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  • 1
    Electronic Resource
    Electronic Resource
    Convective and absolute instabilities in the subcritical Ginzburg-Landau equation (1999)
    Springer
    The European physical journal 11 (1999), S. 517-524 
    Details
    ISSN: 1434-6036
    Keywords: PACS. 47.20.Ky Nonlinearity (including bifurcation theory) - 47.54.+r Pattern selection; pattern formation - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: We study the nature of the instability of the homogeneous steady states of the subcritical real Ginzburg-Landau equation in the presence of group velocity. The shift of the absolute instability threshold of the trivial steady state, induced by the destabilizing cubic nonlinearities, is confirmed by the numerical analysis of the evolution of its perturbations. It is also shown that the dynamics of these perturbations is such that finite size effects may suppress the transition from convective to absolute instability. Finally, we analyze the instability of the subcritical middle branch of steady states, and show, analytically and numerically, that this branch may be convectively unstable for sufficiently high values of the group velocity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s100510050964
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  • 2
    Electronic Resource
    Electronic Resource
    Random walk in dynamically disordered chains: Poisson white noise disorder (1989)
    Springer
    Journal of statistical physics 55 (1989), S. 1027-1052 
    Details
    ISSN: 1572-9613
    Keywords: Random Walk ; Master Equation ; Poisson Noise ; Disordered Systems ; Diffusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Exact solutions are given for a variety of models of random walks in a chain with time-dependent disorder. Dynamic disorder is modeled by white Poisson noise. Models with site-independent (global) and site-dependent (local) disorder are considered. Results are described in terms of an affective random walk in a nondisordered medium. In the cases of global disorder the effective random walk contains multistep transitions, so that the continuous limit is not a diffusion process. In the cases of local disorder the effective process is equivalent to usual random walk in the absence of disorder but with slower diffusion. Difficulties associated with the continuous-limit representation of random walk in a disordered chain are discussed. In particular, we consider explicit cases in which taking the continuous limit and averaging over disorder sources do not commute.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01041077
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