Langevin equation with multi-Poissonian noise

A general master equation is shown to be equivalent to a Langevin equation whose noise is expressed as a linear superposition of Poissonian random variables (multi-Poissonian noise). As typical examples, a birth and death process and a Boltzmann-Langevin equation are given.     

Temperature dependent fission fragment distribution in the Langevin equation

The temperature dependent width of the fission fragment distributions was simulated in the Langevin equation by taking two-parameter exponential form of the fission fragment mass variance at scission point for each fission event. The result can reproduce experimental data well, and it permits to make reliable estimate for unmeasured product yields near symmetry fission.     

Fractional generalized Langevin equation approach to single-file diffusion

Fractional generalized Langevin equation with external force is used to model single-file diffusion. It is found that for external force that varies with power law the solution for such a fractional Langevin equation gives the correct short and long time behavior for the mean square displacement of single-file diffusion when appropriate choice of parameters associated with fractional generalized Langevin equation are used. By considering some special cases of the fractional generalized Langevin equation, a new class of closed analytic expressions for the mean square displacement of single-file diffusion can be obtained. The effective Fokker-Planck equation associated with single-file diffusion is briefly considered.     

Diffusion described with quantum Langevin equation in tilted periodic potential

In this paper, diffusion behavior of Brownian particles moving in a 1D periodic potential landscape has been theoretically investigated by using the general quantum Langevin equation. At first, in the condition of weak disorder, some anomalous diffusive behaviors have been revealed in the process. Then, two types of mean square displacement, ensemble averaged and time averaged mean square displacement, have been investigated in a long time, and the weak ergodicity breaking phenomenon has been revealed. It is shown that the general quantum Langevin equation can exhibit some novel details of the experimental diffusion process.     

Comment on asymptotic properties of coupled Langevin equations

The asymptotic behavior of coupled Langevin equations in the limit of weak noise is studied by general normal form techniques, in the vicinity of a pitchfork bifurcation. The non-Gaussian behavior of the critical variable is established. The conditional probability of the noncritical variable around the center manifold is determined. It is shown that in certain cases the distribution of this later variable may be non-Gaussian.On leave of absence from Facultad de Ciencias Fisicas Y Mathemàticas, Universidad de Chile, Santiago, Chile     

Temperature dependent fission fragment distribution in the Langevin equation

The temperature dependent width of the fission fragment distributions was simulated in the Langevin equation by taking two-parameter exponential form of the fission fragment mass variance at scission point for each fission event. The result can reproduce experimental data well, and it permits to make reliable estimate for unmeasured product yields near symmetry fission.     

Novel perturbation expansion for the Langevin equation

We discuss the randomly driven systemdx/dt= -W(x) +f(t), wheref(t) is a Gaussian random function or stirring force withf(t)f(t)=2(t–t), andW(x) is of the formgx ¹⁺². The parameter is a measure of the nonlinearity of the equation. We show how to obtain the correlation functionsx(t)f(t)···x(t( n)) _f as a power series in. We obtain three terms in the expansion and show how to use Padé approximants to analytically continue the answer in the variable. By using scaling relations, we show how to get a uniform approximation to the equal-time correlation functions valid for allg and.     

Fractional Langevin equation and Riemann-Liouville fractional derivative

In this present work we consider a fractional Langevin equation with Riemann-Liouville fractional time derivative which modifies the classical Newtonian force, nonlocal dissipative force, and long-time correlation. We investigate the first two moments, variances and position and velocity correlation functions of this system. We also compare them with the results obtained from the same fractional Langevin equation which uses the Caputo fractional derivative.     

Langevin representation of Coulomb collisions for bi-Maxwellian plasmas

Langevin model corresponding to the Fokker–Planck equation for bi-Maxwellian particle distribution functions is developed. Rosenbluth potentials and their derivatives are derived in the form of triple hypergeometric functions. The Langevin model is tested in the case of relaxation of the proton temperature anisotropy and implemented into the hybrid expanding box model. First results of this code are presented and discussed.     

Random integral equation formulation of a generalized Langevin equation

In this paper, the generalized Langevin equation introduced by Kubo and Mori is formulated as a random integral equation. We consider (1) the existence and uniqueness of the solution, (2) moments of the solution process, (3) a comparison theorem for solution processes, and (4) the Cauchy polygonal approximation to the solution.     

Langevin equation for self-organized morphologies of thin heteroepitaxial films

The self-organization of nanostructures on strained epitaxial films is expressed as a Langevin equation obtained from an atomistic model of the growth kinetics. The transition rules are based on the incorporation of strain effects into environment-dependent detachment barriers. Comparisons are made with a previous approach based on continuum elasticity to provide an atomistic interpretation of the governing equation for the morphological evolution of strained films.     

A generalized Langevin equation for dealing with nonadditive fluctuations

A suitable extension of the Mori memory-function formalism to the non-Hermitian case allows a multiplicative process to be described by a Langevin equation of non-Markoffian nature. This generalized Langevin equation is then shown to provide for the variable of interest the same autocorrelation function as the well-known theoretical approach developed by Kubo, the stochastic Liouville equation (SLE) theory. It is shown, furthermore, that the present approach does not disregard the influence of the variable of interest on the time evolution of its thermal bath. The stochastic process under study can also be described by a Fokker-Planck-like equation, which results in a Gaussian equilibrium distribution for the variable of interest. The main flaw of the SLE theory, that resulting in an uncorrect equilibrium distribution, is therefore completely eliminated.     

Generalized Langevin equation driven by Lévy processes: A probabilistic, numerical and time series based approach

Lévy processes have been widely used to model a large variety of stochastic processes under anomalous diffusion. In this note we show that Lévy processes play an important role in the study of the Generalized Langevin Equation (GLE). The solution to the GLE is proposed using stochastic integration in the sense of convergence in probability. Properties of the solution processes are obtained and numerical methods for stochastic integration are developed and applied to examples. Time series methods are applied to obtain estimation formulas for parameters related to the solution process. A Monte Carlo simulation study shows the estimation of the memory function parameter. We also estimate the stability index parameter when the noise is a Lévy process.     

Electron Transfer Between Molecules: Study with Langevin Equations

In this paper, we investigate the electron transfer （ET） in donor-acceptor model. The Langevin equation with random forces is used. The oscillations of the primary states observed in experimental data have been shown with this approach. And other features on the dependence of the rate of ET on temperature, free energy, and reorganization energy have also been clearly shown.     

朗之万方程及其在蛋白质折叠动力学中的应用

研究了朗之万方程的动力学性质,并用它模拟了蛋白质分子的折叠过程.首先在相空间中对朗之万方程做连续映射,发现做布朗运动的粒子在位置坐标上存在明显的概率分布,这表明蛋白质折叠过程中分子空间构型是非遍历的.此外,本文还通过数值模拟得到了去折叠态蛋白质的紧密度指标,并验证了它与实验结果以及其他理论方法的一致性.本文还提出了一种利用重整化方法研究熔球体状态蛋白质的理论模型,并提供了考虑疏水基影响的蛋白质折叠过程的模拟思路. 关键词： 朗之万方程 蛋白质折叠非遍历性 紧密度指标 重整化     

Generalized Langevin equations with time-dependent temperature

A generalized Langevin equation describing the evolution of a particle in a heat bath with a time-dependent temperature is derived for a simple model. The temperature is controlled by introducing dissipative terms in the dynamical equations of the heat bath particles. The Langevin equation contains a term that is specifically associated with the variation of the temperature.