分子动力学模拟中非成键相互作用计算的误差估计

高效的非成键相互作用计算对于分子动力学模拟具有核心意义.本文在一个统一的框架下,综述短程相互作用的截断方法、长程静电相互作用的光滑粒子网格Ewald方法和交错网格Ewald方法的误差估计.与传统的误差估计假设体系均匀且无相关性不同,本文介绍的误差估计可以推广到非均匀和有相关性的体系.本文通过具体例子讨论非均匀性和相关性对误差的本质性影响,以及可能的修正方式,并说明误差估计对于提高非成键相互作用的计算精度和速度有重要作用.本文还展示一个针对光滑粒子网格Ewald方法的实用参数优化方法,使得在保证精度的同时选取计算效率近似最优的参数组合成为可能,改善了传统上参数全凭经验选取的局面.     

Methods for computer simulation of crystal sputtering

A computer program for molecular dynamics simulation of sputtering is developed. Numerical methods for the integration of the equations of motion are described. Algorithms for constructing models of single-and polycrystalline targets are proposed. The applicability of various ion-atom and atom-atom interaction potentials to sputtering computations is analyzed.     

Prediction of biaxial buckling behavior of single-layered graphene sheets based on nonlocal plate models and molecular dynamics simulations

The biaxial buckling behavior of single-layered graphene sheets (SLGSs) is studied in the present work. To consider the size-effects in the analysis, Eringen’s nonlocal elasticity equations are incorporated into the different types of plate theory namely as classical plate theory (CLPT), first-order shear deformation theory (FSDT), and higher-order shear deformation theory (HSDT). An exact solution is conducted to obtain the critical biaxial buckling loads of simply-supported square and rectangular SLGSs with various values of side-length and nonlocal parameter corresponding to each type of nonlocal plate model. Then, molecular dynamics (MD) simulations are performed for a series of armchair and zigzag SLGSs with different side-lengths, the results of which are matched with those obtained by the nonlocal plate models to extract the appropriate values of nonlocal parameter relevant to each type of nonlocal elastic plate model and chirality. It is found that the present nonlocal plate models with their proposed proper values of nonlocal parameter have an excellent capability to predict the biaxial buckling response of SLGSs.     

Properties of GaAs single crystals grown by molecular beam epitaxy at low temperatures

Properties of GaAs single crystals grown at low temperatures by molecular beam epitaxy (LTMBE GaAs) have been studied. The results show that excessive arsenic atoms of about 10²⁰ cm⁻³ exist in LTMBE GaAs in the form of arsenic interstitial couples, and cause the dilation in lattice parameter of LTMBE GaAs. The arsenic interstitial couples will be decomposed, and the excessive arsenic atoms will precipitate during the annealing above 300°C. Arsenic precipitates accumulate in the junctions of epilayers with the increase in the temperature of annealing. The depletion regions caused by arsenic precipitates overlap each other in LTMBE GaAs, taking on the character of high resistivity, and the effects of backgating or sidegating are effectively restrained.     

A Python framework to create and simulate models with variable structure in common simulation environments

In modelling and simulation, model complexity increases with the complexity of real systems, often resulting in unfeasibly long simulation times. Variable-structure models, which can change their equation set during run-time, offer a solution. This article introduces an object-oriented approach that describes such models independent of a simulation environment. The problem of changing equations during run-time is addressed using a Python framework. Three tools are already integrated, namely, Dymola, OpenModelica and Matlab/Simulink. With this framework, existing models can be easily reused, and the advantages of different simulation tools can be leveraged. The framework is illustrated using a simple satellite launch example, along with instructions for how to use the framework. The main aim of the framework is to simulate complex models with a few mode changes and thus save simulation time. With two real-world examples and a scalability analysis, it is shown that the framework fulfils these requirements.     

Model development in discrete-event simulation and system dynamics: An empirical study of expert modellers

An empirical study comparing the model development process followed by experts in discrete-event simulation (DES) and system dynamics (SD) modelling is undertaken. verbal protocol analysis (VPA) is used to study the modelling process followed by ten expert modellers (5 SD and 5 DES). Participants are asked to build simulation models based on a case study and to think aloud while modelling. The generated verbal protocols are divided into seven modelling topics: problem structuring, conceptual modelling, data inputs, model coding, verification & validation, results & experimentation and implementation and then analyzed. Our results suggest that all modellers switch between modelling topics, however DES modellers follow a more linear progression. DES modellers focus significantly more on model coding and verification & validation, whereas SD modellers on conceptual modelling. Observations are made revealing some interesting differences in the way the two groups of modellers tackle the case. This paper contributes towards the comparison of DES and SD.     

Application of molecular dynamics computer simulations in the design of a minimal self‐replicating molecular machine

It is commonly agreed that a chemical assembly of molecules can be considered alive if it can ingest resources and convert them into building blocks; has the ability to grow and self‐reproduce; and can evolve. In the design proposed by Rasmussen and Chen (Science 2004, 303, 963) the assembly or protocell could be as simple as a small micellar surfactant aggregate acting as a container, anchoring an informational molecule to its exterior and incorporating a metabolism within the oily interior. We present several examples of modeling such a system with molecular dynamics computer simulations. © 2008 Wiley Periodicals, Inc. Complexity, 2008.     

Modelling and simulation of gas dynamics in an exhaust pipe

The gas dynamics in an exhaust pipe is studied. In particular we focus on the warm up of the catalytic converter in very short times after the engine start. This is done by combustion a small unburnt part of the exhaust gas. This process is classically modelled by gas dynamic equations. Compared to the existing literature we improve the (one-dimensional) modelling approach using a small Mach number technique and a network ansatz for the full exhaust pipe. The final simplified model on one hand still describes the main features and on the other hand it is computationally a few orders of magnitude faster than the original model. Performing numerical simulations we compare the new model to the (classical) full model and to experimental results in the literature.     

Modeling and numerical simulation of linear and nonlinear spacecraft attitude dynamics and gravity gradient moments: A comparative study

In this paper linear and nonlinear models of spacecraft attitude dynamics equations and gravity gradient moments are investigated. In addition, effects of gravity gradient moments on attitude dynamics of the satellite are studied. The purpose of this paper is to present a comparison between nonlinear and linear models of spacecraft attitude dynamics and gravity gradient moments in order to determine divergence of linear approximation from the nonlinear model. Simulation results indicate that designer of spacecraft attitude control subsystem should be meticulous in applying linear approximation of equations especially in low earth orbits. Consequently, finding an upper bound for small angle to keep the linear model valid and precise enough would be a vital part of using linear approximation. Results supported by numerical examples demonstrate various features of this study.     

Computational modelling of fluid structure interaction at nano-scale boundaries with modified Maxwellian velocity distribution

The soft collisions among fluid–fluid and fluid-wall molecules are modeled from first principles. In particular, the assumption of Maxwellian distribution of velocities for thermalized molecules, in both parallel and perpendicular directions to the wall, has been re-evaluated with supporting experimental and/or numerical evidence.It is proposed that the normal component of molecular velocity post collision is conserved for all fluid molecules. The slip effect at the wall boundary, introduced by the surface roughness, is accounted by an accommodation coefficient f. A moving least square method is used to calculate macroscopic velocity values. The influence of molecular interaction on the macroscopic velocity distribution is investigated at 40 MPa and 300 K for slit pore, inclined and stepped wall configurations. The accommodation coefficient values f = 0, 0.07, 0.257, 0.45, 0.681 and 1; and acceleration values ranging from zero to 1 × 10¹¹ m/s² and 250 × 10¹¹ m/s² are used for comparison.The distribution of macroscopic velocity parallel to the wall is studied to observe the effect of the slip behaviour. The detailed study of average of velocity values at various magnitudes of acceleration has shown an evidence of characteristic low and high speed of molecular flows that is considered as significant and a comparison is sought with an equivalent laminar and turbulent flow style behaviour. The two dimensional vector and contour plots of macroscopic velocity provide further insights in understanding Continuum velocity distributions resulting from molecular fluid-wall interaction at nanoscale. The research has highlighted the need to develop molecular dynamics simulation techniques for non-periodic boundary conditions.     

Numerical analysis of the atomic structure and shape of metal nanoparticles

Numerical simulation methods in the framework of molecular dynamics are used to study the emergence and development of amorphous, crystalline, and polycrystalline phases and their spread to the entire volume of a nanoparticle as it increases. Numerical results are presented for the parameters characterizing these processes in metal nanoparticles produced by top-down techniques. The basic features of nanoparticle formation in top-down processes and the properties of the nanoparticle structure are described.     

Asymptotic behavior of a stochastic virus dynamics model with intracellular delay and humoral immunity

In this paper, we formulate a stochastic virus dynamics model with intracellular delay and humoral immunity. By constructing some suitable Lyapunov functions, we show that the solution of stochastic model is going around each of the steady states of the corresponding deterministic model under some conditions. Then, numerical simulations are given to support the theoretical results. Finally, we propose several more effective way to control the spread of the virus by analyzing the sensitivity of the threshold of spread.     

Object-oriented modelling and simulation of a motorcycle

The design of a control oriented motorcycle model for the simulation of two-wheeled vehicles is widely recognized to be a very challenging task, as a complete analytical model is not directly available, due to its complexity and its high sensitivity to parameters' variations. Accordingly, a reliable model should be based on multibody modelling tools endowed with automated symbolic manipulation capabilities. This paper presents a simulation model for the dynamic behaviour of a motorcycle based on the object-oriented modelling paradigm developed in Modelica, within the Dymola environment. Specifically, we illustrate the modular approach to motorcycle modelling and discuss the tire-road interaction model, which is the crucial part of the proposed model. The validity of the proposed simulation model is assessed on real data, measured on an instrumented test vehicle. Further, to perform the verification phase a virtual driver model has been implemented, which allows to track both a roll angle and a target speed profile during different maneuvers. In particular, the behaviour of the driver is modelled as an inverse pendulum, with a rotational degree of freedom along the forward axis. This allows accounting for the driver lean angle, which is necessary to fully capture the real driving behaviour and its effects on the overall vehicle dynamics.     

System dynamic modelling and simulation of hydrodynamic machines

A graph-theoretic framework for the dynamic simulation of hydrodynamic (both axial and radial flow) machines is presented in this article. The physics based analytical models are developed by considering the dynamics of the hydraulic fluid flow and its interaction with the mechanical components. A linear graph is used to capture the topology of the system and the interconnection of the constituent components. Using the graph-theoretic framework, a dynamic model of an automotive hydrodynamic torque converter is developed to simulate its behaviour under different flow conditions. The ability of the model to capture different features of the torque converter will also be demonstrated by simulation. The simulation results are compared with and validated by experimental results in the literature.     

Center-of-mass tomography and probability representation of quantum states for tunneling

We develop a representation of quantum states in which the states are described by fair probability distribution functions instead of wave functions and density operators. We present a one-random-variable tomography map of density operators onto the probability distributions, the random variable being analogous to the center-of-mass coordinate considered in reference frames rotated and scaled in the phase space. We derive the evolution equation for the quantum state probability distribution and analyze the properties of the map. To illustrate the advantages of the new tomography representations, we describe a new method for simulating nonstationary quantum processes based on the tomography representation. The problem of the nonstationary tunneling of a wave packet of a composite particle, an exciton, is considered in detail.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 2, pp. 371–387, February, 2005.     

基于元胞自动机的植物病虫害传播的计算机仿真

利用元胞自动机方法建立植物病虫害传播的数学模型。在此基础上,分别对两种不同病虫害来源的情况进行仿真。仿真结果表明,在参数给定的情况下,无论病虫来源于自身还是外界,植物病虫害的传播均在一定时间后达到稳定状态,不同状态元胞占有率相近;相同参数下,同病虫来源于自身相比,植物病虫从外界入侵时,植物被感染的变化率较低,病虫害传播路径较有规律,有利于病虫害源的确定和病虫害的治理。     

Existence and uniqueness for a kinetic model of population dynamics with character dependence and spatial structure

In this work, we consider a one species population dynamics model with character dependence, spatial structure and a nonlocal renewal process arising as a boundary condition. The individual interaction are based on Boltzmann kinetic-type modeling. Using fixed point arguments and the div-rot lemma, we prove that our model admits a unique global nonnegative solution.     

Calculating ellipse area by the Monte Carlo method and analysing dice poker with Excel at high school

This paper reports on lessons in which 18–19 years old high school students modelled random processes with Excel. In the first lesson, 26 students formulated a hypothesis on the area of ellipse by using the analogy between the areas of circle, square and rectangle. They verified the hypothesis by the Monte Carlo method with a spreadsheet model developed in the lesson. In the second lesson, 27 students analysed the dice poker game. First, they calculated the probability of the hands by combinatorial formulae. Then, they verified the result with a spreadsheet model developed in the lesson. The students were given a questionnaire to find out if they found the lesson interesting and contributing to their mathematical and technological knowledge.     

The DWT power spectrum analysis of the large scale structure in the universe : Method and simulation tests

Based on the discrete wavelet transformation ( DWT), we present a pixelized method of estimating the power spectra of galaxy samples. With local properties of wavelet both in physical and wavenumber spaces, DWT power spectrum is equal to the corresponding band average of Fourier power spectrum. The DWT estimator is optimized in the sense that the spatial resolution is adaptive automatically to the perturbation wavelength to be studied. Under the assumption of ergodicity, the spatial average of local DWT fluctuation modes provides a fair estimation of the ensemble average. We test DWT spectra of four typical cold dark matter (CDM) structure formation models with numerical simulations. To consider the infections of various observation effects to the DWT spectra, we introduce irregular survey geometries, a given sampling rate, radial selection effects and redshift distortion effects into our mock samples. The numerical results show that, owing to its local properties, DWT spectrum is less affected by the sampling rate, survey geometry, and statistical ensemble fluctuations. With fast wavelet decomposition algorithm, DWT can be used to analyze large survey samples, which is of direct significance in precise measurement of the cosmological parameters from the galaxy redshift surveys of next generation.