Rotation Numbers Of Invariant Manifolds Around Unstable Periodic Orbits For The Diamagnetic Kepler Problem

In this paper, a method to construct topological template in terms of symbolic dynamics for the diamagnetic Kepler problem is proposed. To confirm the topological template, rotation numbers of invariant manifolds around unstable periodic orbits in a phase space are taken as an object of comparison. The rotation numbers are determined from the definition and connected with symbolic sequences encoding the periodic orbits in a reduced Poincare section. Only symbolic codes with inverse ordering in the forward mapping can contribute to the rotation of invariant manifolds around the periodic orbits. By using symbolic ordering, the reduced Poincare section is constricted along stable manifolds and a topological template, which preserves the ordering of forward sequences and can be used to extract the rotation numbers, is established. The rotation numbers computed from the topological template are the same as those computed from their original definition.

Metric representation of DNA sequences

A metric representation of DNA sequences is borrowed from symbolic dynamics. In view of this method, the pattern seen in the chaos game representation of DNA sequences is explained as the suppression of certain nucleotide strings in the DNA sequences. Frequencies of short nucleotide strings and suppression of the shortest ones in the DNA sequences can be determined by using the metric representation.

Molecular dynamics simulation of the role of dislocations in microcrack healing

The molecular dynamics method is used to simulate microcrack healing during heating or/and under compressive stress. A centre microcrack in Cu crystal would be sealed under compressive stress or by heating. The role of compressive stress and heating in crack healing was additive. During microcrack healing, dislocation generation and motion occurred. When there were pre-existing dislocations around the microcrack, the critical temperature or compressive stress necessary for microcrack healing would decrease, and, the higher the number of dislocations, the lower the critical temperature or compressive stress. The critical temperature necessary for microcrack healing depended upon the orientation of the crack plane. For example, the critical temperature for the crack along the (001) plane was the lowest, i.e. 770K.

Dislocation dynamics of strain relaxation in epitaxial layers

Many experimental observations have clearly shown that dislocation interaction plays a crucial role in the kinetics of strain relaxation in epitaxial thin films. A set of evolution equations are presented in this article. The key feature of the equations

Formation of Fivefold Deformation Twins in Nanocrystalline Face-Centered-Cubic Copper Based on Molecular Dynamics Simulations

Fivefold deformation twins were reported recently to be observed in the experiment of the nanocrystalline face-centered-cubic metals and alloys. However, they were not predicted previously based on the molecular dynamics (MD) simulations and the reason was thought to be a uniaxial tension considered in the simulations. In the present investigation, through introducing pretwins in grain regions, using the MD simulations, the authors predict out the fivefold deformation twins in the grain regions of the nanocrystal grain cell, which undergoes a uniaxial tension. It is shown in their simulation results that series of Shockley partial dislocations emitted from grain boundaries provide sequential twining mechanism, which results in fivefold deformation twins. (c) 2006 American Institute of Physics.

Molecular Dynamics Simulation of Peeling a DNA Molecule on Substrate

Molecular dynamics (MD) simulations are performed to study adhesion and peeling of a short fragment of single strand DNA (ssDNA) molecule from a graphite surface. The critical peel-off force is found to depend on both the peeling angle and the elasticity of ssDNA. For the short ssDNA strand under investigation, we show that the simulation results can be explained by a continuum model of an adhesive elastic band on substrate. The analysis suggests that it is often the peak value, rather than the mean value, of adhesion energy which determines the peeling of a nanoscale material.

Correlative reference model and molecular dynamics simulation of dislocation emission process

A correlative reference model for computer molecular dynamics simulations is proposed. Based on this model, a flexible displacement boundary scheme is introduced and the dislocations emitted from a crack tip can continuously pass through the border of the inner discrete atomic region and pile up at the outer continuum region. The effect of the emitted dislocations within the plastic zone on the inner atomistic region can be clearly demonstrated. The simulations for a molybdinum crystal show that a full dislocation in a bcc crystal is dissociated into three partial dislocations and interaction between the crack and the emitted dislocations results in gradual decrease of the local stress intensity factor.

Molecular dynamics simulation of hydrogen enhancing dislocation emission

The interactive pair potential between Al and H is obtained based on the ab initio calculation and the Chen-Mobius 3D lattice inversion formula. By utilizing the pair potentials calculated, the effects of hydrogen on the dislocation emission from crack tip have been studied. The simulated result shows that hydrogen can reduce the cohesive strength for Al single crystal, and then the critical stress intensity factor for partial dislocation emission decreases from 0.11 MPa root m (C-H = 0) to 0.075 MPa root m (C-H=0.72%) and 0.06 MPa root m (C-H = 1.44%). This indicates thar hydrogen can enhance the dislocation emission. The simulation also shows that atoms of hydrogen can gather and turn into small bubbles, resulting in enhancement of the equilibrium vacancy concentration.

Get Acquaited with Rarefied Gas Dynamics

以通俗易懂的方式介绍了空气动力学当气体间断分子效应显著时发展起来的特殊分支--稀薄气体动力学。讨论了非平衡现象与稀薄气体动力学的关系。通过与8速度气体模型的间断Boltzmann方程的对比,解释了Boltzmann方程碰撞项的物理意义和数学困难,简要综述了其一般解法。讨论了分子在物体表面的反射和问题的边界条件,着重介绍了直接模拟Monte Carlo(DSMC)方法和为克服低速稀薄流动(如MEMS中流动)中模拟困难的信息保存(IP)方法。

Molecular Dynamics Modeling of Diffusion Bonding

Molecular dynamics simulations on diffusion bonding of Cu-Ag showed that the thickness of the interfacial region depended on the stress. The interfacial region became amorphous during diffusion bonding, and it would normally transform from amorphous into crystalline structure when the structure was cooled to the room temperature.

Molecular Dynamics Simulation of the Uniaxial Tensile Deformation of Nanocrystalline Copper

纳米材料是由尺度在1～100 nm的微小颗粒组成的体系,由于它具有独特的性能而备受关注.本文简要地回顾了分子动力学在纳米材料研究中的应用,并运用它模拟了平均晶粒尺寸从1.79～5.38nm的纳米晶体的力学性质.模拟结果显示:随着晶粒尺寸的减小,系统与晶粒内部的原子平均能量升高,而晶界上则有所下降;纳米晶体的弹性模量要小于普通多晶体,并随着晶粒尺寸的减小而减小;纳米晶铜的强度随着晶粒的减小而减小,显示了反常的Hall-Petch效应;纳米晶体的塑性变形主要是通过晶界滑移与运动,以及晶粒的转动来实现的;位错运动起着次要的、有限的作用;在较大的应变下(约大于5%),位错运动开始起作用;这种作用随着晶粒尺寸的增加而愈加明显.

The Influence of Grain Size and Temperature on the mechanical Deformation of Nanocrystalline Materials: Molecular Dynamics Simulation

Nanocrystalline (nc) materials are characterized by a typical grain size of 1-100nm. The uniaxial tensile deformation of computer-generated nc samples, with several average grain sizes ranging from 5.38 to 1.79nm, is simulated by using molecular dynamics with the Finnis-Sinclair potential. The influence of grain size and temperature on the mechanical deformation is studied in this paper. The simulated nc samples show a reverse Hall-Petch effect. Grain boundary sliding and motion, as well as grain rotation are mainly responsible for the plastic deformation. At low temperatures, partial dislocation activities play a minor role during the deformation. This role begins to occur at the strain of 5%, and is progressively remarkable with increasing average grain size. However, at elevated temperatures no dislocation activity is detected, and the diffusion of grain boundaries may come into play.

Molecular dynamics simulation on dislocation emission process

A correlative reference model for a computer simulation of molecular dynamics is proposed in this paper. Based on this model, a flexible displacement boundary scheme is naturally introduced and the dislocations emitted from a crack tip are presumed to continuously pass through the border of an inner discrete atomic region to pile up at an outer continuum region. The simulations for a Mo crystal show that the interaction between a crack and emitted dislocations results in the decrease in local stress intensity factor gradually.

Molecular Dynamics Simulation of Microstructure of Nanocrystalline Copper

The microstructure of computer generated nanocrystalline coppers is simulated by using molecular dynamics with the Finnis-Sinclair potential, analysed by means of radial distribution functions, coordination number, atomic energy and local crystalline order. The influence of the grain size on the nanocrystalline structure is studied. The results reveal that as the grain size is reduced, the grain boundary shows no significant structural difference, but the grain interior becomes more disordered, and their structural difference diminishes gradually; however, the density and the atomic average energy of the grain boundary present different tendencies from those of the grain interior.

QM/MM and Classical Molecular Dynamics Simulation of Histidine-Tagged Peptide Immobilization on Nickel Surface

The hybrid quantum mechanics (QM) and molecular mechanics (MM) method is employed to simulate the His-tagged peptide adsorption to ionized region of nickel surface. Based on the previous experiments, the peptide interaction with one Ni ion is considered. In the QM/MM calculation, the imidazoles on the side chain of the peptide and the metal ion with several neighboring water molecules are treated as QM part calculated by “GAMESS”, and the rest atoms are treated as MM part calculated by “TINKER”. The integrated molecular orbital/molecular mechanics (IMOMM) method is used to deal with theQMpart with the transitional metal. By using the QM/MM method, we optimize the structure of the synthetic peptide chelating with a Ni ion. Different chelate structures are considered. The geometry parameters of the QM subsystem we obtained by QM/MM calculation are consistent with the available experimental results. We also perform a classical molecular dynamics (MD) simulation with the experimental parameters for the synthetic peptide adsorption on a neutral Ni(1 0 0) surface. We find that half of the His-tags are almost parallel with the substrate, which enhance the binding strength. Peeling of the peptide from the Ni substrate is simulated in the aqueous solvent and in vacuum, respectively. The critical peeling forces in the two environments are obtained. The results show that the imidazole rings are attached to the substrate more tightly than other bases in this peptide.