Overdamped Brownian dynamics in piecewise-defined energy landscapes
We study the overdamped Brownian dynamics of particles moving in piecewise-defined potential energy landscapes U(x), where the height Q of each section is obtained from the exponential distribution p(Q)=aβexp(−aβQ), where β is the reciprocal thermal energy, and a>0. The averaged effective diffusi...
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sg-ntu-dr.10356-1465732023-02-28T19:54:48Z Overdamped Brownian dynamics in piecewise-defined energy landscapes Gray, Thomas H. Yong, Ee Hou School of Physical and Mathematical Sciences Science::Physics Brownian Motion Glass Transition We study the overdamped Brownian dynamics of particles moving in piecewise-defined potential energy landscapes U(x), where the height Q of each section is obtained from the exponential distribution p(Q)=aβexp(−aβQ), where β is the reciprocal thermal energy, and a>0. The averaged effective diffusion coefficient ⟨Deff⟩ is introduced to characterize the diffusive motion: ⟨x2⟩=2⟨Deff⟩t. A general expression for ⟨Deff⟩ in terms of U(x) and p(Q) is derived and then applied to three types of energy landscape: flat sections, smooth maxima, and sharp maxima. All three cases display a transition between subdiffusive and diffusive behavior at a=1, and a reduction to free diffusion as a→∞. The behavior of ⟨Deff⟩ around the transition is investigated and found to depend heavily upon the shape of the maxima: Energy landscapes made up of flat sections or smooth maxima display power-law behavior, while for landscapes with sharp maxima, strongly divergent behavior is observed. Two aspects of the subdiffusive regime are studied: the growth of the mean squared displacement with time and the distribution of mean first-passage times. For the former, agreement between Brownian dynamics simulations and a coarse-grained equivalent was observed, but the results deviated from the random barrier model's predictions. The discrepancy could be a finite-time effect. For the latter, agreement between the characteristic exponent calculated numerically and that predicted by the random barrier model is observed in the large-amplitude limit. Nanyang Technological University Published version T.H.G. acknowledges support from the EPSRC and E.H.Y. acknowledges support from Nanyang Technological University, Singapore, under Grant No. M4081583. 2021-03-02T02:07:07Z 2021-03-02T02:07:07Z 2020 Journal Article Gray, T. H., & Yong, E. H. (2020). Overdamped brownian dynamics in piecewise-defined energy landscapes. Physical Review E, 101(5), 052123-. doi:10.1103/physreve.101.052123 2470-0045 https://hdl.handle.net/10356/146573 10.1103/PhysRevE.101.052123 32575297 2-s2.0-85086302353 5 101 en M4081583 Physical Review E © 2020 American Physical Society (APS). All rights reserved. This paper was published in Physical Review E and is made available with permission of American Physical Society (APS). application/pdf |
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Science::Physics Brownian Motion Glass Transition Gray, Thomas H. Yong, Ee Hou Overdamped Brownian dynamics in piecewise-defined energy landscapes |
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We study the overdamped Brownian dynamics of particles moving in piecewise-defined potential energy landscapes U(x), where the height Q of each section is obtained from the exponential distribution p(Q)=aβexp(−aβQ), where β is the reciprocal thermal energy, and a>0. The averaged effective diffusion coefficient ⟨Deff⟩ is introduced to characterize the diffusive motion: ⟨x2⟩=2⟨Deff⟩t. A general expression for ⟨Deff⟩ in terms of U(x) and p(Q) is derived and then applied to three types of energy landscape: flat sections, smooth maxima, and sharp maxima. All three cases display a transition between subdiffusive and diffusive behavior at a=1, and a reduction to free diffusion as a→∞. The behavior of ⟨Deff⟩ around the transition is investigated and found to depend heavily upon the shape of the maxima: Energy landscapes made up of flat sections or smooth maxima display power-law behavior, while for landscapes with sharp maxima, strongly divergent behavior is observed. Two aspects of the subdiffusive regime are studied: the growth of the mean squared displacement with time and the distribution of mean first-passage times. For the former, agreement between Brownian dynamics simulations and a coarse-grained equivalent was observed, but the results deviated from the random barrier model's predictions. The discrepancy could be a finite-time effect. For the latter, agreement between the characteristic exponent calculated numerically and that predicted by the random barrier model is observed in the large-amplitude limit. |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Gray, Thomas H. Yong, Ee Hou |
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Article |
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Gray, Thomas H. Yong, Ee Hou |
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Gray, Thomas H. |
title |
Overdamped Brownian dynamics in piecewise-defined energy landscapes |
title_short |
Overdamped Brownian dynamics in piecewise-defined energy landscapes |
title_full |
Overdamped Brownian dynamics in piecewise-defined energy landscapes |
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Overdamped Brownian dynamics in piecewise-defined energy landscapes |
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Overdamped Brownian dynamics in piecewise-defined energy landscapes |
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overdamped brownian dynamics in piecewise-defined energy landscapes |
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2021 |
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https://hdl.handle.net/10356/146573 |
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