Volume 25, Issue 1
Approximation of the Mean Escape Time for a Tilted Periodic Potential

Tamra Heberling, Lisa Davis & Tomas Gedeon

Commun. Comput. Phys., 25 (2019), pp. 1-40.

Published online: 2018-09

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  • Abstract

We present a formula approximating the mean escape time (MST) of a particle from a tilted multi-periodic potential well. The potential function consists of a weighted sum of a finite number of component functions, each of which is periodic. For this particular case, the least period of the potential function is a common period amongst all of its component functions. An approximation of the MST for the potential function is derived, and this approximation takes the form of a product of the MSTs for each of the individual periodic component functions. Our first example illustrates the computational advantages of using the approximation for model validation and parameter tuning in the context of the biological application of DNA transcription. We also use this formula to approximate the MST for an arbitrary tilted periodic potential by the product of MSTs of a finite number of its Fourier modes. Two examples using truncated Fourier series are presented and analyzed.

  • Keywords

Brownian Ratchet multi-periodic potential tilted periodic potential Fokker-Plank equation.

  • AMS Subject Headings

60G10 35Q84 60J60 60J65 60H35

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COPYRIGHT: © Global Science Press

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@Article{CiCP-25-1, author = {Tamra Heberling, Lisa Davis and Tomas Gedeon}, title = {Approximation of the Mean Escape Time for a Tilted Periodic Potential}, journal = {Communications in Computational Physics}, year = {2018}, volume = {25}, number = {1}, pages = {1--40}, abstract = {

We present a formula approximating the mean escape time (MST) of a particle from a tilted multi-periodic potential well. The potential function consists of a weighted sum of a finite number of component functions, each of which is periodic. For this particular case, the least period of the potential function is a common period amongst all of its component functions. An approximation of the MST for the potential function is derived, and this approximation takes the form of a product of the MSTs for each of the individual periodic component functions. Our first example illustrates the computational advantages of using the approximation for model validation and parameter tuning in the context of the biological application of DNA transcription. We also use this formula to approximate the MST for an arbitrary tilted periodic potential by the product of MSTs of a finite number of its Fourier modes. Two examples using truncated Fourier series are presented and analyzed.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0133}, url = {http://global-sci.org/intro/article_detail/cicp/12661.html} }
TY - JOUR T1 - Approximation of the Mean Escape Time for a Tilted Periodic Potential AU - Tamra Heberling, Lisa Davis & Tomas Gedeon JO - Communications in Computational Physics VL - 1 SP - 1 EP - 40 PY - 2018 DA - 2018/09 SN - 25 DO - http://dor.org/10.4208/cicp.OA-2017-0133 UR - https://global-sci.org/intro/cicp/12661.html KW - Brownian Ratchet KW - multi-periodic potential KW - tilted periodic potential KW - Fokker-Plank equation. AB -

We present a formula approximating the mean escape time (MST) of a particle from a tilted multi-periodic potential well. The potential function consists of a weighted sum of a finite number of component functions, each of which is periodic. For this particular case, the least period of the potential function is a common period amongst all of its component functions. An approximation of the MST for the potential function is derived, and this approximation takes the form of a product of the MSTs for each of the individual periodic component functions. Our first example illustrates the computational advantages of using the approximation for model validation and parameter tuning in the context of the biological application of DNA transcription. We also use this formula to approximate the MST for an arbitrary tilted periodic potential by the product of MSTs of a finite number of its Fourier modes. Two examples using truncated Fourier series are presented and analyzed.

Tamra Heberling, Lisa Davis & Tomas Gedeon. (1970). Approximation of the Mean Escape Time for a Tilted Periodic Potential. Communications in Computational Physics. 25 (1). 1-40. doi:10.4208/cicp.OA-2017-0133
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