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Title: A unified view of hierarchy approach and formula of differentiation

Abstract

The stochastic differential equation is a powerful tool for describing the dynamics of a dissipative system in which noise characterizes the influence of the environment. For the Ornstein-Uhlenbeck noise, both the formula of differentiation and the hierarchy approach provide efficient numerical simulations, with the stochastic differential equation transformed into a set of coupled, linear ordinary differential equations. We show that while these two deterministic schemes result in different sets of equations, they can be regarded as two representations of an underlying linear-dynamics. Moreover, by manipulating the involved Ornstein-Uhlenbeck noise, we propose a unified algorithm that may reduce to the hierarchy approach or the formula of differentiation in different limits. We further analyze the numerical performance of this algorithm and find that the hierarchy approach appears to be more efficient for our numerical model studies.

Authors:
ORCiD logo; ORCiD logo;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1571839
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Publisher's Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Name: Journal of Chemical Physics Journal Volume: 151 Journal Issue: 16; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics
Country of Publication:
United States
Language:
English

Citation Formats

Yan, Yun-An, Wang, Haobin, and Shao, Jiushu. A unified view of hierarchy approach and formula of differentiation. United States: N. p., 2019. Web. doi:10.1063/1.5126341.
Yan, Yun-An, Wang, Haobin, & Shao, Jiushu. A unified view of hierarchy approach and formula of differentiation. United States. https://doi.org/10.1063/1.5126341
Yan, Yun-An, Wang, Haobin, and Shao, Jiushu. Thu . "A unified view of hierarchy approach and formula of differentiation". United States. https://doi.org/10.1063/1.5126341.
@article{osti_1571839,
title = {A unified view of hierarchy approach and formula of differentiation},
author = {Yan, Yun-An and Wang, Haobin and Shao, Jiushu},
abstractNote = {The stochastic differential equation is a powerful tool for describing the dynamics of a dissipative system in which noise characterizes the influence of the environment. For the Ornstein-Uhlenbeck noise, both the formula of differentiation and the hierarchy approach provide efficient numerical simulations, with the stochastic differential equation transformed into a set of coupled, linear ordinary differential equations. We show that while these two deterministic schemes result in different sets of equations, they can be regarded as two representations of an underlying linear-dynamics. Moreover, by manipulating the involved Ornstein-Uhlenbeck noise, we propose a unified algorithm that may reduce to the hierarchy approach or the formula of differentiation in different limits. We further analyze the numerical performance of this algorithm and find that the hierarchy approach appears to be more efficient for our numerical model studies.},
doi = {10.1063/1.5126341},
journal = {Journal of Chemical Physics},
number = 16,
volume = 151,
place = {United States},
year = {2019},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1063/1.5126341

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Cited by: 3 works
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