Reflection and transmission of plane waves at the interface between anisotropic random discrete media

The Maxwell equations are solved for a random discrete medium using the single-scattering approximation and the condition of immersion in a maximally packed medium. The reflection and transmission factors of plane waves at the interface between vacuum and a random discrete anisotropic medium are determined. The calculated and experimental results on reflection and transmission of plane waves near the edge of a forest as an example of natural anisotropy of a random discrete medium are compared.     

冲击射流激波振荡与抑制

欠膨胀冲击射流具有复杂的激波结构,并伴随产生高幅值的离散频率单音.通过高速摄像获取的纹影图像并结合噪声测量,对欠膨胀冲击射流激波振荡过程、剪切层不稳定波的模态和离散频率单音的产生进行了系列研究.给出了冲击距离为5倍喷嘴出口直径的复杂流动实验结果分析,射流剪切层不稳定波有对称和非对称两种模态,发现不同模态下的离散频率单音...     

Observation of discrete solitons in optically induced real time waveguide arrays

We report the first experimental observation of discrete solitons in an array of optically induced waveguides. The waveguide lattice is induced in real time by illuminating a photorefractive crystal with a pair of interfering plane waves. We demonstrate two types of bright discrete solitons: in-phase self-localized states and the staggered (pi out-of-phase) soliton family. This experiment is the first observation of bright staggered solitons in any physical system. Our scheme paves the way for reconfigurable focusing and defocusing photonic lattices where low-power (mW) discrete solitons can be thoroughly investigated.     

A frequency selective acoustic transducer for directional Lamb wave sensing

A frequency selective acoustic transducer (FSAT) is proposed for directional sensing of guided waves. The considered FSAT design is characterized by a spiral configuration in wavenumber domain, which leads to a spatial arrangement of the sensing material producing output signals whose dominant frequency component is uniquely associated with the direction of incoming waves. The resulting spiral FSAT can be employed both for directional sensing and generation of guided waves, without relying on phasing and control of a large number of channels. The analytical expression of the shape of the spiral FSAT is obtained through the theoretical formulation for continuously distributed active material as part of a shaped piezoelectric device. Testing is performed by forming a discrete array through the points of the measurement grid of a scanning laser Doppler vibrometer. The discrete array approximates the continuous spiral FSAT geometry, and provides the flexibility to test several configurations. The experimental results demonstrate the strong frequency dependent directionality of the spiral FSAT and suggest its application for frequency selective acoustic sensors, to be employed for the localization of broadband acoustic events, or for the directional generation of Lamb waves for active interrogation of structural health.     

Laboratory and modeling study on modulated wave properties

Development of Benjamin?Feir instability is investigated under laboratory conditions and by analytical modeling. Nonlinear properties of the wave train with discrete spectrum are also investigated. The mechanically generated waves are composed of several discrete waves, while the newly generated harmonics are still combined into discrete spectra with the same frequency step. The technique proposed in this study allows us to study accurately the nonlinear variations in main properties of each harmonic with fixed frequency, such as amplitude, phase speed, and wavenumber along the wave tank together with velocities of wave packet crests, especially for the large transient waves. The phase speeds of short waves increase near large transient waves, and the velocities of longer waves are close to the values determined by the linear theory of waves. The relative long wave accompanied by short waves can dramatically change the local kurtosis and skewness of the wave field. They may play an important role for the generation of large transient wave and provide an opportunity for triggering of the freak waves.     

Discrete breathers — Advances in theory and applications

Nonlinear classical Hamiltonian lattices exhibit generic solutions — discrete breathers. They are time-periodic and (typically exponentially) localized in space. The lattices have discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. We will introduce the concept of these localized excitations and review their basic properties including dynamical and structural stability. We then focus on advances in the theory of discrete breathers in three directions — scattering of waves by these excitations, persistence of discrete breathers in long transient processes and thermal equilibrium, and their quantization. The second part of this review is devoted to a detailed discussion of recent experimental observations and studies of discrete breathers, including theoretical modelling of these experimental situations on the basis of the general theory of discrete breathers. In particular we will focus on their detection in Josephson junction networks, arrays of coupled nonlinear optical waveguides, Bose–Einstein condensates loaded on optical lattices, antiferromagnetic layered structures, PtCl based single crystals and driven micromechanical cantilever arrays.     

Effects of reduced discrete coupling on filament tension in excitable media

Wave propagation in the heart has a discrete nature, because it is mediated by discrete intercellular connections via gap junctions. Although effects of discreteness on wave propagation have been studied for planar traveling waves and vortexes (spiral waves) in two dimensions, its possible effects on vortexes (scroll waves) in three dimensions are not yet explored. In this article, we study the effect of discrete cell coupling on the filament dynamics in a generic model of an excitable medium. We find that reduced cell coupling decreases the line tension of scroll wave filaments and may induce negative filament tension instability in three-dimensional excitable lattices.     

On the relation of periodic acoustic emission pulses to slow solitary elastic waves (SSEW): Experiments with radiation-damaged glass in liquids

The periodicity (to 20 hours) of acoustic emission signals from radiation-damaged glass placed into liquid is detected. It is assumed that this periodicity is caused by slow solitary elastic waves (SSEW) with discrete velocities, which arise under experimental conditions. (SSEW were discovered and studied at the Lebedev Physical Institute since 1992.)     

The ion cyclotron resonator in the magnetosphere

Our concern here is to present the idea of the ion cyclotron resonator in the planetary magnetosphere and to discuss briefly the experimental status of the corresponding theory. The resonator confines the ion cyclotron waves to a thin equatorial zone, so that it keeps the wave field from coming into contact with the ionosphere, resulting in a decrease in energy losses. The properties of the resonator are illustrated by adopting a plausible distribution of the magnetic field in the equatorial zone, which yields an expression for the discrete spectrum of the waves just above the gyrofrequency of heavy ions. We show that the resonator is remarkable for many reasons, including the frequency dependence of its size and specific structure of the spectrum.     

Broad-linewidth laser absorption measurements of oxygen between 211 and 235 nm at high temperatures

Absorption coefficient data are presented for molecular oxygen at temperatures between 1100 and 2000 K and discrete wavelengths between 211 and 235 nm. Measurements were made behind reflected shock waves using broad-linewidth ultraviolet laser radiation generated from a frequency-quadrupled, tunable, pulsed Ti:Sapphire laser. Test mixtures consisting of 15% O₂, 15% He and balance Ar were used to minimize the influence of vibrational relaxation on the reflected shock temperature. The experimental results are in good agreement with theoretical calculations and confirm that discrete features from the Schumann–Runge system dominate between 211 and 235 nm at temperatures higher than 1100 K.     

Novel spatial solitons in light-induced photonic bandgap structures

The study of wave propagation in periodic systems is at the frontiers of physics, from fluids to condensed matter physics, and from photonic crystals to Bose-Einstein condensates. In optics, a typical example of periodic system is a closely-spaced waveguide array, in which collective behavior of wave propagation exhibits many intriguing phenomena that have no counterpart in homogeneous media. Even in a linear waveguide array, the diffraction property of a light beam changes due to evanescent coupling between nearby waveguide sites, leading to normal and anomalous discrete diffraction. In a nonlinear waveguide array, a balance between diffraction and self-action gives rise to novel localized states such as spatial “discrete solitons” in the semi-infinite (or total-internal-reflection) gap or spatial “gap solitons” in the Bragg reflection gaps. Recently, in a series of experiments, we have “fabricated” closely-spaced waveguide arrays (photonic lattices) by optical induction. Such photonic structures have attracted great interest due to their novel physics, link to photonic crystals, as well as potential applications in optical switching and navigation. In this review article, we present a brief overview on our experimental demonstrations of a number of novel spatial soliton phenomena in light-induced photonic bandgap structures, including self-trapping of fundamental discrete solitons and more sophisticated lattice gap solitons. Much of our work has direct impact on the study of similar discrete phenomena in systems beyond optics, including sound waves, water waves, and matter waves (Bose-Einstein condensates) propagating in periodic potentials.     

Novel spatial solitons in light-induced photonic bandgap structures

The study of wave propagation in periodic systems is at the frontiers of physics, from fluids to condensed matter physics, and from photonic crystals to Bose-Einstein condensates. In optics, a typical example of periodic system is a closely-spaced waveguide array, in which collective behavior of wave propagation exhibits many intriguing phenomena that have no counterpart in homogeneous media. Even in a linear waveguide array, the diffraction property of a light beam changes due to evanescent coupling between nearby waveguide sites, leading to normal and anomalous discrete diffraction. In a nonlinear waveguide array, a balance between diffraction and self-action gives rise to novel localized states such as spatial “discrete solitons” in the semi-infinite (or total-internal-reflection) gap or spatial “gap solitons” in the Bragg reflection gaps. Recently, in a series of experiments, we have “fabricated” closely-spaced waveguide arrays (photonic lattices) by optical induction. Such photonic structures have attracted great interest due to their novel physics, link to photonic crystals, as well as potential applications in optical switching and navigation. In this review article, we present a brief overview on our experimental demonstrations of a number of novel spatial soliton phenomena in light-induced photonic bandgap structures, including self-trapping of fundamental discrete solitons and more sophisticated lattice gap solitons. Much of our work has direct impact on the study of similar discrete phenomena in systems beyond optics, including sound waves, water waves, and matter waves (Bose-Einstein condensates) propagating in periodic potentials.      

Lie symmetries and nonlocally related systems of the continuous and discrete dispersive long waves system by geometric approach

By using the extended Harrison and Estabrook's differential forms approach, in this paper, we investigate the Lie symmetries of the continuous and discrete dispersive long waves system, respectively. Based on this method, two closed ideals written in terms of a set of differential forms are constructed for the dispersive long waves systems. Furthermore, some invariant solutions are presented for such systems. By a direct computation, it is shown that the discrete dispersive long waves system admits a Kac-Moody-Virasoro type and a Virasoro-like type Lie algebra, respectively. Finally, we present an interesting relationship between the continuous case and a modified dispersive long waves system, which can be used to find nonlocal properties for such systems with each other.     

粉末高速压制成形过程中的应力波分析

应用离散单元法,模拟了粉末高速压制成形过程中的压力传播过程.根据粉末高速压制成形的工艺特性,把一次压制过程分为弹性加载、塑性变形、弹性卸载三个阶段;基于离散单元法的基本理论,分别建立了三个阶段的控制方程;应用PFC2D软件对粉末高速压制过程模腔内部颗粒的运动状态进行了数值模拟,给出了压坯内部的压力分布,得出了实验中无法测量的压坯内部应力传播波形.数值模拟结果显示,压力作用曲线表现出明显的弛豫现象,形成了倾斜度不同的锯齿状加载波形和卸载波形,压坯底层的应力波与实验得到的应力波相符. 关键词： 高速压制成形 离散单元法 接触模型 应力波     

Periodic waves in nonlinear metamaterials

Periodic waves are presented in this Letter. With symbolic computation, equations for monochromatic waves are studied, and analytic periodic waves are obtained. Factors affecting properties of periodic waves are analyzed. Nonlinear metamaterials, with the continuous distribution of the dielectric permittivity obtained, are different from the ones with the discrete distribution.     

Solitary wave solutions as a signature of the instability in the discrete nonlinear Schrödinger equation

The effect of instability on the propagation of solitary waves along one-dimensional discrete nonlinear Schrödinger equation with cubic nonlinearity is revisited. A self-contained quasicontinuum approximation is developed to derive closed-form expressions for small-amplitude solitary waves. The notion that the existence of nonlinear solitary waves in discrete systems is a signature of the modulation instability is used. With the help of this notion we conjecture that instability effects on moving solitons can be qualitative estimated from the analytical solutions. Results from numerical simulations are presented to support this conjecture.     

Interactions of Soliton Waves for a Generalized Discrete KdV Equation

It is well known that soliton interactions in discrete integrable systems often possess new properties which are different from the continuous integrable systems, e.g., we found that there are such discrete solitons in a semidiscrete integrable system(the time variable is continuous and the space one is discrete) that the shorter solitary waves travel faster than the taller ones. Very recently, this kind of soliton was also observed in a full discrete generalized Kd V system(the both of time and space variables are discrete) introduced by Kanki et al. In this paper, for the generalized discrete Kd V(gd Kd V) equation, we describe its richer structures of one-soliton solutions. The interactions of two-soliton waves to the gd Kd V equation are studied. Some new features of the soliton interactions are proposed by rigorous theoretical analysis.     

Two-color operation in high-gain free-electron lasers

Two-color operation in free-electron laser (FEL) amplifiers is studied using a 3D nonlinear polychromatic simulation. We assume the FEL is seeded at two closely spaced wavelengths within the gain band, and study the growth of the seeds and a discrete spectrum of beat waves that are outside the gain band. The beat waves grow parasitically due to electron bunching in the seeded waves with growth rates higher than the seeded waves. Injection of narrow-band seeds ensures a discrete spectrum. An example is discussed corresponding to an x-ray FEL; however, the physics is applicable to all spectral ranges.     

Gravitational waves as a probe of the gravitino mass

If gaugino condensations occur in the early universe, domain walls are produced as a result of the spontaneous breaking of a discrete R symmetry. Those domain walls eventually annihilate with one another, producing the gravitational waves. We show that the gravitational waves can be a probe for measuring the gravitino mass, if the constant term in the superpotential is the relevant source of the discrete R symmetry breaking.     

Vortex solutions of the discrete Gross-Pitaevskii equation starting from the anti-continuum limit

In this paper, we consider the existence, stability and dynamical evolution of dark vortex states in the two-dimensional defocusing discrete nonlinear Schrödinger model, a model of interest both to atomic physics and to nonlinear optics. Our considerations are chiefly based on initializing such vortex configurations at the anti-continuum limit of zero coupling between adjacent sites, and continuing them to finite values of the coupling. Systematic tools are developed for such continuations based on amplitude-phase decompositions and explicit solvability conditions enforcing the vortex phase structure. Regarding the linear stability of such nonlinear waves, we find that in a way reminiscent of their 1d analogs, i.e., of discrete dark solitons, the discrete defocusing vortices become unstable past a critical coupling strength and, subsequently feature a cascade of alternating stabilization-destabilization windows for any finite lattice. Although the results are mainly geared towards the uniform case, we also consider the effect of harmonic trapping potentials often present in experimental atomic physics settings.