Theory of diffusion in finite random media with a dynamic boundary condition

Cáceres, Manuel O.; Matsuda, Hiroaki; Odagaki, Takashi; Prato, Domingo; Lamberti, Walter

doi:10.1103/physrevb.56.5897

Cited by 20 publications

(6 citation statements)

References 14 publications

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“…In Ref. [19], another extension of FEMA was carried out for periodically forced boundary conditions. In the present paper, we obtain, in the guidelines of the expansions developed in FEMA, the exact equations for MFPT and MRT and construct their solutions in the leading relevant order for small bias.…”

Section: Introductionmentioning

confidence: 99%

Survival and residence times in disordered chains with bias

Pury

Cáceres

2002

Phys. Rev. E

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We present a unified framework for first-passage time and residence time of random walks in finite one-dimensional disordered biased systems. The derivation is based on the exact expansion of the backward master equation in cumulants. The dependence on the initial condition, system size, and bias strength is explicitly studied for models with weak and strong disorders. Application to thermally activated processes is also developed.

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Section: Introductionmentioning

confidence: 99%

Survival and residence times in disordered chains with bias

Pury

Cáceres

2002

Phys. Rev. E

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“…In order to calculate the average of the Green function G(z) we need to find its evolution equation, this can be done by using a projector operator technique, see for example [Hernandez et al, 1990a;Hernandez et al, 1990b;Cáceres et al, 1997;Cáceres, 2003Cáceres, , 2004. The average of G(z), i.e.…”

Section: Average Of the Green Functionmentioning

confidence: 99%

Random Evolution in Population Dynamics

Cáceres

2010

Int. J. Bifurcation Chaos

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We present a perturbative formalism to deal with linear random positive maps. We generalize the biological concept of the population growth rate when a Leslie matrix has random elements (i.e. characterizing the macroscopic disorder in the vital parameters). The dominant eigenvalue of which defines the asymptotic dynamics of the mean-value population vector state, is presented as the effective growth rate of a random Leslie model. The problem was reduced to the calculation of the smallest positive rootz 1 of the secular polynomial appearing in the general expression for the mean-value Green function G(z) . This nontrivial polynomial can be obtained order by order in terms of a diagrammatic technique built with Terwiel's cumulants, which have carefully been identified in the present work. By understanding how this smallest positive rootz 1 = 1/λ 1 depends on the model of disorder, one can link the asymptotic population dynamics with the statistical properties of the errors (mutations) in the vital parameters. This eigenvalue has the meaning of an effective Perron-Frobenious eigenvalue for a random positive matrix. Analytical (exact and perturbative calculations) results are presented for several models of disorder.

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“…We will find it useful to define the quantities β k ≡ 1/w + j k , which we assume finite for all k ≥ 1. This class of disorder is known as weak disorder [21,22,23,24]. We also define a measure of the fluctuation of the disorder by F ≡ β 2 − β 2 1 /β 2 1 .…”

Section: Weak Biased Disordered Chainmentioning

confidence: 99%

“…A successful perturbative theory for survival statistics in disordered chains is the finite effective medium approximation (FEMA) [21]. Extensions of FEMA to biased media [22] and periodically forced boundary conditions [23] were presented. A unified framework for the FPT and RT statistics in finite disordered chains with bias was also presented by the authors in reference [24], where exact equations for the quantities averaged over disorder were obtained for both problems and its solutions up to first order in the bias parameter were constructed retaining the full dependence on the system's size and the initial condition.…”

Section: Introductionmentioning

confidence: 99%