2006/08/26 by Niraj Kumar, Kumar, Niraj, Goutam Tripathy +1
Mathematics · Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Stochastic processes and statistical mechanics #Diffusion and Search Dynamics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.cond-mat/0608578
We study front propagation in the reaction diffusion process\n A stackrel\ε\→2A, A stackrel \εt\→3A on a one\ndimensional (1d) lattice with hard core interaction between the particles.\nUsing the leading particle picture, velocity of the front in the system is\ncomputed using different approximate methods, which is in good agreement with\nthe simulation results. It is observed that in certain ranges of parameters,\nthe front velocity varies as a power law of \εt, which is well\ncaptured by our approximate schemes. We also observe that the front dynamics\nexhibits temporal velocity correlations and these must be taken care of in\norder to find the exact estimates for the front diffusion coefficient. This\ncorrelation changes sign depending upon the sign of \εt-D, where D\nis the bare diffusion coefficient of A particles. For \εt=D, the\nleading particle and thus the front moves like an uncorrelated random walker,\nwhich is explained through an exact analysis.\n