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Garbaczewski P, Stephanovich V. Fractional Laplacians in bounded domains: Killed, reflected, censored, and taboo Lévy flights. Phys Rev E 2019; 99:042126. [PMID: 31108727 DOI: 10.1103/physreve.99.042126] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2018] [Indexed: 06/09/2023]
Abstract
The fractional Laplacian (-Δ)^{α/2}, α∈(0,2), has many equivalent (albeit formally different) realizations as a nonlocal generator of a family of α-stable stochastic processes in R^{n}. On the other hand, if the process is to be restricted to a bounded domain, there are many inequivalent proposals for what a boundary-data-respecting fractional Laplacian should actually be. This ambiguity not only holds true for each specific choice of the process behavior at the boundary (e.g., absorbtion, reflection, conditioning, or boundary taboos), but extends as well to its particular technical implementation (Dirichlet, Neumann, etc., problems). The inferred jump-type processes are inequivalent as well, differing in their spectral and statistical characteristics, which may strongly influence the ability of the formalism (if uncritically adopted) to provide an unambiguous description of real geometrically confined physical systems with disorder. Specifically that refers to their relaxation properties and the near-equilibrium asymptotic behavior. In the present paper we focus on Lévy flight-induced jump-type processes which are constrained to stay forever inside a finite domain. This refers to a concept of taboo processes (imported from Brownian to Lévy-stable contexts), to so-called censored processes, and to reflected Lévy flights whose status still remains to be unequivocally settled. As a by-product of our fractional spectral analysis, with reference to Neumann boundary conditions, we discuss disordered semiconducting heterojunctions as the bounded domain problem.
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McKetterick TJ, Giuggioli L. Exact dynamics of stochastic linear delayed systems: application to spatiotemporal coordination of comoving agents. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042135. [PMID: 25375466 DOI: 10.1103/physreve.90.042135] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/14/2014] [Indexed: 06/04/2023]
Abstract
Delayed dynamics result from finite transmission speeds of a signal in the form of energy, mass, or information. In stochastic systems the resulting lagged dynamics challenge our understanding due to the rich behavioral repertoire encompassing monotonic, oscillatory, and unstable evolution. Despite the vast literature, quantifying this rich behavior is limited by a lack of explicit analytic studies of high-dimensional stochastic delay systems. Here we fill this gap for systems governed by a linear Langevin equation of any number of delays and spatial dimensions with additive Gaussian noise. By exploiting Laplace transforms we are able to derive an exact time-dependent analytic solution of the Langevin equation. By using characteristic functionals we are able to construct the full time dependence of the multivariate probability distribution of the stochastic process as a function of the delayed and nondelayed random variables. As an application we consider interactions in animal collective movement that go beyond the traditional assumption of instantaneous alignment. We propose models for coordinated maneuvers of comoving agents applicable to recent empirical findings in pigeons and bats whereby individuals copy the heading of their neighbors with some delay. We highlight possible strategies that individual pairs may adopt to reduce the variance in their velocity difference and/or in their spatial separation. We also show that a minimum in the variance of the spatial separation at long times can be achieved with certain ratios of measurement to reaction delay.
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Affiliation(s)
- Thomas John McKetterick
- Bristol Centre for Complexity Sciences, University of Bristol, Bristol BS8 1UG, United Kingdom and Department of Engineering Mathematics, University of Bristol, Bristol BS8 1UG, Kingdom
| | - Luca Giuggioli
- Bristol Centre for Complexity Sciences, University of Bristol, Bristol BS8 1UG, United Kingdom and Department of Engineering Mathematics, University of Bristol, Bristol BS8 1UG, Kingdom and School of Biological Sciences, University of Bristol, Bristol BS8 1UG, United Kingdom
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Cisternas J, Wehner S, Descalzi O. CO oxidation on Ir(111) surfaces under large non-Gaussian noise. J Chem Phys 2012; 137:064105. [PMID: 22897253 DOI: 10.1063/1.4742191] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jaime Cisternas
- Complex Systems Group, College of Engineering and Applied Sciences, Universidad de los Andes, Santiago, Chile.
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Kolomietz VM, Radionov SV. Non-Markovian diffusion over a potential barrier in the presence of periodic time modulation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:051123. [PMID: 22181385 DOI: 10.1103/physreve.84.051123] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2011] [Revised: 11/03/2011] [Indexed: 05/31/2023]
Abstract
The diffusive non-Markovian motion over a single-well potential barrier in the presence of a weak sinusoidal time modulation is studied. We found nonmonotonic dependence of the mean escape time from the barrier on a frequency of the periodic modulation that is analogous to the stochastic resonance phenomenon. The resonant increase of diffusion over the barrier occurs at the frequency inversely proportional to the mean first-passage time for the motion in the absence of the time modulation.
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Dybiec B, Gudowska-Nowak E, Hänggi P. Escape driven by alpha-stable white noises. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:021109. [PMID: 17358315 DOI: 10.1103/physreve.75.021109] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2006] [Indexed: 05/14/2023]
Abstract
We explore the archetype problem of an escape dynamics occurring in a symmetric double well potential when the Brownian particle is driven by white Lévy noise in a dynamical regime where inertial effects can safely be neglected. The behavior of escaping trajectories from one well to another is investigated by pointing to the special character that underpins the noise-induced discontinuity which is caused by the generalized Brownian paths that jump beyond the barrier location without actually hitting it. This fact implies that the boundary conditions for the mean first passage time (MFPT) are no longer determined by the well-known local boundary conditions that characterize the case with normal diffusion. By numerically implementing properly the set up boundary conditions, we investigate the survival probability and the average escape time as a function of the corresponding Lévy white noise parameters. Depending on the value of the skewness beta of the Lévy noise, the escape can either become enhanced or suppressed: a negative asymmetry parameter beta typically yields a decrease for the escape rate while the rate itself depicts a non-monotonic behavior as a function of the stability index alpha that characterizes the jump length distribution of Lévy noise, exhibiting a marked discontinuity at alpha=1. We find that the typical factor of 2 that characterizes for normal diffusion the ratio between the MFPT for well-bottom-to-well-bottom and well-bottom-to-barrier-top no longer holds true. For sufficiently high barriers the survival probabilities assume an exponential behavior versus time. Distinct non-exponential deviations occur, however, for low barrier heights.
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Affiliation(s)
- B Dybiec
- M. Smoluchowski Institute of Physics, and Mark Kac Center for Complex Systems Research, Jagellonian University, ul. Reymonta 4, 30-059 Kraków, Poland.
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Chaudhury S, Cherayil BJ. Approximate first passage time distribution for barrier crossing in a double well under fractional Gaussian noise. J Chem Phys 2006; 125:114106. [PMID: 16999465 DOI: 10.1063/1.2354089] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The distribution of waiting times, f(t), between successive turnovers in the catalytic action of single molecules of the enzyme beta-galactosidase has recently been determined in closed form by Chaudhury and Cherayil [J. Chem. Phys. 125, 024904 (2006)] using a one-dimensional generalized Langevin equation (GLE) formalism in combination with Kramers' flux-over-population approach to barrier crossing dynamics. The present paper provides an alternative derivation of f(t) that eschews this approach, which is strictly applicable only under conditions of local equilibrium. In this alternative derivation, a double well potential is incorporated into the GLE, along with a colored noise term representing protein conformational fluctuations, and the resulting equation transformed approximately to a Smoluchowski-type equation. f(t) is identified with the first passage time distribution for a particle to reach the barrier top starting from an equilibrium distribution of initial points, and is determined from the solution of the above equation using local boundary conditions. The use of such boundary conditions is necessitated by the absence of definite information about the precise nature of the boundary conditions applicable to stochastic processes governed by non-Markovian dynamics. f(t) calculated in this way is found to have the same analytic structure as the distribution calculated by the flux-over-population method.
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Affiliation(s)
- Srabanti Chaudhury
- Department of Inorganic and Physical Chemistry, Indian Institute of Science, Bangalore 560012, India
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Dybiec B, Gudowska-Nowak E, Hänggi P. Lévy-Brownian motion on finite intervals: Mean first passage time analysis. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:046104. [PMID: 16711875 DOI: 10.1103/physreve.73.046104] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2005] [Indexed: 05/09/2023]
Abstract
We present the analysis of the first passage time problem on a finite interval for the generalized Wiener process that is driven by Lévy stable noises. The complexity of the first passage time statistics (mean first passage time, cumulative first passage time distribution) is elucidated together with a discussion of the proper setup of corresponding boundary conditions that correctly yield the statistics of first passages for these non-Gaussian noises. The validity of the method is tested numerically and compared against analytical formulas when the stability index alpha approaches 2, recovering in this limit the standard results for the Fokker-Planck dynamics driven by Gaussian white noise.
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Affiliation(s)
- B Dybiec
- Marian Smoluchowski Institute of Physics and Mark Kac Center for Complex Systems Research, Jagellonian University, ul. Reymonta 4, 30-059 Kraków, Poland.
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Kim C, Lee EK, Talkner P. Numerical method for solving stochastic differential equations with dichotomous noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:026101. [PMID: 16605392 DOI: 10.1103/physreve.73.026101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2005] [Indexed: 05/08/2023]
Abstract
We propose a numerical method for solving stochastic differential equations with dichotomous Markov noise. The numerical scheme is formulated such that (i) the stochastic formula used follows the Stratonovich-Taylor form over the entire range of noise correlation times, including the Gaussian white noise limit; and (ii) the method is readily applicable to dynamical systems driven by arbitrary types of noise, provided there exists a way to describe the random increment of the stochastic process expressed in the Stratonovich-Taylor form. We further propose a simplified Taylor scheme that significantly reduces the computation time, while still satisfying the moment properties up to the required order. The accuracies and efficiencies of the proposed algorithms are validated by applying the schemes to two prototypical model systems that possess analytical solutions.
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Affiliation(s)
- Changho Kim
- Department of Chemistry and School of Molecular Science (BK21), Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea
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Pogorui AA, Rodríguez-Dagnino RM. Limiting distribution of random motion in a n-dimensional parallelepiped. RANDOM OPERATORS AND STOCHASTIC EQUATIONS 2006. [DOI: 10.1515/156939706779801688] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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Dubkov AA, Spagnolo B. Acceleration of diffusion in randomly switching potential with supersymmetry. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:041104. [PMID: 16383359 DOI: 10.1103/physreve.72.041104] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2004] [Revised: 07/22/2005] [Indexed: 05/05/2023]
Abstract
We investigate the overdamped Brownian motion in a supersymmetric periodic potential switched by Markovian dichotomous noise between two configurations. The two configurations differ from each other by a shift of one-half period. The calculation of the effective diffusion coefficient is reduced to the mean first passage time problem. We derive general equations to calculate the effective diffusion coefficient of Brownian particles moving in arbitrary supersymmetric potential. For the sawtooth potential, we obtain the exact expression for the effective diffusion coefficient, which is valid for the arbitrary mean rate of potential switchings and arbitrary intensity of white Gaussian noise. We find the acceleration of diffusion in comparison with the free diffusion case and a finite net diffusion in the absence of thermal noise. Such a potential could be used to enhance the diffusion over its free value by an appropriate choice of parameters.
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Affiliation(s)
- Alexander A Dubkov
- Radiophysics Department, Nizhni Novgorod State University, 23 Gagarin Ave., 603950 Nizhni Novgorod, Russia.
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Goychuk I, Hänggi P. Fractional diffusion modeling of ion channel gating. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:051915. [PMID: 15600664 DOI: 10.1103/physreve.70.051915] [Citation(s) in RCA: 58] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2004] [Indexed: 05/24/2023]
Abstract
An anomalous diffusion model for ion channel gating is put forward. This scheme is able to describe nonexponential, power-law-like distributions of residence time intervals in several types of ion channels. Our method presents a generalization of the discrete diffusion model by Millhauser, Salpeter, and Oswald [Proc. Natl. Acad. Sci. U.S.A. 85, 1503 (1988)] to the case of a continuous, anomalous slow conformational diffusion. The corresponding generalization is derived from a continuous-time random walk composed of nearest-neighbor jumps which in the scaling limit results in a fractional diffusion equation. The studied model contains three parameters only: the mean residence time, a characteristic time of conformational diffusion, and the index of subdiffusion. A tractable analytical expression for the characteristic function of the residence time distribution is obtained. In the limiting case of normal diffusion, our prior findings [Proc. Natl. Acad. Sci. U.S.A. 99, 3552 (2002)] are reproduced. Depending on the chosen parameters, the fractional diffusion model exhibits a very rich behavior of the residence time distribution with different characteristic time regimes. Moreover, the corresponding autocorrelation function of conductance fluctuations displays nontrivial power law features. Our theoretical model is in good agreement with experimental data for large conductance potassium ion channels.
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Affiliation(s)
- Igor Goychuk
- Institute of Physics, University of Augsburg, Universitätsstrasse 1, D-86135 Augsburg, Germany.
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Dubkov AA, Agudov NV, Spagnolo B. Noise-enhanced stability in fluctuating metastable states. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:061103. [PMID: 15244536 DOI: 10.1103/physreve.69.061103] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2002] [Revised: 04/02/2004] [Indexed: 05/24/2023]
Abstract
We derive general equations for the nonlinear relaxation time of Brownian diffusion in randomly switching potential with a sink. For piece-wise linear dichotomously fluctuating potential with metastable state, we obtain the exact average lifetime as a function of the potential parameters and the noise intensity. Our result is valid for arbitrary white noise intensity and for arbitrary fluctuation rate of the potential. We find noise enhanced stability phenomenon in the system investigated: The average lifetime of the metastable state is greater than the time obtained in the absence of additive white noise. We obtain the parameter region of the fluctuating potential where the effect can be observed. The system investigated also exhibits a maximum of the lifetime as a function of the fluctuation rate of the potential.
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Affiliation(s)
- Alexander A Dubkov
- Radiophysics Department, Nizhni Novgorod State University, 23 Gagarin ave., 603950 Nizhni Novgorod, Russia
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Bena I, Van den Broeck C, Kawai R, Lindenberg K. Drift by dichotomous Markov noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:041111. [PMID: 14682927 DOI: 10.1103/physreve.68.041111] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2003] [Indexed: 05/24/2023]
Abstract
We derive explicit results for the asymptotic probability density and drift velocity in systems driven by dichotomous Markov noise, including the situation in which the asymptotic dynamics crosses unstable fixed points. The results are illustrated on the problem of the rocking ratchet.
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Affiliation(s)
- I Bena
- Département de Physique Théorique, Université de Genève, CH-1211 Genève 4, Switzerland
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Bena I, Van Den Broeck C, Kawai R, Lindenberg K. Nonlinear response with dichotomous noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:045603. [PMID: 12443252 DOI: 10.1103/physreve.66.045603] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2002] [Indexed: 05/24/2023]
Abstract
Dichotomous noise appears in a wide variety of physical and mathematical models. It has escaped attention that the standard results for the long time properties cannot be applied when unstable fixed points are crossed in the asymptotic regime. We show how calculations have to be modified to deal with these cases and present as a first application full analytic results for hypersensitive transport.
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Affiliation(s)
- I Bena
- Limburgs Universitair Centrum, B-3590 Diepenbeek, Belgium
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Laio F, Porporato A, Ridolfi L, Rodriguez-Iturbe I. Mean first passage times of processes driven by white shot noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:036105. [PMID: 11308707 DOI: 10.1103/physreve.63.036105] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2000] [Indexed: 05/23/2023]
Abstract
We consider mean first passage times in systems driven by white shot noise with exponentially distributed jump heights. Simple interpretable results are obtained and the linkage between those results and the steady-state probability density function of the process is presented. The virtual waiting-time or Takács process (constant losses) and the shot noise process with linear losses are analyzed in depth, along with a more complex process with useful implications for the modeling of the soil moisture dynamics in hydrology.
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Affiliation(s)
- F Laio
- Dipartimento di Idraulica Trasporti e Infrastrutture Civili, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy
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Gitterman M. Stochastic resonance in one-dimensional diffusion with one reflecting and one absorbing end point. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:4726-31. [PMID: 11031512 DOI: 10.1103/physreve.61.4726] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/1999] [Indexed: 11/07/2022]
Abstract
An analysis of the nonmonotonic dependence of the mean-free-passage time on the frequency of a periodic signal [stochastic resonance (SR)] for diffusion on a segment with one absorbing and one reflecting end point shows that SR exists only for some restricted values of parameters. SR always exists if the periodic telegraph signal is replaced by a random one. The latter case is considered in detail.
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Affiliation(s)
- M Gitterman
- Department of Physics, Bar-Ilan University, Ramat-Gan, Israel
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Schmid GJ, Reimann P, Hänggi P. Control of reaction rate by asymmetric two-state noise. J Chem Phys 1999. [DOI: 10.1063/1.479619] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Reimann P, Schmid GJ, Hänggi P. Universal equivalence of mean first-passage time and Kramers rate. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:R1-4. [PMID: 11969866 DOI: 10.1103/physreve.60.r1] [Citation(s) in RCA: 51] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/1999] [Indexed: 04/18/2023]
Abstract
We prove that for an arbitrary time-homogeneous stochastic process, Kramers's flux-over-population rate is identical to the inverse of the associated mean first-passage time. In this way the mean first-passage time problem can be treated without making use of the adjoint equation in conjunction with cumbersome boundary conditions.
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Affiliation(s)
- P Reimann
- Theoretische Physik I, Universität Augsburg, 86135 Augsburg, Germany
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Luczka J, Niemiec M, Piotrowski E. Linear systems with randomly interrupted Gaussian white noise. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/26/19/018] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Porr JM, Robinson A, Masoliver J. First-passage-time statistics for diffusion processes with an external random force. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:3240-3245. [PMID: 9964631 DOI: 10.1103/physreve.53.3240] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Christophorov LN. Dichotomous noise with feedback and charge-conformational interactions. J Biol Phys 1996. [DOI: 10.1007/bf00401873] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022] Open
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Luczka J, Niemiec M, Hänggi P. First-passage time for randomly flashing diffusion. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:5810-5816. [PMID: 9964095 DOI: 10.1103/physreve.52.5810] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Gitterman M. Brownian motion in fluctuating media. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:303-306. [PMID: 9963433 DOI: 10.1103/physreve.52.303] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Masoliver J, Porr JM, Weiss GH. Solution to the telegrapher's equation in the presence of reflecting and partly reflecting boundaries. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 48:939-944. [PMID: 9960676 DOI: 10.1103/physreve.48.939] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Kus M, Wódkiewicz K. Mean first-passage time in the presence of telegraph noise and the Ornstein-Uhlenbeck process. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 47:4055-4062. [PMID: 9960479 DOI: 10.1103/physreve.47.4055] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Behn U, Müller R, Talkner P. Mean first-passage time for systems driven by pre-Gaussian noise: Natural boundary conditions. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 47:3970-3974. [PMID: 9960471 DOI: 10.1103/physreve.47.3970] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Porr JM, Masoliver J. Bistability driven by white shot noise. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 47:1633-1641. [PMID: 9960187 DOI: 10.1103/physreve.47.1633] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Doering CR, Gadoua JC. Resonant activation over a fluctuating barrier. PHYSICAL REVIEW LETTERS 1992; 69:2318-2321. [PMID: 10046454 DOI: 10.1103/physrevlett.69.2318] [Citation(s) in RCA: 143] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Foong SK. First-passage time, maximum displacement, and Kac's solution of the telegrapher equation. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 46:R707-R710. [PMID: 9908228 DOI: 10.1103/physreva.46.r707] [Citation(s) in RCA: 29] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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