Small amplitude approximation and stabilities for dislocation motion in a superlattice

Starting from the traveling wave solution, in small amplitude approximation, the Sine-Gordon equation can be re- duced to a generalized Duffing equation to describe the dislocation motion in a superlattice, and the phase plane properties of the system phase plane are described in the absence of an applied field. The stabilities are also discussed in the presence of an applied field. It is pointed out that the separatrix orbit describing the dislocation motion as the kink wave may transfer the energy along the dislocation line, keep its form unchanged, and reveal the soliton wave properties of the dislocation motion. It is stressed that the dislocation motion process is the energy transfer and release process, and the system is stable when its energy is minimum.     

Sound generated by a vortex convected past an elastic sheet

We study the motion and sound generated when a line vortex is convected in a uniform low-Mach flow parallel to a thin elastic sheet. The linearized sheet motion is analyzed under conditions where the unforced sheet (in the absence of the line vortex) is stationary. The vortex passage above the sheet excites a resonance mode of motion, where the sheet oscillates at its least stable eigenmode. The sources of sound in the acoustic problem include the sheet velocity and fluid vorticity. It is shown that the release of trailing-edge vortices, resulting from the satisfaction of the Kutta condition, has two opposite effects on sound radiation: while trailing-edge vortices act to reduce the pressure fluctuations occurring owing to the direct interaction of the line vortex with the unperturbed sheet, they extend and amplify the acoustic signal produced by the motion of the sheet. The sheet motion radiates higher sound levels as the system approaches its critical conditions for instability, where the effect of resonance becomes more pronounced. It is argued that the present theory describes the essential mechanism by which sound is generated as a turbulent eddy is convected in a mean flow past a thin elastic airfoil.     

原子-场强度相关耦合时原子质心平移运动与内态布居的关系

基于原子与腔场共振相互作用及原子-场缀饰态,讨论了驻波腔场中两能级原子与场耦合强度相关时的原子质心的量子化平移运动对原子内态布居间的相互影响。结果表明原子平移运动敏感地依赖于原子的内态布居。特别地,当原子处于两内态等权重同位相迭加态时,平移运动呈现出很稳定的特征。     

Towards a Quantum Bag Dynamics (Ⅲ)-Collective Motion of the Bag

It is showed, that under the adiabatic assumption, the quark-gluon state and the energy of a dynamic bag may be expressed as functions of its collective coordinates and their first time derivatives. The effective-lagrangian and IIamiltonian for the collective motion arethen proposed. The classical equation of coJJective motion is suggested to be used as the self-consistent equation for the force function f(R, R). The bag dynanlics is once again quantized. A set of ellipsoids and their finite combinations is recommended as a complete set of bag shapes because of its Lorentz invariance. The wave function for tlle internal motion of a hadron is therefore a function of the bag shape configuration..It may be used to average intrinsic observables and matrix elements of a hadron over the shape configuration. The zero momentum eigenstate of a hadron is constructed by making use of its translational symmetry. Finite momentum eigenstates are then constructed by Lorentz boosts. Multi-hadron states and hadron interactions are also considered.     

Ehrenfest Time at the Transition from Integrable Motion to Chaotic Motion

Ehrenfest time depends differently on the Planck constant in integrable motion and chaotic motion. We study how its dependence on the Planck constant changes when there is a continuous transition from regular motion to chaotic motion. We find that the dependence is a weighted compromise between its two distinct dependences in regular and chaotic motions. The study is carried out with the system of periodically driven anharmonic oscillator. As the system is quite typical, the result may apply generally.     

The exciton dead layer revisited

Although the exciton in a quantum well is not a rigid ball but distords when its center of mass gets close to a surface, it is mathematically possible to write the exciton energy change from its bulk value as an effective decrease of the well width in which the center of mass would freely move. In the large well limit, the exciton dead layer defined this way is related to the third order term in the expansion of the exciton energy as a function of the inverse well width. A quite precise calculation of this exciton energy is thus necessary to obtain this dead layer. We present a new calculation which relies on a Born-Oppenheimer procedure to decouple the relative motion of the e-h pair from its center of mass motion. This is associated to a quite precise calculation of the relative motion energy, based on our recent work on the exact envelope function for confined motion. We predict that the dead layer increases with the exciton total mass in contradiction with previous results.     

GREEN FUNCTION THEORY AND ITS GLOBAL STRUCTURE

The Green function theory is successful in many fields of theoretical physics and the Bogoliubov-Gor'kov theory system is its important branch that involves many theoretical methods. In the last twenty years many papers have been published, but as all the equations of motion are coupled and their number is infinite, its global structure problem has not been investigated as yet. This paper is devoted to the study of its global structure, the exact decoupling problem, and the uniqueness and completeness problems. Some higher order spectral representation theorems and exact relationships between higher and lower order Green functions are obtained. Thus the equations of motion are decoupled exactly. In this paper it is proved that after cutting off the equations of motion are decoupled exactly and the solution of these equationsystemsmay not be unique. It is also proved that if there is one solution satisfying all the Green function's equations, then there must be a solution set, all of them satisfy all the equations and its number is infinite and the differences between them are arbitrary. By adding some limitations to ImG(x) at the regal axis a uniqueness theorem is proved.     

Note on the Time Reversal Symmetry of Equations of Motion

Rohrlich's recent claim that the equation of motion for a point charge is symmetric under time reversal is shown to be the result of an inappropriate definition. The equation of motion for a charged sphere of finite size, which is claimed, in contrast, to be asymmetric because of the finite propagation time of its (retarded) self-forces, is shown to possess the same asymmetry (or the same symmetry, depending on the definition) as that for a point charge. The arguments apply similarly to other equations of motion.     

Onset of 3D collective surface diffusion in the presence of lateral interactions: Na/Cu(001)

3He spin-echo measurements are used to follow the picosecond motion of sodium atoms on a copper (001) substrate. 2D correlated motion arising from repulsive adsorbate interactions is observed for coverages as low as 0.04 ML. At coverages greater than 0.05 ML there is a pronounced onset of motion perpendicular to the surface. The perpendicular motion is thermally activated and seems related to the basic translational hopping diffusion process. The correlated motion is modeled successfully using a molecular dynamics simulation and a dipolelike lateral interaction. A simple model which relates the apparent height of the atom with its local coverage is shown to reproduce the experimental observations.     

Electric field accompanying the motion of a body in air

Air flow electrization induced by the motion of bodies made of different materials is studied experimentally by detecting a potential appearing at an annular antenna through which the body passes. It is found that the motion of the body is accompanied by the motion of two unlike charges. The positions of the charges relative to the moving body versus its length are determined. Some parameters influencing the value of the charges are considered. It is shown that the kinematics of the body can be determined by recording an electric field accompanying its motion.     

Dynamical symmetries and conservation laws for Korteweg-de Vries equation

The KdV-equation in two space time dimensions with the set of rapidly decreasing test functions as initial conditions is treated in the setting of nonlinear group and Lie algebra representations. The topological properties of the direct and inverse scattering mappings are discussed in detail.The algebra of continuous constants of motion turns out to be generated as in the linear case by three constants of motion and an extension of a representation of the e₂ Lie algebra on space-time symmetries to its enveloping algebra. The integrability of these representations is studied.It is further proved that the “moment problem” does not have a unique solution in this setting.The existence of noncommutative algebras of smooth time independent constants of motion is pointed out.     

Low-dimensionality energy landscapes: Magnetic switching mechanisms and rates

In this paper we propose a new method for the study and visualization of dynamic processes in magnetic nanostructures, and for the accurate calculation of rates for such processes. The method is illustrated for the case of switching of a grain of an exchange-coupled recording medium, which switches through domain wall nucleation and motion, but is generalizable to other rate processes such as vortex formation and annihilation. The method involves calculating the most probable (lowest energy) switching path and projecting the motion onto that path. The motion is conveniently visualized in a two-dimensional (2D) projection parameterized by the dipole and quadrupole moment of the grain. The motion along that path can then be described by a Langevin equation, and its rate can be computed by the classic method of Kramers [4]. The rate can be evaluated numerically, or in an analytic approximation—interestingly, the analytic result for domain-wall switching is very similar to that obtained by Brown in 1963 for coherent switching, except for a factor proportional to the domain-wall volume. Thus in addition to its lower coercivity, an exchange-coupled medium has the additional advantage (over a uniform medium) of greater thermal stability, for a fixed energy barrier.     

A meta-analysis on the effects of haphazard motion of tiny/nano-sized particles on the dynamics and other physical properties of some fluids

Decline in the theoretical and empirical review of Brownian motion is worth noticing, not just because its relevance lies in the field of mathematical physics but due to unavailability of statistical technique. The ongoing debate on transport phenomenon and thermal performance of various fluids in the presence of haphazard motion of tiny particles as explained by Albert Einstein using kinetic theory and Robert Brown is further clinched in this report. This report presents the outcome of detailed inspections of the significance of Brownian motion on the flow of various fluids as reported in forty-three (43) published articles using the method of slope linear regression through the data point. The technique of slope regression through the data points of each physical property of the flow and Brownian motion parameter was established and used to generate four forest plots. The outcome of the study indicates that an increase in Brownian motion corresponds to an enhancement of haphazard motion of tiny particles. In view of this, there would always be a significant difference between the corresponding effects when Brownian motion is small and large in magnitude. Maximum heat transfer rate can be achieved due to Brownian motion in the presence of thermal radiation, thermal convective and mass convective at the wall in three-dimensional flow. In the presence of heat convective and mass convective at the wall, and thermal radiation, a significant increase in Nusselt number due to Brownian motion is guaranteed. A decrease in the concentration of fluid substance due to an increase in Brownian motion is bound to occur. This is not achievable in the case of high entropy generation and homogeneous-heterogeneous quartic autocatalytic kind of chemical reaction.     

Breathing motion of a kink-bag system in (1 + 1) dimensions: Inertia of the vacuum confined in a bag

We examine the breathing motion of a (1 + 1)-dimensional hybrid bag where the confined quarks are coupled with a solitonic chiral field at the bag boundary. The hybrid bag is a toy model for the (1 + 3)-dimensional skyrmion-bag system and its breathing motion has close connection with the excited states of a nucleon such as the Roper resonance. The collective lagrangian for the motion is derived microscopically by focusing on the polarized Dirac sea inside the bag. The mass parameter of the motion is decreased compared with the MIT-bag one owing to the negative contribution from the inertia of the confined vacuum. As a result, the spectra of the motion do not have too low excitation energies despite that the potential energy surface is softened by the vacuum effect.     

周期弯晶作为束流控制元件的动力学稳定性

在经典力学框架内和偶极近似下,引入正弦平方势,把粒子运动方程化为具有阻尼项和受迫项的广义摆方程。利用Melnikov方法讨论了沟道运动次谐分叉及其稳定性, 导出了周期弯晶的临界条件和退道长度。结果表明, 要试图获得高的引出效率, 除了要求弯晶长度必须小于退道长度外, 还必须保证沟道粒子的运动是稳定的。对临界条件的分析表明, 系统的稳定性与它的参数有关, 只须适当调节系统参数, 就可以保证周期弯晶作为引出元件的稳定性。In the classical mechanics frame and with a dipole approximation the particle motion equation in the periodic bent crystal is reduced to the general pendulum equation with a damping term and the forced term by using the sine squared potential． This paper discusses the problem of the sub harmonic bifurcation of the periodic orbit and the stabilities of the channeling motion by using Melnikov method, so as to derive the critical condition and the dechanneling length of the periodic bent crystal. The results show that channeling motion must be stable in addition that the crystal length is smaller than the dechanneling length in order to ensure higher extracted efficiency. The analysis of the critical condition shows that the system stabilities are related to its parameters. Just by properly regulating the parameters of the system, the dynamic stabilities by the use of periodic bent crystal as beam control cell can be ensured.     

W-symmetry and the rigid particle

We prove that W₃ is the gauge symmetry of the scale-invariant rigid particle, whose action is given by the integrated extrinsic curvature of its world line. This is achieved by showing that its equations of motion can be written in terms of the Boussinesq operator. The W₃ generators T and W then appear respectively as functions of the induced world line metric and the extrinsic curvature. We also show how the equations of motion for the standard relativistic particle arise from those of the rigid particle whenever it is consistent to impose the “zero-curvature gauge”, and how to rewrite them in terms of the KdV operator. The relation between particle models and integrable systems is further pursued in the case of the spinning particle, whose equations of motion are closely related to the SKdV operator. We also partially extend our analysis in the supersymmetric domain to the scale-invariant rigid particle by explicitly constructing a supercovariant version of its action.     

Particle motion in guide potentials and the collective nuclear motion

The motion of a particle which is constrained by a guide potential to move on a curve is studied in the framework of the Generator Coordinate Method (GCM). In the limit of narrow guide potentials a differential equation for the wave function of the constrained motion is obtained which differs from the corresponding Schrödinger equation by an additional potential. This additional potential is due to the embedding of the curve in the space and depends on the form of the guide potential and on the curvature of the curve. Nonadiabatic transitions in the constrained motion are possible for finite widths of the guide potential. The coupling terms are given explicitly and it is shown that an adiabatic limit exists. Since the GCM can equally well describe the collective motion of nuclei, some insight into the more complicated problem of collective motion is obtained from its analogies to the studied problem of constrained particle motion: The collective motion of a nucleus can be considered as the motion of a particle with variable mass along a curve in a guide potential which is given by the interaction potential between the nucleons. It is shown that Schrödinger's quantized kinetic energy is correctly used in the cranking model and that the additional potential terms mentioned above are included there by the definition of the collective potential energy. Approximations to the idealized GCM used here are discussed and the connection with the method of Born, Oppenheimer and Villars is indicated.     

Kinetic equation for the dilute Lorentz gas with attractive forces

The kinetic equation for the dilute Lorentz gas of particles with repulsive-attractive potential, is derived. For that purpose the distribution function is decomposed into two parts: the one corresponding to the bounded motion of the marked particle and the second corresponding to its unbounded motion; only the second part, as representing the diffusion, is considered.After the appropriate modification of the projection operator, a general kinetic equation for the diffusion part of the distribution function is obtained. The low density limit of the scattering operator of this equation is found. The regions of bounded motion are excluded in the integration over position space.For the square-well potential, the Laplace-transformed kinetic equation is also given in full detail.