First-passage distributions in a collective model of anomalous diffusion with tunable exponent
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Amitai-2010-First-passage distributions in a collective model of anomalous diffusion with tunable exponent.pdf
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Author(s)
Amitai, Assaf
Kantor, Yacov
Kardar, Mehran
Date Issued
January 2010
Journal
Physical Review E
Publisher
American Physical Society
Citation
Amitai, Assaf, Yacov Kantor, and Mehran Kardar. “First-passage distributions in a collective model of anomalous diffusion with tunable exponent.” Physical Review E 81.1 (2010): 011107. © 2010 The American Physical Society
Version
Final published version
Abstract
We consider a model system in which anomalous diffusion is generated by superposition of underlying linear modes with a broad range of relaxation times. In the language of Gaussian polymers, our model corresponds to Rouse (Fourier) modes whose friction coefficients scale as wave number to the power 2−z. A single (tagged) monomer then executes subdiffusion over a broad range of time scales, and its mean square displacement increases as t[superscript α] with α=1/z. To demonstrate nontrivial aspects of the model, we numerically study the absorption of the tagged particle in one dimension near an absorbing boundary or in the interval between two such boundaries. We obtain absorption probability densities as a function of time, as well as the position-dependent distribution for unabsorbed particles, at several values of α. Each of these properties has features characterized by exponents that depend on α. Characteristic distributions found for different values of α have similar qualitative features, but are not simply related quantitatively. Comparison of the motion of translocation coordinate of a polymer moving through a pore in a membrane with the diffusing tagged monomer with identical α also reveals quantitative differences.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.81.011107
