基于分数阶环境热浴的非各态历经判据研究

本文从分数阶谱形式的气固耦合模型出发, 理论推导出具有幂律记忆核的广义朗之万方程. 研究气体分子在自由场和简谐势场中的动力学演化和长时渐进行为, 着重分析三种各态历经判据: Khinchin判据、Lee判据以及内在判据和外在表现的适用性. 研究结果表明: Khinchin判据适用于广义朗之万方程描述的所有扩散和输运过程; Lee判据并不适用于布朗运动, 只能用来区分不同类型的扩散过程; 而内在判据和外在表现不仅能够把非各态历经分为两类, 同时可以揭示非各态历经的物理内在根源.     

基于三磷酸腺苷调节的分子马达单向能量跃迁模型

分子马达的梯跳运动和在过阻尼溶液中动力学原理尚未揭示清楚, 从分子马达输运特点和实验现象出发, 构建满足朗之万方程的单向能量跃迁模型, 并通过Monte Carlo方法分析了分子马达的随机动力学行为. 结果表明, 在合适的跃迁能量作用下, 分子马达可以利用噪声进行稳定的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; 轨道周期势虽影响分子马达速度的大小但不会改变其运动方向, 分子马达运动方向由跃迁能量决定; 另外, 虽然在不同的噪声强度时平均速度不为零, 但是分子马达系统的高效输运对噪声有一定选择性. 关键词： 分子马达 能量跃迁 朗之万方程 噪声强度     

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     

用一种分数阶算法研究非马尔可夫过程中阻尼与涨落的竞争机制

基于分数阶朗之万方程和随机行走理论, 建立了一种用于研究非马尔可夫系统中随机变量随时间演化的数值模拟算法, 称之为分数阶随机行走模拟法. 进一步运用此算法分别数值研究了无阻尼有涨落、 有阻尼无涨落和阻尼与涨落兼备三种情况下, 受欠扩散分数阶朗之万方程约束的随机变量随时间的演化行为. 结果显示阻尼和涨落存在竞争关系: 高斯型涨落的影响会随着时间的增长被"抹平", 从而凸显阻尼使系统趋于平衡的作用; 而长尾型涨落则由于包含"小概率大贡献"事件, 使得长时间演化之后系统变量仍以一定概率出现突然变化. 关键词： 非马尔可夫 欠扩散 阻尼与涨落 分数阶朗之万方程     

蛋白质动力学理论研究中的计算机模拟方法

蛋白质是生物体中一种十分重要的高分子物质。蛋白质分子有着自身所特有的化学、物理结构;在溶液中蛋白质分子不仅自身不同部分间存在着相互作用,而且还与溶剂分子间发生着复杂的相互作用,这些都很大程度上影响到分子的结构和演变过程。为了对蛋白质分子进行模拟,很有必要建立适当的描述蛋白质分子结构的模型,引入合理的模型基元间的相互作用,并采用有效的方法进行模拟,本着贴近现实和方便模拟的原则,在本文中我们系统地总结了近年来蛋白质动力学及其物理特性,特别对其模型、势能及模拟方法进行了着重介绍。为了增加一些感性认识,文中还就实验分析、折叠的协作性、搜寻保守残基和动力学过程的熵效应和阻挫效应等几个专题进行了应用介绍。     

蛋白质动力学理论研究中的计算机模拟方法

蛋白质是生物体中一种十分重要的高分子物质。蛋白质分子有着自身所特有的化学、物理结构;在溶液中蛋白质分子不仅自身不同部分间存在着相互作用,而且还与溶剂分子间发生着复杂的相互作用,这些都很大程度上影响到分子的结构和演变过程。为了对蛋白质分子进行模拟,很有必要建立适当的描述蛋白质分子结构的模型,引入合理的模型基元间的相互作用,并采用有效的方法进行模拟,本着贴近现实和方便模拟的原则,在本文中我们系统地总结了近年来蛋白质动力学及其物理特性,特别对其模型、势能及模拟方法进行了着重介绍。为了增加一些感性认识,文中还就实验分析、折叠的协作性、搜寻保守残基和动力学过程的熵效应和阻挫效应等几个专题进行了应用介绍。     

布朗运动仿真实验的设计与实现

介绍了布朗运动仿真实验的设计与实现方法,利用"位置朗之万方程"的数值离散化,最大程度还原真实的布朗运动.通过对仿真实验数据的定量分析,并计算出了阿伏加德罗常量的近似值.     

互联网流量控制的朗之万模型及相变分析

为互联网中的流量控制协议构建恰当模型,从而阐明具体协议算法与网络宏观性能间的关系,一直是互联网研究者面临的重大挑战.本文通过逻辑演绎,建立了互联网传输控制协议下流量的朗之万方程.在此基础上,细致分析了主动队列管理算法的有效性,在理论上证明了此类算法存在从畅通态到拥塞态到瘫痪态的相变过程,并给出了相变临界点与系统参数的显式关系.本建模与分析方法虽以具体的主动队列管理算法为例,但其方法可以应用于一般的网络流量控制问题. 关键词： 互联网 流量控制 朗之万方程 相变     

用发光法测定DnaJ类分子伴侣MRJ对虫荧光素酶体外重折叠的促进作用

蛋白质的折叠使新翻译合成的多肽变成有生物功能的空间结构，因此蛋白质折叠是后基因组时代的重要工作。而在由白质折叠过程中，必须依靠分子伴侣的相互作用，才能保证蛋白质折叠向正确的方向进行。MBJ是一类新发现的DnaJ类分子伴侣，已证实它有调节ATP酶活性和阻止多聚谷氨酰胺凝聚的作用。我们用胍变性的虫荧光素酶作为蛋白质恢复功能活性的分子模型，用生物发光法研究了MRJ对蛋白质重新折叠的作用，发现MRJ确实有促进变性虫荧光素酶重新折叠并恢复其催化活力的功能。而且这种过程需要另一类Hsp60和Hsp70的协助，而这三种分子伴侣组合在一起，功效最好。实验中还发现，MRJ对虫荧光素酶恢复的促进作用是与ATP密切相关的。发光分析是研究分子伴侣促进蛋白质折叠过程的一种灵敏、精确和快速的技术手段。     

细胞丛状化分布对二维耦合体系尺度选择效应的影响

采用随机模拟方法对体系的化学朗之万方程进行了数值模拟，考察了二维耦合细胞体系中，细胞的丛状化分布对于因内噪声作用而产生的尺度选择效应所带来的影响.研究发现，当体系处于Hopf分岔点附近时，由于耦合作用使得处于最佳状态的一定数目的细胞呈现丛状化聚集在一起，而这种丛状化分布的“团队精神”可以极大地提高体系的工作效率，表现为体系对外界刺激信号的响应能力(信噪比)达到极大值.同时还观察到，体系对外界刺激最为敏感时对应的最佳细胞丛尺度大小不随耦合强度的改变而变化，而体系输出信号的信噪比，随着耦合强度的增加有增大趋势.这些现象表明，细胞的丛状化分布将极大地增强细胞中钙离子信号对外界刺激的响应效果.生物体系本身可能具有这种特性，并利用它来改善和提高感受外界信息的能力.     

Subordinated diffusion and continuous time random walk asymptotics

Anomalous transport is usually described either by models of continuous time random walks (CTRWs) or, otherwise, by fractional Fokker-Planck equations (FFPEs). The asymptotic relation between properly scaled CTRW and fractional diffusion process has been worked out via various approaches widely discussed in literature. Here, we focus on a correspondence between CTRWs and time and space fractional diffusion equation stemming from two different methods aimed to accurately approximate anomalous diffusion processes. One of them is the Monte Carlo simulation of uncoupled CTRW with a Le?vy α-stable distribution of jumps in space and a one-parameter Mittag-Leffler distribution of waiting times. The other is based on a discretized form of a subordinated Langevin equation in which the physical time defined via the number of subsequent steps of motion is itself a random variable. Both approaches are tested for their numerical performance and verified with known analytical solutions for the Green function of a space-time fractional diffusion equation. The comparison demonstrates a trade off between precision of constructed solutions and computational costs. The method based on the subordinated Langevin equation leads to a higher accuracy of results, while the CTRW framework with a Mittag-Leffler distribution of waiting times provides efficiently an approximate fundamental solution to the FFPE and converges to the probability density function of the subordinated process in a long-time limit.     

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.     

QUALITATIVE AND QUANTITATIVE ANALYSIS OF STOCHASTIC PROCESSES BASED ON MEASURED DATA, II: APPLICATIONS TO EXPERIMENTAL DATA

Analysis of stochastic processes governed by the Langevin equation is discussed. The analysis is based on a general method for non-parametric estimation of deterministic and random terms of the Langevin equation directly from given data. Separate estimation of the terms corresponds to the decomposition of process dynamics into deterministic and random components. Part I of the paper presented several possibilities for qualitative and quantitative analysis of process dynamics based on such decomposition. In Part II, some of these analysis possibilities are applied to experimental datasets from metal cutting and laser-beam welding.     

QUALITATIVE AND QUANTITATIVE ANALYSIS OF STOCHASTIC PROCESSES BASED ON MEASURED DATA, I: THEORY AND APPLICATIONS TO SYNTHETIC DATA

Analysis of stochastic processes governed by the Langevin equation is discussed. The analysis is based on a general method for non-parametric estimation of deterministic and random terms of the Langevin equation directly from given data. Separate estimation of the terms corresponds to decomposition of process dynamics into deterministic and random components. Such decomposition provides a basis for qualitative and quantitative analysis of process dynamics. In Part I, the following analysis possibilities are described and illustrated using various synthetic datasets: (1) qualitative inspection of the estimated terms presented as fields, (2) reconstruction of the deterministic and stochastic evolution of the process and (3) approximation of the deterministic term by an analytical function and quantitative treatment of the equations obtained. In Part II, these analysis possibilities are applied to experimental datasets from metal cutting and laser-beam welding.     

On the quantum-mechanical Fokker-Planck and Kramers-Chandrasekhar equation

In the classical theory of Brownian motion we can consider the Langevin equation as an infinitesimal transformation between the coordinates and momenta of a Brownian particle, given probabilistically, since the impulse appearing is characterized by a Gaussian random process. This probabilistic infinitesimal transformation generates a streaming on the distribution function, expressed by the classical Fokker-Planck and Kramers-Chandrasekhar equations. If the laws obeyed by the Brownian particle are quantum mechanical, we can reinterpret the Langevin equation as an operator relation expressing an infinitesimal transformation of these operators. Since the impulses are independent of the coordinates and momenta we can think of them as c numbers described by a Gaussian random process. The so resulting infinitesimal operator transformation induces a streaming on the density matrix. We may associate, according to Weyl functions with operators. The function associated with the density matrix is the Wigner function. Expressing, then, these operator relations in terms of these functions we can express the streaming as a continuity equation of the Wigner function. We find that in this parametrization the extra terms which appear are the same as in the classical theory, augmenting the usual Wigner equation.     

Reconstructing Free Energy Profiles from Nonequilibrium Relaxation Trajectories

Reconstructing free energy profiles is an important problem in bimolecular reactions, protein folding or allosteric conformational changes. Nonequilibrium trajectories are readily measured experimentally, but their statistical significance and relation to equilibrium system properties still call for rigorous methods of assessment and interpretation. Here we introduce methods to compute the equilibrium free energy profile of a given variable from a set of short nonequilibrium trajectories, obtained by externally driving a system out of equilibrium and subsequently observing its relaxation. This protocol is not suitable for the Jarzynski equality since the irreversible work on the system is instantaneous. Assuming that the variable of interest satisfies an overdamped Langevin equation, which is frequently used for modeling biomolecular processes, we show that the trajectories sample a nonequilibrium stationary distribution that can be calculated in closed form. This allows for the estimation of the free energy via an inversion procedure that is analogous to that used in equilibrium and bypasses more complicated path integral methods, which we derive for comparison. We generalize the inversion procedure to systems with a diffusion constant that depends on the reaction coordinate, as is the case in protein folding, as well as to protocols in which the trajectories are initiated at random points. Using only a statistical pool of tens of synthetic trajectories, we demonstrate the versatility of these methods by reconstructing double and multi-well potentials, as well as a proposed profile for the hydrophobic collapse of a protein.     

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 in field theory

A new approach to quantum field theory is developed based on the Langevin equation (stochastic quantization). Applications to conventional and gauge theories are discussed, as well as various extensions; the Langevin difference equation, the complex Langevin equation in Minkowski space, etc.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 66–76, March, 1986.     

Modelling gaze shift as a constrained random walk

In this paper gaze shifts are considered as a realization of a stochastic process with non-local transition probabilities in a saliency field that represents a landscape upon which a constrained random walk is performed. The search is driven by a Langevin equation whose random term is generated by a Levy distribution, and by a Metropolis algorithm. Results of the simulations are compared with experimental data, and a notion of complexity is introduced to quantify the behavior of the system in different conditions.