2014/07/28 by Patrick Dondl, Dondl, Patrick W., Michael Scheutzow +1
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1407.7379
We consider a discretized version of the quenched Edwards-Wilkinson model for\nthe propagation of a driven interface through a random field of obstacles. Our\nmodel consists of a system of ordinary differential equations on a\nd-dimensional lattice coupled by the discrete Laplacian. At each lattice\npoint, the system is subject to a constant driving force and a random obstacle\nforce impeding free propagation. The obstacle force depends on the current\nstate of the solution and thus renders the problem non-linear. For independent\nand identically distributed obstacle strengths with exponential moment we prove\nballistic propagation (i.e., propagation with a positive velocity) of the\ninterface if the driving force is large enough. For a specific case of\ndependent obstacles, we show that no stationary solution exists, but still the\npropagation of the front is not ballistic.\n