Lattice Boltzmann Simulation of Sedimentation of a Single Elastic Dumbbell in a Newtonian Fluid

Based on the lattice Boltzmann method (LBM), the sedimentations of a single elastic dumbbell in a Newtonian fluid under different initial positions and orientations, and also that of the elastic dumbbells with different free lengths of the spring under the same initial conditions have been simulated. All of the numerical results show that the final orientations of the elastic dumbbells are in the same horizontal direction, and the final positions of their centroids are all on the centerline of the tube no matter what the initial positions and orientations of the elastic dumbbell or the free lengths of the spring are. When the elastic dumbbell finally falls down vertically, the two circular cylinders of the elastic dumbbell rotate around their own symmetry-axis respectively, and their angular velocities are equal but opposite to each other. For the sedimentations of the elastic dumbbells with different free lengths of the spring, the shorter of the free length is, the faster the final angular velocity and vertical velocity of the circular cylinder will be.     

Lattice Boltzmann simulations of a dumbbell moving in a Poiseuille flow

In this paper, the lattice Boltzmann method is applied to simulate a dumbbell moving in a pressure-driven flow in a planar channel with the stress-integration method for the evaluation of hydrodynamic force acting on the cylinders. The simulation results show that the dumbbell also has the important feature of the Segr\'e--Silberberg effect like a particle in a Poiseuille flow. The dumbbell trajectories, orientations, the cylinders vertical velocities and angular velocities all reach their equilibrium values separately independent of their initial positions. It is also found that the dumbbell equilibrium positions depend on the flow Reynolds number, blockage ratio and elastic coefficient. This study is expected to be helpful to understand the dynamics of polymer solutions, polymer synthesis and reaction, etc.     

Influence of Focusing on Phonon Propagation and Thermal Conductivity in Single Crystal Films with Different Types of Anisotropy of Elastic Energy

The influence of the anisotropy of elastic energy on the phonon propagation and phonon transport in single crystal nanofilms with different types of anisotropy of elastic energy in a Knudsen flow of a phonon gas is studied. The angular distribution of phonon mean free paths in the planes of the films and in their cross section is analyzed. The physical reasons leading to the dependence of the thermal conductivity on the orientation of the film planes and the directions of the heat flux relative to the crystal axes are studied. An analysis of the effect of focusing on the phonon propagation made it possible to explain the qualitative difference between the anisotropy of phonon mean free paths in films of cubic nanocrystals of various types having different orientations of the planes.     

Anisotropy of the mean free paths of phonons in single-crystal films of germanium,silicon, and diamond at low temperatures

The physical aspects of the influence of the elastic energy anisotropy of crystals on the anisotropy of the mean free paths of phonons in single-crystal films of germanium, silicon, and diamond in the diffuse scattering of phonons at the boundaries of the samples have been considered. It has been shown that, for sufficiently wide films of germanium, silicon, and diamond with the {100} and {111} orientations and the lengths of less than or equal to their width, the phonon mean free paths are isotropic (independent of the direction of the temperature gradient in the plane of the film). The anisotropy of the phonon mean free paths depends primarily on the orientation of the film plane and is determined by the focusing and defocusing of phonon modes. For single-crystal films of germanium, silicon, and diamond with the {100} and {111} orientations and lengths much larger than their width, the phonon mean free paths are anisotropic.     

Quasi-stationary states in a circular geometry

The quasi-stationary final states of decaying two-dimensional turbulence on a circular domain, with an initial flow field containing either no or a substantial amount of angular momentum, have been investigated numerically. The production of angular momentum is almost absent for these flows on a circular domain with a no-slip wall. Its presence or absence essentially determines the character of the quasi-stationary final state. Based on a minimum-enstrophy principle a diagram is constructed that provides insight into the development of the typical late-time flow patterns on a circular domain with a no-slip wall. The quasi-stationary final states found in the present numerical study can be understood based on the predictions from the minimum-enstrophy principle.     

Effect of the geometry of workpiece on polishing velocity in free annular polishing

Base on Coulomb friction model, the workpieces with different geometry rotating in free annular polishing are simulated. From simulation, the following conclusions are drawn. The angular velocity of workpiece is higher than that of polishing pad if the ring rotates uncontrolled in free annular polishing. The circular workpiece can synchronize with polishing pad through controlling the rotation of ring, which depends on the radii of ring and workpiece, the friction coefficients of polishing pad-workpiece and ring-workpiece,and the angular velocity of polishing pad. The workpiece with sharp corner cannot contact with the ring contiguously, which causes the contact state changing and the angular velocity of workpiece fluctuating ceaselessly, and this type of workpiece should be controlled with clamp to rotate synchronistically with the polishing pad.     

弹簧的质心

依据圆柱形弹簧的劲度系数公式和胡克定律,导出了形变前后有重量的弹簧上同一点相对于弹簧固定端的距离关系式,给出了弹簧非均匀形变的数学表述,讨论了弹簧的质量分布和质心位置问题.     

Lyapunov instability of two-dimensional fluids: Hard dumbbells

We generalize Benettin's classical algorithm for the computation of the full Lyapunov spectrum to the case of a two-dimensional fluid composed of linear molecules modeled as hard dumbbells. Each dumbbell, two hard disks of diameter sigma with centers separated by a fixed distance d, may translate and rotate in the plane. We study the mixing between these qualitatively different degrees of freedom and its influence on the full set of Lyapunov exponents. The phase flow consists of smooth streaming interrupted by hard elastic collisions. We apply the exact collision rules for the differential offset vectors in tangent space to the computation of the Lyapunov exponents, and of time-averaged offset-vector projections into various subspaces of the phase space. For the case of a homogeneous mass distribution within a dumbbell we find that for small enough d/sigma, depending on the density, the translational part of the Lyapunov spectrum is decoupled from the rotational part and converges to the spectrum of hard disks. (c) 1998 American Institute of Physics.     

Mixtures of polar and nonpolar molecules

The site-site Ornstein-Zernike (SSOZ) equation with mean spherical approximation closure is solved analytically for a mixture of hard dumbbells and polar hard dumbbells. The solution reduces to that of the pure polar hard dumbbell fluid at the polar species density rather than the total density. The thermodynamic properties of the mixture are obtained using the zero-pole approximation (ZPA) to the free energy. The mixture is shown to separate into two mixed phases, one rich in the nonpolar species and the other rich in the polar species. This phase separation terminates in an upper critical solution temperature. The excess thermodynamic functions are presented and the mixture exhibits both positive and negative values of the excess volume. The negative values of the excess volume occur in mixtures rich in the polar component.     

Kinetic Monte Carlo simulations of heteroepitaxial growth with an atomistic model of elasticity

We have implemented Kinetic Monte Carlo (KMC) simulations of growth of heteroepitaxial thin films. A simple cubic Solid-on-Solid (SOS) model is used to describe the atomic configurations and nearest neighbor bonds are used to describe the energetics. Elastic effects are modeled using harmonic springs between atoms displaced from their lattice positions. The misfit strain is a consequence of different equilibrium spring lengths for the substrate and film. The consistency of this elastic model with continuum theories for strained surfaces has been shown by performing elastic energy calculations for various morphologies. KMC simulations for submonolayer deposition show scaling behavior in the island size distribution. The resulting island shapes are predominantly square and do not show any shape transitions in the physically relevant range of conditions. This method gives a detailed understanding of elastic interactions and their interplay with surface diffusion in heteroepitaxial systems.     

Fidelity of Two-Particle Wave Packets Moving around the Schwarzschild Spacetime

Fidelity for two-particle wave packets of spin- particles moving around the Schwarzschild spacetime is discussed. Both acceleration and gravity cause to produce a Wigner rotation that transforms the wave packet as it moves along a specified path in the gravitational field. For considered circular paths, the fidelity between the spin parts of initial and final states of the system, called the spin fidelity, is obtained as a function of angular velocity, elapsed proper time and radius of circular paths. For fixed elapsed proper time and angular momentum of the centroid, there always exists one circular orbit with determined radius on which the fidelity of spin parts is minimum. Using a numerical approach, the behavior of the spin fidelity in terms of the angular velocity, as well as the radius of paths is described for both the spin singlet and spin triplet states.     

影响单电子非线性汤姆孙散射因素的研究

应用电子汤姆孙散射的经典理论，通过理论分析和计算机模拟，研究了超短超强激光脉冲作用下电子产生的辐射脉冲的性质.计算表明，在这种情况下，电子的辐射通常以阿秒脉冲列的形式出现.讨论了不同激光场参数（包括激光强度、脉宽、初相位和偏振态）、不同电子初始状态（初始速度和位置）对辐射脉冲的时间和空间特性的影响.通常在相对论光强条件下，激光强度越大，电子辐射越强，脉宽越窄，中心频率越大，并且方向性越好；电子在线偏振激光中产生的辐射效率，比在同样强度下圆偏振激光中产生的效率更高；无论入射光是线偏振光，还是圆偏振光,辐射场呈现较复杂的偏振态, 并且它与辐射方向有关.当电子具有一定的初始能量时，通常辐射场的振幅随电子初始能量的增大而增大.不管电子的初始能量以及运动方向如何，做相对论运动的电子产生的辐射趋向于出现在靠近电子运动方向的角度区域.     

Simulation of the dynamics of a two-dimensional dislocation-disclination ensemble

A computer code for simulating the dynamics of an arbitrary 2D dislocation-disclination ensemble is developed. The code is constructed according to the molecular-dynamics principles; individual interacting particles are taken to be edge dislocations and dipoles of partial wedge disclinations. Pure copper is considered as an example for simulating the glide of one dislocation near an immobile dipole for various orientations of the dipole and under various initial conditions of the problem. The dislocation dynamics is shown to be mainly determined by the distribution of the elastic field of the disclination dipole rather than by the initial velocity of the dislocation.     

The interaction of a screw dislocation with point defects in bcc iron

In this study, we calculate the interaction energy of intrinsic point defects vacancies and interstitials) with screw dislocations in body-centered cubic iron. First (we calculate the dipole tensor of a defect in the bulk crystal using molecular statics. Using a formulation based on linear elasticity theory, we calculate the interaction energy of the defect and the dislocation using both isotropic and anisotropic strain fields. Second, we perform atomistic calculations using molecular statics methods to directly calculate the interaction energy. Results from these two methods are compared. We verify that continuum methods alone are unable to correctly predict the interactions of defects and dislocations near the core. Although anisotropic theory agrees qualitatively with atomistics far from the core, it cannot predict which dumbbell orientations are stable and any continuum calculations must be used with caution. Spontaneous absorption by the core of both vacancies and dumbbells is seen. This paper demonstrates and discusses the differences between continuum and atomistic calculations of interaction energy between a dislocation core and a point defect.     

VIBRATION OF A COMPLIANT TOWER IN THREE-DIMENSIONS

The three-dimensional motion of an offshore compliant tower using both rigid and flexible beam models is studied in this paper. The tower is modelled as a beam supported by a torsional spring at the base with a point mass at the free end. The torsional spring constant is the same in all directions. When the beam is considered rigid, the two-degree-of-freedom model is employed. The two degrees constitute the two angular degrees of spherical co-ordinates, and the resulting equations are coupled and non-linear. When the beam is considered as elastic, three displacements are obtained as functions of the axial co-ordinate and time; again with coupled and non-linear equations of motion. The free and the forced responses due to deterministic loads are presented. The free responses of the rigid and elastic beams show rotating elliptical paths when viewed from above. The rate at which the path rotates depends on the initial conditions. When a harmonic transverse loading is applied in one direction, the displacement in that direction shows subharmonic resonance of order 1/2 and 1/3 while the displacement in the perpendicular direction is affected minimally. Next, in addition to the harmonic load in one direction, a transverse load is applied in the perpendicular direction. The transverse load varies exponentially with depth but is constant with time. It is found that the transverse load affects the transverse displacements in the perpendicular direction minimally.     

On Collisions Times of ‘Self-Sorting’ Interacting Particles in One-Dimension with Random Initial Positions and Velocities

We investigate a one-dimensional system of N particles, initially distributed with random positions and velocities, interacting through binary collisions. The collision rule is such that there is a time after which the N particles do not interact and become sorted according to their velocities. When the collisions are elastic, we derive asymptotic distributions for the final collision time of a single particle and the final collision time of the system as the number of particles approaches infinity, under different assumptions for the initial distributions of the particles’ positions and velocities. For comparison, a numerical investigation is carried out to determine how a non-elastic collision rule, which conserves neither momentum nor energy, affects the median collision time of a particle and the median final collision time of the system.     

用智能手机App Video Physics研究竖直平面内的圆周运动

本实验用智能手机App Video Physics追踪小球在竖直平面内做圆周运动的情况,研究了不同质量的小球从同一高度静止释放到达最低点的速度关系,研究了从不同高度静止释放小球的速度与运动轨迹之间的关系,计算了小球在圆形轨道上运动时的向心力、角速度,以及当小球与圆形轨道等高静止释放时小球的脱离点速度.     

Features of X-ray diffraction at elastic deformations near the dislocation axis in section topography techniques

Features of the formation of an x-ray diffraction image by x-ray section topography are considered for a strongly distorted region near the dislocation axis in silicon single crystals. The results of experimental investigations and numerical calculations of the diffraction contrast and section topographs of rectilinear dislocations are presented for their different orientations and positions in the scattering triangle in silicon single crystals. A comparison and an analysis of the experimental topographs and the simulated images lead to the conclusion that the structure of the image of a dislocation strongly depends on its position and orientation in the scattering triangle. It has been found that each point of the strongly distorted region of the elastic field of a dislocation becomes a source of a new wave field propagating under the dislocation in a new scattering triangle. This new field interferes with the primary wave field forming the observed diffraction image of a dislocation. The addition of these waves with regard to their amplitudes and phases results in a large variety of images of defects. A comparison of different dislocation orientations in the Borrmann triangle allowed us to evaluate the role of different effects determined by the interference of the initial and newly formed wave fields, to determine on this basis the main dislocation parameters, and to optimize the diffraction conditions of the topographic measurement for the investigation of elastic-field characteristics.     

An improved penalty immersed boundary method for fluid–flexible body interaction

An improved penalty immersed boundary (pIB) method has been proposed for simulation of fluid–flexible body interaction problems. In the proposed method, the fluid motion is defined on the Eulerian domain, while the solid motion is described by the Lagrangian variables. To account for the interaction, the flexible body is assumed to be composed of two parts: massive material points and massless material points, which are assumed to be linked closely by a stiff spring with damping. The massive material points are subjected to the elastic force of solid deformation but do not interact with the fluid directly, while the massless material points interact with the fluid by moving with the local fluid velocity. The flow solver and the solid solver are coupled in this framework and are developed separately by different methods. The fractional step method is adopted to solve the incompressible fluid motion on a staggered Cartesian grid, while the finite element method is developed to simulate the solid motion using an unstructured triangular mesh. The interaction force is just the restoring force of the stiff spring with damping, and is spread from the Lagrangian coordinates to the Eulerian grids by a smoothed approximation of the Dirac delta function. In the numerical simulations, we first validate the solid solver by using a vibrating circular ring in vacuum, and a second-order spatial accuracy is observed. Then both two- and three-dimensional simulations of fluid–flexible body interaction are carried out, including a circular disk in a linear shear flow, an elastic circular disk moving through a constricted channel, a spherical capsule in a linear shear flow, and a windsock in a uniform flow. The spatial accuracy is shown to be between first-order and second-order for both the fluid velocities and the solid positions. Comparisons between the numerical results and the theoretical solutions are also presented.     

像散光束的光束参数与光强二阶矩的关系

采用光束的二阶强度矩的方法讨论三维像散光束的光束特性。通过计算像散光束在自由空间、球面光学系统中的传输特性以及坐标系旋转时的变换特性 ,给出了光束的束腰位置、束腰半径、瑞利长度、有效波面曲率半径、近场和远场的方位角、光束的光束参数积等参数与光强二阶矩之间的关系。