Structures and Dynamics of a Two-Dimensional Confined Dusty Plasma System

The influence of the confining potential strength and temperature on the structures and dynamics of a two-dimensional （2D） dusty plasma system is investigated through molecular dynamic （MD） simulation. The circular symmetric confining potential leads to the nonuniform packing of particles, that is, an inner core with a hexagon lattice surrounded by a few outer circular shells. Under the appropriate confining potential and temperature, the particle trajectories on middle shells form a series of concentric and nested hexagons due to tangential movements of particles. Mean square displacement, self-diffusion constant, pair correlation function, and the nearest bond are used to characterize the structural and dynamical properties of the system. With the increase of the confining potential, the radial and tangential movements of particles have different behaviors. With the increase of temperature, the radial and tangential motions strengthen, particle trajectories gradually become disordered, and the system gradually changes from a crystal or liquid state to a gas state.     

二维荷电粒子维格纳晶格:边界效应

采用一种非线性的优化方法,研究了处于硬壁限制势下二维带电多粒子系统的基态,分析不同形状边界对系统基态构型的影响.由于圆形边界对称性高,基态结构和抛物限制势下情况相似.在正方形边界下,当系统粒子数N<66时,荷电粒子形成方形晶格;当N≥66时,由于边界影响被削弱,内层粒子形成六角维格纳晶格.进一步分析了椭圆和矩形边界对维格纳晶格的影响.     

Influence of the long-range forces in non-Gaussian random-packing dynamics

In this paper, we perform molecular dynamics (MD) simulations to study the random packing of spheres with different particle size distributions. In particular, we deal with non-Gaussian distributions by means of the Lévy distributions. The initial positions as well as the radii of five thousand non-overlapping particles are assigned inside a confining rectangular box. After that, the system is allowed to settle under gravity towards the bottom of the box. Both the translational and rotational movements of each particle are considered in the simulations. In order to deal with interacting particles, we take into account both the contact and long-range cohesive forces. The normal viscoelastic force is calculated according to the nonlinear Hertz model, whereas the tangential force is calculated through an accurate nonlinear-spring model. Assuming a molecular approach, we account for the long-range cohesive forces using a Lennard-Jones (LJ)-like potential. The packing processes are studied assuming different long-range interaction strengths.     

Coulomb clusters: melting and potential barriers

The melting of two-dimensional and three-dimensional Coulomb micro- and macroclusters is studied. Temperature dependences of radial and angular square deviations of particles are investigated. The melting of microclusters has two stages: at lower temperature there is a transition from a frozen phase to a state with a rotatory reorientation of “crystalline” shells relative to each other, different pairs of shells melting at different temperatures. In the case of large N and high triangular symmetry inside the cluster, orientational melting takes place only for external pairs of shells. In this case external shells lose their order. At higher temperature a transition with a loss of radial shell order occurs. The origin of two-stage melting is in the smallness of the barrier energy relative to the rotation of shells in comparison with the barrier corresponding to the radial disordering of shells. It is shown also that the temperatures of orientational and total melting are at 5–15 times lower than the temperatures of disappearance of corresponding potential barriers. The influence of confinement anisotropy on the character of cluster melting is considered. It is found that at some degree of anisotropy the melting becomes one stage. The last is connected with an increase of the ratios of barriers of intershell rotation to barriers of jumps of a particle between the shells.     

Competition between two forms of ordering in finite Coulomb clusters

The lowest-energy state of spherical clusters made up of single-species charged particles in a three-dimensional confining potential is investigated by molecular dynamics simulations for a system size of 5 x 10(3) to 1.2 x 10(5). The energy per particle is compared between shell-structured clusters and spherical finite-bcc lattices with relaxed surfaces. The shell structure in the interior is the lowest-energy configuration for ion numbers lower than about 10(4), while for higher ion numbers, an interior with bcc ordering surrounded by a few shells on the outside has lower energy. The formation of a small bcc lattice (nucleation) in the shell-structured cluster of 2 x 10(4) ions is observed.     

Ion current generation in the field ion microscope: I. dynamic approach

The numbers of gas particles arriving at unit tip surface in unit time from a field free region are derived as functions of velocity components for a spherical tip. It is shown that a considerable fraction of the gas particles arrives at the tip having large tangential velocities. The simple model of collision of a particle with a metal surface is used and the trajectories and rebounds of particles are tracked. The principal method to calculate the total ion current is shown. The capture probability of particles by the dipole attraction potential is shown to increase when the tip temperature is lowered, the field strength is increased, the mass ratio of the gas atom to the metal atom increases and the gas temperature is lowered.     

Orbital and epicyclic motion of charged test particles around non-rotating Einstein-Æther black holes

The study of charged test particle dynamics in the combined black hole gravitational field and magnetic field around it could provide important theoretical insight into astrophysical processes around such compact object. We have explored the orbital and epicyclic motion of charged test particles in the background of non-rotating Einstein-Æther black holes in the presence of external uniform magnetic field. We numerically integrate the equations of motion and analyze the trajectories of the charged test particles. We examined the stability of circular orbits using effective potential technique and study the characteristics of innermost stable circular orbits. We analyze the key features of quasi-harmonic oscillations of charged test particles nearby the stable circular orbits in an equatorial plane of the black hole, and investigate the radial profiles of the frequencies of latitudinal as well as radial harmonic oscillations in dependence on the strength of magnetic field, mass of the black hole and dimensionless coupling constants of the theory. We demonstrate that the magnetic field and dimensionless parameters of the theory have strong influence on charged particle motion around Einstein-Æther black holes.     

Dynamic Simulation of Random Packing of Polydispersive Fine Particles

In this paper, we perform molecular dynamic (MD) simulations to study the two-dimensional packing process of both monosized and random size particles with radii ranging from 1.0 to 7.0 μm. The initial positions as well as the radii of five thousand fine particles were defined inside a rectangular box by using a random number generator. Both the translational and rotational movements of each particle were considered in the simulations. In order to deal with interacting fine particles, we take into account both the contact forces and the long-range dispersive forces. We account for normal and static/sliding tangential friction forces between particles and between particle and wall by means of a linear model approach, while the long-range dispersive forces are computed by using a Lennard-Jones-like potential. The packing processes were studied assuming different long-range interaction strengths. We carry out statistical calculations of the different quantities studied such as packing density, mean coordination number, kinetic energy, and radial distribution function as the system evolves over time. We find that the long-range dispersive forces can strongly influence the packing process dynamics as they might form large particle clusters, depending on the intensity of the long-range interaction strength.     

Rigid and differential plasma crystal rotation induced by magnetic fields

Observations show that plasma crystals, suspended in the sheath of a radio-frequency discharge, rotate under the influence of a vertical magnetic field. Depending on the discharge conditions, two different cases are observed: a rigid-body rotation (all the particles move with a constant angular velocity) and sheared rotation (the angular velocity of particles has a radial distribution). When the discharge voltage is increased sufficiently, the particles may even reverse their direction of motion. A simple analytical model is used to explain qualitatively the mechanism of the observed particle motion and its dependence on the confining potential and discharge conditions. The model takes into account electrostatic, ion drag, neutral drag, and effective interparticle interaction forces. For the special case of rigid-body rotation, the confining potential is reconstructed. Using data for the radial dependence of particle rotation velocity, the shear stresses are estimated. The critical shear stress at which shear-induced melting occurs is used to roughly estimate the shear elastic modulus of the plasma crystal. The latter is also used to estimate the viscosity contribution due to elasticity in the plasma liquid. Further development is suggested in order to quantitatively implement these ideas.     

Two-dimensional Abrikosov-vortex microclusters: Shell structure and melting

Melting of two-dimensional Abrikosov-vortex microclusters in a type-II superconductor island with thickness less than the coherence length has been studied. Equilibrium configurations corresponding to local and global minima of potential energy for clusters with N=1–50 particles are calculated. The temperature dependences of the structure and of mean-square radial and angular vortex displacements are investigated. It is shown that vortex microclusters melt in two stages: first the frozen-out phase transfers to a state corresponding to rotational reorientation of crystalline shells with respect to one another, followed by a transition to a state with no radial order at a substantially higher temperature. The reason for this is that the barrier to shell rotation is significantly lower than that to radial breakdown of shells. Fiz. Tverd. Tela (St. Petersburg) 39, 1005–1010 (June 1997)     

Melting properties of two-dimensional multi-species colloidal systems in a parabolic trap

The angular and radial melting properties of two-dimensional classical systems consisting of different types of particles confined in a parabolic trap are studied through modified Monte Carlo simulations. A universal behavior of the angular melting process is found, which occurs in multiple steps due to shell depended melting temperatures. The melting sequence of the different shells is determined by two major factors: (1) the confinement strength which each shell is subjected to, and (2) the specific structure of each shell. Further, a continuous radial disordering of the particle types forming a single circular shell is found and analyzed. This phenomenon has never been observed before in two-dimensional mono-dispersive systems. This continuous radial disordering results from the high energy barrier between different particle types in multi-species systems.     

完美涡旋光中微米级粒子的受力与力矩特性分析

基于紧聚焦方法在几何焦平面处获得了完美涡旋光场,理论分析了该光场中微米级尺寸微粒受到的光学力与轨道矩。结果表明,该完美涡旋光可以在横平面上捕获微粒并驱动其绕光轴做轨道旋转运动,微粒受到的轨道矩随着拓扑荷的增大先增大后趋近于稳定。此外,分析了圆偏振、径向偏振和方位角偏振完美涡旋光对微粒施加的光学力和轨道矩。结果表明完美涡旋光的偏振态在一定程度上会影响微粒的轨道运动,圆偏振完美涡旋光更适合用于诱导微粒轨道旋转。     

Structure and melting of dipole clusters

Two-dimensional clusters of particles, repelling due to dipole-dipole interactions and confined by an external parabolic potential, are considered. The model describes different physical systems, particularly electrons in semiconductor structures, or electrons above a drop of He near a metal electrode, a drop of colloid liquid etc. Two kinds of ordering are in competition in the clusters: a triangular lattice and a shell structure. The ground-state configurations corresponding to the local and global minima of the potential energy for clusters with N = 1 – 40 “particles” are calculated. The structure, the potential energy and the radial and angular r.m.s. displacements as functions of temperature are also calculated. Analysing these quantities the melting of clusters is studied. One- or two-stage melting occurs depending on the number of particles in the cluster. In the case of clusters consisting of two shells melting has two stages: at lower temperature reorientation of neighbouring shells (“orientational melting”) arises; at much higher temperatures the radial shell order disappears. In clusters consisting of more than two shells total melting occurs as a first-order one-stage transition (analogously to a dipole crystal). This is connected with the barrier of rotation being less than the barrier of interchange of particles between shells for small microclusters while the barriers are of equal order for clusters with a greater number of particles.     

Structure and melting of dipole clusters

Two-dimensional microclusters made up of particles repelled by the dipole law and confined by an external quadratic potential are considered. The model describes a number of physical systems, in particular, electrons in semiconductor structures near a metallic electrode, indirect excitons in coupled semiconductor dots etc. Two competing types of particle ordering in clusters have been revealed: formation of a triangular lattice and of a shell structure. Equilibrium configurations of clusters with N=1–40 particles are calculated. Temperature dependences of the structure, potential energy, and mean-square radial and angular displacements are studied. These characteristics are used to investigate cluster melting. Melting occurs in one or two stages, depending on N. Melting of a two-shell microcluster takes place in two stages: at low temperatures—from the frozen phase to a state with rotationally reoriented “crystalline” shells with respect to one another, followed by a transition involving breakdown of radial order. Melting in a cluster made up of a larger number of shells occurs in one stage. This is due to the fact that the potential barrier to intershell rotation is substantially lower than that to particle jumping from one shell to another for small N, and of the same order of magnitude for large N. A method is proposed for predicting the character of melting in shell clusters by comparing the potential barriers for shell rotation and intershell particle jumping. Fiz. Tverd. Tela (St. Petersburg) 40, 1379–1386 (July 1998)     

Adiabatic description of impenetrable particles in an infinitely deep potential well

In the framework of adiabatic approximation the energy spectrum and wave functions of two impenetrable particles in an infinitely deep potential well are considered for two cases of approximation of the effective confining potential of the ??slow?? subsystem. In case of the quadraticterm approximation the obtained energy spectrum is equidistant. The probability distribution in the range of ??fast?? particle has a symmetric shape while that in the range of the ??slow?? particle is asymmetric and the peak of localization of the system in its ground state is shifted towards the ??fast?? particle. In the first excited state the center of the probability distribution of the ??slow?? particle is shifted towards the impenetrable wall.     

Models of spherical shells as sources of Majumdar–Papapetrou type spacetimes

By starting with a seed Newtonian potential–density pair we construct relativistic thick spherical shell models for a Majumdar–Papapetrou type conformastatic spacetime. As a simple example, we considerer a family of Plummer–Hernquist type relativistic spherical shells. As a second application, these structures are then used to model a system composite by a dust disk and a halo of matter. We study the equatorial circular motion of test particles around such configurations. Also the stability of the orbits is analyzed for radial perturbation using an extension of the Rayleigh criterion. The models considered satisfying all the energy conditions.     

Hydrodynamic pair attractions between driven colloidal particles

Colloidal spheres driven through water along a circular path by an optical ring trap display unexpected dynamical correlations. We use Stokesian dynamics simulations and a simple analytical model to demonstrate that the path's curvature breaks the symmetry of the two-body hydrodynamic interaction, resulting in particle pairing. The influence of this effective nonequilibrium attraction diminishes as either the temperature or the stiffness of the radial confinement increases. We find a well-defined set of dynamically paired states whose stability relies on hydrodynamic coupling in curving trajectories.     

Event-driven simulations of insulating grains in an external electric field

In this work we employ event-driven particle dynamics simulations for a system of spherical insulating grains interacting with an external electric field. This system resembles the electrostatic particle separation present on some industrial processes. Here, the particles collide inelastically with each other and with the container walls, for a constant normal and tangential restitution coefficients. During the collisions, the grains can acquire electric charge due to triboelectric contact charging, since two different species of insulating particles are mixed. Particle-particle electric interactions are not considered. Grains are also subjected to the gravitational field and rotation, and are confined in a cubic box with thermal walls in order to prevent the static equilibrium state. We calculate the mass and charge density profile, and the particle charge distribution for different values of the electric field and temperature of the walls. The particle charge distribution and the effect of particle sizes on the separation process were also investigated.     

Heating of Powders in the Fire Ball of an Induction Plasma

A theoretical model has been developed for the calculation of the trajectories and temperature histories of particles injected in the fire-ball of an inductively coupled plasma. Calculations were made for alumina particles of different diameters ranging between 10 and 250 ?m. The particles were injected through a water cooled probe upstream of the fire-ball. The results shows that the internal plasma recirculation in the coil region is responsable for the bouncing of the particles on the fire-ball. Particles of the order of 10 ?m and smaler are entrained in the fire-ball by the inward radial flow caused by the electromagnetic pumping, and are subsequently completely evaporated. Larger particles, depending on their initial position and velocity of injection, could by-pass the plasma fire-ball, and in some cases, end up deposited on the wall of the plasma confining tube. Particles with diameters larger than 100 ?m were found to pass straight through the fire-ball when injected close to the center line of the torch.     

Theorie der spontanen Magnetisierung kleiner ferromagnetischer Teilchen

With a modified conception of the Néel sublattices a molecular field theory is developed for small ferromagnetic particles. They are treated as a system of neighboring shells. These are supposed to consist each of atoms with equal average properties and are coupled to the next neighbors by an (exchange-) interaction. To simplify the numerical calculations the model was further modified by taking together all shells of the interior to form a core. Calculations of the temperature dependence of the spontaneous magnetization and of Curie-temperatures have been done for some particle forms and sizes of the f.c.c., b.c.c. and hexagonal lattices. The results are discussed and compared to experimental data of other authors from small particles of nickel, iron and cobalt.