Journal article
Effective transport properties of lattices
- Abstract:
- The method of multiple scales is used to calculate the effective macroscopic transport properties of a random walk on a periodic lattice with arbitrary, spatially-dependent transition rates. In contrast to the standard multiple-scales approach for continuous media, the fast scale here is discrete, and only the slow scale is continuous. The solution is found as the discrete probability distribution of finding the particle at a particular node in the unit cell, modulated by a continuous slow function of the position of the unit cell in the macroscopic material. This last function represents the macroscopic drift-diffusion of the particle, with drift and diffusion coefficients calculated in terms of the individual transition probabilities.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, pdf, 548.6KB, Terms of use)
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- Publisher copy:
- 10.1137/16M1092039
Authors
- Publisher:
- Society for Industrial and Applied Mathematics
- Journal:
- SIAM Journal on Applied Mathematics More from this journal
- Volume:
- 77
- Issue:
- 5
- Pages:
- 1631–1652
- Publication date:
- 2017-09-14
- Acceptance date:
- 2017-04-18
- DOI:
- EISSN:
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1095-712X
- ISSN:
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0036-1399
- Keywords:
- Pubs id:
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pubs:690300
- UUID:
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uuid:5429032f-8f68-4c4d-a842-7340e7d41cdc
- Local pid:
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pubs:690300
- Source identifiers:
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690300
- Deposit date:
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2017-04-20
Terms of use
- Copyright holder:
- Society for Industrial and Applied Mathematics
- Copyright date:
- 2017
- Notes:
- Copyright © by SIAM. This is the accepted manuscript version of the article. The final version is available online from SIAM at: https://doi.org/10.1137/16M1092039
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