孤立波在一维复合颗粒链中传播特性的模拟研究

采用分子动力学方法模拟研究了孤立波在重轻颗粒相间排列的一维复合颗粒链中的传播特性.结果发现,在轻重颗粒的质量比较大或较小时,散射作用较弱,颗粒的速度和孤立波的速度衰减较慢.在轻重颗粒的质量比为中等时,散射作用较强,颗粒的速度和孤立波的速度衰减较快.孤立波在通过重-轻颗粒界面时,存在有增速效应,可以提高孤立波的传播速度.并且,轻重颗粒的质量比越小增速效应越强.在散射作用和增速效应的共同作用下,改变轻重颗粒的质量比可以调控孤立波在重-轻颗粒链中的传播时间.     

Gain/loss effect on bright solitary wave in a cigar-shaped attractive condensate in the presence of expulsive parabolic potential

<正>Taking into account both gain/loss and time-dependent atomic scattering length,this paper analytically derives an exact bright solitary wave in a cigar-shaped attractive condensate in the presence of an expulsive parabolic potential. Due to the balance of the scattering length and gain/loss,the bright solitary wave is shown to have constant amplitude. Especially,it is found that the bright solitary wave is accelerated by expulsive force,whose velocity can be modulated by changing the axial and transverse angular frequencies.The results are in good agreement with the experimental observations by Khaykovich et al(2002 Science 296 1290).     

Simulation studies of the scattering of a solitary wave by a mass impurity in a chain of nonlinear oscillators

We have simulated large amplitude motion in cyclic one-dimensional lattices of Morse potential oscillators with a mass impurity, and have observed an unexpected persistence of solitary wave behavior for which we are unable to discover a satisfactory explanation. In solitary wave motion as a function of cycle length and of initial energy, the most common feature of the dynamics is an initial energy plateau with regular oscillatory energy exchange between the solitary wave and other excitations of the lattice, followed by rapid decay. Some systems show no decay at all through 1000 impurity interactions, while others show no significant plateau before decaying. For some cycle lengths there are energy bands in which the solitary wave propagates indefinitely long, with small amplitude oscillatory exchange of energy with the lattice. No regularities were found.     

基于温度效应的无限长压电圆杆纵波分析

利用有限变形理论,以无限长压电圆杆为研究对象,考虑了在横向惯性、等效泊松比效应以及在热电弹藕合共同作用下,基于Hamilton原理,并引入Euler方程推导出压电圆杆的纵向波动方程.采用Jacobi椭圆函数展开法,求解压电圆杆的波动方程和对应的解.最后,通过Matlab软件得到不同波速比下的色散曲线.以及温度场对压电圆杆的波形、波幅和波数的影响曲线.数值分析结果表明:随着温度的升高,波速逐渐降低,温度场的改变可影响和控制孤立波的传播特性.     

Propagation dynamics on the Fermi-Pasta-Ulam lattices

The spatiotemporal propagation of a momentum excitation on the finite Fermi-Pasta-Ulam lattices is investigated. The competition between the solitary wave and phonons gives rise to interesting propagation behaviors. For a moderate nonlinearity, the initially excited pulse may propagate coherently along the lattice for a long time in a solitary wave manner accompanied by phonon tails. The lifetime of the long-transient propagation state exhibits a sensitivity to the nonlinear parameter. The solitary wave decays exponentially during the final loss of stability, and the decay rate varying with the nonlinear parameter exhibits two different scaling laws. This decay is found to be related to the largest Lyapunov exponent of the corresponding Hamiltonian system, which manifests a transition from weak to strong chaos. The mean-free-path of the solitary waves is estimated in the strong chaos regime, which may be helpful to understand the origin of anomalous conductivity in the Fermi-Pasta-Ulam lattice.     

Binary collision approximation for solitary waves in a Y-shaped granular chain

We implement a binary collision approximation to study solitary wave propagation in a two-dimensional double Y-shaped granular chain. The solitary wave was transmitted and reflected when it met the interface of the bifurcated branches of the Y-shaped granular chains. We obtain the analytic results of the ratios of the transmitted and reflected speeds to the incident speed of the solitary wave, the maximum force between the two neighbor beads in a solitary wave, and the total time taken by the pulse to pass through each branch. All of the analytic results are in good agreement with the experimental observations from Daraio et al. [Phys. Rev. E 82 036603 (2010)]. Moreover, we also discuss the delay effects on the arrival of split pulses, and predict the recombination of the split waves traveling in branches in the final stem of asymmetric systems. The prediction of pulse recombination is verified by our numerical results.     

Behavior of reaction-diffusion waves with fast activator diffusion near propagation threshold

Numerical simulation is performed to analyze behavior of reaction-diffusion waves in a medium whose parameters are near both the propagation threshold and diffusive (oscillatory) instability boundary. The wave decays in the subthreshold parameter region and propagates at a constant velocity in the parameter region well above the threshold. Just above the threshold, the wave velocity exhibits alternate intervals of chaotic and constant-amplitude oscillations. The transition from steady to chaotic propagation is a sequence of period-doubling bifurcations that occupies a narrow interval of the bifurcation parameter. In the subthreshold region, the wave decay time is a random function of the bifurcation parameter increasing on average toward the threshold.     

Determination of heavy-meson wave functions from B decays

We extract the B, D, and meson wave functions from the CLEO data of the decays and in the perturbative QCD framework. In this formalism, various logarithmic corrections are organized to give the Wilson evolution from the W boson mass down to the characteristic scale of a decay process, which is of order of the b quark mass, and the Sudakov evolution from the characteristic scale to a lower factorization scale of order . With large logarithms organized, the b quark decay amplitudes are evaluated reliably in perturbation theory. Below the factorization scale, QCD dynamics is regarded as being nonperturbative, and absorbed into meson wave functions. Because of their universality, the heavy-meson wave functions determined in this work, can be employed to make predictions of other decay modes. We also observe that the dependence of heavy meson wave functions on intrinsic parton transverse momenta plays an important role in the explanation of data. Received: 18 February 1999 / Revised version: 24 June 1999 / Published online: 3 November 1999     

Formation of solitary structures and envelope solitons in electron acoustic wave in inner magnetosphere plasma with suprathermal ions

The propagation of electron acoustic solitary waves is investigated in magnetized two-temperature electron plasma with supra-thermal ion. By using the reductive perturbation technique, the Korteweg de-Vries (KdV) equation is derived. Later solving this equation, a solitary wave solution has been derived. These are mainly in astrophysical plasmas where changes of local charge density, temperature, and energy of particles produce considerable effects on the plasma system. The effects of supra-thermality, density, and Mach number on solitary structures are studied in detail. The results show that the supra-thermal index (κ) and ion to electron temperature ratio (σ) alters the regime where solitary waves may exist. While studying the solitary profile for different parametric variation some interesting conclusion can be drawn; it is shown that the solitary profile becomes flatter. This can be due to the thermal energy associated with the hot electrons. However, with the increase in ion density with respect to the cold electrons' density, the solitary waves become steeper and sharper. This is due to the comparatively heavier mass of ions. The density of cold electron also increases the solitary structures in a similar manner. The higher the density of cold electrons, sharper will be the profile. The above findings will be helpful in understanding many astrophysical phenomena and data obtained by space missions. For a further study, we keep the investigation of the formation of other kinds of stationary structures like shocks, double layers, etc.     

Ion acoustic solitary wave in an inhomogeneous plasma with non-uniform temperature

A modifiedK-dV equation, which describes the propagation of an ion acoustic solitary wave in an inhomogeneous plasma with both density and temperature gradients, is derived. It is shown that, the velocity of a solitary wave increases as it propagates towards regions of increasing temperature.     

Modulational instability of relativistic ion-acoustic waves in aplasma with trapped electrons

The association between the modified Korteweg-de Vries solitary wave and the modulationally unstable envelope solitary wave in a weakly relativistic unmagnetized plasma with trapped electrons is discussed. The effect of trapped electrons modifies the nonlinearity of the nonlinear Schrodinger equation and gives rise to the propagation of the modulationally unstable ion-acoustic solitary wave. The amplitude of the envelope solitary wave increases while the number of trapped electrons decreases. The velocity of the solitary wave decreases with increasing ionic temperature and increasing particle velocities. The ion oscillation mode, which satisfies the nonlinear dispersion relation, is also derived. The theory is applied to explain space observations of the solar energetic flows in interplanetary space and of the energetic particle events in the Earth's magnetosphere     

Nonlinear dynamics of the interface between fluids at the suppression of Kelvin–Helmholtz instability by a tangential electric field

The nonlinear dynamics of the interface between ideal dielectric fluids in the presence of tangential discontinuity of the velocity at the interface and the stabilizing action of the horizontal electric field is examined. It is shown that the regime of motion of the interface where liquids move along the field lines occurs in the state of neutral equilibrium where electrostatic forces suppress Kelvin–Helmholtz instability. The equations of motion of the interface describing this regime can be reduced to an arbitrary number of ordinary differential equations describing the propagation and interaction of structurally stable solitary waves, viz. rational solitons. It is shown that weakly interacting solitary waves recover their shape and velocity after collision, whereas strongly interacting solitary waves can form a wave packet (breather).     

Field theory on a non‐commutative plane: a non‐perturbative study

The 2d gauge theory on the lattice is equivalent to the twisted Eguchi–Kawai model, which we simulated at N ranging from 25 to 515. We observe a clear large N scaling for the 1‐ and 2‐point function of Wilson loops, as well as the 2‐point function of Polyakov lines. The 2‐point functions agree with a universal wave function renormalization. The large N double scaling limit corresponds to the continuum limit of non‐commutative gauge theory, so the observed large N scaling demonstrates the non‐perturbative renormalizability of this non‐commutative field theory. The area law for the Wilson loops holds at small physical area as in commutative 2d planar gauge theory, but at large areas we find an oscillating behavior instead. In that regime the phase of the Wilson loop grows linearly with the area. This agrees with the Aharonov‐Bohm effect in the presence of a constant magnetic field, identified with the inverse non‐commutativity parameter. Next we investigate the 3d λϕ⁴ model with two non‐commutative coordinates and explore its phase diagram. Our results agree with a conjecture by Gubser and Sondhi in d = 4, who predicted that the ordered regime splits into a uniform phase and a phase dominated by stripe patterns. We further present results for the correlators and the dispersion relation. In non‐commutative field theory the Lorentz invariance is explicitly broken, which leads to a deformation of the dispersion relation. In one loop perturbation theory this deformation involves an additional infrared divergent term. Our data agree with this perturbative result. We also confirm the recent observation by Ambjø rn and Catterall that stripes occur even in d = 2, although they imply the spontaneous breaking of the translation symmetry.     

Growth of discontinuities in chemically reacting relativistic fluids

A relativistic theory is developed to study the growth of weak discontinuities propagating in a chemically reacting fluid mixture. The velocity of propagation is determined, which fully agrees with classical results in the nonrelativistic limit. The growth equation for the wave propagation in relativistic fluid flows with nonequilibrium effects is obtained and solved. The wave amplitude is determined as a function of time. The relativistic and relaxation effects on the global behavior of the wave amplitude are studied analytically. It is concluded that if the wave is of a compressive nature and its initial amplitude is greater than a critical value, then the discontinuity grows until it develops into a shock wave after a finite critical timet _c . But on the other hand if the initial wave amplitude is less than the critical one, the wave decays and damps out ultimately. It is shown that both relativistic and relaxation effects help in stabilizing the wave propagation by increasing the critical timet _c for the breakdown of the wave due to nonlinear steepening.     

Fermi-Pasta-Ulam β 格点链系统能量载流子研究

Fermi-Pasta-Ulam (FPU) β格点链中能量输运的载流子是孤子还是声子一直存在较多的争议. 本文通过单脉冲方法, 明确了一个能量波包在该格点链系统中从声子波包转变成为孤子波包的条件, 即波包能量达到一定阈值. 基于纯四次势链的声子真空效应, 构造了由FPU-β链与纯四次势链构成的双段链系统. 通过对比研究双段链系统和单段FPU-β链中的热流, 发现低温下声子是FPU-β链中能量的主要载流子, 而随着温度的升高孤子逐步取代声子成为能量的主要载流子. 关键词： Fermi-Pasta-Ulam格点链 声子 孤子 热传导     

First passage time in a two-layer system

As a first step in the first passage problem for passive tracer in stratified porous media, we consider the case of a two-dimensional system consisting of two layers with different convection velocities. Using a lattice generating function formalism and a variety of analytic and numerical techniques, we calculate the asymptotic behavior of the first passage time probability distribution. We show analytically that the asymptotic distribution is a simple exponential in time for any choice of the velocities. The decay constant is given in terms of the largest eigenvalue of an operator related to a half-space Green's function. For the anti-symmetric case of opposite velocities in the layers, we show that the decay constant for system lengthL crosses over fromL ^–2 behavior in the diffusive limit toL ^–1 behavior in the convective regime, where the crossover lengthL ^* is given in terms of the velocities. We also have formulated a general self-consistency relation, from which we have developed a recursive approach which is useful for studying the short-time behavior.     

修正高阶非线性薛定锷方程的解析孤波解

解析求解了考虑喇曼自频移效应后的修正高阶非线性薛定锷方程.为了获得精确解,引入了非线性增益和失谐效应.结果给出精确亮孤波解和暗孤波解的表达式,同时给出了两种解存在的参量条件,并且指出亮孤波解存在于负三阶色散区,而暗孤波解存在于正三阶色散区.     

Extended Schwinger-Boson theory of the two-dimensional spin-1/2 anisotropic Heisenberg antiferromagnets

The properties of the possible solitary electromagnetic waves, propagating in two-dimensional SIS Josephson junction without dissipative losses are investigated on the basis of the local theory of the junction. A classification of the waves in the junction with respect to the Swihart velocity is made. It is shown that allowed and forbidden areas for the wave numbers, wave frequency and wave amplitude exist. The cut-off frequency for the solitary waves which velocity is greater than the Swihart velocity can be smaller than the Josephson plasma frequency and moreover these waves can propagate only in a junction that is large in the direction perpendicular to the propagation direction. On the contrary the solitary waves which velocity is smaller than the Swihart velocity request junction size in the above direction to be smaller than a critical one. The investigated two-dimensional solitary waves can be connected with one or two quanta of the magnetic flux.     

Shocks in non-loaded bead chains with impurities

We numerically investigate the problem of the propagation of a shock in an horizontal non-loaded granular chain with a bead interaction force exponent varying from unity to large values. When is close to unity we observed a cross-over between a nonlinearity-dominated regime and a solitonic one, the latest being the final steady state of the propagating wave. In the case of large values of the deformation field given by the numerical simulations is completely different from the one obtained by analytical calculation. In the following we studied the interaction of these shock waves with a mass impurity placed in the bead chain. Two different physical pictures emerge whether we consider a light or a heavy impurity mass. The scatter of the shock wave with a light impurity yields damped oscillations of the impurity which then behave as a solitary wave source. Differently an heavy impurity is just shifted by the shock and the transmitted wave loses its solitonic character being fragmented into waves of decreasing amplitudes. Received 23 June 1999     

Nonlinear waves in elastic media

We ask about the possible existence of solitary waves in infinite, homogeneous, isotropic, elastic media. Namely, can a nonlinear localized wave packet propagate without altering its shape in such materials? We consider one- dimensional propagation both of body and surface waves. In the first case we show, under rather general assumptions, that if a wave packet propagates without altering its shape it must, of necessity, be a solution of a linear wave equation and in this sense, (body) solitary waves do not exist. Surface solitary waves may however exist: a model equation is derived in which nonlinear and dispersive effects balance each other to allow for waves-both periodic and solitary-of constant shape. It is conceivable they are of some relevance in seismology.