First-passage distributions in a collective model of anomalous diffusion with tunable exponent
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...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Physical Society
2010
|
| Online Access: | http://hdl.handle.net/1721.1/56292 https://orcid.org/0000-0002-1112-5912 |
| _version_ | 1826203243720474624 |
|---|---|
| author | Amitai, Assaf Kantor, Yacov Kardar, Mehran |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Amitai, Assaf Kantor, Yacov Kardar, Mehran |
| author_sort | Amitai, Assaf |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T12:33:53Z |
| format | Article |
| id | mit-1721.1/56292 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:33:53Z |
| publishDate | 2010 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/562922022-09-28T08:38:12Z First-passage distributions in a collective model of anomalous diffusion with tunable exponent Amitai, Assaf Kantor, Yacov Kardar, Mehran Massachusetts Institute of Technology. Department of Physics Kardar, Mehran Kardar, Mehran 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. 2010-07-14T15:03:57Z 2010-07-14T15:03:57Z 2010-01 2009-09 Article http://purl.org/eprint/type/JournalArticle 1539-3755 1550-2376 http://hdl.handle.net/1721.1/56292 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 https://orcid.org/0000-0002-1112-5912 en_US http://dx.doi.org/10.1103/PhysRevE.81.011107 Physical Review E Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | Amitai, Assaf Kantor, Yacov Kardar, Mehran First-passage distributions in a collective model of anomalous diffusion with tunable exponent |
| title | First-passage distributions in a collective model of anomalous diffusion with tunable exponent |
| title_full | First-passage distributions in a collective model of anomalous diffusion with tunable exponent |
| title_fullStr | First-passage distributions in a collective model of anomalous diffusion with tunable exponent |
| title_full_unstemmed | First-passage distributions in a collective model of anomalous diffusion with tunable exponent |
| title_short | First-passage distributions in a collective model of anomalous diffusion with tunable exponent |
| title_sort | first passage distributions in a collective model of anomalous diffusion with tunable exponent |
| url | http://hdl.handle.net/1721.1/56292 https://orcid.org/0000-0002-1112-5912 |
| work_keys_str_mv | AT amitaiassaf firstpassagedistributionsinacollectivemodelofanomalousdiffusionwithtunableexponent AT kantoryacov firstpassagedistributionsinacollectivemodelofanomalousdiffusionwithtunableexponent AT kardarmehran firstpassagedistributionsinacollectivemodelofanomalousdiffusionwithtunableexponent |