Conserving the linear momentum in stochastic dynamics: Dissipative particle dynamics as a general strategy to achieve local thermostatization in molecular dynamics simulations

Stochastic dynamics is a widely employed strategy to achieve local thermostatization in molecular dynamics simulation studies; however, it suffers from an inherent violation of momentum conservation. Although this short‐coming has little impact on structural and short‐time dynamic properties, it can be shown that dynamics in the long‐time limit such as diffusion is strongly dependent on the respective thermostat setting. Application of the methodically similar dissipative particle dynamics (DPD) provides a simple, effective strategy to ensure the advantages of local, stochastic thermostatization while at the same time the linear momentum of the system remains conserved. In this work, the key parameters to employ the DPD thermostats in the framework of periodic boundary conditions are investigated, in particular the dependence of the system properties on the size of the DPD‐region as well as the treatment of forces near the cutoff. Structural and dynamical data for light and heavy water as well as a Lennard–Jones fluid have been compared to simulations executed via stochastic dynamics as well as via use of the widely employed Nose–Hoover chain and Berendsen thermostats. It is demonstrated that a small size of the DPD region is sufficient to achieve local thermalization, while at the same time artifacts in the self‐diffusion characteristic for stochastic dynamics are eliminated. © 2016 Wiley Periodicals, Inc.     

From Nosé–Hoover chain to Nosé–Hoover network: design of non-Hamiltonian equations of motion for molecular-dynamics with multiple thermostats

A systematic algorithm to design multiple thermostat systems in the framework of the Nosé–Hoover type non-Hamiltonian formulation is presented. Using ‘non uniform’ time transformations in a generalised Hamiltonian equation, we develop the non-Hamiltonian equations of motion for multiple thermostat systems having an arbitrary number of thermostats and arbitrary connections between a physical system and thermostats (‘Nosé–Hoover network’). We then present the algorithm to construct the Nosé–Hoover network equations based on a simple diagram only. On the basis of this algorithm, recursively attached Nosé–Hoover thermostats are introduced as an example of the Nosé–Hoover network and its high efficiency in sampling the canonical distribution for an one-dimensional double-well system is illustrated by numerical calculations.     

The Kac Equation with a Thermostatted Force Field

We consider the Kac equation with a thermostatted force field and prove the existence of a global in time solution that converges weakly to a stationary state. As there is no an obvious candidate for the entropy functional, in this case, the convergence result is obtained via Fourier transform techniques.     

Large-scale simulations of sodium silicate glasses

Half million and million atom systems of sodium silicate glass have been simulated using classical molecular dynamics, and their structures have been examined. Although the structural features are reasonable for the intended glasses, and have a lower configurational energy than smaller systems, they contain features which are indicative of an effective internal, or configurational, temperature higher than the target temperature. This observation is ascribed to the use of a thermostat which controls only the kinetic energy, or momenta, of the particles, and because of the non-equilibrium nature of the simulations, there is no requirement that the potential, or configurational, energy and kinetic energy be coupled. The use of alternative thermostats is suggested.     

Symmetry of Lyapunov spectrum

The symmetry of the spectrum of Lyapunov exponents provides a useful quantitative connection between properties of dynamical systems consisting ofN interacting particles coupled to a thermostat, and nonequilibrium statistical mechanics. We obtain here sufficient conditions for this symmetry and analyze the structure of 1/N corrections ignored in previous studies. The relation of the Lyapunov spectrum symmetry with some other symmetries of dynamical systems is discussed.     

低温条件下半导体材料禁带宽度的测量

介绍用硅三级管作为样品，在低温１５０Ｋ－２５０Ｋ范围内，测量其ＰＮ结正向特征，可精确求得玻耳兹曼常量及硅半导体材料禁带宽度的值。     

Representation of Quantum Brownian Motion in the Collective Coordinate Method

We consider two explicitly solvable models of quantum random processes described by the Langevin equation, namely, those for a free quantum Brownian particle and for a quantum Brownian harmonic oscillator. The Hamiltonian (string) realization of the models reveals a soliton-like structure of classical solutions. Accordingly, the zero-mode collective coordinate method turns out to be an adequate means for describing the quantum dynamics of the models.