Nodal patterns of floaters in surface waves

We argue theoretically and demonstrate experimentally that in a standing wave floating particles drift towards the nodes or anti-nodes depending on their hydrophilic or hydrophobic properties. We explain this effect as the breakdown of Archimedes' law by a surface tension, which creates a difference between the masses of the floater and displaced liquid, making the particle effectively inertial. We describe analytically the motion of a small floating particle in a small-amplitude wave and show that the drift appears as a second order effect in wave amplitude. We confirm experimentally that indeed the clustering rate is proportional to the square of the wave amplitude. In the case of surface random waves we show experimentally that the inertial effects significantly change the statistics of floater distribution on a liquid surface. The analysis of particle concentration moments and probability distribution functions shows that particle concentrate on a multi-fractal set with caustics.     

Standing Waves in the Lorentz-Covariant World

When Einstein formulated his special relativity, he developed his dynamics for point particles. Of course, many valiant efforts have been made to extend his relativity to rigid bodies, but this subject is forgotten in history. This is largely because of the emergence of quantum mechanics with wave-particle duality. Instead of Lorentz-boosting rigid bodies, we now boost waves and have to deal with Lorentz transformations of waves. We now have some nderstanding of plane waves or running waves in the covariant picture, but we do not yet have a clear picture of standing waves. In this report, we show that there is one set of standing waves which can be Lorentz-transformed while being consistent with all physical principle of quantum mechanics and relativity. It is possible to construct a representation of the Poincaré group using harmonic oscillator wave functions satisfying space-time boundary conditions. This set of wave functions is capable of explaining the quantum bound state for both slow and fast hadrons. In particular it can explain the quark model for hadrons at rest, and Feynman’s parton model hadrons moving with a speed close to that of light.     

Specificity of the phenomenon of acoustoelasticity in a two-dimensional internally structured medium

A two-dimensional model of a microstructured medium is considered in the form of a square lattice consisting of elastically interacting circular particles with translational and rotational degrees of freedom. The interactions between the particles are modeled by a set of elastic springs. Differential equations are derived to describe the propagation and interaction of acoustic waves in such a medium. The relation between the velocities of wave propagation and the small strain arising in the structure under external action is determined. Analytical expressions that determine the difference between the squares of the velocities of both longitudinal and shear waves propagating in two mutually perpendicular directions in a medium with an externally induced anisotropy are derived and analyzed.     

Particle paths in Stokes’ edge wave

We treat the particle motion in Stokes’ linear edge wave along a uniformly sloping beach. By a rotation of the coordinate frame, we show that there is no particle motion in the direction orthogonal to the sloping beach, and conclude that particles have a longshore drift in the direction of wave propagation which decreases with depth and distance from the shoreline. We discuss the application of this rotated coordinate frame to higher mode (Ursell) and weakly nonlinear (Whitham) edge waves, and show that the weakly nonlinear case is identical to that for two-dimensional deep-water Stokes waves.     

The de Broglie wave packet for a simple stationary state

A simple stationary state is set up by combining the two de Broglie waves from two particles traveling in one direction with equal and opposite velocities. By considering the waves forming this state from the point of view of all possible observers moving in the same direction, it is shown that the basic standing wave pattern does not alter, but that the particle will be confined to a small region stationary relative to this pattern. This region is similar in extent to that confining a free particle, the natural internal frequency of the particle being raised. This agrees with previous suggestions that a particle in a stationary state without angular momentum is stationary.     

Optical absorption by small metallic particles

We study theoretically the dependence of absorption by small metallic particles on particle shape and wave polarization in the IR frequency range. We examine the electric and magnetic absorption by small particles. The particles may be either larger or smaller than the electron mean free path. We show that for asymmetric particles smaller than the mean free path the light-induced conductivity is a tensor. We also show that the total absorption and the electric-to-magnetic absorption ratio are strongly dependent on particle shape and wave polarization. Finally, we construct curves representing the dependence of the ratio of the electric and magnetic contributions to absorption on the degree of particle asymmetry for different wave polarizations. Similar curves are constructed for the ratio of the components of the light-induced conductivity tensor. Zh. éksp. Teor. Fiz. 112, 661–678 (August 1997)     

Theory of periodic and solitary space charge waves in extrinsic semiconductors

We present a theory of the existence and stability of traveling periodic and solitary space charge wave solutions to a standard rate equation model of electrical conduction in extrinsic semiconductors which includes effects of field-dependent impurity impact ionization. A nondimensional set of equations is presented in which the small parameter β = (dielectric relaxation time) / (characteristic impurity time) 1 plays a crucial role for our singular perturbation analysis. For a narrow range of wave velocities a phase plane analysis gives a set of limit cycle orbits corresponding to periodic traveling waves. while for a unique value of wave velocity we find a homoclinic orbit corresponding to a moving solitary space charge wave of the type experimentally observed in p-type germanium. A linear stability analysis reveals all waves to be unstable under current bias on the infinite one-dimensional line. Finally, we conjecture that solitary waves may be stable in samples of finite length under voltage bias.     

Effect of solid dust particles on the propagation of shock wave in planar and non-planar gasdynamics

The aim of the present study is to analyze the propagation of shock wave along the characteristic path in planar and non-planar unsteady compressible ideal gas flow in presence of small solid dust particles. The analytical solution of the governing quasilinear hyperbolic system is computed in the characteristic plane and it is found that this analytical linear solution in this plane can exhibit non-linear phenomenon in the physical plane. The effect of the dust particles on the evolutionary behavior of the propagating shock wave in ideal gas flow is discussed. The transport equations leading to the evolution of shock wave is determined which introduces the conditions of shock formation. The growth and decay of compressive waves and expansive waves, respectively, in planar and non-planar ideal gas dynamics influenced by the presence of small solid dust particles, is discussed.     

Vector rogue waves in binary mixtures of Bose-Einstein condensates

We study numerically rogue waves in the two-component Bose-Einstein condensates which are described by the coupled set of two Gross-Pitaevskii equations with variable scattering lengths. We show that rogue wave solutions exist only for certain combinations of the nonlinear coefficients describing two-body interactions. We present the solutions for the combinations of these coefficients that admit the existence of rogue waves.     

Numerical Study of the Instability in a Maxwellian Beam-Plasma System II. Many Wave Regime

The relaxation of the beam-plasma system with several preliminarily excited unstable waves in its spectrum is investigated on the basis of computer simulations. The nature of the waves and particles interaction during the instability development is analysed. It is shown that the destroying of the amplitude oscillations of the single wave after saturation in the presence of additional waves is caused by the well known effect of resonance overlapping. A chaotization of the motion of the beam particles occurs even in the case when the amplitudes of the neighbouring waves are small.     

On the interaction of two beating electrostatic waves with plasma electrons

This paper is devoted to the study of the interaction of particles with two beating plasma waves. We follow the instructional article by Ott and Dum. According to them, the sum of wave actions during the interaction is constant, supposing the effect of trapped particles on the beat can be neglected. In the present paper, this problem is solved more generally, just for the case of trapped and also untrapped particles in the wave. Our study shows that the sum of wave actions is constant also in the case when the influence of the trapped particles on the amplitudes of two waves was considered. On the contrary this conclusion is not valid if it is supposed that two original waves are amplitude modulated e.g. by the influence of the interaction of the beat with particles. The author is deeply indebted to Dr. Ladislav Krlín for guidance and encouragement throughout the course of this work.     

Unstable Surface Waves in Running Water

We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for a general class of shear flows with inflection points and the maximal unstable wave number is found. Comparison to the rigid-wall setting testifies that the free surface has a destabilizing effect. For a class of unstable shear flows, the bifurcation of nontrivial periodic traveling waves is demonstrated at all wave numbers. We show the linear instability of small nontrivial waves that appear after bifurcation at an unstable wave number of the background shear flow. The proof uses a new formulation of the linearized water-wave problem and a perturbation argument. An example of the background shear flow of unstable small-amplitude periodic traveling waves is constructed for an arbitrary vorticity strength and for an arbitrary depth, illustrating that vorticity has a subtle influence on the stability of free-surface water waves.     

在兴奋-抑制混沌神经元网络中有序波的自发形成

大脑皮层在一定条件下可以自发出现螺旋波和平面波,为了了解这些有序波的产生机制,构造了一个双层的二维神经元网络.该网络由最近邻兴奋性耦合和长程抑制性耦合层组成,采用修改后的Hindmarsh-Rose神经元模型研究了该混沌神经元网络从具有随机相位分布的初态演化是否能自发出现各种有序波.数值模拟结果表明:当抑制性耦合强度比较小时,系统一般不会自发出现有序波;在兴奋性耦合强度足够大的情况下,抑制性耦合强度越大,系统越容易产生有序波.系统出现不同的有序波与系统初态和耦合强度有密切关系,适当选择兴奋性和抑制性耦合的耦合强度,系统会自发出现迷宫斑图、平面波、单螺旋波、多螺旋波、旋转方向相反的螺旋波对、双臂螺旋波、靶波、向内方形波等有序波斑图.螺旋波、迷宫斑图和内向方形波出现概率分别达到27.5%, 21.5%和10.0%,这里的迷宫斑图是由不同传播方向的许多平面波组成,其他有序波出现概率比较小.研究结果有助于理解发生在大脑皮层中的自组织现象.     

Velocity locking of incoherent nonlinear wave packets

We show both theoretically and experimentally in an optical fiber system that a set of incoherent nonlinear waves irreversibly evolves to a specific equilibrium state, in which the individual wave packets propagate with identical group velocities. This intriguing process of velocity locking can be explained in detail by simple thermodynamic arguments based on the kinetic wave theory. Accordingly, the selection of the velocity-locked state is shown to result from the natural tendency of the isolated wave system to approach the state that maximizes the nonequilibrium entropy.     

Spin waves on chains of YIG particles: dispersion relations,Faraday rotation,and power transmission

We calculate the dispersion relations for spin waves on a periodic chain of spherical or cylindrical Yttrium Iron Garnet (YIG) particles. We use the quasistatic approximation, appropriate when kd ? 1, where k is the wave number and d the interparticle spacing. In this regime, because of the magnetic dipole-dipole interaction between the localized magnetic excitations on neighboring particles, dispersive spin waves can propagate along the chain. The waves are analogous to plasmonic waves generated by electric dipole-dipole interactions between plasmons on neighboring metallic particles. The spin waves can be longitudinal (L), transverse (T), or elliptically polarized. We find that a linearly polarized spin wave undergoes a Faraday rotation as it propagates along the chain. The amount of Faraday rotation can be tuned by varying the off-diagonal component of the permeability tensor. We also discuss the possibility of wireless power transmission along the chain using these coupled spin waves.     

Stoneley (interfacial) waves between two magneto-electro-elastic half planes

We investigated the propagation properties of Stoneley waves between two magneto-electro-elastic half planes. Magneto-electro-elastic materials are assumed to possess hexagonal (6 mm) symmetry. Twenty-five sets of magneto-electrical interface conditions were adopted and generalized frequency equations were derived and solved numerically. It was found that, for each set of interface conditions, existing Stoneley waves are always non-dispersive. Numerical results further show that material properties have a significant effect on both the number and velocity of Stoneley waves, and that, although different magneto-electrical interface conditions could influence the existence of Stoneley waves, they have no effect on wave velocities.     

Rogue waves in nonlinear Schrödinger models with variable coefficients: Application to Bose–Einstein condensates

We explore the form of rogue wave solutions in a select set of case examples of nonlinear Schrödinger equations with variable coefficients. We focus on systems with constant dispersion, and present three different models that describe atomic Bose–Einstein condensates in different experimentally relevant settings. For these models, we identify exact rogue wave solutions. Our analytical findings are corroborated by direct numerical integration of the original equations, performed by two different schemes. Very good agreement between numerical results and analytical predictions for the emergence of the rogue waves is identified. Additionally, the nontrivial fate of small numerically induced perturbations to the exact rogue wave solutions is also discussed.     

Superluminal Behaviour of Modified Bessel Waves

Much experimental evidence of superluminal phenomena has been available by electromagnetic wave propagation experiments, with the results showing that the phase time describes the barrier traversal time. Based on the extrapolated phase time approach and numerical methods, we show that, in contrast to the ordinary Bessel waves of real argument, the group velocities of modified Bessel waves are superluminal. We obtain the following results. The group velocities increase with the increase of propagation distance, which is similar to the evanescent plane- wave cases. For large wave numbers, the group velocities fall off as the wave numbers increase, which is similar to the evanescent plane-wave cases. For small wave numbers, the group velocities increase with the increase of wave numbers, this is different from the evanescent plane-wave cases.     

Unified boundary integral equation for the scattering of elastic and acoustic waves: solution by the method of moments

A unified boundary integral equation (BIE) is developed for the scattering of elastic and acoustic waves. Traditionally, the elastic and acoustic wave problems are solved separately with different BIEs. The elastic wave case is represented in a vector BIE with the traction and displacement vectors as unknowns whereas the acoustic wave case is governed by a scalar BIE with velocity potential or pressure as unknowns. Although these two waves can be unified in the form of a partial differential equation, the unified form in its BIE counterpart has not been reported. In this work, we derive the unified BIE for these two waves and then show that the acoustic wave case can be derived from this BIE by introducing a shielding loss for small shear modulus approximation; hence only one code needs to be maintained for both elastic and acoustic wave scattering. We also derive the asymptotic Green's tensor for zero shear modulus and solve the corresponding vector equation. We employ the method of moments, which has been widely used in electromagnetics, as a numerical tool to solve the BIEs involved. Our numerical experiments show that it can also be used robustly in elastodynamics and acoustics.