Stochastic processes with finite correlation time: Modeling and application to the generalized Langevin equation

Srokowski, T.

doi:10.1103/physreve.64.031102

Cited by 12 publications

(4 citation statements)

References 49 publications

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“…56, which is exact, in contrast to other methods. 57,62,63 Briefly, the Wiener-Khintchin theorem is exploited, which connects the spectral density…”

Section: Random Forcementioning

confidence: 99%

Collective Langevin dynamics of conformational motions in proteins

Lange

Grubmüller

2006

The Journal of Chemical Physics

137

181

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Functionally relevant slow conformational motions of proteins are, at present, in most cases inaccessible to molecular dynamics (MD) simulations. The main reason is that the major part of the computational effort is spend for the accurate description of a huge number of high frequency motions of the protein and the surrounding solvent. The accumulated influence of these fluctuations is crucial for a correct treatment of the conformational dynamics; however, their details can be considered irrelevant for most purposes. To accurately describe long time protein dynamics we here propose a reduced dimension approach, collective Langevin dynamics (CLD), which evolves the dynamics of the system within a small subspace of relevant collective degrees of freedom. The dynamics within the low-dimensional conformational subspace is evolved via a generalized Langevin equation which accounts for memory effects via memory kernels also extracted from short explicit MD simulations. To determine the memory kernel with differing levels of regularization, we propose and evaluate two methods. As a first test, CLD is applied to describe the conformational motion of the peptide neurotensin. A drastic dimension reduction is achieved by considering one single curved conformational coordinate. CLD yielded accurate thermodynamical and dynamical behaviors. In particular, the rate of transitions between two conformational states agreed well with a rate obtained from a 150 ns reference molecular dynamics simulation, despite the fact that the time scale of the transition (approximately 50 ns) was much longer than the 1 ns molecular dynamics simulation from which the memory kernel was extracted.

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“…56, which is exact, in contrast to other methods. 57,62,63 Briefly, the Wiener-Khintchin theorem is exploited, which connects the spectral density…”

Section: Random Forcementioning

confidence: 99%

Collective Langevin dynamics of conformational motions in proteins

Lange

Grubmüller

2006

The Journal of Chemical Physics

137

181

View full text Add to dashboard Cite

show abstract

“…Therefore, the complete characterization of the process u(t) is given by 17) where the function Ψ(t, τ ) is defined as…”

Section: Shot Noisementioning

confidence: 99%

“…This approximation leads to the study of linear stochastic differential equations with arbitrary noises. Besides the simplicity of this kind of equations they were the subject of numerous theoretical investigation [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] , and also they provide non-trivial models for the study of many different mechanism of relaxation in physics, biology and another research areas.…”

Section: Introductionmentioning

confidence: 99%

Functional characterization of generalized Langevin equations

Budini¹,

Cáceres²

2004

J. Phys. A: Math. Gen.

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We present an exact functional formalism to deal with linear Langevin equations with arbitrary memory kernels and driven by any noise structure characterized through its characteristic functional. No others hypothesis are assumed over the noise, neither the fluctuation dissipation theorem. We found that the characteristic functional of the linear process can be expressed in terms of noise's functional and the Green function of the deterministic (memory-like) dissipative dynamics. This object allow us to get a procedure to calculate all the Kolmogorov hierarchy of the non-Markov process.As examples we have characterized through the 1-time probability a noiseinduced interplay between the dissipative dynamics and the structure of different noises. Conditions that lead to non-Gaussian statistics and distributions with long tails are analyzed. The introduction of arbitrary fluctuations in fractional Langevin equations have also been pointed out.

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“…The study of non-Markovian Langevin equations have received a lot of attention [32][33][34][35][36][37][38][39][40]. From a rigorous point of view, these equations can only be completely characterized after knowing the full Kolmogorov hierarchy [1,2], i.e., any n-joint probability, or equivalently any n-time correlation.…”

Section: Introductionmentioning

confidence: 99%

Functional characterization of linear delay Langevin equations

Budini

Cáceres²

2004

Phys. Rev. E

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We present an exact functional characterization of linear delay Langevin equations driven by any noise structure defined through its characteristic functional. This method relies on the possibility of finding an explicitly analytical expression for each realization of the delayed stochastic process in terms of those of the driving noise. General properties of the transient dissipative dynamics are analyzed. The corresponding interplay with a color Gaussian noise is presented. As a full application of our functional method we study a model for population growth with non-Gaussian fluctuations: the Gompertz model driven by multiplicative white shot noise.

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Stochastic processes with finite correlation time: Modeling and application to the generalized Langevin equation

Abstract: The kangaroo process (KP) is characterized by various forms of the covariance and can serve as a useful model of random noises. We discuss properties of that process for the exponential, stretched exponential and algebraic (power-law) covariances.

Cited by 12 publications

References 49 publications

Collective Langevin dynamics of conformational motions in proteins

Collective Langevin dynamics of conformational motions in proteins

Functional characterization of generalized Langevin equations

Functional characterization of linear delay Langevin equations

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