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Analysis of white noise limits for stochastic systems with two fast relaxation times
 Multiscale Model. Simul
"... Abstract. In this paper we present a rigorous asymptotic analysis for stochastic systems with two fast relaxation times. The mathematical model analyzed in this paper consists of a Langevin equation for the particle motion with timedependent force constructed through an infinite dimensional Gaussia ..."
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Abstract. In this paper we present a rigorous asymptotic analysis for stochastic systems with two fast relaxation times. The mathematical model analyzed in this paper consists of a Langevin equation for the particle motion with timedependent force constructed through an infinite dimensional Gaussian noise process. We study the limit as the particle relaxation time as well as the correlation time of the noise tend to zero and we obtain the limiting equations under appropriate assumptions on the Gaussian noise. We show that the limiting equation depends on the relative magnitude of the two fast time scales of the system. In particular, we prove that in the case where the two relaxation times converge to zero at the same rate there is a drift correction, in addition to the limiting Itô integral, which is not of Stratonovich type. If, on the other hand, the colored noise is smooth on the scale of particle relaxation then the drift correction is the standard Stratonovich correction. If the noise is rough on this scale then there is no drift correction. Strong (i.e. pathwise) techniques are used for the proof of the convergence theorems.
Dense Gas Theory and Fluctuating Hydrodynamics Based on Extended Thermodynamics
"... Nonequilibrium phenomena with evident spatiotemporal changes in physical quantities are notably interdisciplinary and encountered in engineering, physics, chemistry, biology and so on. For example, such phenomena appear in mesoscopic scale fluid flow, shock waves in the field of highspeed hydrody ..."
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Nonequilibrium phenomena with evident spatiotemporal changes in physical quantities are notably interdisciplinary and encountered in engineering, physics, chemistry, biology and so on. For example, such phenomena appear in mesoscopic scale fluid flow, shock waves in the field of highspeed hydrodynamics, ultrasonic waves. In particular, in mesoscopic systems, the effects of fluctuations become essentially significant. These phenomena have been studied from the view point of thermodynamics. For strongly nonequilibrium phenomena, I. Müller, T. Ruggeri and I. S. Liu proposed, developed and applied the extended thermodynamics (ET) theory. ET can be used to describe phenomena beyond the applicable range of wellknown theory, that is, thermodynamics of irreversible processes (TIP) proposed by L. Onsager, C. Eckart, J. Meixner and I. Prigogine. For phenomena with fluctuations, the LandauLifshitz (LL) theory, a fluctuating hydrodynamics theory based on TIP has shown scope for future study. However, ET and LL have the following problems: 1. ET is presently limited to rarefied monatomic gases.
Sunder Sethuraman
, 2013
"... Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the aut ..."
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Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Downloaded 9May2016 14:01:28 Link to item