomalous diffusion in the absence of reaction. Applying renormalization group (RG) theory to a field theoretic description of the reaction-diffusion process and the matching theory to the RG trajectory integrals of the systems, we find that for d<2 the density of particles decays as c(t)∼t[sup -ν] with the dynamic exponent ν=d/(2+γ¯) in the absence of input and the density grows as c(I)∼I[sup μ] with the static exponent μ=d/(d+2+γ¯) in the presence of input with γ¯=β[sup 2]γ/4π. For d>2 the behavior is mean-filed like. The results confirm the Racz’s conjecture about the relation between the static and the dynamic exponents μ=ν/(1+ν) for a single species reaction-diffusion system even in disordered media. © 2000 American Institute of Physics.
ACCESSION #
6028295

 

Related Articles

  • The effect of strongly anisotropic turbulent mixing on critical behavior: Renormalization group analysis of two nonstandard systems. Antonov, N.; Malyshev, A. // Theoretical & Mathematical Physics;Apr2011, Vol. 167 Issue 1, p444 

    We consider the effect of strongly anisotropic turbulent mixing on the critical behavior of two systems: a φ critical dynamics model describing universal properties of metastable states in the vicinity of a firstorder phase transition and a reaction-diffusion system near the point of a...

  • Effects of turbulent transfer on critical behavior. Antonov, N.; Kapustin, A.; Malyshev, A. // Theoretical & Mathematical Physics;Oct2011, Vol. 169 Issue 1, p1470 

    Using the field theory renormalization group, we study the critical behavior of two systems subjected to turbulent mixing. The first system, described by the equilibrium model A, corresponds to the relaxational dynamics of a nonconserved order parameter. The second system is the strongly...

  • Numerical Calculation of Scaling Exponents of Percolation Process in the Framework of Renormalization Group Approach. Adzhemyan, L. Ts.; Hnatič, M.; Kompaniets, M.; Lučivjanský, T.; Mižišin, L. // EPJ Web of Conferences;2016, Vol. 108, p02005-p.1 

    The renormalization group theory is used to the study of the directed bond percolation (Gribov process) near its second-order phase transition between absorbing and active state. We present a numerical calculation of the renormalization group functions in the ϵ-expansion where ϵ is the...

  • Persistence of zero velocity fronts in reaction diffusion systems. Kramer, Lorenz; Gottwald, Georg; Krinsky, Valentin I.; Pumir, Alain; Barelko, Viktor V. // Chaos;Sep2000, Vol. 10 Issue 3 

    Steady, nonpropagating, fronts in reaction diffusion systems usually exist only for special sets of control parameters. When varying one control parameter, the front velocity may become zero only at isolated values (where the Maxwell condition is satisfied, for potential systems). The...

  • Simulations of anisotropic front propagation in the H[sub 2]+O[sub 2] reaction on a Rh(110) surface. Makeev, A.; Imbihl, R. // Journal of Chemical Physics;9/1/2000, Vol. 113 Issue 9 

    A mathematical model is presented which reproduces the experimental results of anisotropic front propagation in the bistable H[sub 2]+O[sub 2] reaction on a Rh(110) surface. A model represented by a system of two coupled nonlinear reaction-diffusion equations incorporates the chemical diffusion...

  • Universal scaling for diffusion-controlled reactions among traps. Torquato, S.; Yeong, C.L.Y. // Journal of Chemical Physics;6/1/1997, Vol. 106 Issue 21, p8814 

    Determines the mean survival time associated with diffusion-controlled reactions among the static traps. Consideration of the broad class of model particulate and digitized-based models; Universal curve for the mean survival time for a wide range of porosities.

  • Interaction of Turing and flow-induced chemical instabilities. Dawson, S. Ponce; Lawniczak, A.; Kapral, R. // Journal of Chemical Physics;4/1/1994, Vol. 100 Issue 7, p5211 

    The interaction between the Turing instability and the instability induced by a differential flow is studied in the Selkov model. Both instabilities give rise to the formation of spatial patterns, and for a range of parameter values, these patterns can compete. The effect of anisotropic...

  • Diffusion-stress relations in polymer mixtures. Curtiss, C.F.; Bird, R. Byron // Journal of Chemical Physics;12/8/1999, Vol. 111 Issue 22, p10362 

    Studies teh diffusion-stress relations in polymer mixtures. Linearization of the time-evolution equation of the singlet distribution function; Derivation of the Maxwell-Stefan equations for the mass flux.

  • Intergradient simulations of dissipative quasi-particle interactions with solutions of a three-component three-dimensional reaction-diffusion system. Liehr, A. W.; Moskalenko, A.; Bode, M.; Purwins, H. G. // AIP Conference Proceedings;2001, Vol. 574 Issue 1, p257 

    © 2001 American Institute of Physics.

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics