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.     

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.     

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.     

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.     

Real-space renormalization group for Langevin dynamics in absence of translational invariance

A novel exact dynamical real-space renormalization group for a Langevin equation derivable from a Euclidean Gaussian action is presented. It is demonstrated rigorously that an algebraic temporal law holds for the Green function on arbitrary structures of infinite extent. In the case of fractals it is shown on specific examples that two different fixed points are found, at variance with periodic structures. Connection with the growth dynamics of interfaces is also discussed.     

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.     

Fluctuations of time averages for Langevin dynamics in a binding force field

We derive a simple formula for the fluctuations of the time average x(t) around the thermal mean (eq) for overdamped brownian motion in a binding potential U(x). Using a backward Fokker-Planck equation, introduced by Szabo, Schulten, and Schulten in the context of reaction kinetics, we show that for ergodic processes these finite measurement time fluctuations are determined by the Boltzmann measure. For the widely applicable logarithmic potential, ergodicity is broken. We quantify the large nonergodic fluctuations and show how they are related to a superaging correlation function.     

Derivation of a Fokker–Planck equation for generalized Langevin dynamics

A Fokker–Planck equation describing the statistical properties of Brownian particles acted upon by long-range stochastic forces with power-law correlations is derived. In contrast with previous approaches (Wang, Phys. Rev. A 45 (1992) 2), it is shown that the distribution of Brownian particles after release from a point source is broader than Gaussian and described by a Fox function. Transport is shown to be ballistic at short times and either sub-diffusive or super-diffusive at large times. The imposition of occasional trapping events onto the Brownian dynamics can result in confined diffusion (d/dtx²→0) at long times when the mean trapping time is divergent. It is suggested that such dynamics describe protein motions in cell membranes.     

Langevin dynamics deciphers the motility pattern of swimming parasites

The parasite African trypanosome swims in the bloodstream of mammals and causes the highly dangerous human sleeping sickness. Cell motility is essential for the parasite's survival within the mammalian host. We present an analysis of the random-walk pattern of a swimming trypanosome. From experimental time-autocorrelation functions for the direction of motion we identify two relaxation times that differ by an order of magnitude. They originate from the rapid deformations of the cell body and a slower rotational diffusion of the average swimming direction. Velocity fluctuations are athermal and increase for faster cells whose trajectories are also straighter. We demonstrate that such a complex dynamics is captured by two decoupled Langevin equations that decipher the complex trajectory pattern by referring it to the microscopic details of cell behavior.     

An optimization method for fly’s eye integrator

By analyzing how aberrations affect the performance of a fly’s eye integrator, an efficient method to optimize the performance is put forward. A fly’s eye integrator to be used to homogenize the beam of laser diode stack is designed as an example. The optimization method achieves optimized homogeneous illumination by minimizing the aberrations that degrade the homogeneity and transmission efficiency. By this means, it is possible to substitute two spherical lenses for the Fourier lens, which is usually used in a conventional fly’s eye integrator. This helps to reduce the cost without degrading its performance.     

Langevin dynamics of financial systems: A second-order analysis

We address the issue of stock market fluctuations within Langevin Dynamics (LD) and the thermodynamics definitions of multifractality in order to study its second-order characterization given by the analogous specific heat C_q, where q is an analogous temperature relating the moments of the generating partition function for the financial data signals. Due to non-linear and additive noise terms within the LD, we found that C_q can display a shoulder to the right of its main peak as also found in the S&P500 historical data which may resemble a classical phase transition at a critical point. Received 6 November 2000 and Received in final form 26 March 2001     

Study of fission dynamics with the three-dimensional Langevin equations

The dynamics of fission has been studied by solving one- and three-dimensional Langevin equations with dissipation generated through the chaos weighted wall and window friction formula. The average prescission neutron multiplicities, fission probabilities and the mean fission times have been calculated in a broad range of the excitation energy for compound nuclei ²¹⁰Po and ²²⁴Th formed in the fusion-fission reactions ⁴He + ²⁰⁶Pb , ¹⁶O + ²⁰⁸Pb and results compared with the experimental data. The analysis of the results shows that the average prescission neutron multiplicities, fission probabilities and the mean fission times calculated by one- and three-dimensional Langevin equations are different from each other, and also the results obtained based on three-dimensional Langevin equations are in better agreement with the experimental data.     

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.     

Generalized Langevin dynamics simulation: numerical integration and application of the generalized Langevin equation with an exponential model for the friction kernel

An efficient procedure is introduced for a generalized Langevin dynamics simulation when the exponential model is taken for the friction kernel. The leap frog algorithm is used for numerical integration of the generalized Langevin equation. Simulation with this model has been performed on a cyclic undecapeptide, cyclosporin A (CPA). By comparison with the results obtained from previous simulations, the method proves to be reliable and efficient in the simulation of CPA.     

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.     

An ideal integrator in a radiometer

Radio Physics and Electronics Institute, Armenian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 31, No. 8, pp. 903–906, August, 1988.     

Langevin dynamics of a π4-model with long range interactions

The Dominicis-Peliti generating functional (GF) method is used for the investigation of a Langevin dynamics of the π⁴-model: the symmetric double-well on-site potential and the infinite range interparticle interaction. We limit ourselves to the range above the temperature of the second order phase transition. The role of the 1/N-fluctuations (where N is the number of particles) is systematically investigated by using the steepest descent method. It is shown that the functional Legendre transformation directly results in the kinetic equation for the complete correlation function. Although this equation resembles the mode coupling equations used to describe the glass transition, it is qualitatively different. The solutions of this non-linear equation are investigated. It is shown that 1/N-fluctuations do not result in a breaking or ergodicity if the mean-field correlator is ergodic. On the other hand, if the mean-field correlator is nonergodic (e.g. if the time is much less than the inverse Kramers rate) then 1/N-fluctuations restore the ergodicity with characteristic relaxation time proportional to N.