Diffusion through permeable interfaces: Fundamental equations and their application to first-passage and local time statistics
The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we obtain such an equation from a microscopic description using a la...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2022-09-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.4.L032039 |
| _version_ | 1797210631851474944 |
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| author | Toby Kay Luca Giuggioli |
| author_facet | Toby Kay Luca Giuggioli |
| author_sort | Toby Kay |
| collection | DOAJ |
| description | The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we obtain such an equation from a microscopic description using a lattice random walk model. The sought after Fokker-Planck description and the corresponding backward Kolmogorov equation are employed to investigate first-passage and local time statistics and gain new insights. Among them a surprising phenomenon, in the case of a semibounded domain, is the appearance of a regime of dependence and independence on the location of the permeable barrier in the mean first-passage time. The new formalism is completely general: it allows to study the dynamics in the presence of multiple permeable barriers as well as reactive heterogeneities in bounded or unbounded domains and under the influence of external forces. |
| first_indexed | 2024-04-24T10:13:40Z |
| format | Article |
| id | doaj.art-30f6096dbd0d44cc8335ac21d4146adf |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:13:40Z |
| publishDate | 2022-09-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-30f6096dbd0d44cc8335ac21d4146adf2024-04-12T17:24:20ZengAmerican Physical SocietyPhysical Review Research2643-15642022-09-0143L03203910.1103/PhysRevResearch.4.L032039Diffusion through permeable interfaces: Fundamental equations and their application to first-passage and local time statisticsToby KayLuca GiuggioliThe diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we obtain such an equation from a microscopic description using a lattice random walk model. The sought after Fokker-Planck description and the corresponding backward Kolmogorov equation are employed to investigate first-passage and local time statistics and gain new insights. Among them a surprising phenomenon, in the case of a semibounded domain, is the appearance of a regime of dependence and independence on the location of the permeable barrier in the mean first-passage time. The new formalism is completely general: it allows to study the dynamics in the presence of multiple permeable barriers as well as reactive heterogeneities in bounded or unbounded domains and under the influence of external forces.http://doi.org/10.1103/PhysRevResearch.4.L032039 |
| spellingShingle | Toby Kay Luca Giuggioli Diffusion through permeable interfaces: Fundamental equations and their application to first-passage and local time statistics Physical Review Research |
| title | Diffusion through permeable interfaces: Fundamental equations and their application to first-passage and local time statistics |
| title_full | Diffusion through permeable interfaces: Fundamental equations and their application to first-passage and local time statistics |
| title_fullStr | Diffusion through permeable interfaces: Fundamental equations and their application to first-passage and local time statistics |
| title_full_unstemmed | Diffusion through permeable interfaces: Fundamental equations and their application to first-passage and local time statistics |
| title_short | Diffusion through permeable interfaces: Fundamental equations and their application to first-passage and local time statistics |
| title_sort | diffusion through permeable interfaces fundamental equations and their application to first passage and local time statistics |
| url | http://doi.org/10.1103/PhysRevResearch.4.L032039 |
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