1
|
Bley M, Dzubiella J, Moncho-Jordá A. Active binary switching of soft colloids: stability and structural properties. SOFT MATTER 2021; 17:7682-7696. [PMID: 34342324 DOI: 10.1039/d1sm00670c] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We employ reactive dynamical density functional theory (R-DDFT) and reactive Brownian dynamics (R-BD) simulations to study the non-equilibrium structure and phase behavior of an active dispersion of soft Gaussian colloids with binary interaction switching, i.e., we consider a one-component colloidal system in which every particle can individually switch stochastically between two interaction states (here, sizes 'big' and 'small') at predefined rates. We consider the influence of switching activity on the inhomogeneous density profiles of the colloids confined by various external potentials, as well as on their pair structure and phase behavior in bulk solutions. For the latter, we extend the R-DDFT method to incorporate the Percus test-particle route. Our results demonstrate that switching activity strongly modifies the steady-state density profiles and structural (pair) correlations. In particular, the switching rate interpolates from a near-equilibrium binary colloidal mixture of two states at very low rates to a non-equilibrium, 'one-state liquid' at very high rates characterized by one, average interaction size. The latter limit can be described by an equivalent effective one-component (EOC) equilibrium system, for which the exact analytical expression for the effective pair potential is a diffusion-weighted superposition of the active systems' pair potentials. This leads to the interesting fact that under certain conditions an interacting switching system can behave like a non-interacting (ideal) gas in the limit of high switching rates. Moreover, for colloids that are unstable (i.e., demix) near equilibrium, we demonstrate that phase separation and micro-clustering in both confinement and bulk can be dynamically controlled by the switching rate, and vanish for high rates. All R-DDFT results are in excellent agreement with our R-BD simulations.
Collapse
Affiliation(s)
- Michael Bley
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder Straße 3, D-79104 Freiburg, Germany.
| | | | | |
Collapse
|
2
|
Berezhkovskii AM, Bezrukov SM. Effect of stochastic gating on channel-facilitated transport of non-interacting and strongly repelling solutes. J Chem Phys 2017; 147:084109. [PMID: 28863525 DOI: 10.1063/1.4986902] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Ligand- or voltage-driven stochastic gating-the structural rearrangements by which the channel switches between its open and closed states-is a fundamental property of biological membrane channels. Gating underlies the channel's ability to respond to different stimuli and, therefore, to be functionally regulated by the changing environment. The accepted understanding of the gating effect on the solute flux through the channel is that the mean flux is the product of the flux through the open channel and the probability of finding the channel in the open state. Here, using a diffusion model of channel-facilitated transport, we show that this is true only when the gating is much slower than the dynamics of solute translocation through the channel. If this condition breaks, the mean flux could differ from this simple estimate by orders of magnitude.
Collapse
Affiliation(s)
- Alexander M Berezhkovskii
- Section on Molecular Transport, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Sergey M Bezrukov
- Section on Molecular Transport, Eunice Kennedy Shriver National Institute of Child Health and Human Development, National Institutes of Health, Bethesda, Maryland 20892, USA
| |
Collapse
|
3
|
Kolb JJ, Angioletti-Uberti S, Dzubiella J. Communication: Resonance reaction in diffusion-influenced bimolecular reactions. J Chem Phys 2016; 144:081102. [DOI: 10.1063/1.4942998] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Jakob J. Kolb
- Institut für Physik, Humboldt-Universität zu Berlin, 12489 Berlin, Germany
| | - Stefano Angioletti-Uberti
- International Center for Soft Matter Research, Beijing University of Chemical Technology, Beijing 100029, China
| | - Joachim Dzubiella
- Institut für Physik, Humboldt-Universität zu Berlin, 12489 Berlin, Germany
- Institut für Weiche Materie und Funktionale Materialen, Helmholtz-Zentrum Berlin für Materialien und Energie, 14109 Berlin, Germany
| |
Collapse
|
4
|
Ray S, Mondal D, Bag BC. Resonant activation in a colored multiplicative thermal noise driven closed system. J Chem Phys 2014; 140:204105. [DOI: 10.1063/1.4878235] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
|
5
|
Ghosh PK, Li MS, Bag BC. Periodic force induced stabilization or destabilization of the denatured state of a protein. J Chem Phys 2011; 135:114101. [PMID: 21950844 DOI: 10.1063/1.3635774] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We have studied the effects of an external sinusoidal force in protein folding kinetics. The externally applied force field acts on the each amino acid residues of polypeptide chains. Our simulation results show that mean protein folding time first increases with driving frequency and then decreases passing through a maximum. With further increase of the driving frequency the mean folding time starts increasing as the noise-induced hoping event (from the denatured state to the native state) begins to experience many oscillations over the mean barrier crossing time period. Thus unlike one-dimensional barrier crossing problems, the external oscillating force field induces both stabilization or destabilization of the denatured state of a protein. We have also studied the parametric dependence of the folding dynamics on temperature, viscosity, non-Markovian character of bath in presence of the external field.
Collapse
|
6
|
Klik I, Chang CR. Complex conjugate eigenvalues in the spectrum of an operator for resonant activation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:042101. [PMID: 21599219 DOI: 10.1103/physreve.83.042101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/19/2009] [Revised: 02/28/2011] [Indexed: 05/30/2023]
Abstract
We consider the exit problem for an overdamped Brownian particle in a potential undergoing dichotomic fluctuations. The system exhibits resonant activation. We compute the corresponding exit times distribution and show that the resonance is associated with the presence of a finite number of complex conjugate eigenvalue pairs in the spectrum of the evolution equation. The properties of these eigenvalues and their influence on the exit times distribution and on the possible dynamics of the system are discussed in detail.
Collapse
Affiliation(s)
- Ivo Klik
- Department of Physics, National Taiwan University, Taipei, Taiwan.
| | | |
Collapse
|
7
|
Li JH, Chen QH, Zhou XF. Transport and its enhancement caused by coupling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:041104. [PMID: 20481674 DOI: 10.1103/physreve.81.041104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2009] [Revised: 01/06/2010] [Indexed: 05/29/2023]
Abstract
Using the Weiss mean-field approximation theory and the particles' transport theory for the spatially periodic stochastic systems, we derive an exact analytical expression for the stationary probability current of a coupled lattice system driven by dichotomous noise. It is shown that, for this coupled lattice system, the spatial asymmetry of the system, the asymmetry of the dichotomous noise, and the coupling among nearest neighbors are the ingredients for the stationary probability current. By applying our theory to two special models, we find that (1) the coupling can lead to the directional transport of the particles (even when the potential and the dichotomous noise are symmetric) and (2) the coupling among nearest neighbors can enhance the transport of the particles in some circumstances. Our results are applied to a device of two-dimensional Josephson-junction arrays and a large protein motors cluster.
Collapse
Affiliation(s)
- Jing-hui Li
- Faculty of Science, Ningbo University, Ningbo 315211, People's Republic of China
| | | | | |
Collapse
|
8
|
Pan C, Tan X, Yu Y, Sun G, Kang L, Xu W, Chen J, Wu P. Resonant activation through effective temperature oscillation in a Josephson tunnel junction. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:030104. [PMID: 19391880 DOI: 10.1103/physreve.79.030104] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/10/2008] [Indexed: 05/27/2023]
Abstract
We experimentally investigated the thermal escape from a metastable state in a Josephson tunnel junction subjected to an oscillating effective temperature. A minimum of the average escape time is observed at certain oscillation frequency. Our results confirm that the resonant activation can be caused not only by the oscillating barrier but also by the oscillating temperature. The linear dependence of the minimum average escape time on the resonant frequency suggests that the correlation between the oscillation and the escape process leads to the resonant escape.
Collapse
Affiliation(s)
- Cheng Pan
- Department of Physics and National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China
| | | | | | | | | | | | | | | |
Collapse
|
9
|
Ghosh PK, Bag BC, Ray DS. Noise correlation-induced splitting of Kramers’ escape rate from a metastable state. J Chem Phys 2007; 127:044510. [PMID: 17672710 DOI: 10.1063/1.2756042] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A correlation between two noise processes driving the thermally activated particles in a symmetric triple-well potential may cause a symmetry breaking and a difference in relative stability of the two side wells with respect to the middle one. This leads to an asymmetric localization of population and splitting of Kramers' rate of escape from the middle well, ensuring a preferential distribution of the products in the course of a parallel reaction.
Collapse
Affiliation(s)
- Pulak Kumar Ghosh
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
| | | | | |
Collapse
|
10
|
Bag BC, Hu CK. Escape through an unstable limit cycle driven by multiplicative colored non-Gaussian and additive white Gaussian noises. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:042101. [PMID: 17500937 DOI: 10.1103/physreve.75.042101] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2006] [Revised: 01/30/2007] [Indexed: 05/15/2023]
Abstract
In a previous paper [Bag and Hu, Phys. Rev. E 73, 061107 (2006)], we studied the mean lifetime (MLT) for the escape of a Brownian particle through an unstable limit cycle driven by multiplicative colored Gaussian and additive Gaussian white noises and found resonant activation (RA) behavior. In the present paper we switch from Gaussian to non-Gaussian multiplicative colored noise. We find that in the RA phenomenon, the minimum appears at a smaller noise correlation time (tau) for non-Gaussian noises compared to Gaussian noises in the plot of MLT vs tau for a fixed noise variance; the same plot for a given noise strength increases linearly and the increasing rate is smaller for non-Gaussian noises than for the Gaussian noises; the plot of logarithm of inverse of MLT vs inverse of the strength of additive noise is Arrhenius-like for Gaussian colored noise and it becomes similar to the quantum-Kramers rate if the multiplicative noise is non-Gaussian.
Collapse
|
11
|
Ghosh PK, Bag BC, Ray DS. Interference of stochastic resonances: splitting of Kramers' rate. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:032101. [PMID: 17500739 DOI: 10.1103/physreve.75.032101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2007] [Revised: 02/19/2007] [Indexed: 05/15/2023]
Abstract
We consider the escape of particles located in the middle well of a symmetric triple well potential driven sinusoidally by two forces such that the potential wells rock as in stochastic resonance and the height of the potential barrier oscillates symmetrically about a mean as in resonant activation. It has been shown that depending on their phase difference the application of these two synchronized signals may lead to a splitting of time averaged Kramers' escape rate and a preferential product distribution in a parallel chemical reaction in the steady state.
Collapse
Affiliation(s)
- Pulak Kumar Ghosh
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | | | | |
Collapse
|
12
|
Li JH, Han YX. Escape over a fluctuating potential barrier with three-state Markovian noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:041118. [PMID: 17155033 DOI: 10.1103/physreve.74.041118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2006] [Indexed: 05/12/2023]
Abstract
We consider the escape over a fluctuating potential barrier with a three-state Markovian noise. The resonant activations (RA's) for the mean first-passage times as functions of the transition rates gamma(1), gamma(2), and gamma(3) of the three-state Markovian noise are obtained, respectively. The effect of the three values of the three-state Markovian noise on the RA's is investigated.
Collapse
Affiliation(s)
- Jing-hui Li
- Faculty of Science, Ningbo University, Ningbo 315211, China
| | | |
Collapse
|
13
|
Ghosh PK, Ray DS. A parametric variant of resonant activation: Two-state model approach. J Chem Phys 2006; 125:124102. [PMID: 17014161 DOI: 10.1063/1.2348867] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Mean first passage time of a periodically driven particle for its escape over a fluctuating barrier with wells remaining unbiased exhibits a resonance when the frequency of the driving field is varied. This parametric variant of resonant activation and associated features of noise induced transition are realized in terms of a two-state model to estimate analytically several quantifiers of the escape event. Numerical simulation on a continuous double-well model collaborates our theoretical analysis.
Collapse
Affiliation(s)
- Pulak Kumar Ghosh
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
| | | |
Collapse
|
14
|
Bag BC, Hu CK. Escape through an unstable limit cycle: resonant activation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:061107. [PMID: 16906809 DOI: 10.1103/physreve.73.061107] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2006] [Indexed: 05/11/2023]
Abstract
We consider a Brownian particle acted on by a linear conservative force, a nonlinear frictional force, and multiplicative colored and additive white noises; the frictional force can be negative when the external energy supply is large enough. We numerically calculate the mean first passage time (MFPT) for the particle to escape from an unstable limit cycle and find resonant activation, i.e., the MFPT first decreases, followed by a rise after passing through a minimum with increasing noise correlation time tau for a fixed noise variance. For fixed noise strength of the multiplicative noise the MFPT increases linearly with tau. This is in sharp contrast to the case of fluctuations of nonlinear potentials, in which the MFPT first increases nonlinearly before reaching a limiting value. Our model could be useful for understanding some biological processes.
Collapse
|
15
|
Ghosh PK, Barik D, Bag BC, Ray DS. Quantum escape kinetics over a fluctuating barrier. J Chem Phys 2005; 123:224104. [PMID: 16375467 DOI: 10.1063/1.2135781] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The escape rate of a particle over a fluctuating barrier in a double-well potential exhibits resonance at an optimum value of correlation time of fluctuation. This has been shown to be important in several variants of kinetic model of chemical reactions. We extend the analysis of this phenomenon of resonant activation to quantum domain to show how quantization significantly enhances resonant activation at low temperature due to tunneling.
Collapse
Affiliation(s)
- Pulak Kumar Ghosh
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India
| | | | | | | |
Collapse
|
16
|
|
17
|
Zhao YK, Li JH, Zhao XG. Transitions and transport for a spatially periodic stochastic system with locally coupled oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:031113. [PMID: 15524512 DOI: 10.1103/physreve.70.031113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2003] [Revised: 12/05/2003] [Indexed: 05/24/2023]
Abstract
In this paper, with a special model, we investigate the spatially periodic stochastic system with locally coupled oscillators subject to a constant force F. A nonequilibrium second-order phase transition is found when F=0. This phase transition is reentrant when the additive noise is weak. With varying the constant force F, a continuous or discontinuous transition between the states with positive and negative mean fields (mu>0 and mu<0) is observed, which is not a phase transition. The mean field or current sometimes exhibits hysteresis as a function of F. With the variation of the force F, when hysteresis of the mean field or current versus F appears, a nonzero probability current with definite direction will occur at the point F=0. The correlation between the additive and multiplicative noises has an effect on the transitions and the transport.
Collapse
Affiliation(s)
- Ying-Kui Zhao
- Graduate School of China Academy of Engineering Physics, P.O. Box 2101, Beijing 100088, China
| | | | | |
Collapse
|
18
|
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.
Collapse
Affiliation(s)
- Alexander A Dubkov
- Radiophysics Department, Nizhni Novgorod State University, 23 Gagarin ave., 603950 Nizhni Novgorod, Russia
| | | | | |
Collapse
|
19
|
Samanta HS, Bhattacharjee JK, Ramaswamy R. Approach to equilibrium in adiabatically evolving potentials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:056114. [PMID: 15244890 DOI: 10.1103/physreve.69.056114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2003] [Indexed: 05/24/2023]
Abstract
For a potential function (in one dimension) which evolves from a specified initial form V(i)(x) to a different V(f)(x) asymptotically, we study the evolution, in an overdamped dynamics, of an initial probability density to its final equilibrium. There can be unexpected effects that can arise from the time dependence. We choose a time variation of the form V(x,t) = V(f)(x) + (V(i) - V(f)) e(-lambda t). For a V(f)(x), which is double welled and a V(i)(x) which is simple harmonic, we show that, in particular, if the evolution is adiabatic, this results in a decrease in the Kramers time characteristic of V(f)(x). Thus the time dependence makes diffusion over a barrier more efficient. There can also be interesting resonance effects when V(i)(x) and V(f)(x) are two harmonic potentials displaced with respect to each other that arise from the coincidence of the intrinsic time scale characterizing the potential variation and the Kramers time. Both these features are illustrated through representative examples.
Collapse
Affiliation(s)
- H S Samanta
- Department of Theoretical Physics, Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700 032, India.
| | | | | |
Collapse
|
20
|
Flomenbom O, Klafter J. Resonant activation in discrete systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:051109. [PMID: 15244810 DOI: 10.1103/physreve.69.051109] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2003] [Indexed: 05/24/2023]
Abstract
The resonant activation phenomenon (RAP) in a discrete system is studied using the master equation formalism. We show that the RAP corresponds to a nonmonotonic behavior of the frequency dependent first passage time probability density function (PDF). An analytical expression for the resonant frequency is introduced, which, together with numerical results, helps understand the RAP behavior in the space spanned by the transition rates for the case of reflecting and absorbing boundary conditions. The limited range of system parameters for which the RAP occurs is discussed. We show that a minimum and a maximum in the mean first passage time can be obtained when both boundaries are absorbing. Relationships to some biological systems are suggested.
Collapse
Affiliation(s)
- O Flomenbom
- School of Chemistry, Raymond & Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel
| | | |
Collapse
|
21
|
Talkner P, Łuczka J. Rate description of Fokker-Planck processes with time-dependent parameters. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:046109. [PMID: 15169071 DOI: 10.1103/physreve.69.046109] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2003] [Indexed: 05/24/2023]
Abstract
The reduction of a continuous Markov process with multiple metastable states to a discrete rate process is investigated in the presence of slow time-dependent parameters such as periodic external forces or slowly fluctuating barrier heights. A quantitative criterion is provided under which condition a kinetic description with time-dependent frozen rates applies and nonadiabatic corrections to the frozen rates are obtained. Finally it is shown how the long-time behavior of the underlying continuous process can be retrieved from the knowledge of the discrete process by means of an appropriate random decoration of the discrete states. As a particular example of the presented theory an overdamped bistable Brownian oscillator with periodic driving is discussed.
Collapse
Affiliation(s)
- Peter Talkner
- Universität Augsburg, Institut für Physik, Universitätsstrasse 1, D-86135 Augsburg, Germany
| | | |
Collapse
|
22
|
Chvosta P, Reineker P. Analysis of stochastic resonances. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 68:066109. [PMID: 14754271 DOI: 10.1103/physreve.68.066109] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2003] [Revised: 09/04/2003] [Indexed: 11/07/2022]
Abstract
We investigate the one-dimensional diffusion of a particle in a piecewise linear potential superimposed with a step of a harmonically modulated height. Employing the matching conditions, we solve the corresponding Fokker-Planck equation and we analyze nonlinear features of the particle's mean position as a function of time. We present detailed results in two physically relevant cases. First, we take the unperturbed potential as a symmetrical up-oriented tip, which is placed between two reflecting boundaries and we add the jump at the tip coordinate. The setting yields resonance-like behavior of the stationary-response amplitude. Second, if the discontinuity at origin is combined with the constant force in the symmetrical region between the boundaries, the stationary response displays a time-independent shift against the potential slope. The driving-induced force exhibits a resonance-like behavior both with respect to the diffusion constant and the slope of the unperturbed potential.
Collapse
Affiliation(s)
- Petr Chvosta
- Department of Macromolecular Physics, Faculty of Mathematics and Physics, Charles University, V Holesovickách 2, CZ-180 00 Praha, Czech Republic.
| | | |
Collapse
|
23
|
Yu Y, Han S. Resonant escape over an oscillating barrier in underdamped Josephson tunnel junctions. PHYSICAL REVIEW LETTERS 2003; 91:127003. [PMID: 14525391 DOI: 10.1103/physrevlett.91.127003] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2003] [Indexed: 05/24/2023]
Abstract
The escape from a metastable state over an oscillating barrier of an underdamped Josephson tunnel junction has been experimentally investigated with oscillation frequency well separated from the plasma frequency of the junction. The resonant escape, namely, a minimum of the average escape time as a function of the oscillation frequency, was observed. For the oscillation frequency much smaller than the "resonant frequency," the average escape time is the average of the times required to cross over each of the barriers. On the other hand, for the oscillation frequency much greater than the "resonant frequency," the average escape time is that required to cross the average barrier.
Collapse
Affiliation(s)
- Yang Yu
- Department of Physics and Astronomy, University of Kansas, Lawrence, Kansas 66045, USA
| | | |
Collapse
|
24
|
Iwaniszewski J. Mean escape time over a fluctuating barrier. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:027105. [PMID: 14525151 DOI: 10.1103/physreve.68.027105] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2002] [Indexed: 05/24/2023]
Abstract
An approximate method for studying activation over a fluctuating barrier of potential is proposed. It involves considering separately the slow and fast components of barrier fluctuations, and it applies for any value of their correlation time tau. It gives exact results for the limiting values tau-->0 and tau--> infinity, and the agreement with numerics in between is also excellent, both for dichotomic and Gaussian barrier perturbations.
Collapse
Affiliation(s)
- Jan Iwaniszewski
- Institute of Physics, Nicolaus Copernicus University, Grudziacedil;dzka 5, 87-100 Toruń, Poland.
| |
Collapse
|
25
|
Fa KS, Lenzi EK. Power law diffusion coefficient and anomalous diffusion: analysis of solutions and first passage time. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:061105. [PMID: 16241197 DOI: 10.1103/physreve.67.061105] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2002] [Revised: 03/14/2003] [Indexed: 05/04/2023]
Abstract
We investigate one-dimensional equations for the diffusion with a nonconstant diffusion coefficient inside the second derivative and between the derivatives. In particular, we employ the diffusion coefficient D(x) proportional to /x/(-theta)(theta in R) and a quartic potential. These diffusion equations present a rich variety of behaviors associated with different regimes. Results of two approaches are analyzed and compared. We also investigate the mean first passage time of these systems. We show that the system with the coefficient D(x) between the derivatives can produce different behaviors for the mean first passage time in comparison with those obtained by the system with the coefficient inside the derivatives.
Collapse
Affiliation(s)
- Kwok Sau Fa
- Departamento de Física, Universidade Estadual de Maringá, Maringá-PR, Brazil
| | | |
Collapse
|
26
|
Freund JA, Schimansky-Geier L, Hänggi P. Frequency and phase synchronization in stochastic systems. CHAOS (WOODBURY, N.Y.) 2003; 13:225-238. [PMID: 12675429 DOI: 10.1063/1.1500497] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
The phenomenon of frequency and phase synchronization in stochastic systems requires a revision of concepts originally phrased in the context of purely deterministic systems. Various definitions of an instantaneous phase are presented and compared with each other with special attention paid to their robustness with respect to noise. We review the results of an analytic approach describing noise-induced phase synchronization in a thermal two-state system. In this context exact expressions for the mean frequency and the phase diffusivity are obtained that together determine the average length of locking episodes. A recently proposed method to quantify frequency synchronization in noisy potential systems is presented and exemplified by applying it to the periodically driven noisy harmonic oscillator. Since this method is based on a threshold crossing rate pioneered by Rice the related phase velocity is termed the Rice frequency. Finally, we discuss the relation between the phenomenon of stochastic resonance and noise-enhanced phase coherence by applying the developed concepts to the periodically driven bistable Kramers oscillator.
Collapse
Affiliation(s)
- Jan A Freund
- Institut für Physik, Humboldt-Universität zu Berlin, Invalidenstr. 110, D-10115 Berlin, Germany.
| | | | | |
Collapse
|
27
|
Fa KS. Linear Langevin equation with time-dependent drift and multiplicative noise term: exact study. Chem Phys 2003. [DOI: 10.1016/s0301-0104(02)00942-4] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
|
28
|
Shepherd TD, Hernandez R. An optimized mean first passage time approach for obtaining rates in activated processes. J Chem Phys 2002. [DOI: 10.1063/1.1516590] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
29
|
Li JH. Effect of asymmetry on stochastic resonance and stochastic resonance induced by multiplicative noise and by mean-field coupling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:031104. [PMID: 12366096 DOI: 10.1103/physreve.66.031104] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2001] [Indexed: 05/23/2023]
Abstract
In the paper, we investigate the effect of asymmetry of the potential on stochastic resonance (SR) for a model with an asymmetric bistable potential and driven by additive noise, the signal-to-noise ratio (SNR) for a model with a monostable potential and driven by additive and multiplicative noises, and the SNR for a mean-field coupled model with infinite globally coupling oscillators driven by additive noises. It is shown that for the first model,the asymmetry of the potential can weaken the phenomenon of SR; for the second and third models, a SR induced by multiplicative noise and a different one caused by mean-field coupling are found.
Collapse
Affiliation(s)
- Jing-hui Li
- Center for Nonlinear Studies, Institute of Applied Physics and Computational Mathematics, P.O. Box 800928, Beijing 100088, People's Republic of China
| |
Collapse
|
30
|
Dybiec B, Gudowska-Nowak E. Influence of the barrier shape on resonant activation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:026123. [PMID: 12241253 DOI: 10.1103/physreve.66.026123] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2002] [Revised: 04/29/2002] [Indexed: 05/23/2023]
Abstract
The escape of a Brownian particle over a dichotomously fluctuating barrier is investigated for various shapes of the barrier. The problem of resonant activation is revisited with the attention on the effect of the barrier shape on optimal value of the mean escape time in the system. The characteristic features of resonant behavior are analyzed for situations when the barrier switches either between different heights representing erection of a barrier and formation of a well, respectively, or it proceeds through "on" and "off" positions.
Collapse
Affiliation(s)
- Bartłomiej Dybiec
- Marian Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Kraków, Poland.
| | | |
Collapse
|
31
|
Rozenfeld R, Freund JA, Neiman A, Schimansky-Geier L. Noise-induced phase synchronization enhanced by dichotomic noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:051107. [PMID: 11735900 DOI: 10.1103/physreve.64.051107] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2001] [Indexed: 05/23/2023]
Abstract
We study the nonlinear response of a stochastic bistable system driven by both a weak periodic signal and a dichotomic noise in terms of stochastic phase synchronization. We show that the effect of noise-induced phase synchronization can be significantly enhanced by the addition of a dichotomic noise.
Collapse
Affiliation(s)
- R Rozenfeld
- Institut für Physik, Humboldt-Universität zu Berlin, D-10115 Berlin, Germany
| | | | | | | |
Collapse
|
32
|
Shepherd TD, Hernandez R. Chemical reaction dynamics with stochastic potentials below the high-friction limit. J Chem Phys 2001. [DOI: 10.1063/1.1386422] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
33
|
Mielke A. Effective rate equations for the overdamped motion in fluctuating potentials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:021106. [PMID: 11497561 DOI: 10.1103/physreve.64.021106] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/18/2000] [Indexed: 05/23/2023]
Abstract
We discuss physical and mathematical aspects of the overdamped motion of a Brownian particle in fluctuating potentials. It is shown that such a system can be described quantitatively by fluctuating rates if the potential fluctuations are slow compared to relaxation within the minima of the potential, and if the position of the minima does not fluctuate. Effective rates can be calculated; they describe the long-time dynamics of the system. Furthermore, we show the existence of a stationary solution of the Fokker-Planck equation that describes the motion within the fluctuating potential under some general conditions. We also show that a stationary solution of the rate equations with fluctuating rates exists.
Collapse
Affiliation(s)
- A Mielke
- Institut für Theoretische Physik, Ruprecht Karls Universität, Philosophenweg 19, D-69120 Heidelberg, Germany
| |
Collapse
|
34
|
Li JH, Hänggi P. Spatially periodic stochastic system with infinite globally coupled oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:011106. [PMID: 11461224 DOI: 10.1103/physreve.64.011106] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2001] [Indexed: 05/23/2023]
Abstract
In this paper we study a spatially periodic stochastic system with infinite globally coupled oscillators driven by a constant force F. With two typical models we show that when F=0 there is a nonequilibrium transition between the state with zero mean field (s=0) and the state with nonzero mean field (s not equal 0). For model I, the transition is not a phase transition, while for the model II it is (second order). In addition, we find that for coupled oscillators driven only by additive noises, when F=0 a transport may emerge if the nonzero mean field breaks the symmetry of the systems. With varying F a continuous or discontinuous transition between state s>0 and state s<0 will appear. The mean field or current sometimes exhibits hysteresis as a function of F.
Collapse
Affiliation(s)
- J H Li
- Lehrstuhl für Theoretische Physik I, Institut für Physik, Universität Augsburg, Universitässtrasse 1, D-86135 Augsburg, Germany
| | | |
Collapse
|
35
|
Chapter 2 Phase synchronization: From periodic to chaotic and noisy. ACTA ACUST UNITED AC 2001. [DOI: 10.1016/s1383-8121(01)80005-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
|
36
|
Gitterman M. Symmetry breaking in one-dimensional diffusion. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:8820-2. [PMID: 11138192 DOI: 10.1103/physreve.62.8820] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2000] [Indexed: 11/07/2022]
Abstract
The mean free passage time for one-dimensional diffusion on a line segment under the influence of a deterministic telegraph signal proves to be a nonmonotonic function of the signal rate ("stochastic resonance") if symmetry breaking takes place. The symmetry breaking may be expressed either in nonsymmetric boundary conditions (one end absorbing and the other reflecting) or in a nonsymmetric telegraph signal. The latter case is considered in detail. It turns out that the larger the asymmetry of a telegraph signal, the wider the range of parameters for which a stochastic resonance occurs.
Collapse
Affiliation(s)
- M Gitterman
- Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel
| |
Collapse
|
37
|
Rozenfeld R, Neiman A, Schimansky-Geier L. Stochastic resonance enhanced by dichotomic noise in a bistable system. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:R3031-R3034. [PMID: 11088871 DOI: 10.1103/physreve.62.r3031] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2000] [Indexed: 05/23/2023]
Abstract
We study linear responses of a stochastic bistable system driven by dichotomic noise to a weak periodic signal. We show that the effect of stochastic resonance can be greatly enhanced in comparison with the conventional case when dichotomic forcing is absent, that is, both the signal-to-noise ratio and the spectral power amplification reach much greater values than in the standard stochastic resonance setup.
Collapse
Affiliation(s)
- R Rozenfeld
- Institute for Physics, Humboldt University at Berlin, D-10115, Berlin, Germany
| | | | | |
Collapse
|
38
|
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.
Collapse
Affiliation(s)
- M Gitterman
- Department of Physics, Bar-Ilan University, Ramat-Gan, Israel
| |
Collapse
|
39
|
Mantegna RN, Spagnolo B. Experimental investigation of resonant activation. PHYSICAL REVIEW LETTERS 2000; 84:3025-3028. [PMID: 11019003 DOI: 10.1103/physrevlett.84.3025] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/1999] [Indexed: 05/23/2023]
Abstract
We experimentally investigate the escape from a metastable state over a fluctuating barrier of a physical system. The system is switching between two states under electronic control of a dichotomous noise. We measure the escape time and its probability density function as a function of the correlation rate of the dichotomous noise in a frequency interval spanning more than four frequency decades. We observe resonant activation, namely a minimum of the average escape time as a function of the correlation rate. We detect two regimes in the study of the shape of the escape time probability distribution: (i) a regime of exponential and (ii) a regime of nonexponential probability distribution.
Collapse
Affiliation(s)
- RN Mantegna
- Istituto Nazionale per la Fisica della Materia, Unita di Palermo, and Dipartimento di Energetica ed Applicazioni di Fisica, Universita di Palermo, Viale delle Scienze, I-90128, Palermo, Italy
| | | |
Collapse
|
40
|
Iwaniszewski J, Kaufman IK, McClintock PV, McKane AJ. Resonances while surmounting a fluctuating barrier. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 61:1170-1175. [PMID: 11046390 DOI: 10.1103/physreve.61.1170] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/1999] [Indexed: 05/23/2023]
Abstract
Electronic analog experiments on escape over a fluctuating potential barrier are performed for the case when the fluctuations are caused by Ornstein-Uhlenbeck noise (OUN). In its dependence on the relation between the two OUN parameters (the correlation time tau and noise strength Q) the nonmonotonic variation of the mean escape time T as a function of tau can exhibit either a minimum (resonant activation), or a maximum (inhibition of activation), or both these effects. The possible resonant nature of these features is discussed. We claim that T is not a good quantity to describe the resonancelike character of the problem. Independently of the specific relation between the OUN parameters, the resonance manifests itself as a maximal lowering of the potential barrier during the escape event, and it appears for tau of the order of the relaxation time toward the metastable state.
Collapse
Affiliation(s)
- J Iwaniszewski
- School of Physics and Chemistry, Lancaster University, Lancaster LA1 4YB, United Kingdom and Institute of Physics, Nicholas Copernicus University, Grudzi&acedil;dzka 5, 87-100 Torun, Poland
| | | | | | | |
Collapse
|
41
|
Mielke A. Noise induced stability in fluctuating, bistable potentials. PHYSICAL REVIEW LETTERS 2000; 84:818-821. [PMID: 11017381 DOI: 10.1103/physrevlett.84.818] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/1999] [Indexed: 05/23/2023]
Abstract
The overdamped motion of a Brownian particle in an asymmetric, bistable, fluctuating potential shows noise induced stability: For intermediate fluctuation rates the mean occupancy of minima with an energy above the absolute minimum is enhanced. The model works as a detector for potential fluctuations being not too fast and not too slow. This effect occurs due to the different time scales in the problem. We present a detailed analysis of this effect using the exact solution of the Fokker-Planck equation for a simple model. Further we show that for not too fast fluctuations the system can be well described by effective rate equations. The results of the rate equations agree quantitatively with the exact results.
Collapse
Affiliation(s)
- A Mielke
- Institut fur Theoretische Physik, Ruprecht-Karls-Universitat, Philosophenweg 19, D-69120 Heidelberg, Federal Republic of Germany
| |
Collapse
|
42
|
Berezhkovskii AM, Szabo A, Weiss GH, Zhou HX. Reaction dynamics on a thermally fluctuating potential. J Chem Phys 1999. [DOI: 10.1063/1.480348] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
43
|
Li JH, Hu B, Xing DY, Dong JM. Escape over a fluctuating barrier with additive and multiplicative noise. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:6443-8. [PMID: 11970560 DOI: 10.1103/physreve.60.6443] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/1999] [Indexed: 04/18/2023]
Abstract
The mean first passage time (MFPT) over the fluctuating potential barrier is investigated in the presence of additive and multiplicative noises. It is shown that the MFPT over the fluctuating potential barrier displays a resonant activation (RA). The effect of the additive and multiplicative noises and the correlation between them on the RA is that the additive and multiplicative noises can weaken the RA; but the correlation between them can enhance it. The susceptibility of the RA to the multiplicative noise is far larger than that to the additive one. In addition, we find that the transition rate (i.e., the inverse of the MFPT) over the fluctuating potential barrier can be suppressed by the positive correlation and show a minimum as the function of the noises' strengths.
Collapse
Affiliation(s)
- J H Li
- Department of Physics and Centre for Nonlinear Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
| | | | | | | |
Collapse
|
44
|
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
|
45
|
Li JH, Xing DY, Dong JM, Hu B. Resonant activations for a fluctuating barrier system driven by dichotomous noise and Gaussian white noise. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:1324-8. [PMID: 11969891 DOI: 10.1103/physreve.60.1324] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/13/1999] [Indexed: 04/18/2023]
Abstract
We consider the escape over a fluctuating barrier in the presence of a dichotomous noise and a Gaussian white noise. It is shown that the mean first passage time (MFPT) over the fluctuating barrier displays two resonant activations. One is the resonant activation of the MFPT as a function of the flipping rate of the fluctuating potential barrier; the other is the resonant activation of the MFPT as a function of the transition rate of the dichotomous noise. In addition, we find that the dichotomous noise can weaken the former resonant activation, but enhance the latter one. By further study, we find that, when the fluctuating potential barrier is driven by two or more dichotomous noises, there are three or more resonant activations.
Collapse
Affiliation(s)
- J H Li
- Department of Physics and National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210008, China
| | | | | | | |
Collapse
|
46
|
Neiman A, Schimansky-Geier L, Moss F, Shulgin B, Collins JJ. Synchronization of noisy systems by stochastic signals. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:284-92. [PMID: 11969761 DOI: 10.1103/physreve.60.284] [Citation(s) in RCA: 70] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/1998] [Revised: 04/05/1999] [Indexed: 11/07/2022]
Abstract
We study, in terms of synchronization, the nonlinear response of noisy bistable systems to a stochastic external signal, represented by Markovian dichotomic noise. We propose a general kinetic model which allows us to conduct a full analytical study of the nonlinear response, including the calculation of cross-correlation measures, the mean switching frequency, and synchronization regions. Theoretical results are compared with numerical simulations of a noisy overdamped bistable oscillator. We show that dichotomic noise can instantaneously synchronize the switching process of the system. We also show that synchronization is most pronounced at an optimal noise level-this effect connects this phenomenon with aperiodic stochastic resonance. Similar synchronization effects are observed for a stochastic neuron model stimulated by a stochastic spike train.
Collapse
Affiliation(s)
- A Neiman
- Center for Neurodynamics, University of Missouri at St. Louis, St. Louis, Missouri 63121, USA
| | | | | | | | | |
Collapse
|
47
|
Fu HX, Cao L, Wu DJ. Effect of correlation between additive and multiplicative noises on the activation from a double well. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 59:R6235-8. [PMID: 11969727 DOI: 10.1103/physreve.59.r6235] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/1998] [Indexed: 04/18/2023]
Abstract
We study the thermal activation problem of a bistable system driven by correlated additive and multiplicative noises by means of numerical simulation. We find that in the colored noise case the suppression effect of the positive correlation decreases and finally is released as the autocorrelation time tau of the colored noise grows. When tau is large enough, negative correlation becomes more suppressive than the positive correlation. Such phenomena are ascribed to the collaboration between noises as well as the memory effect of the multiplicative colored noise.
Collapse
Affiliation(s)
- H X Fu
- Department of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | | | | |
Collapse
|
48
|
Berdichevsky V, Gitterman M. Stochastic resonance in a bistable piecewise potential: analytical solution. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/29/18/001] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
|
49
|
Reimann P, Bartussek R, Hänggi P. Reaction rates when barriers fluctuate: A singular perturbation approach. Chem Phys 1998. [DOI: 10.1016/s0301-0104(98)00077-9] [Citation(s) in RCA: 40] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
|
50
|
Reimann P, Elston TC. Kramers Rate for Thermal Plus Dichotomous Noise Applied to Ratchets. PHYSICAL REVIEW LETTERS 1996; 77:5328-5331. [PMID: 10062776 DOI: 10.1103/physrevlett.77.5328] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|