Product measures and dynamics for solid-on-solid interfaces

A two-species asymmetric exclusion process is considered with general transition rates subject only to the constraint of charge conservation. Conditions for the existence of a stationary product measure are found in both the cases of odd-even parallel dynamics and continuous-time dynamics. The results are then applied to a one-dimensional restricted solid-on-solid model, considered as a model of driven interfacial growth, showing a nontrivial dependence of the stationary measure on the external driving field. The dependence of the growth velocity on the slope of the interface is given and interface shapes in finite volume with opposite boundary conditions are investigated numerically     

Contact angle hysteresis in a solid-on-solid model

The hysteresis of the contact angle of a sessile drop on top of a disordered substrate is studied within a two-dimensional solid-on-solid model using Monte Carlo dynamics. Numerical and analytical evidence is given to show that there is always a hysteresis even for small densities of impurities.     

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.     

The Langevin dynamics of vibrated powders

We present a microscopic theory of the relaxational behaviour of a granular pile submitted to vibration, elucidating the different roles of collective and independent-particle relaxation. We write down and solve Langevin equations for these processes, which have an explicit coupling. The analysis of the solution in terms of independent-particle and collective relaxations provides a consistent framework for the interpretation of experimental results.     

Finite-size corrections for inclined interfaces in two dimensions: Exact results for Ising and solid-on-solid models

Analysis of finite-size corrections for the surface tension and surface stiffness coefficients in two-dimensional models with inclined interfaces is presented. We obtain a universal leading contribution proportional to (lnL)/L for the 2D system of sizeL. By explicit calculations for restricted and unrestricted solid-on-solid models and the square lattice Ising model, we demonstrate the Gaussian nature of rough interfaces with fixed ends, and derive the leading 1/L-type corrections for appropriate surface quantities.     

半刚性聚电解质链与带相反电荷颗粒复合体系的动力学模拟

用Langevin动力学研究了半刚性聚电解质链与带相反电荷球状颗粒在溶液中的复合体系，并研究了链的拉伸性质.具体考察了带电颗粒的电量以及溶液中盐离子浓度对复合体系的影响.链两端没有施加外力的情况下，当溶液中盐离子浓度较低时，复合体系呈现一种串珠状结构；当溶液中盐离子浓度较高时，复合体系转变为一种聚集态结构.链的两端施加外力的情况下，带电颗粒从链上脱落的过程可以分为两步. 关键词： 聚电解质链 Langevin动力学 Debye-Hückel长度     

Langevin dynamics simulations of phase separation in a one-component system

Langevin dynamics computer simulations have been performed for a two-dimensional Lennard-Jones fluid quenched into the coexistence region of its liquid-vapor phase diagram. For late stages of the phase-separation process, the average radius of the liquid clusters is found to grow proportional to (time)^1/4. This growth law is analyzed theoretically and compared to recent molecular dynamics and Monte Carlo results. Details of the different simulation methods are critically discussed.     

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.     

A population-level model from the microscopic dynamics in Escherichia coli chemotaxis via Langevin approximation

Recent extensive studies of Escherichia coli (E. coli) chemotaxis have achieved a deep understanding of its mi- croscopic control dynamics. As a result, various quantitatively predictive models have been developed to describe the chemotactic behavior of E. coli motion. However, a population-level partial differential equation (PDE) that rationally incorporates such microscopic dynamics is still insufficient. Apart from the traditional Keller-Segel (K-S) equation, many existing population-level models developed from the microscopic dynamics are integro-PDEs. The difficulty comes mainly from cell tumbles which yield a velocity jumping process. Here, we propose a Langevin approximation method that avoids such a difficulty without appreciable loss of precision. The resulting model not only quantitatively repro- duces the results of pathway-based single-cell simulators, but also provides new inside information on the mechanism of E. coli chemotaxis. Our study demonstrates a possible alternative in establishing a simple population-level model that allows for the complex microscopic mechanisms in bacterial chemotaxis.     

A simple and effective Verlet-type algorithm for simulating Langevin dynamics

We present a revision to the well known Störmer–Verlet algorithm for simulating second order differential equations. The revision addresses the inclusion of linear friction with associated stochastic noise, and we analytically demonstrate that the new algorithm correctly reproduces diffusive behaviour of a particle in a flat potential. For a harmonic oscillator, our algorithm provides the exact Boltzmann distribution for any value of damping, frequency and time step for both underdamped and overdamped behaviour within the usual stability limit of the Verlet algorithm. Given the structure and simplicity of the method, we conclude that this approach can trivially be adapted for contemporary applications, including molecular dynamics with extensions such as molecular constraints.     

Localised distributions and criteria for correctness in complex Langevin dynamics

Complex Langevin dynamics can solve the sign problem appearing in numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive distribution, which is effectively sampled during the stochastic process. In the context of a simple model, we study this distribution by solving the Fokker–Planck equation as well as by brute force and relate the results to the recently derived criteria for correctness. We demonstrate analytically that it is possible that the distribution has support in a strip in the complexified configuration space only, in which case correct results are expected.     

分形基底上受限固-固模型动力学性质的数值模拟研究

为了探讨非完整基底结构对生长表面动力学行为的影响,本文在具有相同分形维数而不同谱维数的谢尔宾斯基箭头和蟹状分形基底上对受限固-固(restricted solid-on-solid,RSOS)模型的生长过程进行了大量的数值模拟研究.通过计算表面宽度和饱和表面极值高度的统计行为对生长表面的动力学行为进行了分析.结果表明,分形基底结构对生长表面的动力学行为具有显著的影响.尽管在两种基底上受限固-固模型的表面宽度均表现出很好的动力学标度行为,仍然满足Family-Vicsek标度规律,但由此计算得到的动力学标度指数并不相同.饱和生长表面的极值高度并不能满足三种常用的极值统计分布,即Weibull,Gumbel和Frechet分布,而是能很好地符合Asym2Sig分布.     

Non-Markovian Diffusion Over a Saddle with a Generalized Langevin Equation

The diffusion over a simple parabolic barrier is exactly solved with a non-Markovian Generalized Langevin Equation. For a short relaxation time, the problem is shown to be similar to a Markovian one, with a smaller effective friction. But for longer relaxation time, the average trajectory starts to oscillate and the system can have a very fast first passage over the barrier. For very long relaxation times, the solution tends to a zero-friction limit. PACS: 02.50.EY, 05.40.−a, 25.70.Jj     

耦合系统的朗之万动力学产生法

提出一种朗之万动力学方法获取处于热平衡态耦合系统内部振子坐标,数值模拟了单端固定简谐振子链的时间演化行为,并将其平衡性质与解析解进行了比较.结果表明了朗之万动力学方法的有效性.推广应用于非简谐四次方型耦合系统,模拟得到振子的四次方均坐标,与理论值验证;以模拟结果作为样本点计算哈密顿量,其能量分布与Boltzmann分布相符.     

科赫分形基底上受限固-固模型动力学标度行为的数值研究

为分析基底结构对离散生长模型动力学性质的影响, 本文在随机游走指数十分接近而分形维数和谱维数均不相同的科赫格子和科赫曲线分形基底上对受限固-固(restricted solid-on-solid)模型的生长过程进行数值模拟研究. 通过分析表面宽度和饱和表面极值高度的统计行为发现: 随机游走的动力学指数能够对饱和粗化表面的动力学行为起主要贡献. 尽管分形基底具有不同的分形维数和谱维数, 但是在两种分形基底上得到了在误差范围内相同的粗造度指数. 两种分形基底上饱和表面相对生长高度极大(小)值分布分别可以很好的塌缩在一起, 且很好的满足Asym2Sig函数分布.     

From shape to randomness: A classification of Langevin stochasticity

The Langevin equation–perhaps the most elemental stochastic differential equation in the physical sciences–describes the dynamics of a random motion driven simultaneously by a deterministic potential field and by a stochastic white noise. The Langevin equation is, in effect, a mechanism that maps the stochastic white-noise input to a stochastic output: a stationary steady state distribution in the case of potential wells, and a transient extremum distribution in the case of potential gradients. In this paper we explore the degree of randomness of the Langevin equation’s stochastic output, and classify it à la Mandelbrot into five states of randomness ranging from “infra-mild” to “ultra-wild”. We establish closed-form and highly implementable analytic results that determine the randomness of the Langevin equation’s stochastic output–based on the shape of the Langevin equation’s potential field.     

Langevin simulation of scalar fields: Additive and multiplicative noises and lattice renormalization

We consider the Langevin lattice dynamics for a spontaneously broken λ?⁴$\lambda {?}^4$ scalar field theory where both additive and multiplicative noise terms are incorporated. The lattice renormalization for the corresponding stochastic Ginzburg–Landau–Langevin and the subtleties related to the multiplicative noise are investigated.     

Comparison of modern Langevin integrators for simulations of coarse-grained polymer melts

For a wide range of phenomena, current computational ability does not always allow for atomistic simulations of high-dimensional molecular systems to reach time scales of interest. Coarse-graining (CG) is an established approach to alleviate the impact of computational limits while retaining the same algorithms used in atomistic simulations. It is important to understand how algorithms such as Langevin integrators perform on non-trivial CG molecular systems, and in particular how large of an integration time step can be used without introducing unacceptable amounts of error into averaged quantities of interest. To investigate this, we examined three different Langevin integrators on a CG polymer melt: the recently developed BAOAB method by Leimkuhler and Matthews [J. Chem. Phys. 138 (17), 05B601_1 (2013)], the Grønbech-Jensen and Farago method [Mol. Phys. 111 (8), 983-991 (2013)], or G-JF, and the frequently used Brünger–Brooks–Karplus integrator [Chem. Phys. Lett. 105 (5), 495-500 (1984)], known as BBK. We compute and analyse key statistical properties for each. Our results indicate that the integrators perform similarly for a small friction parameter; however outside this regime, the use of large integration steps produces significant deviations from the predicted diffusivity and steady-state distributions for all methods examined with the exception of G-JF.     

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.