Effect of Vacancy Defects on the Young's Modulus and Fracture Strength of Graphene: A Molecular Dynamics Study

The Young's modulus of graphene with various rectangular and circular vacancy defects is investigated by molecular dynamics simulation. By comparing with the results calculated from an effective spring model, it is demonstrated that the Young's modulus of graphene is largely correlated to the size of vacancy defects perpendicular to the stretching direction. And a linear reduction of Young's modulus with the increasing concentration of mono‐atomic‐vacancy defects (i.e., the slope of ?0.03) is also observed. The fracture behavior of graphene, including the fracture strength, crack initiation and propagation are then studied by the molecular dynamics simulation, the effective spring model, and the quantized fracture mechanics. The blunting effect of vacancy edges is demonstrated, and the characterized crack tip radius of 4.44 Å is observed.     

Note on the fractal dimension of hard sphere trajectories

Using Monte Carlo molecular dynamics, a new, careful study is made of the approach of the trajectory of a typical particle in a hard sphere fluid to that of a Brownian particle, discussed before by Powles and Quirke and Rapaport. The apparent fractal dimension of the trajectory, as a function of reduced length scale,(), characterizes the transition from mechanical to Brownian motion and differs markedly from 2 in all present computer simulations.     

Exclusion process and droplet shape

We use a mathematical isomorphism between the one-dimensional exclusion process and the two-dimensional stochastic Ising model in the low-temperature limit to describe the typical instantaneous shape of a supercritical droplet. We derive, specifically, the exact asymptotic distribution of the boundaries of a (+1) spin region, confined to Z ₊ ² and subjected to a positive magnetic field. In an appropriate scaling, the boundary distribution converges to a deterministic continuum limit.On leave at the EPFL, CH-1015 Lausanne, Switzerland.     

Heat conductivity of three periodic Hard Disks via nonequilibrium molecular dynamics

We use a driving field, of the type first suggested by Evans, to generate a steady heat current in the simplest possible system, a two-dimensional periodic fluid of three hard disks. Hard-disk motion equations can be conveniently derived from repulsive constant-force or linear-force potentials by considering the infinitely repulsive limit of these potentials. We show that the isoenergetic and isokinetic forms of the nonequilibrium equations of motion generate steady-state heat conductivities differing by terms of order 1/N, whereN is the number of particles. The resulting conductivities appear to vary as the logarithm of the driving field strength. Even at low fields, the three-body periodic-system results lie well below Enskog's infinite-system prediction.     

钙钛矿结构中的简谐子软模

利用复合空间型方法,在自由边界条件下解出了钙钛矿结构有限尺寸晶体的简谐振动方程.计算结果给出了收敛的简谐子谱分布,并发现了许多简谐子软模.用这些软模花样说明了钛酸钡晶体冷却时发生具有a畴和c畴结构的铁电相变.理论表明铁电相变过程涉及屏蔽电荷的激发及其在界面的缓慢扩散,以最后得出各个电畴内部的均匀自发极化 关键词： 晶格动力学 简谐子 软模 钛酸钡     

Droplet dynamics for asymmetric Ising model

Nucleation from a metastable state is studied for an anisotropic Ising model at very low temperatures. It turns out that the critical nucleus as well as configurations on a typical path to it differ from the Wulff shape of an equilibrium droplet.     

随机波动率模型下含违约风险的欧式衍生产品的套期保值

研究了含违约风险的欧式未定权益的最优套期保值问题. 假定含违约风险衍生产品的标的资产满足Heston随机波动率模型, 则利用局部风险最小化方法获得含违约风险衍生产品的最优套期保值策略. 此外, 还考虑了在一个特别情况下, 研究了含违约风险的欧式看涨期权的最优套期保值问题, 并通过特征函数和傅里叶反演公式给出了明确的局部风险最小化套期保值策略.     

Chaotic resonance: A simulation

Stochastic resonance is a statistical phenomenon that has been observed in periodically modulated, noise-driven, bistable systems. The characteristic signatures of the effect include an increase in the signal-to-noise of the output as noise is added to the system, and exponentially decreasing peaks in the probability density as a function of residence times in one state. Presented are the results of a numerical simulation where these same signatures were observed by adding achaotic driving term instead of a white noise term. Although the probability distributions of the noise and chaos inputs were significantly different, the stochastic and chaotic resonances were equal within the experimental error.     

Nonequilibrium dynamics of a diffusion-limited reaction driven by a cluster-memory mechanism

The diffusion-limited reaction A+AA+B is studied in general dimension. The asymptotic decay of the system is found to depend nontrivially upon the initial concentration of A particles for certain ranges of the diffusion constant, backward reaction rate, and total concentration of particles. This nonequilibrium behavior is due to the formation of clusters centered about the initial A particles. A perturbative analysis ind=1 shows that the transition to the nonequilibrium dynamics is sharp and is quite similar to another previously studied reaction A+AA. Ford>1, a scaling argument is presented which describes the dependence of the asymptotic decay on the initial concentration of A particles and the equilibrium concentration for large backward reaction rates. Monte Carlo data are shown which confirm the analytic work ind=1, 2, and 3.