Stationary and dynamical properties of finite N-unit Langevin models subjected to multiplicative noises

We have studied the finite N-unit Langevin model subjected to multiplicative noises, by using the augmented moment method (AMM), as a continuation of our previous paper [H. Hasegawa, J. Phys. Soc. Japan 75 (2006) 033001]. Effects of couplings on stationary and dynamical properties of the model have been investigated. The difference and similarity between the results of diffusive and sigmoid couplings are studied in details. Time dependences of average and fluctuations in local and global variables calculated by the AMM are in good agreement with those of direct simulations (DSs). We also discuss stationary distributions of local and global variables with the use of the Fokker–Planck equation (FPE) method and DSs. It is demonstrated that stationary distributions show much variety when multiplicative noise and external inputs are taken into account.     

Intrinsic noise analysis and stochastic simulation on transforming growth factor beta signal pathway

A typical biological cell lives in a small volume at room temperature; the noise effect on the cell signal transduction pathway may play an important role in its dynamics. Here, using the transforming growth factor-β signal transduction pathway as an example, we report our stochastic simulations of the dynamics of the pathway and introduce a linear noise approximation method to calculate the transient intrinsic noise of pathway components. We compare the numerical solutions of the linear noise approximation with the statistic results of chemical Langevin equations, and find that they are quantitatively in agreement with the other. When transforming growth factor-β dose decreases to a low level, the time evolution of noise fluctuation of nuclear Smad2-Smad4 complex indicates the abnormal enhancement in the transient signal activation process.     

Stochastic aspects of biological locomotion

Various aspects of random walks undertaken by motile bacteria and migrating leukocytes are discussed, including the motions of these cells when responding to gradients of chemoattractants. Brief reference also is made to studies of particle movements within the cytoplasm of eucaryotic cells.Presented at the Symposium on Random Walks, Gaithersburg, MD, June 1982.     

各向异性颗粒PDF输运方程及其颗粒湍流扩散

根据Minier的模型,获得颗粒所见流体脉动速度的朗之万模型,并推导颗粒所见流体湍流脉动速度自关联函数,该函数具有各向异性的特征,进一步由流体脉动速度朗之万模型和颗粒运动方程获得相应的颗粒PDF输运方程.为描述在网格生成湍流中的颗粒扩散运动,将颗粒PDF输运方程作相应的简化,获得一个具有颗粒湍流各向异性的解析解,将方程的解与Wellsand Stock的颗粒湍流扩散实验结果进行比较,获得了很好的结果.揭示了具有各向异性特征的颗粒PDF输运方程的优越性.     

从布朗运动的发现到RR方法

对朗之万方程研究的历史和现状进行了全面的综合评述。     

一类受Poisson干扰的Markov过程应跳性逼近

对于随机微分方程约束下受Poison干扰的Markov过程,给出了一种具有应跳性的轨道逼近方法:将每条轨道分解为若干连续阶段,在每个阶段中建立了相应的常微分方程,并采用Runge-Kuta方法求解。该方法已用于研究Langevin方程和Dufing-VanderPol振子。     

Adiabatic elimination for systems of Brownian particles with nonconstant damping coefficients

We discuss the problem of eliminating the momentum variable in the phase space Langevin equations for a system of Brownian particles in two related situations: (i) position-dependent damping and (ii) existence of hydrodynamic interactions. We discuss the problems associated with the conventional elimination and we develop an alternative elimination procedure, in the Lagevin framework, which leads to the correct Smoluchowski equation. We give a heuristic argument on the basis of stochastic differential equations for the Smoluchowski limit and establish rigorously the limit for the general case of position-dependent friction and diffusion coefficents.     

重核熔合耗散动力学

用双中心核态参数描写重核熔合过程,以一个布朗粒子通过二次势位垒的简化模型得到了熔合几率的解析表达式.在两碰撞核的接触处,颈部变量的变化遵守高斯分布,而沿拉长方向的初始平均动能由表面摩擦模型所确定.计算了几个对称和近似对称的反应系统的熔合激发函数,并与实验结果进行了比较.讨论了颈部增长和初始能量损失对熔合障碍产生的效应. Dissipative dynamics of fusion of massive nuclei is studied in terms of the two center shape parameterization. Fusion probability is obtained analytically from a Brownian particle passing over a parabolic potential barrier along the elongation coordinate. The neck variable at the initial contact shape is supposed to be a Gaussian distribution. Fusion probabilities of several symmetric or nearly symmetric systems in central collisions are calculatedand compared with experimental data. Effects of neck folding...     

Quantum dissipative Higgs model

By using a continuum of oscillators as a reservoir, we present a classical and a quantum-mechanical treatment for the Higgs model in the presence of dissipation. In this base, a fully canonical approach is used to quantize the damped particle on a spherical surface under the action of a conservative central force, the conjugate momentum is defined and the Hamiltonian is derived. The equations of motion for the canonical variables and in turn the Langevin equation are obtained. It is shown that the dynamics of the dissipative Higgs model is not only determined by a projected susceptibility tensor that obeys the Kramers–Kronig relations and a noise operator but also the curvature of the spherical space. Due to the gnomonic projection from the spherical space to the tangent plane, the projected susceptibility displays anisotropic character in the tangent plane. To illuminate the effect of dissipation on the Higgs model, the transition rate between energy levels of the particle on the sphere is calculated. It is seen that appreciable probabilities for transition are possible only if the transition and reservoir’s oscillators frequencies to be nearly on resonance.     

Conservative Langevin dynamics of solid-on-solid interfaces

We study the dynamics of an interface between two phases in interaction with a wall in the case when the evolution is dominated by surface diffusion. For this, we use an SOS model governed by a conservative Langevin equation and suitable boundary conditions. In the partial wetting case, we study various scaling regimes and show oscillatory behavior in the relaxation of the interface toward its equilibrium shape. We also consider complete wetting and the structure of the precursor film.     

肌球蛋白Ⅵ分子马达周期势场下的弹性扩散模型

肌球蛋白Ⅵ分子马达因其特殊的结构及胞内功能,其动力学原理成为研究的热点. 从肌球蛋白Ⅵ自身结构和实验现象出发,建立其弹性扩散模型,并通过Monte Carlo方法分析了肌球蛋白Ⅵ满足朗之万方程的随机动力学行为. 结果表明,在环境噪声作用下,具有弹性势能和轨道周期势能的肌球蛋白Ⅵ可以进行梯跳运动和有效的输运,但负载力会减弱分子马达系统的输运能力;当弹性系数一定时,弹性链越长平均速度越小,当弹性链长度一定时,合理选择弹性系数平均速度可达到最大值;另外,负载力的存在使肌球蛋白Ⅵ在接触位点的平均驻留时间呈指数增加.关键词：分子马达肌球蛋白Ⅵ朗之万方程弹性扩散模型     

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 dynamics of an interface near a wall

We study dynamical contact angles and precursor films using Langevin dynamics for SOS type models, near a wall which favors spreading. We first solve exactly the Gaussian model and discuss various asymptotic regimes. This is only appropriate to partial wetting. We then consider more general models. Using local equilibrium and scaling arguments, we derive the shape of the dynamical profile and the speed of the precursor film which exists when the spreading coefficient is strictly positive. Long-range potentials lead to a layered structure of the precursor film. We also consider the case of a meniscus in a capillary.     

Quantization of Christ—Lee Model Using the WKB Approximation

The Hamilton-Jacobi formalism for constrained systems is applied to the Christ-Lee model. The equations of motion are obtained and the action integral is determined in the configuration space. This enables us to quantize the Christ-Lee model by using the WKB approximation.     

(e,2e)反应中冲量近似的理论研究

利用冲量近似理论和玻恩近似方法, 以氢原子(1s)为例, 在共面不对称几何条件下用多种模型分别计算了若干入射能、 散射角情形下电子碰撞电离(e, 2e) 反应的三重微分散射截面. 与其他的理论方法和实验数据进行了比较, 分析了曲线结构差异及原因, 对其适用范围进行了研究, 并探讨了交换效应的贡献, 验证了早期的研究.关键词：扭曲波冲量近似平面波冲量近似三重微分截面