Dynamical consequences of a constraint on the Langevin thermostat in molecular cluster simulation

We investigate some unusual behaviour observed while performing molecular dynamics simulations of small molecular clusters using a constrained Langevin thermostat. Atoms appear to be thermalised to different temperatures that depend on their mass and on the total number of particles in the system. The deviation from the zeroth law of thermodynamics can be considerable for small systems of heavy and light particles. We trace this behaviour to the absence of thermal noise acting on the centre of mass of the system. This is demonstrated by solving the stochastic dynamics for the constrained thermostat and comparing the results with simulation data. By removing the constraint, the Langevin thermostat may be restored to its intended behaviour. We also investigate a Langevin thermostat constrained to have zero total force acting on its centre of mass, and find similar deficiencies.     

Pseudo-random number generation for Brownian Dynamics and Dissipative Particle Dynamics simulations on GPU devices

Brownian Dynamics (BD), also known as Langevin Dynamics, and Dissipative Particle Dynamics (DPD) are implicit solvent methods commonly used in models of soft matter and biomolecular systems. The interaction of the numerous solvent particles with larger particles is coarse-grained as a Langevin thermostat is applied to individual particles or to particle pairs. The Langevin thermostat requires a pseudo-random number generator (PRNG) to generate the stochastic force applied to each particle or pair of neighboring particles during each time step in the integration of Newton’s equations of motion. In a Single-Instruction-Multiple-Thread (SIMT) GPU parallel computing environment, small batches of random numbers must be generated over thousands of threads and millions of kernel calls. In this communication we introduce a one-PRNG-per-kernel-call-per-thread scheme, in which a micro-stream of pseudorandom numbers is generated in each thread and kernel call. These high quality, statistically robust micro-streams require no global memory for state storage, are more computationally efficient than other PRNG schemes in memory-bound kernels, and uniquely enable the DPD simulation method without requiring communication between threads.     

Spectral element modeling for extended Timoshenko beams

Periodic lattice structures such as the large space lattice structures and carbon nanotubes may take the extension-transverse shear-bending coupled vibrations, which can be well represented by the extended Timoshenko beam theory. In this paper, the spectrally formulated finite element model (simply, spectral element model) has been developed for extended Timoshenko beams and applied to some typical periodic lattice structures such as the armchair carbon nanotube, the periodic plane truss, and the periodic space lattice beam.     

Molecular dynamics simulation on mechanicalproperty of carbon nanotube torsional deformation

In this paper torsional deformation of the carbon nanotubes is simulated by molecular dynamics method. The Brenner potential is used to set up thesimulation system. Simulation results show that the carbon nanotubes can bear larger torsional deformation, for the armchair type (10,10) single wall carbon nanotubes, with a yielding phenomenon taking place when the torsional angle is up to 63$^{\circ}$(1.1rad). The influence of carbon nanotube helicity in torsional deformation is very small. The shear modulus of single wall carbon nanotubes should be several hundred GPa, not 1\,GPa as others reports.     

Impact of thermostat on interfacial thermal conductance prediction from non-equilibrium molecular dynamics simulations

The knowledge of interfacial thermal conductance (ITC) is key to understand thermal transport in nanostructures. The non-equilibrium molecular dynamics (NEMD) simulation is a useful tool to calculate the ITC. In this study, we investigate the impact of thermostat on the prediction of the ITC. The Langevin thermostat is found to result in larger ITC than the Nose-Hoover thermostat. In addition, the results from NEMD simulations with the Nose-Hoover thermostat exhibit strong size effect of thermal reservoirs. Detailed spectral heat flux decomposition and modal temperature calculation reveal that the acoustic phonons in hot and cold thermal reservoirs are of smaller temperature difference than optical phonons when using the Nose-Hoover thermostat, while phonons in the Langevin thermostat are of identical temperatures. Such a non-equilibrium state of phonons in the case of the Nose-Hoover thermostat reduces the heat flux of low-to-middle-frequency phonons. We also discuss how enlarging the reservoirs or adding an epitaxial rough wall to the reservoirs affects the predicted ITC, and find that these attempts could help to thermalize the phonons, but still underestimate the heat flux from low-frequency phonons.     

轴压和扭转复合载荷作用下氮化硼纳米管屈曲行为的分子动力学模拟

采用分子动力学方法模拟了氮化硼纳米管在轴压和扭转复合荷载作用下的屈曲和后屈曲行为.在各加载比例下,给出了初始线性变形阶段和后屈曲阶段原子间相互作用力的变化,确定了屈曲临界荷载关系.通过对屈曲模态的细致研究,从微观变形机理上分析了纳米管对不同外荷载力学响应的差异.研究结果表明,扶手型和锯齿型纳米管均呈现出非线性的屈曲临界荷载关系,复合加载下的屈曲行为具有强烈的尺寸依赖性.温度升高将导致屈曲临界荷载的下降,且温度的影响随加载比例的变化而变化.无论在简单加载或复合加载中,同尺寸的碳纳米管均比氮化硼纳米管具有更强地抵抗屈曲荷载的能力.     

温度、应变率和空位缺陷对氮化硼纳米管压缩性能的影响

采用分子动力学方法,分别模拟了完好的和含有缺陷的氮化硼纳米管的轴向压缩过程。原子间的相互作用采用Tersoff多体势函数来描述。结果表明,同尺寸的锯齿型氮化硼纳米管的临界轴向压缩强度高于扶手型氮化硼纳米管,这与碳纳米管的研究结果一致。发现纳米管的压缩强度,如临界轴向内力在低温下受温度影响明显,并且和应变率的大小有关。然而,应变率对纳米管的弹性变形没有影响。另外,还发现空位缺陷降低了纳米管的力学性能。与完好的纳米管相比,含有缺陷的纳米管轴向压缩强度对于温度的影响并不敏感。     

Peierls相变与磁场中碳纳米管的场发射

应用紧束缚模型和WKB方法研究碳纳米管的out-of-plane型Peierls相变,及其对碳纳米管的场发射的影响.结果发现Peierls相变会在室温出现,并使碳纳米管费米面附近出现能隙,导致碳纳米管发生金属—半导体转变,从而抑制碳纳米管的场发射.磁场也会抑制Peierls形变,Peierls相变和磁场相互竞争影响碳纳米管的能带结构,从而影响碳纳米管的场发射. 关键词： 场发射 碳纳米管 Peierls相变     

多壁碳纳米管外壁高温蒸发的分子动力学模拟

采用经典分子动力学（MD）方法,使用EDIP（environment-dependent interatomic potential)势描述C纳米管内C原子之间相互作用,对多壁C纳米管由于Stone-Wales缺陷引起外层管高温剥落蒸发现象进行了计算模拟.研究结果表明,高温下多壁C纳米管外层管Stone-Wales缺陷处C原子剧烈振动导致C—C键断裂形成悬键,并逐渐向四周扩散导致外层管剥落蒸发.利用Lindemann指数作为判据,得出多壁C纳米管外层管出现剥落蒸发的温度为2290 K左右,与Huang Jianyu等实验中观测到多壁C纳米管外层管剥落蒸发现象产生的温度2000 ℃基本一致. 关键词： 多壁C纳米管 分子动力学 Stone-Wales缺陷 剥落蒸发     

Work fluctuation theorems for harmonic oscillators

The work fluctuations of an oscillator in contact with a thermostat and driven out of equilibrium by an external force are studied experimentally and theoretically within the context of fluctuation theorems. The oscillator dynamics is modeled by a second order Langevin equation. Both the transient and stationary state fluctuation theorems hold and the finite time corrections are very different from those of a first order Langevin equation. The periodic forcing of the oscillator is also studied; it presents new and unexpected short time convergences. Analytical expressions are given in all cases.     

碳纳米管包裹的硅纳米线复合结构的热稳定性研究

采用经典分子动力学方法模拟一定直径[111]晶向的硅纳米线填充不同扶手椅型单壁碳纳米管复合结构的加热过程, 通过可视化和能量分析的方法判断复合结构中硅纳米线和碳纳米管的热稳定性. 通过讨论碳纳米管的空间限制作用和分子间相互作用力的关系, 对碳纳米管和硅纳米线的热稳定性变化进行初步解释. 研究发现碳纳米管中硅纳米线的热稳定性和碳纳米管的直径关系密切: 当管径较小时, 硅纳米线的热稳定性有所提高, 当管径增大到一定大小时, 硅纳米线的热稳定性会突然显著地下降, 直到硅纳米线与管壁不存在分子间相互作用力, 硅纳米线的热稳定性才会恢复. 而硅纳米线填充到碳纳米管中对碳纳米管的热稳定性有着明显的降低作用.     

Electromechanical actuation of CNT/PVDF composite films based on a bridge configuration

Bridged strips consisting of carbon nanotubes and poly(vinylidene fluoride) are developed, which exhibit notable deflection in response to very low driven voltages( 1 V), because of both the excellent conductivity of the unique carbon nanotube film and the powerful thermal expansion capability of the polymer. The actuators demonstrate periodic vibrations motivated by the alternating signals. The amplitude of displacement is dependent not only on the driven voltage but also on the applied frequency. The mechanism of actuation is confirmed to be the thermal power induced by the electrical heating. By accelerating the dissipation of heat, the vibration response at higher frequencies can be significantly enhanced.The useful locomotion shows great promise in potential applications such as miniature smart devices and micro power generators.     

缺陷对碳纳米管摩擦与运动行为的影响

本文采用分子动力学方法研究了公度、无公度情况下含空位、Stone-Thrower-Wales(STW)型缺陷的单壁碳纳米管(SWCNT)在石墨基底上的摩擦与运动行为.结果表明,公度时缺陷的存在导致了界面局部无公度,减小了摩擦.随着碳纳米管底部STW缺陷的增多,碳纳米管变形增大,侧向力波动的幅值减小,局部无公度性增强,摩擦减小.含空位缺陷的碳纳米管所受的摩擦力明显大于含STW缺陷的碳纳米管,原因在于含空位缺陷的碳纳米管在运动的后期出现了明显的翻转现象,增大了能量耗散.无公度时,碳纳米管与石墨基底间的摩擦力很小,缺陷对其摩擦力影响不大,原因在于无论是否含有缺陷,碳纳米管与石墨组成的界面的无公度性差别不大.     

A novel method for studying the buckling of nanotubes considering geometrical imperfections

Buckling of nanotubes has been studied using many methods such as molecular dynamics (MD), molecular mechanics, and continuum-based shell theories. In MD, motion of the individual atoms is tracked under applied temperature and pressure, ensuring a reliable estimate of the material response. The response thus simulated varies for individual nanotubes and is only as accurate as the force field used to model the atomic interactions. On the other hand, there exists a rich literature on the understanding of continuum mechanics-based shell theories. Based on the observations on the behavior of nanotubes, there have been a number of shell theory-based approaches to study the buckling of nanotubes. Although some of these methods yield a reasonable estimate of the buckling stress, investigation and comparison of buckled mode shapes obtained from continuum analysis and MD are sparse. Previous studies show that the direct application of shell theories to study nanotube buckling often leads to erroneous results. The present study reveals that a major source of this error can be attributed to the departure of the shape of the nanotube from a perfect cylindrical shell. Analogous to the shell buckling in the macro-scale, in this work, the nanotube is modeled as a thin-shell with initial imperfection. Then, a nonlinear buckling analysis is carried out using the Riks method. It is observed that this proposed approach yields significantly improved estimate of the buckling stress and mode shapes. It is also shown that the present method can account for the variation of buckling stress as a function of the temperature considered. Hence, this can prove to be a robust method for a continuum analysis of nanosystems taking in the effect of variation of temperature as well.     

Understanding the loading dependence of self-diffusion in carbon nanotubes

The influence of flexible walls on the self-diffusion of CH4 in an isolated single walled carbon nanotube, as an example, is studied by molecular dynamics simulations. By simulating the carbon nanotube as a flexible framework we demonstrate that the flexibility has a crucial influence on self-diffusion at low loadings. We show how this influence can be incorporated in a simulation of a rigid nanotube by using a Lowe-Andersen thermostat which works on interface-fluid collisions. The reproduction of the results of a flexible carbon nanotube by a rigid nanotube simulation is excellent.     

Optimization of the calculations of the electronic structure of carbon nanotubes

A method is proposed for calculating the electronic structure and physical properties (in particular, Young’s modulus) of nanotubes, including single-walled carbon nanotubes. This method explicitly accounts for the periodic boundary conditions for the geometric structure of nanotubes and makes it possible to decrease considerably (by a factor of 10–10³) the time needed to calculate the electronic structure with minimum error. In essence, the proposed method consists in changing the geometry of the structure by partitioning nanotubes into sectors with the introduction of the appropriate boundary conditions. As a result, it becomes possible to reduce substantially the size of the unit cell of the nanotube in two dimensions, so that the number of atoms in a new unit cell of the modified nanotube is smaller than the number of atoms in the initial unit cell by a factor equal to an integral number. A decrease in the unit cell size and the corresponding decrease in the number of atoms provide a means for drastically reducing the computational time, which, in turn, substantially decreases with an increase in the degree of partition, especially for nanotubes with large diameters. The results of the calculations performed for carbon and non-carbon (boron nitride) nanotubes demonstrate that the electronic structures, densities of states, and Young’s moduli determined within the proposed approach differ insignificantly from those obtained by conventional computational methods.     

Mass conservative finite volume discretization of the continuity equations in multi-component mixtures

The Stefan–Maxwell equations for multi-component diffusion result in a system of coupled continuity equations for all species in the mixture. We use a generalization of the exponential scheme to discretize this system of continuity equations with the finite volume method. The system of continuity equations in this work is obtained from a non-singular formulation of the Stefan–Maxwell equations, where the mass constraint is not applied explicitly. Instead, all mass fractions are treated as independent unknowns and the constraint is a result of the continuity equations, the boundary conditions, the diffusion algorithm and the discretization scheme. We prove that with the generalized exponential scheme, the mass constraint can be satisfied exactly, although it is not explicitly applied. A test model from the literature is used to verify the correct behavior of the scheme.     

周向畸变对跨声速风扇低阶强迫振动的影响研究

边界层抽吸式推进系统(BLI)因具有降低未来商用飞机燃油消耗率的巨大潜力而备受关注.但风扇叶片作为关键组件,需要受到由于边界层吸入而导致的畸变来流的挑战.基于本团队前期在NASA Rotor 67进行的数值模拟,在设计转速附近风扇因受到二阶激励而以一阶弯曲的形式发生低阶模态振动,同时,激发的强度足以引起叶片振动.由于来...     

Longitudinal vibration and stability analysis of carbon nanotubes conveying viscous fluid

Nowadays, carbon nanotubes (CNT) play an important role in practical applications in fluidic devices. To this end, researchers have studied various aspects of vibration analysis of a behavior of CNT conveying fluid. In this paper, based on nonlocal elasticity theory, single-walled carbon nanotube (SWCNT) is simulated. To investigate and analyze the effect of internal fluid flow on the longitudinal vibration and stability of SWCNT, the equation of motion for longitudinal vibration is obtained by using Navier-Stokes equations. In the governing equation of motion, the interaction of fluid-structure, dynamic and fluid flow velocity along the axial coordinate of the nanotube and the nano-scale effect of the structure are considered. To solve the nonlocal longitudinal vibration equation, the approximate Galerkin method is employed and appropriate simply supported boundary conditions are applied. The results show that the axial vibrations of the nanotubesstrongly depend on the small-size effect. In addition, the fluid flowing in nanotube causes a decrease in the natural frequency of the system. It is obvious that the system natural frequencies reach zero at lower critical flow velocities as the wave number increases. Moreover, the critical flow velocity decreases as the nonlocal parameter increases.     

Raman spectra of polycrystalline bismuth titanate nanotubes

The Raman spectra of bismuth titanate Bi₄Ti₃O₁₂ nanotubes synthesized by the template method on an Al₂O₃ membrane have been studied. The samples prepared represent an array of oriented ∼50-μm-long nanotubes with coalescing smooth walls. The nanotube wall thickness is varied from 20 to 50 nm, and the nanotube inside diameter is about 200 nm. The Raman spectra of the nanotubes demonstrate a broadening of the lines corresponding to the stretching and bending vibrations of TiO₆ octahedra. In the low-frequency spectral range corresponding to vibrations of Bi ions with respect to the oxygen octahedra, a transformation due to strong mechanical stresses generated during the formation of the nanotubes has been observed.