The multiple time step r-RESPA procedure and polarizable potentials based on induced dipole moments

In the present study, we present an accelerating scheme based on the reversible multiple time step r-RESPA method to be used in molecular dynamics simulations with polarizable potentials based on induced dipole moments. Even if the induced dipoles are estimated with an iterative self-consistent procedure, this scheme significantly reduces the CPU time needed to perform a molecular dynamics simulation, up to a factor 2, as compared to the Car–Parrinello method where additional dynamical variables are introduced for the treatment of the induced dipoles. The tests show that stable and reliable molecular dynamics trajectories can be generated with that scheme, and that the physical properties derived from the trajectories are equivalent to those computed with the classical all atom iterative approach and the Car–Parrinello one.     

Conformational temperature characterizing the folding of a protein

The time sequences of the molecular dynamics simulation for the folding process of a protein is analyzed with the inherent structure landscape which focuses on the configurational dynamics of the system. Time-dependent energy and entropy for inherent structures are introduced, and from these quantities a conformational temperature is defined. The conformational temperature follows the time evolution of a slow relaxation process and reaches the bath temperature when the system is equilibrated. We show that the nonequilibrium system is described by two temperatures, one for fast vibration and the other for slow configurational relaxation, while the equilibrium system is described by one temperature. The proposed formalism is applicable widely for systems with many metastable states.     

Multiple-time scale accelerated molecular dynamics: addressing the small-barrier problem

We present a method for accelerated molecular-dynamics simulation in systems with rare-event dynamics that span a wide range of time scales. Using a variant of hyperdynamics, we detect, on the fly, groups of recurrent states connected by small energy barriers and we modify the potential-energy surface locally to consolidate them into large, coarse states. In this way, fast motion between recurrent states is treated within an equilibrium formalism and dynamics can be simulated over the longer time scale of the slow events. We apply the method to simulate cluster diffusion and the initial growth of Co on Cu(001),where time scales spanning more than 6 orders of magnitude are present, and show that the method correctly follows the slow events, so that much larger times can be simulated than with accelerated molecular dynamics alone.     

Late stage, non-equilibrium dynamics in the dipolar Ising model

Magnetic domain structures are a fascinating area of study with interest deriving both from technological applications and fundamental scientific questions. The nature of the striped magnetic phases observed in ultra-thin films is one such intriguing system. The non-equilibrium dynamics of such systems as they evolve toward equilibrium has only recently become an area of interest and previous work on model systems showed evidence of complex, slow dynamics with glass-like properties as the stripes order mesoscopically. To aid in the characterization of the observed phases and the nature of the transitions observed in model systems we have developed an efficient method for identifying clusters or domains in the spin system, where the clusters are based on the stripe orientation. Thus we are able to track the growth and decay of such clusters of stripes in a Monte Carlo simulation and observe directly the nature of the slow dynamics. We have applied this method to consider the growth and decay of ordered domains after a quench from a saturated magnetic state to temperatures near and well below the critical temperature in the 2D dipolar Ising model. We discuss our method of identifying stripe domains or clusters of stripes within this model and present the results of our investigations.     

平衡和非平衡方法计算相对结合自由能的精度和效率比较

Estimation of protein-ligand binding affinity within chemical accuracy is one of the grand challenges in structure-based rational drug design. With the efforts over three decades, free energy methods based on equilibrium molecular dynamics (MD) simulations have become mature and are nowadays routinely applied in the community of computational chemistry. On the contrary, nonequilibrium MD simulation methods have attracted less attention, despite their underlying rigor in mathematics and potential advantage in efficiency. In this work, the equilibrium and nonequilibrium simulation methods are compared in terms of accuracy and convergence rate in the calculations of relative binding free energies. The proteins studied are T4-lysozyme mutant L99A and COX-2. For each protein, two ligands are studied. The results show that the nonequilibrium simulation method can be competitively as accurate as the equilibrium method, and the former is more efficient than the latter by considering the convergence rate with respect to the cost of wall clock time. In addition, Bennett acceptance ratio, which is a bidirectional post-processing method, converges faster than the unidirectional Jarzynski equality for the nonequilibrium simulations.     

液态Co物性的平衡及非平衡分子动力学模拟

本文采用EAM作用势,通过平衡分子动力学(EMD)模拟的方法计算了Co熔体的自扩散系数、剪切粘度等物理性质.同时采用非平衡分子动力学(NEMD)方法计算了Co的剪切粘度.研究表明有关传输性质的计算是可与实验比较的,能够反映出液态Co典型的动力学特性.     

Study of thermal properties of the metastable supersaturated vapor with the restricted ensemble

The pressure and internal energy data at different densities of the supersaturated Argon vapor at the reduced temperatures 0.7 and 0.8 are obtained by the restricted canonical ensemble Monte Carlo simulation method [D.S. Corti, P. Debenedetti, Chem. Eng. Sci. 49 (1994) 2717]. In order to maintain the system in its one-phase state, different constraints on the density fluctuations have been imposed, varying with densities approaching and beyond the spinodal. The results are comparable with a molecular dynamics simulation study [A. Linhart, C.C. Chen, J. Vrabec, H. Hasse, J. Chem. Phys. 122 (2005) 144506] on the same system. The current study verifies the conclusion drawn by the simulation work that clustering of Argon atoms exists even in the vicinity of the spinodal. Compared with molecular dynamics simulations, our method can give the equilibrium properties of a metastable fluid, for example internal energies.     

Boundary-equilibrium bifurcations in piecewise-smooth slow-fast systems

In this paper we study the qualitative dynamics of piecewise-smooth slow-fast systems (singularly perturbed systems) which are everywhere continuous. We consider phase space topology of systems with one-dimensional slow dynamics and one-dimensional fast dynamics. The slow manifold of the reduced system is formed by a piecewise-continuous curve, and the differentiability is lost across the switching surface. In the full system the slow manifold is no longer continuous, and there is an O(?) discontinuity across the switching manifold, but the discontinuity cannot qualitatively alter system dynamics. Revealed phase space topology is used to unfold qualitative dynamics of planar slow-fast systems with an equilibrium point on the switching surface. In this case the local dynamics corresponds to so-called boundary-equilibrium bifurcations, and four qualitative phase portraits are uncovered. Our results are then used to investigate the dynamics of a box model of a thermohaline circulation, and the presence of a boundary-equilibrium bifurcation of a fold type is shown.     

Histogram reweighting method for dynamic properties

The histogram reweighting technique, widely used to analyze Monte Carlo data, is shown to be applicable to dynamic properties obtained from molecular dynamics simulations. The theory presented here is based on the fact that the correlation functions in systems in thermodynamic equilibrium are averages over initial conditions of trajectory functions, the latter depending on the volume of the system, the total number of particles, and the classical Hamiltonian. Thus, the well-known histogram reweighting method can be almost straightforwardly applied to reconstruct the probability distribution of initial states at different thermodynamic conditions, without extra computational effort. Correlation functions and transport coefficients are obtained with this method from few simulation data sets.     

The investigation of solid–solid phase transformation at CuAlNi alloy using molecular dynamics simulation

In this study the thermodynamic and structural properties of a CuAlNi model alloy (3A) system were investigated using a molecular dynamics (MD) simulation method. The interactions between atoms were modelled by the Sutton-Chen embedded atom method (SCEAM) based on many-body interactions. It was observed that at the end of thermal process the thermo-elastic phase transformation occurred in the model alloy system. In order to analyse the structures obtained from MD simulation, techniques such as thermodynamic parameters and radial distribution function (RDF) were used. The local atomic order in the model alloy was analysed using Honeycutt–Andersen (HA) method.     

The canonical equilibrium of constrained molecular models

In order to increase the efficiency of the computer simulation of biological molecules, it is very common to impose holonomic constraints on the fastest degrees of freedom; normally bond lengths, but also possibly bond angles. Since the maximum time step required for the stability of the dynamics is proportional to the shortest period associated with the motions of the system, constraining the fastest vibrations allows to increase it and, assuming that the added numerical cost is not too high, also increase the overall efficiency of the simulation. However, as any other element that affects the physical model, the imposition of constraints must be assessed from the point of view of accuracy: both the dynamics and the equilibrium statistical mechanics are model-dependent, and they will be changed if constraints are used. In this review, we investigate the accuracy of constrained models at the level of the equilibrium statistical mechanics distributions produced by the different dynamics. We carefully derive the canonical equilibrium distributions of both the constrained and unconstrained dynamics, comparing the two of them by means of a “stiff” approximation to the latter. We do so both in the case of flexible and hard constraints, i.e., when the value of the constrained coordinates depends on the conformation and when it is a constant number. We obtain the different correcting terms associated with the kinetic energy mass-metric tensor determinants, but also with the details of the potential energy in the vicinity of the constrained subspace (encoded in its first and second derivatives). This allows us to directly compare, at the conformational level, how the imposition of constraints changes the thermal equilibrium of molecular systems with respect to the unconstrained case. We also provide an extensive review of the relevant literature, and we show that all models previously reported can be considered special cases of the most general treatments presented in this work. Finally, we numerically analyze a simple methanol molecule in order to illustrate the theoretical concepts in a practical case.     

Effects of the System Temperature on Dust Cluster Formation in Plasma

Effects of the system temperature on dust aggregation in plasmas are investigated using two‐dimensional molecular dynamics simulations. It is shown that as the system temperature increases, the boundary of the clusters becomes gradually irregular (i.e., deviating from sphere‐like), and the cluster system gradually changes from solid to liquid and finally to gas state. The mean square displacement, mean nearest‐neighbor distance in the clusters, cluster size and coupling parameter of the system are obtained and the properties of the system structure and dynamics are investigated. The time τ needed for reaching equilibrium for different temperatures is obtained. It is shown that τ firstly decreases and then increases with the temperature, indicating that there is an optimum temperature allowing a dust aggregation to reach an equilibrium state most rapidly. The simulation results agree qualitatively with the experimental observations. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Time scale bridging in atomistic simulation of slow dynamics: viscous relaxation and defect activation

Atomistic simulation methods are known for timescale limitations in resolving slow dynamical processes. Two well-known scenarios of slow dynamics are viscous relaxation in supercooled liquids and creep deformation in stressed solids. In both phenomena the challenge to theory and simulation is to sample the transition state pathways efficiently and follow the dynamical processes on long timescales. We present a perspective based on the biased molecular simulation methods such as metadynamics, autonomous basin climbing (ABC), strain-boost and adaptive boost simulations. Such algorithms can enable an atomic-level explanation of the temperature variation of the shear viscosity of glassy liquids, and the relaxation behavior in solids undergoing creep deformation. By discussing the dynamics of slow relaxation in two quite different areas of condensed matter science, we hope to draw attention to other complex problems where anthropological or geological-scale time behavior can be simulated at atomic resolution and understood in terms of micro-scale processes of molecular rearrangements and collective interactions. As examples of a class of phenomena that can be broadly classified as materials ageing, we point to stress corrosion cracking and cement setting as opportunities for atomistic modeling and simulations.     

矩形波纹过模周期慢波结构色散特性及其单模工作分析

 通过数值模拟，给出了一种求解矩形波纹过模周期慢波结构TM_0n模的色散关系的简便方法；研究了周期慢波系统平均半径、波纹周期、波纹幅度等结构参数对本征模式色散特性的影响；讨论了周期慢波系统中表面波与体积波的存在条件；分析了过模周期慢波系统仍能工作在单模状态下的原因。结果表明，过模周期慢波系统中，当结构参数满足一定条件，且与束电压、束半径匹配，使电子束与TM₀₁模同步点位于π模附近，此时TM₀₁模的总场是表面波，在两种选模机制作用下系统可实现TM₀₁单模工作。     

Thermodynamics of one-dimensional nonlinear lattices

Analytic equations were obtained for the thermodynamic parameters of one-dimensional lattices of particles with the Toda and Morse interaction potentials in a canonical Gibbs ensemble. For the same systems, equations were derived for molecular dynamics simulations of thermodynamic processes. Stochastic differential equations were solved with simulating the thermostat by Langevin sources with random forced. Analytic equations for thermodynamic parameters (energy, temperature, and pressure) excellently coincided with molecular dynamics simulation results. The kinetics of system relaxation to the thermodynamic equilibrium state was analyzed. The advantages of simulating the physical properties of systems in a canonical compared with microcanonical ensemble were demonstrated.     

具有多分界面的非线性电路中的非光滑分岔

本文分析了具有多分界面的非线性电路在不同时间尺度下的快慢动力学行为. 在一定的参数条件下,系统的周期解为簇发解,表现出明显的快慢效应. 根据状态变量变化的快慢,把全系统划分为快子系统和慢子系统两组. 根据快慢分析法将慢变量看作快子系统的控制参数,分析了快子系统的平衡点在向量场不同区域内的稳定性. 非光滑系统的分岔与向量场的分界面密切相关,对于具有快慢效应的两时间尺度非光滑系统,快子系统的分岔则取决于分界面两侧平衡点的性质. 通过在临界面引入广义Jacobi矩阵,讨论了快子系统非光滑分岔的类型,即多次穿越分 关键词： 非线性电路 多分界面 非光滑分岔 快慢效应     

Test of a Fokker-Planck-Kramers equation treatment for short-time dynamics of diffusion-controlled reactions by molecular dynamics simulation in Lennard-Jones fluids

We test the extended Harris (EXH) theory for the dynamics of diffusion-controlled reactions using the molecular dynamics simulations in Lennard-Jones fluids. The EXH theory is based on the Fokker-Planck-Kramers equation in which the inertia effect on the molecular migration is taken into account. The time dependence of the theoretical survival probabilities of the reactant agrees with the simulation results if the potential of mean force and the initial equilibrium distribution are appropriately taken into account. The position dependence of the diffusion coefficient is not necessary in explaining the simulation results. On the other hand, the simulation results cannot be reproduced if the two-body or the uniform potentials are employed in the theoretical calculations.     

Non-Abelian Berry phase in a quantum mechanical environment

We investigate a quantum physical system that can be naturally separated into fast and slow moving components. A modification of the conventional molecular Born-Oppenheimer approximation is considered by taking the intermolecular position vector to be a slowlyvarying quantum mechanical parameter. It is found that the fast motion (electronic degrees of freedom) induces a non-Abelian vector potential (Berry connection) into the dynamics of the slow system (nucleus), thereby modifying the commutation relations of the slow variables.