Kim, E-J. and Hollerbach, R. (2016) Time-dependent probability density function in cubic stochastic processes. Physical Review E, 94 (5). ISSN 2470-0045
Abstract
We report time-dependent Probability Density Functions (PDFs) for a nonlinear stochastic process with a cubic force by novel analytical and computational studies. Analytically, a transition probability is formulated by using a path integral and is computed by the saddle-point solution (instanton method) and a new nonlinear transformation of time. The predicted PDF p(x, t) is in general given as a time integral and useful PDFs with explicit dependence on x and t are presented in certain limits (e.g. in the short and long time limits). Numerical simulations of the FokkerPlanck equation provide exact time evolution of the PDFs and confirm analytical predictions in the limit of weak noise. In particular, we show that non-equilibrium PDFs behave drastically differently from the stationary PDFs in regards to the asymmetry (skewness) and kurtosis. Specifically, while stationary PDFs are symmetric, transient PDFs are skewed; transient PDFs are much broader than stationary PDFs, with the kurtosis larger and smaller than 3, respectively. We elucidate the effect of nonlinear interaction on the strong fluctuations and intermittency in relaxation process.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 American Physical Society. This is an author produced version of a paper subsequently published in Physical Review E. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 23 Nov 2016 15:44 |
Last Modified: | 21 Mar 2018 00:51 |
Published Version: | http://doi.org/10.1103/PhysRevE.94.052118 |
Status: | Published |
Publisher: | American Physical Society |
Refereed: | Yes |
Identification Number: | 10.1103/PhysRevE.94.052118 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:108219 |