Brownian Flights over a Fractal Nest and First-Passage Statistics on Irregular Surfaces

Levitz, Pierre; Grebenkov, Denis S.; Zinsmeister, Michel; Kolwankar, Kiran M.; Sapoval, B.

doi:10.1103/physrevlett.96.180601

Cited by 54 publications

(41 citation statements)

References 18 publications

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“…(37) can be seen as the spectral representation of the inverse of the Dirichlet-to-Neumann operator, M −1 p , which is equal to DG 0 (s, p|s 0 ) according to Eq. (22). As a consequence, the Laplace transform can be inverted to get…”

Section: B Spectral Representation Via Dirichlet-to-neumann Operatormentioning

confidence: 99%

Probability distribution of the boundary local time of reflected Brownian motion in Euclidean domains

Grebenkov

2019

Phys. Rev. E

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How long does a diffusing molecule spend in a close vicinity of a confining boundary or a catalytic surface? This quantity is determined by the boundary local time, which plays thus a crucial role in the description of various surface-mediated phenomena such as heterogeneous catalysis, permeation through semi-permeable membranes, or surface relaxation in nuclear magnetic resonance. In this paper, we obtain the probability distribution of the boundary local time in terms of the spectral properties of the Dirichlet-to-Neumann operator. We investigate the short-time and long-time asymptotic behaviors of this random variable for both bounded and unbounded domains. This analysis provides complementary insights onto the dynamics of diffusing molecules near partially reactive boundaries.

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Section: B Spectral Representation Via Dirichlet-to-neumann Operatormentioning

confidence: 99%

Probability distribution of the boundary local time of reflected Brownian motion in Euclidean domains

Grebenkov

2019

Phys. Rev. E

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“…A broad range of length scales makes questionable the use of a single dimensionless diffusion coefficient p. 2. The boundary of these media is often irregular that may considerably influence the signal attenuation, either by diffusional screening [inhomogeneous accessibility for diffusing particles, see (15)(16)(17)(18)(19)(20)(21)(22)88)] or by enhancing susceptibility-induced magnetic field gradients [see (89) and references therein].…”

Section: What Can One Do In Porous Media?mentioning

confidence: 99%

Laplacian eigenfunctions in NMR. II. Theoretical advances

Grebenkov

2009

Concepts Magnetic Resonance

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In this article, theoretical advances in the study of restricted diffusion in NMR that have been achieved by using Laplacian eigenfunctions are described. The macroscopic signal is represented as the characteristic function of a random phase shift that a nucleus acquires during its motion in an inhomogeneous magnetic field. The moments of this random variable are written in a matrix form that is based on Laplacian eigenfunctions. This article focuses on the zeroth, first, and second moments which provide the major contribution to the macroscopic signal. The asymptotic behavior of the macroscopic signal in both short-time and long-time regimes is considered when the diffusion length is either much smaller or much larger than the size of a diffusion-confining domain, respectively. Apparent diffusion coefficient, localization regime, inverse spectral problem, and many other issues are discussed.

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“…Some authors [2,3,[8][9][10]16,[19][20][21][22][23][24][25][45][46][47][48] have used scaling arguments to improve our understanding of certain aspects of diffusion-limited reactions which occur in fractal spaces (porous) or on fractal boundaries (rough). The scaling arguments, numerical and experimental studies [2,3,[8][9][10]16,[19][20][21][22][23][24][25][45][46][47][48] have shown that reaction rates follow approximately a power law relation in time. The scaling form for the current is…”

Section: Introductionmentioning

confidence: 99%

Diffusion-controlled potentiostatic current transients on realistic fractal electrodes

Jha

Sangal

Kant

2008

Journal of Electroanalytical Chemistry

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Brownian Flights over a Fractal Nest and First-Passage Statistics on Irregular Surfaces

Abstract: flights over a fractal nest and first-passage statistics on irregular surfaces.

Cited by 54 publications

References 18 publications

Probability distribution of the boundary local time of reflected Brownian motion in Euclidean domains

Probability distribution of the boundary local time of reflected Brownian motion in Euclidean domains

Laplacian eigenfunctions in NMR. II. Theoretical advances

Diffusion-controlled potentiostatic current transients on realistic fractal electrodes

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