Nonlinear Standing Langmuir Waves

The structure of stationary nonlinear standing Langmuir waves is examined in a self-consistent manner. A singularity for the stationary wave function is found which may cause the Langmuir waves to collapse, or expand indefinitely.     

Stable Directions for Small Nonlinear Dirac Standing Waves

We prove that for a Dirac operator, with no resonance at thresholds nor eigenvalue at thresholds, the propagator satisfies propagation and dispersive estimates. When this linear operator has only two simple eigenvalues sufficiently close to each other, we study an associated class of nonlinear Dirac equations which have stationary solutions. As an application of our decay estimates, we show that these solutions have stable directions which are tangent to the subspaces associated with the continuous spectrum of the Dirac operator. This result is the analogue, in the Dirac case, of a theorem by Tsai and Yau about the Schrödinger equation. To our knowledge, the present work is the first mathematical study of the stability problem for a nonlinear Dirac equation     

Fluorescence of a Liquid Drop with a Dye Excited by Femtosecond Laser Pulses

Results of investigations into the spectral and power characteristics of two-photon fluorescence of a liquid drop with the Rhodamine 6G dye irradiated by femtosecond laser pulses are presented. It is demonstrated that stimulated emission of two types is realized in drops with the concentrated dye solution, namely, superfluorescence within the drop volume and lasing on whispering gallery modes.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 15–19, April, 2005.     

液体表面低频声波的非线性声光效应

实现了液体表面上低频声波的光衍射,得到了稳定的、具有高阶衍射的高反衬衍射图样.理论上首次考虑到表面声波中的高次谐波,得到了相应的非线性条件下衍射强度分布的解析表达式,并将这种非线性理论与实验结果进行对比.对比结果表明,非线性理论与实验结果有更高的吻合程度.     

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.     

Solitary Waves in Spherical Bessel Lattice

The analytical solitary waves solution to (3+1)-dimensional Gross-Pitaevskii equation with varying coefficients and an spherical Bessel lattice potential is obtained, which is in the form of self-similar solitary waves. The properties and the stability of the solitary waves family are discussed in detail.     

Nonlinear Concentration Waves in an Imperfect Reacting Diffusion System

A nonlinear differential equation describing the evolution of the intermediate reagent concentration is derived for the generalized Schlogl model of a chemical reaction in an imperfect system. It is demonstrated that concentration waves corresponding to a periodic analytic solution of the evolutionary equation arise in the imperfect system. Conditions of existence of periodic and solitary waves are formulated depending on the concentration of the initial component and the imperfection parameters of the examined system. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 81–84, July, 2005.     

Nonlinear Waves in an Inhomogeneous Fluid Filled Elastic Tube

In a thin-walled, homogeneous, straight, long, circular, and incompressible fluid filled elastic tube, small but finite long wavelength nonlinear waves can be describe by a KdV (Korteweg de Vries) equation, while the carrier wave modulations are described by a nonlinear Schrödinger equation (NLSE). However if the elastic tube is slowly inhomogeneous, then it is found, in this paper, that the carrier wave modulations are described by an NLSE-like equation. There are soliton-like solutions for them, but the stability and instability regions for this soliton-like waves will change, depending on what kind of inhomogeneity the tube has.     

Mathematical Modeling of Nonlinear Waves in an Elastic Cylindrical Shell Surrounded by an Elastic Medium and Containing a Viscous Incompressible Liquid

A mathematical model is proposed for a Kirchhoff–Love-type nonlinear elastic cylindrical shell surrounded by an elastic medium and containing a viscous incompressible liquid. The model is used to analyze wave processes both analytically and numerically. On the basis of the proposed computational algorithm, a software package is developed, which makes it possible to plot diagrams and to obtain numerical solutions to Cauchy problems with initial conditions taken in the form of exact solutions to dynamic equations of shells in the absence of the liquid.     

Generation of Vortices by Nonlinear Waves on the Surface of a Viscous Liquid

Physics of Wave Phenomena - Time dependence of the average vorticity amplitude is measured for vortices at lattice sites on the surface of water-glycerin solutions after excitation of two...     

Depth Resolved Structural Studies in Multilayers Using X-ray Standing Waves

X-ray based characterization techniques are powerful tools for the study of atomic scale structure of materials. However, high penetrating power of X-rays make them less suitable for depth selective studies, as required in the characterization of multilayer structures. In the present work, it is shown that depth selectivity of the techniques like, X-ray fluorescence, X-ray absorption spectroscopy and nuclear resonance fluorescence can be greatly enhanced by generating X-ray standing waves inside the multilayer structure. The concentration profiles of various elements can be obtained with a depth resolution of the order of 0.1 nm. Depth dependent information about the local structure around a given atom can be obtained from XAFS under standing wave conditions. It is demonstrated that detection of nuclear resonance fluorescence by tuning the energy of the incident X-rays to a Mössbauer transition can yield depth profile of a particular isotope, and can be used for self-diffusion studies. The techniques of X-ray reflectivity and conversion electron Mössbauer spectroscopy are used to provide useful complementary information.     

Nonlinear Waves in Nonuniform Complex Astrocloud

The global nonlinear gravito‐electrostatic eigen‐fluctuation behaviors in large‐scale non‐uniform complex astroclouds in quasi‐neutral hydrodynamic equilibrium are methodologically analyzed. Its composition includes warm lighter electrons, ions; and massive bi‐polar multi‐dust grains (inertial) with partial ionization sourced, via plasma‐contact electrification, in the cloud plasma background. The multi‐fluidic viscous drag effects are conjointly encompassed. The naturalistic equilibrium inhomogeneities, gradient forces and nonlinear convective dynamics are considered without any recourse to the Jeans swindle against the traditional perspective. An inho‐mogeneous multiscale analytical method is meticulously applied to derive a new conjugated non‐integrable coupled (via zeroth‐order factors) pair of variable‐coefficient inhomogeneous Korteweg de‐Vries Burger (i ‐KdVB) equations containing unique form of non‐uniform linear self‐consistent gradient‐driven sinks. A numerical illustrative scheme is procedurally constructed to examine the canonical fluctuations. It is seen that the eigenspectrum coevolves as electrostatic rarefactive damped oscillatory shock‐like structures and self‐gravitational compressive damped oscillatory shock‐like patterns . The irregular damping nature is attributable to the i ‐KdVB sinks. The aperiodicity in the hybrid rapid small downstream wavetrains is speculated to be deep‐rooted in the quasi‐linear gravito‐electrostatic interplay. The phase‐evolutionary dynamics grow as atypical non‐chaotic fixed‐point attractors . We, finally, indicate tentative astronomical applications relevant in large‐scale cosmic structure formation aboard facts and faults. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Asymmetry in Negative Refraction of Nonlinear Waves

Recently, inwardly propagating waves （called antiwaves, AWs） in nonlinear oscillatory systems have attracted much attention. An interesting negative refraction phenomenon has been observed in a bidomain system where one medium supports forwardly propagating waves （normal waves, NWs） and the other AWs. In this paper we find that negative refraction （NR） in nonlinear media has an asymmetric property, i.e., NR can be observed only by applying wave source with proper frequency to one medium, but not the other. Moreover, NR appears always when the incident waves are dense and the refractional waves are sparse. This asymmetry is a particular feature for nonlinear NR, which can neither be observed in linear refraction processes （both positive and negative refractions） nor in nonlinear positive refraction. The mechanism underlying the asymmetry of nonlinear NR are fully understood based on the competition of nonlinear waves.     

Relativistic Spherical Plasma Waves in a Collisional and Warm Plasma

Under Lagrange coordinates, the relativistic spherical plasma wave in a collisional and warm plasma is discussed theoretically. Within the Lagrange coordinates and using the Maxwell and hydrodynamics equations, a wave equation describing the relativistic spherical wave is derived. The damped oscillating spherical wave solution is obtained analytically using the perturbation theory. Because of the coupled effects of spherical geometry,thermal pressure, and collision effect, the electron damps the periodic oscillation. The oscillation frequency and the damping rate of the wave are related to not only the collision and thermal pressure effect but also the space coordinate. Near the center of the sphere, the thermal pressure significantly reduces the oscillation period and the damping rate of the wave, while the collision effect can strongly influence the damping rate. Far away from the spherical center, only the collision effect can reduce the oscillation period of the wave, while the collision effect and thermal pressure have weak influence on the damping rate.     

Asymmetry in Negative Refraction of Nonlinear Waves

Recently, inwardly propagating waves (called antiwaves, AWs) in nonlinear oscillatory systems have attracted much attention. An interesting negative refraction phenomenon has been observed in a bidomain system where one medium supports forwardly propagating waves (normal waves, NWs) and the other AWs. In this paper we find that negative refraction (NR) in nonlinear media has an asymmetric property, i.e., NR can be observed only by applying wave source withproper frequency to one medium, but not the other. Moreover, NR appears always when the incident waves are dense and the refractional waves are sparse. This asymmetry is a particular feature for nonlinear NR, which can neither be observed in linear refraction processes (both positive and negative refractions) nor in nonlinear positive refraction. The mechanism underlying the asymmetry of nonlinear NR are fully understood based on the competition of nonlinear waves.     

Two-Photon Excited Fluorescence and Molecular Reorientations in Liquid Solutions

Theoretical expressions are derived that relate the two-photon excited fluorescence depolarisation experiments to the molecular symmetry and the rotational motions of fluorescent molecules. Diffusive rotational motions in liquid solvents are considered, as well as the influence of fast unresolved motions (e.g. librations). The results obtained are compared with one-photon excited fluorescence depolarisation experiments. The derived theoretical expressions can be applied for detailed analyses of the molecular rotation in solvent. Several of the results are useful for determining and assigning the components of two-photon absorption tensors.     

Beam Displacement in a Layered Configuration due to Formation of Standing Waves

We obtain a large positive lateral shift of a light beam reflected from a layered configuration due to the formation of the unusual standing wave, which acts like the forward surface wave. An explicitly analytic condition to obtain the large lateral shift is presented. Finally we present a numerical simulation for the lateral displacement of a Gaussian beam.     

二维平板间驻波声流的MRT-LBM数值研究

采用多松弛时间格子玻尔兹曼方法（Multiple Relaxation Time Lattice Boltzmann Method,MRT-LBM）对二维平板间的驻波声流进行数值模拟,模拟结果与Rayleigh流近似解析解相符,研究黏度和板间宽度对驻波声流的影响,得到不同黏度下x=L/4截面无量纲水平速度分布和x=L/2截面无量纲竖直速度分布,板间宽度对边界层内声流区域厚度的影响及驻波声流的形成过程,结果表明MRT-LBM模型能有效模拟驻波声流效应.