2015-05-07
associated with the lattice background; the nonlinearity is derived from the inclusion of cubic nonlinearity. Often the background potential is periodic...dispersion branch we can find discrete evolution equations for the envelope associated with the lattice NLS equation (1) by looking for solutions of...spatial operator in the above NLS equation can be elliptic, hyperbolic or parabolic . We remark that further reduction is possible by going into a moving
Variation principle for nonlinear wave propagation
International Nuclear Information System (INIS)
Watanabe, T.; Lee, Y.C.; Nishikawa, Kyoji; Hojo, H.; Yoshida, Y.
1976-01-01
Variation principle is derived which determines stationary nonlinear propagation of electrostatic waves in the self-consistent density profile. Example is given for lower-hybrid waves and the relation to the variation principle for the Lagrangian density of electromagnetic fluids is discussed
Nonlinear radial propagation of drift wave turbulence
International Nuclear Information System (INIS)
Prakash, M.
1985-01-01
We study the linear and the nonlinear radial propagation of drift wave energy in an inhomogeneous plasma. The drift mode excited in such a plasma is dispersive in nature. The drift wave energy spreads out symmetrically along the direction of inhomogeneity with a finite group velocity. To study the effect of the nonlinear coupling on the propagation of energy in a collision free plasma, we solve the Hasegawa-Mima equation as a mixed initial boundary-value problem. The solutions of the linearized equation are used to check the reliability of our numerical calculations. Additional checks are also performed on the invariants of the system. Our results reveal that a pulse gets distorted as it propagates through the medium. The peak of the pulse propagates with a finite velocity that depends on the amplitude of the initial pulse. The polarity of propagation depends on the initial parameters of the pulse. We have also studied drift wave propagation in a resistive plasma. The Hasegawa-Wakatani equations are used to investigate this problem
Jefrey, A
1964-01-01
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat
Nonlinear magnetoacoustic wave propagation with chemical reactions
Margulies, Timothy Scott
2002-11-01
The magnetoacoustic problem with an application to sound wave propagation through electrically conducting fluids such as the ocean in the Earth's magnetic field, liquid metals, or plasmas has been addressed taking into account several simultaneous chemical reactions. Using continuum balance equations for the total mass, linear momentum, energy; as well as Maxwell's electrodynamic equations, a nonlinear beam equation has been developed to generalize the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation for a fluid with linear viscosity but nonlinear and diffraction effects. Thermodynamic parameters are used and not tailored to only an adiabatic fluid case. The chemical kinetic equations build on a relaxing media approach presented, for example, by K. Naugolnukh and L. Ostrovsky [Nonlinear Wave Processes in Acoustics (Cambridge Univ. Press, Cambridge, 1998)] for a linearized single reaction and thermodynamic pressure equation of state. Approximations for large and small relaxation times and for magnetohydrodynamic parameters [Korsunskii, Sov. Phys. Acoust. 36 (1990)] are examined. Additionally, Cattaneo's equation for heat conduction and its generalization for a memory process rather than a Fourier's law are taken into account. It was introduced for the heat flux depends on the temperature gradient at an earlier time to generate heat pulses of finite speed.
Wave propagation in non-linear media
Broer, L.J.F.
1965-01-01
The problem of the propagation of electromagnetic waves through solids is essentially one of interaction between light quanta and matter. The most fundamental and general treatment of this subject is therefore undoubtedly based on the quantummechanical theory of this interaction. Nevertheless, a
Nonlinear propagation of short wavelength drift-Alfven waves
DEFF Research Database (Denmark)
Shukla, P. K.; Pecseli, H. L.; Juul Rasmussen, Jens
1986-01-01
Making use of a kinetic ion and a hydrodynamic electron description together with the Maxwell equation, the authors derive a set of nonlinear equations which governs the dynamics of short wavelength ion drift-Alfven waves. It is shown that the nonlinear drift-Alfven waves can propagate as two-dim...
Wave propagation in elastic medium with heterogeneous quadratic nonlinearity
International Nuclear Information System (INIS)
Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin
2011-01-01
This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter β when the nonlinearity distribution in the layer is a stochastic process.
Controlling wave propagation through nonlinear engineered granular systems
Leonard, Andrea
We study the fundamental dynamic behavior of a special class of ordered granular systems in order to design new, structured materials with unique physical properties. The dynamic properties of granular systems are dictated by the nonlinear, Hertzian, potential in compression and zero tensile strength resulting from the discrete material structure. Engineering the underlying particle arrangement of granular systems allows for unique dynamic properties, not observed in natural, disordered granular media. While extensive studies on 1D granular crystals have suggested their usefulness for a variety of engineering applications, considerably less attention has been given to higher-dimensional systems. The extension of these studies in higher dimensions could enable the discovery of richer physical phenomena not possible in 1D, such as spatial redirection and anisotropic energy trapping. We present experiments, numerical simulation (based on a discrete particle model), and in some cases theoretical predictions for several engineered granular systems, studying the effects of particle arrangement on the highly nonlinear transient wave propagation to develop means for controlling the wave propagation pathways. The first component of this thesis studies the stress wave propagation resulting from a localized impulsive loading for three different 2D particle lattice structures: square, centered square, and hexagonal granular crystals. By varying the lattice structure, we observe a wide range of properties for the propagating stress waves: quasi-1D solitary wave propagation, fully 2D wave propagation with tunable wave front shapes, and 2D pulsed wave propagation. Additionally the effects of weak disorder, inevitably present in real granular systems, are investigated. The second half of this thesis studies the solitary wave propagation through 2D and 3D ordered networks of granular chains, reducing the effective density compared to granular crystals by selectively placing wave
A nonlinear wave equation in nonadiabatic flame propagation
International Nuclear Information System (INIS)
Booty, M.R.; Matalon, M.; Matkowsky, B.J.
1988-01-01
The authors derive a nonlinear wave equation from the diffusional thermal model of gaseous combustion to describe the evolution of a flame front. The equation arises as a long wave theory, for values of the volumeric heat loss in a neighborhood of the extinction point (beyond which planar uniformly propagating flames cease to exist), and for Lewis numbers near the critical value beyond which uniformly propagating planar flames lose stability via a degenerate Hopf bifurcation. Analysis of the equation suggests the possibility of a singularity developing in finite time
Nonlinear propagation of Alfven waves in cometary plasmas
International Nuclear Information System (INIS)
Lakhina, G.S.; Shukla, P.K.
1987-07-01
Large amplitude Alfven waves propagating along the guide magnetic field in a three-component plasma are shown to be modulationally unstable due to their nonlinear interaction with nonresonant electrostatic density fluctuations. A new class of subsonic Alfven soliton solutions are found to exist in the three-component plasma. The Alfven solitons can be relevant in explaining the properties of hydromagnetic turbulence near the comets. (author). 15 refs
Theory for stationary nonlinear wave propagation in complex magnetic geometry
International Nuclear Information System (INIS)
Watanabe, T.; Hojo, H.; Nishikawa, Kyoji.
1977-08-01
We present our recent efforts to derive a systematic calculation scheme for nonlinear wave propagation in the self-consistent plasma profile in complex magnetic-field geometry. Basic assumptions and/or approximations are i) use of the collisionless two-fluid model with an equation of state; ii) restriction to a steady state propagation and iii) existence of modified magnetic surface, modification due to Coriolis' force. We discuss four situations: i) weak-field propagation without static flow, ii) arbitrary field strength with flow in axisymmetric system, iii) weak field limit of case ii) and iv) arbitrary field strength in nonaxisymmetric torus. Except for case iii), we derive a simple variation principle, similar to that of Seligar and Whitham, by introducing appropriate coordinates. In cases i) and iii), we derive explicit results for quasilinear profile modification. (auth.)
Propagation of nonlinear ion acoustic wave with generation of long-wavelength waves
International Nuclear Information System (INIS)
Ohsawa, Yukiharu; Kamimura, Tetsuo
1978-01-01
The nonlinear propagation of the wave packet of an ion acoustic wave with wavenumber k 0 asymptotically equals k sub(De) (the electron Debye wavenumber) is investigated by computer simulations. From the wave packet of the ion acoustic wave, waves with long wavelengths are observed to be produced within a few periods for the amplitude oscillation of the original wave packet. These waves are generated in the region where the original wave packet exists. Their characteristic wavelength is of the order of the length of the wave packet, and their propagation velocity is almost equal to the ion acoustic speed. The long-wavelength waves thus produced strongly affect the nonlinear evolution of the original wave packet. (auth.)
Wave propagation in a strongly nonlinear locally resonant granular crystal
Vorotnikov, K.; Starosvetsky, Y.; Theocharis, G.; Kevrekidis, P. G.
2018-02-01
In this work, we study the wave propagation in a recently proposed acoustic structure, the locally resonant granular crystal. This structure is composed of a one-dimensional granular crystal of hollow spherical particles in contact, containing linear resonators. The relevant model is presented and examined through a combination of analytical approximations (based on ODE and nonlinear map analysis) and of numerical results. The generic dynamics of the system involves a degradation of the well-known traveling pulse of the standard Hertzian chain of elastic beads. Nevertheless, the present system is richer, in that as the primary pulse decays, secondary ones emerge and eventually interfere with it creating modulated wavetrains. Remarkably, upon suitable choices of parameters, this interference "distills" a weakly nonlocal solitary wave (a "nanopteron"). This motivates the consideration of such nonlinear structures through a separate Fourier space technique, whose results suggest the existence of such entities not only with a single-side tail, but also with periodic tails on both ends. These tails are found to oscillate with the intrinsic oscillation frequency of the out-of-phase motion between the outer hollow bead and its internal linear attachment.
Directional nonlinear guided wave mixing: Case study of counter-propagating shear horizontal waves
Hasanian, Mostafa; Lissenden, Cliff J.
2018-04-01
While much nonlinear ultrasonics research has been conducted on higher harmonic generation, wave mixing provides the potential for sensitive measurements of incipient damage unencumbered by instrumentation nonlinearity. Studies of nonlinear ultrasonic wave mixing, both collinear and noncollinear, for bulk waves have shown the robust capability of wave mixing for early damage detection. One merit of bulk wave mixing lies in their non-dispersive nature, but guided waves enable inspection of otherwise inaccessible material and a variety of mixing options. Co-directional guided wave mixing was studied previously, but arbitrary direction guided wave mixing has not been addressed until recently. Wave vector analysis is applied to study variable mixing angles to find wave mode triplets (two primary waves and a secondary wave) resulting in the phase matching condition. As a case study, counter-propagating Shear Horizontal (SH) guided wave mixing is analyzed. SH wave interactions generate a secondary Lamb wave mode that is readily receivable. Reception of the secondary Lamb wave mode is compared for an angle beam transducer, an air coupled transducer, and a laser Doppler vibrometer (LDV). Results from the angle beam and air coupled transducers are quite consistent, while the LDV measurement is plagued by variability issues.
Gusev, Vitalyi E; Ni, Chenyin; Lomonosov, Alexey; Shen, Zhonghua
2015-08-01
Theory accounting for the influence of hysteretic nonlinearity of micro-inhomogeneous material on flexural wave in the plates of continuously varying thickness is developed. For the wedges with thickness increasing as a power law of distance from its edge strong modifications of the wave dynamics with propagation distance are predicted. It is found that nonlinear absorption progressively disappearing with diminishing wave amplitude leads to complete attenuation of acoustic waves in most of the wedges exhibiting black hole phenomenon. It is also demonstrated that black holes exist beyond the geometrical acoustic approximation. Applications include nondestructive evaluation of micro-inhomogeneous materials and vibrations damping. Copyright © 2015 Elsevier B.V. All rights reserved.
Nonlinear wave propagation through a ferromagnet with damping in ...
Indian Academy of Sciences (India)
magnetic waves in a ferromagnet can be reduced to an integro-differential equation. Keywords. Solitons; integro-differential equations; reductive perturbation method. PACS Nos 41.20 Jb; 05.45 Yv; 03.50 De; 78.20 Ls. 1. Introduction. The phenomenon of propagation of electromagnetic waves in ferromagnets are not only.
Nonlinear acoustic wave propagating in one-dimensional layered system
International Nuclear Information System (INIS)
Yun, Y.; Miao, G.Q.; Zhang, P.; Huang, K.; Wei, R.J.
2005-01-01
The propagation of finite-amplitude plane sound in one-dimensional layered media is studied by the extended method of transfer matrix formalism. For the periodic layered system consisting of two alternate types of liquid, the energy distribution and the phase vectors of the interface vibration are computed and analyzed. It is found that in the pass-band, the second harmonic of sound wave can propagate with the characteristic modulation
Propagation of nonlinear waves over submerged step: wave separation and subharmonic generation
Monsalve, Eduardo; Maurel, Agnes; Pagneux, Vincent; Petitjeans, Philippe
2015-11-01
Water waves can be described in simplified cases by the Helmholtz equation. However, even in these cases, they present a high complexity, among which their dispersive character and their nonlinearities are the subject of the present study. Using Fourier Transform Profilometry, we study experimentally the propagation of waves passing over a submerged step. Because of the small water depth after the step, the wave enters in a nonlinear regime. In the shallow water region, the second harmonic leads to two types of waves: bound waves which are slaves of the fundamental frequency with wavenumber 2 k (ω) , and free waves which propagate according to the usual dispersion relation with wavenumber k (2 ω) . Because of the presence of these two waves, beats are produced at the second harmonic with characteristic beat length. In this work, for the first time we extended this analysis to the third and higher harmonics. Next, the region after the step is limited to a finite size L with a reflecting wall. For certain frequencies and L- values, the spectral component becomes involved, with the appearance of sub harmonics. This regime is analyzed in more details, suggesting a transition to a chaotic and quasi-periodic wave behavior.
Propagation of Quasi-plane Nonlinear Waves in Tubes
Directory of Open Access Journals (Sweden)
P. Koníček
2002-01-01
Full Text Available This paper deals with possibilities of using the generalized Burgers equation and the KZK equation to describe nonlinear waves in circular ducts. A new method for calculating of diffraction effects taking into account boundary layer effects is described. The results of numerical solutions of the model equations are compared. Finally, the limits of validity of the used model equations are discussed with respect to boundary conditions and the radius of the circular duct. The limits of applicability of the KZK equation and the GBE equation for describing nonlinear waves in tubes are discussed.
Energy Technology Data Exchange (ETDEWEB)
Ruderman, M S
1988-08-01
Nonlinear Alfven surface wave propagation at a magnetic interface in a compressible fluid is considered. It is supposed that the magnetic field directions at both sides of the interface and the direction of wave propagation coincide. The equation governing time-evolution of nonlinear small-amplitude waves is derived by the method of multiscale expansions. This equation is similar to the equation for nonlinear Alfven surface waves in an incompressible fluid derived previously. The numerical solution of the equation shows that a sinusoidal disturbance overturns, i.e. infinite gradients arise.
Nonlinear wave propagation studies, dispersion modeling, and signal parameters correction
Czech Academy of Sciences Publication Activity Database
Převorovský, Zdeněk
..: ..., 2004, 00. [European Workshop on FP6-AERONEWS /1./. Naples (IT), 13.09.2004-16.09.2004] EU Projects: European Commission(XE) 502927 - AERO-NEWS Institutional research plan: CEZ:AV0Z2076919 Keywords : nodestructive testing * nonlinear elastic wave spectroscopy Subject RIV: BI - Acoustics
Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, Claes; Bigoni, Daniele
2016-01-01
We introduce a new stabilized high-order and unstructured numerical model for modeling fully nonlinear and dispersive water waves. The model is based on a nodal spectral element method of arbitrary order in space and a -transformed formulation due to Cai, Langtangen, Nielsen and Tveito (1998). In...
International Nuclear Information System (INIS)
Matsuda, Y.; Crawford, F.W.
1975-01-01
An economical low-noise plasma simulation model originated by Denavit is applied to a series of problems associated with electrostatic wave propagation in a one-dimensional, collisionless, Maxwellian plasma, in the absence of magnetic field. The model is described and tested, first in the absence of an applied signal, and then with a small amplitude perturbation. These tests serve to establish the low-noise features of the model, and to verify the theoretical linear dispersion relation at wave energy levels as low as 10 -6 of the plasma thermal energy: Better quantitative results are obtained, for comparable computing time, than can be obtained by conventional particle simulation models, or direct solution of the Vlasov equation. The method is then used to study propagation of an essentially monochromatic plane wave. Results on amplitude oscillation and nonlinear frequency shift are compared with available theories
Propagation of Quasi-plane Nonlinear Waves in Tubes
P. Koníček; M. Bednařík; M. Červenka
2002-01-01
This paper deals with possibilities of using the generalized Burgers equation and the KZK equation to describe nonlinear waves in circular ducts. A new method for calculating of diffraction effects taking into account boundary layer effects is described. The results of numerical solutions of the model equations are compared. Finally, the limits of validity of the used model equations are discussed with respect to boundary conditions and the radius of the circular duct. The limits of applicabi...
Nonlinear Wave Propagation and Solitary Wave Formation in Two-Dimensional Heterogeneous Media
Luna, Manuel
2011-05-01
Solitary wave formation is a well studied nonlinear phenomenon arising in propagation of dispersive nonlinear waves under suitable conditions. In non-homogeneous materials, dispersion may happen due to effective reflections between the material interfaces. This dispersion has been used along with nonlinearities to find solitary wave formation using the one-dimensional p-system. These solitary waves are called stegotons. The main goal in this work is to find two-dimensional stegoton formation. To do so we consider the nonlinear two-dimensional p-system with variable coefficients and solve it using finite volume methods. The second goal is to obtain effective equations that describe the macroscopic behavior of the variable coefficient system by a constant coefficient one. This is done through a homogenization process based on multiple-scale asymptotic expansions. We compare the solution of the effective equations with the finite volume results and find a good agreement. Finally, we study some stability properties of the homogenized equations and find they and one-dimensional versions of them are unstable in general.
The nonlinear distortion of propagation cones of lower hybrid wave in an inhomogeneous plasma
International Nuclear Information System (INIS)
Sanuki, Heiji; Ogino, Tatsuki.
1976-12-01
Nonlinear propagation of externally driven waves in the lower hybrid frequency range in an inhomogeneous plasma are investigated. The results of finite temperature, inhomogeneity of the plasma and density depression due to the ponderomotive force are emphasized since these effects are responsible for the propagation characteristics of the waves. The results shows that the waves are localized in a spatial wave packet that propagates into the plasma center along the conical trajectory which makes a small angle with respect to the confining magnetic field. (auth.)
Nonlinear wave propagation in discrete and continuous systems
Rothos, V. M.
2016-09-01
In this review we try to capture some of the recent excitement induced by a large volume of theoretical and computational studies addressing nonlinear Schrödinger models (discrete and continuous) and the localized structures that they support. We focus on some prototypical structures, namely the breather solutions and solitary waves. In particular, we investigate the bifurcation of travelling wave solution in Discrete NLS system applying dynamical systems methods. Next, we examine the combined effects of cubic and quintic terms of the long range type in the dynamics of a double well potential. The relevant bifurcations, the stability of the branches and their dynamical implications are examined both in the reduced (ODE) and in the full (PDE) setting. We also offer an outlook on interesting possibilities for future work on this theme.
Propagation of multidimensional nonlinear waves and kinematical conservation laws
Prasad, Phoolan
2017-01-01
This book formulates the kinematical conservation laws (KCL), analyses them and presents their applications to various problems in physics. Finally, it addresses one of the most challenging problems in fluid dynamics: finding successive positions of a curved shock front. The topics discussed are the outcome of collaborative work that was carried out mainly at the Indian Institute of Science, Bengaluru, India. The theory presented in the book is supported by referring to extensive numerical results. The book is organised into ten chapters. Chapters 1–4 offer a summary of and briefly discuss the theory of hyperbolic partial differential equations and conservation laws. Formulation of equations of a weakly nonlinear wavefront and those of a shock front are briefly explained in Chapter 5, while Chapter 6 addresses KCL theory in space of arbitrary dimensions. The remaining chapters examine various analyses and applications of KCL equations ending in the ultimate goal-propagation of a three-dimensional curved sho...
Nonlinear sausage-wave propagation in a magnetic slab in an incompressible fluid
International Nuclear Information System (INIS)
Ruderman, M.S.
1993-01-01
Long nonlinear sausage-wave propagation in a magnetic slab in an incompressible plasma is considered. The governing equation is derived with the aid of the reductive perturbation method. The solutions of this equation in the form of periodic waves of permanent shape are found numerically. (Author)
Wave propagation in photonic crystals and metamaterials: Surface waves, nonlinearity and chirality
Energy Technology Data Exchange (ETDEWEB)
Wang, Bingnan [Iowa State Univ., Ames, IA (United States)
2009-01-01
Photonic crystals and metamaterials, both composed of artificial structures, are two interesting areas in electromagnetism and optics. New phenomena in photonic crystals and metamaterials are being discovered, including some not found in natural materials. This thesis presents my research work in the two areas. Photonic crystals are periodically arranged artificial structures, mostly made from dielectric materials, with period on the same order of the wavelength of the working electromagnetic wave. The wave propagation in photonic crystals is determined by the Bragg scattering of the periodic structure. Photonic band-gaps can be present for a properly designed photonic crystal. Electromagnetic waves with frequency within the range of the band-gap are suppressed from propagating in the photonic crystal. With surface defects, a photonic crystal could support surface modes that are localized on the surface of the crystal, with mode frequencies within the band-gap. With line defects, a photonic crystal could allow the propagation of electromagnetic waves along the channels. The study of surface modes and waveguiding properties of a 2D photonic crystal will be presented in Chapter 1. Metamaterials are generally composed of artificial structures with sizes one order smaller than the wavelength and can be approximated as effective media. Effective macroscopic parameters such as electric permittivity ϵ, magnetic permeability μ are used to characterize the wave propagation in metamaterials. The fundamental structures of the metamaterials affect strongly their macroscopic properties. By designing the fundamental structures of the metamaterials, the effective parameters can be tuned and different electromagnetic properties can be achieved. One important aspect of metamaterial research is to get artificial magnetism. Metallic split-ring resonators (SRRs) and variants are widely used to build magnetic metamaterials with effective μ < 1 or even μ < 0. Varactor based
Nonlinear propagation of intense electromagnetic waves in weakly-ionized plasmas
International Nuclear Information System (INIS)
Shukla, P.K.
1993-01-01
The nonlinear propagation of intense electromagnetic waves in weakly-ionized plasmas is considered. Stimulated scattering mechanisms involving electromagnetic and acoustic waves in an unmagnetized plasma are investigated. The growth rate and threshold for three-wave decay interactions as well as modulational and filamentation instabilities are presented. Furthermore, the electromagnetic wave modulation theory is generalized for weakly ionized collisional magnetoplasmas. Here, the radiation envelope is generally governed by a nonlinear Schroedinger equation. Accounting for the dependence of the attachment frequency on the radiation intensity, ponderomotive force, as well as the differential Joule heating nonlinearity, the authors derive the equations for the nonthermal electron density and temperature perturbations. The various nonlinear terms in the electron motion are compared. The problems of self-focusing and wave localization are discussed. The relevance of the investigation to ionospheric modification by powerful electromagnetic waves is pointed out
Oblique propagation of nonlinear hydromagnetic waves: One- and two-dimensional behavior
International Nuclear Information System (INIS)
Malara, F.; Elaoufir, J.
1991-01-01
The one- and two-dimensional behavior of obliquely propagating hydromagnetic waves is analyzed by means of analytical theory and numerical simulations. It is shown that the nonlinear evolution of a one-dimensional MHD wave leads to the formation of a rotational discontinuity and a compressive steepened quasi-linearly polarized pulse whose structure is similar to that of a finite amplitude magnetosonic simple wave. For small propagation angles, the pulse mode (fast or slow) depends on the value of β with respect to unity while for large propagation angles the wave mode is fixed by the sign of the initial density-field correlation. The two-dimensional evolution shows that an MHD wave is unstable against a small-amplitude long-wavelength modulation in the direction transverse to the wave propagation direction. A two-dimensional magnetosonic wave solution is found, in which the density fluctuation is driven by the corresponding total pressure fluctuation, exactly as in the one-dimensional simple wave. Along with the steepening effect, the wave experiences both wave front deformation and a self-focusing effect which may eventually lead to the collapse of the wave. The results compare well with observations of MHD waves in the Earth's foreshock and at comets
Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials.
Kourakis, I; Shukla, P K
2005-07-01
We investigate the nonlinear propagation of electromagnetic waves in left-handed materials. For this purpose, we consider a set of coupled nonlinear Schrödinger (CNLS) equations, which govern the dynamics of coupled electric and magnetic field envelopes. The CNLS equations are used to obtain a nonlinear dispersion, which depicts the modulational stability profile of the coupled plane-wave solutions in left-handed materials. An exact (in)stability criterion for modulational interactions is derived, and analytical expressions for the instability growth rate are obtained.
The propagation of nonlinear rayleigh waves in layered elastic half-space
International Nuclear Information System (INIS)
Ahmetolan, S.
2004-01-01
In this work, the propagation of small but finite amplitude generalized Rayleigh waves in an elastic half-space covered by a different elastic layer of uniform and finite thickness is considered. The constituent materials are assumed to be homogeneous, isotropic, compressible hyperelastic. Excluding the harmonic resonance phenomena, it is shown that the nonlinear self modulation of generalized Rayleigh waves is governed asymptotically by a nonlinear Schrodinger (NLS) equation. The stability of the solutions and the existence of solitary wave-type solutions a NLS are strongly depend on the sign of the product of the coefficients of the nonlinear and dipersion terms of the equation.Therefore the analysis continues with the examination of dependence of these coefficients on the nonlinear material parameters. Three different models have been considered which are nonlinear layer-nonlinear half space, linear layer-nonlinear half space and nonlinear layer-linear half space. The behavior of the coefficients of the NLS equation was also analyzed the limit as h(thickness of the layer) goes to zero and k(the wave number) is constant. Then conclusions are drawn about the effect of nonlinear material parameters on the wave modulation. In the numerical investigations both hypothetical and real material models are used
International Nuclear Information System (INIS)
Yu-Lin, Feng; Xiao-Zhou, Liu; Jie-Hui, Liu; Li, Ma
2009-01-01
Based on an equivalent medium approach, this paper presents a model describing the nonlinear propagation of acoustic waves in a viscoelastic medium containing cylindrical micropores. The influences of pores' nonlinear oscillations on sound attenuation, sound dispersion and an equivalent acoustic nonlinearity parameter are discussed. The calculated results show that the attenuation increases with an increasing volume fraction of micropores. The peak of sound velocity and attenuation occurs at the resonant frequency of the micropores while the peak of the equivalent acoustic nonlinearity parameter occurs at the half of the resonant frequency of the micropores. Furthermore, multiple scattering has been taken into account, which leads to a modification to the effective wave number in the equivalent medium approach. We find that these linear and nonlinear acoustic parameters need to be corrected when the volume fraction of micropores is larger than 0.1%
PetClaw: A scalable parallel nonlinear wave propagation solver for Python
Alghamdi, Amal; Ahmadia, Aron; Ketcheson, David I.; Knepley, Matthew; Mandli, Kyle; Dalcin, Lisandro
2011-01-01
We present PetClaw, a scalable distributed-memory solver for time-dependent nonlinear wave propagation. PetClaw unifies two well-known scientific computing packages, Clawpack and PETSc, using Python interfaces into both. We rely on Clawpack to provide the infrastructure and kernels for time-dependent nonlinear wave propagation. Similarly, we rely on PETSc to manage distributed data arrays and the communication between them.We describe both the implementation and performance of PetClaw as well as our challenges and accomplishments in scaling a Python-based code to tens of thousands of cores on the BlueGene/P architecture. The capabilities of PetClaw are demonstrated through application to a novel problem involving elastic waves in a heterogeneous medium. Very finely resolved simulations are used to demonstrate the suppression of shock formation in this system.
Highly Nonlinear Wave Propagation in Elastic Woodpile Periodic Structures
2016-08-03
called a nanopteron, is not only motivated theoretically and numerically, but are also visualized experimentally by means of a laser Doppler vibrometer...velocity, which clearly follow the prin- cipal solitary wave (highlighted in red color ). It should be noted that the velocities involved in the
Directory of Open Access Journals (Sweden)
Mati Goldberg
Full Text Available A new paradigm has recently emerged in brain science whereby communications between glial cells and neuron-glia interactions should be considered together with neurons and their networks to understand higher brain functions. In particular, astrocytes, the main type of glial cells in the cortex, have been shown to communicate with neurons and with each other. They are thought to form a gap-junction-coupled syncytium supporting cell-cell communication via propagating Ca(2+ waves. An identified mode of propagation is based on cytoplasm-to-cytoplasm transport of inositol trisphosphate (IP(3 through gap junctions that locally trigger Ca(2+ pulses via IP(3-dependent Ca(2+-induced Ca(2+ release. It is, however, currently unknown whether this intracellular route is able to support the propagation of long-distance regenerative Ca(2+ waves or is restricted to short-distance signaling. Furthermore, the influence of the intracellular signaling dynamics on intercellular propagation remains to be understood. In this work, we propose a model of the gap-junctional route for intercellular Ca(2+ wave propagation in astrocytes. Our model yields two major predictions. First, we show that long-distance regenerative signaling requires nonlinear coupling in the gap junctions. Second, we show that even with nonlinear gap junctions, long-distance regenerative signaling is favored when the internal Ca(2+ dynamics implements frequency modulation-encoding oscillations with pulsating dynamics, while amplitude modulation-encoding dynamics tends to restrict the propagation range. As a result, spatially heterogeneous molecular properties and/or weak couplings are shown to give rise to rich spatiotemporal dynamics that support complex propagation behaviors. These results shed new light on the mechanisms implicated in the propagation of Ca(2+ waves across astrocytes and the precise conditions under which glial cells may participate in information processing in the brain.
Spectro-spatial analysis of wave packet propagation in nonlinear acoustic metamaterials
Zhou, W. J.; Li, X. P.; Wang, Y. S.; Chen, W. Q.; Huang, G. L.
2018-01-01
The objective of this work is to analyze wave packet propagation in weakly nonlinear acoustic metamaterials and reveal the interior nonlinear wave mechanism through spectro-spatial analysis. The spectro-spatial analysis is based on full-scale transient analysis of the finite system, by which dispersion curves are generated from the transmitted waves and also verified by the perturbation method (the L-P method). We found that the spectro-spatial analysis can provide detailed information about the solitary wave in short-wavelength region which cannot be captured by the L-P method. It is also found that the optical wave modes in the nonlinear metamaterial are sensitive to the parameters of the nonlinear constitutive relation. Specifically, a significant frequency shift phenomenon is found in the middle-wavelength region of the optical wave branch, which makes this frequency region behave like a band gap for transient waves. This special frequency shift is then used to design a direction-biased waveguide device, and its efficiency is shown by numerical simulations.
Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis
Jeffrey, Alan
1971-01-01
The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)
Hysteresis, Discrete Memory, and Nonlinear Wave Propagation in Rock: A New Paradigm
International Nuclear Information System (INIS)
Guyer, R.A.; McCall, K.R.; Boitnott, G.N.
1995-01-01
The structural elements in a rock are characterized by their density in Preisach-Mayergoyz space (PM space). This density is found for a Berea sandstone from stress-strain data and used to study the response of the sandstone to elaborate pressure protocols. Hysteresis with discrete memory, in agreement with experiment, is found. The relationship between strain, quasistatic modulus, and dynamic modulus is established. Nonlinear wave propagation, the production of copious harmonics, and nonlinear attenuation are demonstrated. PM space is shown to be the central construct in a new paradigm for the description of the elastic behavior of consolidated materials
Wave propagation in a bounded plasma with striction nonlinearity taken into account
International Nuclear Information System (INIS)
Brazhnik, V.A.; Grishaev, V.I.; Demchenko, V.V.; Pavlov, S.S.; Panchenko, V.I.; AN Ukrainskoj SSR, Kharkov. Fiziko-Tekhnicheskij Inst. Nizkikh Temperatur)
1981-01-01
Electromagnetic wave propagation in plasma is analyzed with striction nonlinearity taken into account. The reflection of a circularly polarized wave falling on a layer of homogeneous magnetoactive plasma is analytically investigated under conditions of linear skinning. The large amplitude TE-type wave propagation along the layer of isotropic plasma is numerically determined. It is shown that the distribution of the electric field amplitude essentially differs from the one predicted from the linear theory. Some periodic distributions across the layer become possible, in particular numerical modelling makes it possible to study the evolution of solitons generated by a monochromatic pump field in an inhomogeneous plasma layer bounded by ideally conducting surfaces. It is shown that generated solitons interact with those reflected from the boundary without any change of their form [ru
Nonlinear and linear wave equations for propagation in media with frequency power law losses
Szabo, Thomas L.
2003-10-01
The Burgers, KZK, and Westervelt wave equations used for simulating wave propagation in nonlinear media are based on absorption that has a quadratic dependence on frequency. Unfortunately, most lossy media, such as tissue, follow a more general frequency power law. The authors first research involved measurements of loss and dispersion associated with a modification to Blackstock's solution to the linear thermoviscous wave equation [J. Acoust. Soc. Am. 41, 1312 (1967)]. A second paper by Blackstock [J. Acoust. Soc. Am. 77, 2050 (1985)] showed the loss term in the Burgers equation for plane waves could be modified for other known instances of loss. The authors' work eventually led to comprehensive time-domain convolutional operators that accounted for both dispersion and general frequency power law absorption [Szabo, J. Acoust. Soc. Am. 96, 491 (1994)]. Versions of appropriate loss terms were developed to extend the standard three nonlinear wave equations to these more general losses. Extensive experimental data has verified the predicted phase velocity dispersion for different power exponents for the linear case. Other groups are now working on methods suitable for solving wave equations numerically for these types of loss directly in the time domain for both linear and nonlinear media.
Identification and determination of solitary wave structures in nonlinear wave propagation
International Nuclear Information System (INIS)
Newman, W.I.; Campbell, D.K.; Hyman, J.M.
1991-01-01
Nonlinear wave phenomena are characterized by the appearance of ''solitary wave coherent structures'' traveling at speeds determined by their amplitudes and morphologies. Assuming that these structures are briefly noninteracting, we propose a method for the identification of the number of independent features and their respective speeds. Using data generated from an exact two-soliton solution to the Korteweg-de-Vries equation, we test the method and discuss its strengths and limitations. 41 refs., 2 figs
The effects of nonlinear wave propagation on the stability of inertial cavitation
International Nuclear Information System (INIS)
Sinden, D; Stride, E; Saffari, N
2009-01-01
In the context of forecasting temperature and pressure fields generated by high-intensity focussed ultrasound, the accuracy of predictive models is critical for the safety and efficacy of treatment. In such fields 'inertial' cavitation is often observed. Classically, estimations of cavitation thresholds have been based on the assumption that the incident wave at the surface of a bubble is the same as in the far-field, neglecting the effect of nonlinear wave propagation. By modelling the incident wave as a solution to Burgers' equation using weak shock theory, the effects of nonlinear wave propagation on inertial cavitation are investigated using both numerical and analytical techniques. From radius-time curves for a single bubble, it is observed that there is a reduction in the maximum size of a bubble undergoing inertial cavitation and that the inertial collapse occurs earlier in contrast with the classical case. Corresponding stability thresholds for a bubble whose initial radius is slightly below the critical Blake radius are calculated, providing a lower bound for the onset of instability. Bifurcation diagrams and frequency-response curves are presented associated with the loss of stability. The consequences and physical implications of the results are discussed with respect to the classical results.
Nonlinear and diffraction effects in propagation of N-waves in randomly inhomogeneous moving media.
Averiyanov, Mikhail; Blanc-Benon, Philippe; Cleveland, Robin O; Khokhlova, Vera
2011-04-01
Finite amplitude acoustic wave propagation through atmospheric turbulence is modeled using a Khokhlov-Zabolotskaya-Kuznetsov (KZK)-type equation. The equation accounts for the combined effects of nonlinearity, diffraction, absorption, and vectorial inhomogeneities of the medium. A numerical algorithm is developed which uses a shock capturing scheme to reduce the number of temporal grid points. The inhomogeneous medium is modeled using random Fourier modes technique. Propagation of N-waves through the medium produces regions of focusing and defocusing that is consistent with geometrical ray theory. However, differences up to ten wavelengths are observed in the locations of fist foci. Nonlinear effects are shown to enhance local focusing, increase the maximum peak pressure (up to 60%), and decrease the shock rise time (about 30 times). Although the peak pressure increases and the rise time decreases in focal regions, statistical analysis across the entire wavefront at a distance 120 wavelengths from the source indicates that turbulence: decreases the mean time-of-flight by 15% of a pulse duration, decreases the mean peak pressure by 6%, and increases the mean rise time by almost 100%. The peak pressure and the arrival time are primarily governed by large scale inhomogeneities, while the rise time is also sensitive to small scales.
International Nuclear Information System (INIS)
Mirzade, Fikret Kh.
2005-01-01
The propagation of longitudinal strain wave in a plate with quadratic nonlinearity of elastic continuum was studied in the context of a model that takes into account the joint dynamics of elastic displacements in the medium and the concentration of the nonequilibrium laser-induced point defects. The input equations of the problem are reformulated in terms of only the total displacements of the medium points. In this case, the presence of structural defects manifests itself in the emergence of a delayed response of the system to the propagation of the strain-related perturbations, which is characteristic of media with relaxation or memory. The model equations describing the nonlinear displacement wave were derived with allowance made for the values of the relaxation parameter. The influence of the generation and relaxation of lattice defects on the propagation of this wave was analyzed. It is shown that, for short relaxation times of defects, the strain can propagate in the form of shock fronts. In the case of longer relaxation times, shock waves do not form and the strain wave propagates only in the form of solitary waves or a train of solitons. The contributions of the finiteness of the defect-recombination rate to linear and nonlinear elastic modulus, and spatial dispersion are determined
Yuldashev, Petr V; Ollivier, Sébastien; Karzova, Maria M; Khokhlova, Vera A; Blanc-Benon, Philippe
2017-12-01
Linear and nonlinear propagation of high amplitude acoustic pulses through a turbulent layer in air is investigated using a two-dimensional KZK-type (Khokhlov-Zabolotskaya-Kuznetsov) equation. Initial waves are symmetrical N-waves with shock fronts of finite width. A modified von Kármán spectrum model is used to generate random wind velocity fluctuations associated with the turbulence. Physical parameters in simulations correspond to previous laboratory scale experiments where N-waves with 1.4 cm wavelength propagated through a turbulence layer with the outer scale of about 16 cm. Mean value and standard deviation of peak overpressure and shock steepness, as well as cumulative probabilities to observe amplified peak overpressure and shock steepness, are analyzed. Nonlinear propagation effects are shown to enhance pressure level in random foci for moderate initial amplitudes of N-waves thus increasing the probability to observe highly peaked waveforms. Saturation of the pressure level is observed for stronger nonlinear effects. It is shown that in the linear propagation regime, the turbulence mainly leads to the smearing of shock fronts, thus decreasing the probability to observe high values of steepness, whereas nonlinear effects dramatically increase the probability to observe steep shocks.
Energy Technology Data Exchange (ETDEWEB)
Chabchoub, A., E-mail: achabchoub@swin.edu.au [Centre for Ocean Engineering Science and Technology, Swinburne University of Technology, Hawthorn, Victoria 3122 (Australia); Kibler, B.; Finot, C.; Millot, G. [Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 6303 CNRS, Université de Bourgogne, 21078 Dijon (France); Onorato, M. [Dipartimento di Fisica, Università degli Studi di Torino, Torino 10125 (Italy); Istituto Nazionale di Fisica Nucleare, INFN, Sezione di Torino, Torino 10125 (Italy); Dudley, J.M. [Institut FEMTO-ST, UMR 6174 CNRS- Université de Franche-Comté, 25030 Besançon (France); Babanin, A.V. [Centre for Ocean Engineering Science and Technology, Swinburne University of Technology, Hawthorn, Victoria 3122 (Australia)
2015-10-15
The dynamics of waves in weakly nonlinear dispersive media can be described by the nonlinear Schrödinger equation (NLSE). An important feature of the equation is that it can be derived in a number of different physical contexts; therefore, analogies between different fields, such as for example fiber optics, water waves, plasma waves and Bose–Einstein condensates, can be established. Here, we investigate the similarities between wave propagation in optical Kerr media and water waves. In particular, we discuss the modulation instability (MI) in both media. In analogy to the water wave problem, we derive for Kerr-media the Benjamin–Feir index, i.e. a nondimensional parameter related to the probability of formation of rogue waves in incoherent wave trains.
Kim, Kihong; Phung, D K; Rotermund, F; Lim, H
2008-01-21
We develop a generalized version of the invariant imbedding method, which allows us to solve the electromagnetic wave equations in arbitrarily inhomogeneous stratified media where both the dielectric permittivity and magnetic permeability depend on the strengths of the electric and magnetic fields, in a numerically accurate and efficient manner. We apply our method to a uniform nonlinear slab and find that in the presence of strong external radiation, an initially uniform medium of positive refractive index can spontaneously change into a highly inhomogeneous medium where regions of positive or negative refractive index as well as metallic regions appear. We also study the wave transmission properties of periodic nonlinear media and the influence of nonlinearity on the mode conversion phenomena in inhomogeneous plasmas. We argue that our theory is very useful in the study of the optical properties of a variety of nonlinear media including nonlinear negative index media fabricated using wires and split-ring resonators.
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
Control of Wave Propagation and Effect of Kerr Nonlinearity on Group Index
International Nuclear Information System (INIS)
Hazrat, Ali; Iftikhar, Ahmed; Ziauddin
2013-01-01
We use four-level atomic system and control the wave propagation via forbidden decay rate. The Raman gain process becomes dominant on electromagnetically induced transparency (EIT) medium by increasing the forbidden decay rate via increasing the number of atoms [G.S. Agarwal and T.N. Dey, Phys. Rev. A 74 (2006) 043805 and K. Harada, T. Kanbashi, and M. Mitsunaga, Phys. Rev. A 73 (2006) 013803]. The behavior of wave propagation is dramatically changed from normal (subluminal) to anomalous (superluminal) dispersion by increasing the forbidden decay rate. The system can also give a control over the group velocity of the light propagating through the medium via Kerr field. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Nonlinear surface Alfven waves
International Nuclear Information System (INIS)
Cramer, N.F.
1991-01-01
The problem of nonlinear surface Alfven waves propagating on an interface between a plasma and a vacuum is discussed, with dispersion provided by the finite-frequency effect, i.e. the finite ratio of the frequency to the ion-cyclotron frequency. A set of simplified nonlinear wave equations is derived using the method of stretched co-ordinates, and another approach uses the generation of a second-harmonic wave and its interaction with the first harmonic to obtain a nonlinear dispersion relation. A nonlinear Schroedinger equation is then derived, and soliton solutions found that propagate as solitary pulses in directions close to parallel and antiparallel to the background magnetic field. (author)
Directory of Open Access Journals (Sweden)
Y. Nariyuki
2006-01-01
Full Text Available Nonlinear relations among frequencies and phases in modulational instability of circularly polarized Alfvén waves are discussed, within the context of one dimensional, dissipation-less, unforced fluid system. We show that generation of phase coherence is a natural consequence of the modulational instability of Alfvén waves. Furthermore, we quantitatively evaluate intensity of wave-wave interaction by using bi-coherence, and also by computing energy flow among wave modes, and demonstrate that the energy flow is directly related to the phase coherence generation. We first discuss the modulational instability within the derivative nonlinear Schrödinger (DNLS equation, which is a subset of the Hall-MHD system including the right- and left-hand polarized, nearly degenerate quasi-parallel Alfvén waves. The dominant nonlinear process within this model is the four wave interaction, in which a quartet of waves in resonance can exchange energy. By numerically time integrating the DNLS equation with periodic boundary conditions, and by evaluating relative phase among the quartet of waves, we show that the phase coherence is generated when the waves exchange energy among the quartet of waves. As a result, coherent structures (solitons appear in the real space, while in the phase space of the wave frequency and the wave number, the wave power is seen to be distributed around a straight line. The slope of the line corresponds to the propagation speed of the coherent structures. Numerical time integration of the Hall-MHD system with periodic boundary conditions reveals that, wave power of transverse modes and that of longitudinal modes are aligned with a single straight line in the dispersion relation phase space, suggesting that efficient exchange of energy among transverse and longitudinal wave modes is realized in the Hall-MHD. Generation of the longitudinal wave modes violates the assumptions employed in deriving the DNLS such as the quasi
Ginter, S
2000-07-01
Ultrasound (US) thermotherapy is used to treat tumours, located deep in human tissue, by heat. It features by the application of high intensity focused ultrasound (HIFU), high local temperatures of about 90 degrees C and short treating time of a few seconds. Dosage of the therapy remains a problem. To get it under control, one has to know the heat source, i.e. the amount of absorbed US power, which shows nonlinear influences. Therefore, accurate simulations are essential. In this paper, an improved simulation model is introduced which enables accurate investigations of US thermotherapy. It combines nonlinear US propagation effects, which lead to generation of higher harmonics, with a broadband frequency-power law absorption typical for soft tissue. Only the combination of both provides a reliable calculation of the generated heat. Simulations show the influence of nonlinearities and broadband damping for different source signals on the absorbed US power density distribution.
Propagation of the nonlinear plastic stress waves in semi-infinite bar
Directory of Open Access Journals (Sweden)
Edward Włodarczyk
2017-03-01
Full Text Available This paper presents the propagation longitudinal nonlinear plastic stress in thin semi-infinite rod or in wire. The rod is characterized by a nonlinear strain hardening model within the scope a plastic strain. The modulus of strain hardening is a decreasing function of the strain. The frontal bar end is suddenly launching to the velocity V, and subsequently moves with this one. General solution of this boundary value problem of the Lagrangian coordinate (material description and of the Eulerian one (spatial description has been presented. There has been carried out the physical interpretation of the obtained results by means of Lagrangian and Eulerian methods. The results of this paper may be utilized in scientific researches and in engineering practice.
Louisnard, O
2012-01-01
The bubbles involved in sonochemistry and other applications of cavitation oscillate inertially. A correct estimation of the wave attenuation in such bubbly media requires a realistic estimation of the power dissipated by the oscillation of each bubble, by thermal diffusion in the gas and viscous friction in the liquid. Both quantities and calculated numerically for a single inertial bubble driven at 20 kHz, and are found to be several orders of magnitude larger than the linear prediction. Viscous dissipation is found to be the predominant cause of energy loss for bubbles small enough. Then, the classical nonlinear Caflish equations describing the propagation of acoustic waves in a bubbly liquid are recast and simplified conveniently. The main harmonic part of the sound field is found to fulfill a nonlinear Helmholtz equation, where the imaginary part of the squared wave number is directly correlated with the energy lost by a single bubble. For low acoustic driving, linear theory is recovered, but for larger drivings, namely above the Blake threshold, the attenuation coefficient is found to be more than 3 orders of magnitude larger then the linear prediction. A huge attenuation of the wave is thus expected in regions where inertial bubbles are present, which is confirmed by numerical simulations of the nonlinear Helmholtz equation in a 1D standing wave configuration. The expected strong attenuation is not only observed but furthermore, the examination of the phase between the pressure field and its gradient clearly demonstrates that a traveling wave appears in the medium. Copyright © 2011 Elsevier B.V. All rights reserved.
Non-reciprocal wave propagation in one-dimensional nonlinear periodic structures
Directory of Open Access Journals (Sweden)
Benbiao Luo
2018-01-01
Full Text Available We study a one-dimensional nonlinear periodic structure which contains two different spring stiffness and an identical mass in each period. The linear dispersion relationship we obtain indicates that our periodic structure has obvious advantages compared to other kinds of periodic structures (i.e. those with the same spring stiffness but two different mass, including its increased flexibility for manipulating the band gap. Theoretically, the optical cutoff frequency remains unchanged while the acoustic cutoff frequency shifts to a lower or higher frequency. A numerical simulation verifies the dispersion relationship and the effect of the amplitude-dependent signal filter. Based upon this, we design a device which contains both a linear periodic structure and a nonlinear periodic structure. When incident waves with the same, large amplitude pass through it from opposite directions, the output amplitude of the forward input is one order magnitude larger than that of the reverse input. Our devised, non-reciprocal device can potentially act as an acoustic diode (AD without an electrical circuit and frequency shifting. Our result represents a significant step forwards in the research of non-reciprocal wave manipulation.
Nonlinear hyperbolic waves in multidimensions
Prasad, Phoolan
2001-01-01
The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and provides a self-contained account and gradual development of mathematical methods for studying successive positions of these fronts.Nonlinear Hyperbolic Waves in Multidimensions includes all introductory material on nonlinear hyperbolic waves and the theory of shock waves. The author derives the ray theory for a nonlinear wavefront, discusses kink phenomena, and develops a new theory for plane and curved shock propagation. He also derives a full set of conservation laws for a front propagating in two space dimensions, and uses these laws to obtain successive positions of a front with kinks. The treatment includes examples of the theory applied to converging wavefronts...
Wave Propagation in Linear and Nonlinear Photonic Band-Gap Materials
National Research Council Canada - National Science Library
Venakides, Stephanos
2003-01-01
.... Development of 3D boundary element code for EM scattering off photonic crystal slabs. Development of 2D FDTD code that includes nonlinearities and use in studying resonant phenomena. Nonlinear Effects...
Nonlinear waves and weak turbulence
Zakharov, V E
1997-01-01
This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive conservative media. Emphasis is on waves on the surface of an ideal fluid and on Rossby waves in the atmosphere. Although the book deals mainly with weakly nonlinear waves, it is more than simply a description of standard perturbation techniques. The goal is to show that the theory of weakly interacting waves is naturally related to such areas of mathematics as Diophantine equations, differential geometry of waves, Poincaré normal forms, and the inverse scattering method.
Nonlinear modulation of ionization waves
International Nuclear Information System (INIS)
Bekki, Naoaki
1981-01-01
In order to investigate the nonlinear characteristics of ionization waves (moving-striations) in the positive column of glow discharge, a nonlinear modulation of ionization waves in the region of the Pupp critical current is analysed by means of the reductive perturbation method. The modulation of ionization waves is described by a nonlinear Schroedinger type equation. The coefficients of the equation are evaluated using the data of the low pressure Argon-discharge, and the simple solutions (plane wave and envelope soliton type solutions) are presented. Under a certain condition an envelope soliton is propagated through the positive column. (author)
Hamilton, Mark F.
1990-12-01
This report discusses five projects all of which involve basic theoretical research in nonlinear acoustics: (1) pulsed finite amplitude sound beams are studied with a recently developed time domain computer algorithm that solves the KZK nonlinear parabolic wave equation; (2) nonlinear acoustic wave propagation in a liquid layer is a study of harmonic generation and acoustic soliton information in a liquid between a rigid and a free surface; (3) nonlinear effects in asymmetric cylindrical sound beams is a study of source asymmetries and scattering of sound by sound at high intensity; (4) effects of absorption on the interaction of sound beams is a completed study of the role of absorption in second harmonic generation and scattering of sound by sound; and (5) parametric receiving arrays is a completed study of parametric reception in a reverberant environment.
David, P
2013-01-01
Propagation of Waves focuses on the wave propagation around the earth, which is influenced by its curvature, surface irregularities, and by passage through atmospheric layers that may be refracting, absorbing, or ionized. This book begins by outlining the behavior of waves in the various media and at their interfaces, which simplifies the basic phenomena, such as absorption, refraction, reflection, and interference. Applications to the case of the terrestrial sphere are also discussed as a natural generalization. Following the deliberation on the diffraction of the "ground? wave around the ear
Bell, T. F.
1984-01-01
A theory is presented of the nonlinear gyroresonance interaction that takes place in the magnetosphere between energetic electrons and coherent VLF waves propagating in the whistler mode at an arbitrary angle psi with respect to the earth's magnetic field B-sub-0. Particularly examined is the phase trapping (PT) mechanism believed to be responsible for the generation of VLF emissions. It is concluded that near the magnetic equatorial plane gradients of psi may play a very important part in the PT process for nonducted waves. Predictions of a higher threshold value for PT for nonducted waves generally agree with experimental data concerning VLF emission triggering by nonducted waves.
Wave propagation in ordered, disordered, and nonlinear photonic band gap materials
Energy Technology Data Exchange (ETDEWEB)
Lidorikis, Elefterios [Iowa State Univ., Ames, IA (United States)
1999-12-10
Photonic band gap materials are artificial dielectric structures that give the promise of molding and controlling the flow of optical light the same way semiconductors mold and control the electric current flow. In this dissertation the author studied two areas of photonic band gap materials. The first area is focused on the properties of one-dimensional PBG materials doped with Kerr-type nonlinear material, while, the second area is focused on the mechanisms responsible for the gap formation as well as other properties of two-dimensional PBG materials. He first studied, in Chapter 2, the general adequacy of an approximate structure model in which the nonlinearity is assumed to be concentrated in equally-spaced very thin layers, or 6-functions, while the rest of the space is linear. This model had been used before, but its range of validity and the physical reasons for its limitations were not quite clear yet. He performed an extensive examination of many aspects of the model's nonlinear response and comparison against more realistic models with finite-width nonlinear layers, and found that the d-function model is quite adequate, capturing the essential features in the transmission characteristics. The author found one exception, coming from the deficiency of processing a rigid bottom band edge, i.e. the upper edge of the gaps is always independent of the refraction index contrast. This causes the model to miss-predict that there are no soliton solutions for a positive Kerr-coefficient, something known to be untrue.
Nonlinear propagation of the extraordinary mode in a hot magnetoplasma
International Nuclear Information System (INIS)
Khiet, Tu; Furutani, Y.; Ichikawa, Y.H.
1978-07-01
Kinetic theory for a nonlinear propagation of quasi-monochromatic extraordinary waves is presented. It reveals that propagation of an envelope of the extraordinary carriers is described by the nonlinear Schroedinger equation. In a cold plasma limit, a detailed analysis is carried out on a behaviour of the envelope of the upper- and the lower-hybrid waves at respective resonant frequency ranges. (author)
Tubaldi, Eleonora; Amabili, Marco; Païdoussis, Michael P.
2017-05-01
In deformable shells conveying pulsatile flow, oscillatory pressure changes cause local movements of the fluid and deformation of the shell wall, which propagate downstream in the form of a wave. In biomechanics, it is the propagation of the pulse that determines the pressure gradient during the flow at every location of the arterial tree. In this study, a woven Dacron aortic prosthesis is modelled as an orthotropic circular cylindrical shell described by means of the Novozhilov nonlinear shell theory. Flexible boundary conditions are considered to simulate connection with the remaining tissue. Nonlinear vibrations of the shell conveying pulsatile flow and subjected to pulsatile pressure are investigated taking into account the effects of the pulse-wave propagation. For the first time in literature, coupled fluid-structure Lagrange equations of motion for a non-material volume with wave propagation in case of pulsatile flow are developed. The fluid is modeled as a Newtonian inviscid pulsatile flow and it is formulated using a hybrid model based on the linear potential flow theory and considering the unsteady viscous effects obtained from the unsteady time-averaged Navier-Stokes equations. Contributions of pressure and velocity propagation are also considered in the pressure drop along the shell and in the pulsatile frictional traction on the internal wall in the axial direction. A numerical bifurcation analysis employs a refined reduced order model to investigate the dynamic behavior of a pressurized Dacron aortic graft conveying blood flow. A pulsatile time-dependent blood flow model is considered by applying the first harmonic of the physiological waveforms of velocity and pressure during the heart beating period. Geometrically nonlinear vibration response to pulsatile flow and transmural pulsatile pressure, considering the propagation of pressure and velocity changes inside the shell, is here presented via frequency-response curves, time histories, bifurcation
Wave transmission in nonlinear lattices
International Nuclear Information System (INIS)
Hennig, D.; Tsironis, G.P.
1999-01-01
The interplay of nonlinearity with lattice discreteness leads to phenomena and propagation properties quite distinct from those appearing in continuous nonlinear systems. For a large variety of condensed matter and optics applications the continuous wave approximation is not appropriate. In the present review we discuss wave transmission properties in one dimensional nonlinear lattices. Our paradigmatic equations are discrete nonlinear Schroedinger equations and their study is done through a dynamical systems approach. We focus on stationary wave properties and utilize well known results from the theory of dynamical systems to investigate various aspects of wave transmission and wave localization. We analyze in detail the more general dynamical system corresponding to the equation that interpolates between the non-integrable discrete nonlinear Schroedinger equation and the integrable Albowitz-Ladik equation. We utilize this analysis in a nonlinear Kronig-Penney model and investigate transmission and band modification properties. We discuss the modifications that are effected through an electric field and the nonlinear Wannier-Stark localization effects that are induced. Several applications are described, such as polarons in one dimensional lattices, semiconductor superlattices and one dimensional nonlinear photonic band gap systems. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
Ak, Turgut; Aydemir, Tugba; Saha, Asit; Kara, Abdul Hamid
2018-06-01
Propagation of nonlinear shock waves for the generalised Oskolkov equation and dynamic motions of the perturbed Oskolkov equation are investigated. Employing the unified method, a collection of exact shock wave solutions for the generalised Oskolkov equations is presented. Collocation finite element method is applied to the generalised Oskolkov equation for checking the accuracy of the proposed method by two test problems including the motion of shock wave and evolution of waves with Gaussian and undular bore initial conditions. Considering an external periodic perturbation, the dynamic motions of the perturbed generalised Oskolkov equation are studied depending on the system parameters with the help of phase portrait and time series plot. The perturbed generalised Oskolkov equation exhibits period-3, quasiperiodic and chaotic motions for some special values of the system parameters, whereas the generalised Oskolkov equation presents shock waves in the absence of external periodic perturbation.
International Nuclear Information System (INIS)
Balashova, E.V.; Lemanov, V.V.; Sherman, A.B.
1986-01-01
Generation process of a surface acoustic wave with summarized frequency in collinear propagation of two surface acoustic waves in SrTiO 3 crystal near crystal-phase transition O n → D 4h (T c ≅ 105 K) is investigated. Anomalous increase of a nonlinear parameter Γ ∼ (T-T c ) -1 attributed to a fluctuation mechanism is observed. It is shown that the presence of a surface layer in SrTiO 3 having a higher, than in crystal volume, temperature of phase transition results in summarized frequency signal oscillation
1984-09-01
Asymptotic Results for a Model Equation for Low Reynolds Number Flow, SIAM J. Appi. Math., 35, July 1978. 3. A. S. Yokes : Group Theoretical Aspects of...Quadratic and Cubic Invariants in’ Classical Mechanics, J. Math. Anal. Appl.,’ 74, 342, (1980). 5. A. S. Pokas , P. A. Lagerstrom: On the Use of Lie...Mathematical Methods in Hydrodynamics and %Integrability in Dynamical System, pp. 237-241. 24. 14. J. Ablovitz and A. S. Pokas : A Direct Linearization
Wave modulation in a nonlinear dispersive medium
International Nuclear Information System (INIS)
Kim, Y.C.; Khadra, L.; Powers, E.J.
1980-01-01
A model describing the simultaneous amplitude and phase modulation of a carrier wave propagating in a nonlinear dispersive medium is developed in terms of nonlinear wave-wave interactions between the sidebands and a low frequency wave. It is also shown that the asymmetric distribution of sidebands is determined by the wavenumber dependence of the coupling coefficient. Digital complex demodulation techniques are used to study modulated waves in a weakly ionized plasma and the experimental results support the analytical model
Wave equations for pulse propagation
International Nuclear Information System (INIS)
Shore, B.W.
1987-01-01
Theoretical discussions of the propagation of pulses of laser radiation through atomic or molecular vapor rely on a number of traditional approximations for idealizing the radiation and the molecules, and for quantifying their mutual interaction by various equations of propagation (for the radiation) and excitation (for the molecules). In treating short-pulse phenomena it is essential to consider coherent excitation phenomena of the sort that is manifest in Rabi oscillations of atomic or molecular populations. Such processes are not adequately treated by rate equations for excitation nor by rate equations for radiation. As part of a more comprehensive treatment of the coupled equations that describe propagation of short pulses, this memo presents background discussion of the equations that describe the field. This memo discusses the origin, in Maxwell's equations, of the wave equation used in the description of pulse propagation. It notes the separation into lamellar and solenoidal (or longitudinal and transverse) and positive and negative frequency parts. It mentions the possibility of separating the polarization field into linear and nonlinear parts, in order to define a susceptibility or index of refraction and, from these, a phase and group velocity. The memo discusses various ways of characterizing the polarization characteristics of plane waves, that is, of parameterizing a transverse unit vector, such as the Jones vector, the Stokes vector, and the Poincare sphere. It discusses the connection between macroscopically defined quantities, such as the intensity or, more generally, the Stokes parameters, and microscopic field amplitudes. The material presented here is a portion of a more extensive treatment of propagation to be presented separately. The equations presented here have been described in various books and articles. They are collected here as a summary and review of theory needed when treating pulse propagation
Ye, W; Bel-Brunon, A; Catheline, S; Combescure, A; Rochette, M
2018-01-01
In this study, visco-hyperelastic Landau's model, which is widely used in acoustical physic field, is introduced into a finite element formulation. It is designed to model the nonlinear behaviour of finite amplitude shear waves in soft solids, typically, in biological tissues. This law is used in finite element models based on elastography, experiments reported in Jacob et al, the simulations results show a good agreement with the experimental study: It is observed in both that a plane shear wave generates only odd harmonics and a nonplane wave generates both odd and even harmonics in the spectral domain. In the second part, a parametric study is performed to analyse the influence of different factors on the generation of odd harmonics of plane wave. A quantitative relation is fitted between the odd harmonic amplitudes and the non-linear elastic parameter of Landau's model, which provides a practical guideline to identify the non-linearity of homogeneous tissues using elastography experiment. Copyright © 2017 John Wiley & Sons, Ltd.
International Nuclear Information System (INIS)
Wu, Ru-Shan; Wang, Benfeng; Hu, Chunhua
2015-01-01
We derived the renormalized nonlinear sensitivity operator and the related inverse thin-slab propagator (ITSP) for nonlinear tomographic waveform inversion based on the theory of nonlinear partial derivative operator and its De Wolf approximation. The inverse propagator is based on a renormalization procedure to the forward and inverse transition matrix scattering series. The ITSP eliminates the divergence of the inverse Born series for strong perturbations by stepwise partial summation (renormalization). Numerical tests showed that the inverse Born T-series starts to diverge at moderate perturbation (20% for the given model of Gaussian ball with a radius of 5 wavelength), while the ITSP has no divergence problem for any strong perturbations (up to 100% perturbation for test model). In addition, the ITSP is a non-iterative, marching algorithm with only one sweep, and therefore very efficient in comparison with the iterative inversion based on the inverse-Born scattering series. This convergence and efficiency improvement has potential applications to the iterative procedure of waveform inversion. (paper)
Alghamdi, Amal Mohammed
2012-04-01
Clawpack, a conservation laws package implemented in Fortran, and its Python-based version, PyClaw, are existing tools providing nonlinear wave propagation solvers that use state of the art finite volume methods. Simulations using those tools can have extensive computational requirements to provide accurate results. Therefore, a number of tools, such as BearClaw and MPIClaw, have been developed based on Clawpack to achieve significant speedup by exploiting parallel architectures. However, none of them has been shown to scale on a large number of cores. Furthermore, these tools, implemented in Fortran, achieve parallelization by inserting parallelization logic and MPI standard routines throughout the serial code in a non modular manner. Our contribution in this thesis research is three-fold. First, we demonstrate an advantageous use case of Python in implementing easy-to-use modular extensible scalable scientific software tools by developing an implementation of a parallelization framework, PetClaw, for PyClaw using the well-known Portable Extensible Toolkit for Scientific Computation, PETSc, through its Python wrapper petsc4py. Second, we demonstrate the possibility of getting acceptable Python code performance when compared to Fortran performance after introducing a number of serial optimizations to the Python code including integrating Clawpack Fortran kernels into PyClaw for low-level computationally intensive parts of the code. As a result of those optimizations, the Python overhead in PetClaw for a shallow water application is only 12 percent when compared to the corresponding Fortran Clawpack application. Third, we provide a demonstration of PetClaw scalability on up to the entirety of Shaheen; a 16-rack Blue Gene/P IBM supercomputer that comprises 65,536 cores and located at King Abdullah University of Science and Technology (KAUST). The PetClaw solver achieved above 0.98 weak scaling efficiency for an Euler application on the whole machine excluding the
Wan, Xiang; Tse, Peter W.; Zhang, Xuhui; Xu, Guanghua; Zhang, Qing; Fan, Hongwei; Mao, Qinghua; Dong, Ming; Wang, Chuanwei; Ma, Hongwei
2018-04-01
Under the discipline of nonlinear ultrasonics, in addition to second harmonic generation, static component generation is another frequently used nonlinear ultrasonic behavior in non-destructive testing (NDT) and structural health monitoring (SHM) communities. However, most previous studies on static component generation are mainly based on using longitudinal waves. It is desirable to extend static component generation from primary longitudinal waves to primary Lamb waves. In this paper, static component generation from the primary Lamb waves is studied. Two major issues are numerically investigated. First, the mode of static displacement component generated from different primary Lamb wave modes is identified. Second, cumulative effect of static displacement component from different primary Lamb wave modes is also discussed. Our study results show that the static component wave packets generated from the primary S0, A0 and S1 modes share the almost same group velocity equal to the phase velocity of S0 mode tending to zero frequency c plate . The finding indicates that whether the primary mode is S0, A0 or S1, the static components generated from these primary modes always share the nature of S0 mode. This conclusion is also verified by the displacement filed of these static components that the horizontal displacement field is almost uniform and the vertical displacement filed is antisymmetric across the thickness of the plate. The uniform distribution of horizontal displacement filed enables the static component, regardless of the primary Lamb modes, to be a promising technique for evaluating microstructural damages buried in the interior of a structure. Our study also illustrates that the static components are cumulative regardless of whether the phase velocity of the primary and secondary waves is matched or not. This observation indicates that the static component overcomes the limitations of the traditional nonlinear Lamb waves satisfying phase velocity
Matsumoto, Takuma; Shibata, Kazunari
We have performed MHD simulations of Alfven wave propagation along an open ux tube in the solar atmosphere. In our numerical model, Alfven waves are generated by the photospheric granular motion. As the wave generator, we used a derived temporal spectrum of the photo-spheric granular motion from G-band movies of Hinode/SOT. It is shown that the total energy ux at the corona becomes larger and the transition region height becomes higher in the case when we use the observed spectrum rather than white/pink noise spectrum as the wave gener-ator. This difference can be explained by the Alfven wave resonance between the photosphere and the transition region. After performing Fourier analysis on our numerical results, we have found that the region between the photosphere and the transition region becomes an Alfven wave resonant cavity. We have conrmed that there are at least three resonant frequencies, 1, 3 and 5 mHz, in our numerical model. Alfven wave resonance is one of the most effective mechanisms to explain the dynamics of the spicules and the sufficient energy ux to heat the corona.
Schamel, Hans; Eliasson, Bengt
2016-05-01
Quantum statistics and electron trapping have a decisive influence on the propagation characteristics of coherent stationary electrostatic waves. The description of these strictly nonlinear structures, which are of electron hole type and violate linear Vlasov theory due to the particle trapping at any excitation amplitude, is obtained by a correct reduction of the three-dimensional Fermi-Dirac distribution function to one dimension and by a proper incorporation of trapping. For small but finite amplitudes, the holes become of cnoidal wave type and the electron density is shown to be described by a ϕ ( x ) 1 / 2 rather than a ϕ ( x ) expansion, where ϕ ( x ) is the electrostatic potential. The general coefficients are presented for a degenerate plasma as well as the quantum statistical analogue to these steady state coherent structures, including the shape of ϕ ( x ) and the nonlinear dispersion relation, which describes their phase velocity.
International Nuclear Information System (INIS)
Singh, Kh.I.; Das, G.C.
1993-01-01
Soliton propagations are studied in a relativistic multicomponent ion-beam plasma through the derivation of Korteweg-deVries (K-dV) and modified K-dV (mK-dV) equations. A generalization of the mK-dV equation involving higher order nonlinearities gives a transitive link between the K-dV and mK-dV equations for isothermal plasma, and the validity of this generalized equation throughout the whole range of negative ion concentrations is investigated through the derivation of Sagdeev potential. Parallel discussion of various K-dV solitons enlightening the experimental implications is also made. (author). 22 refs
Wave propagation in elastic solids
Achenbach, Jan
1984-01-01
The propagation of mechanical disturbances in solids is of interest in many branches of the physical scienses and engineering. This book aims to present an account of the theory of wave propagation in elastic solids. The material is arranged to present an exposition of the basic concepts of mechanical wave propagation within a one-dimensional setting and a discussion of formal aspects of elastodynamic theory in three dimensions, followed by chapters expounding on typical wave propagation phenomena, such as radiation, reflection, refraction, propagation in waveguides, and diffraction. The treat
Nonlinear operators and their propagators
International Nuclear Information System (INIS)
Schwartz, C.
1997-01-01
Mathematical physicists are familiar with a large set of tools designed for dealing with linear operators, which are so common in both the classical and quantum theories; but many of those tools are useless with nonlinear equations of motion. In this work a general algebra and calculus is developed for working with nonlinear operators: The basic new tool being the open-quotes slash product,close quotes defined by A(1+εB) =A+εA/B+O(ε 2 ). For a generic time development equation, the propagator is constructed and then there follows the formal version of time dependent perturbation theory, in remarkable similarity to the linear situation. A nonperturbative approximation scheme capable of producing high accuracy computations, previously developed for linear operators, is shown to be applicable as well in the nonlinear domain. A number of auxiliary mathematical properties and examples are given. copyright 1997 American Institute of Physics
Wave propagation in electromagnetic media
Davis, Julian L
1990-01-01
This is the second work of a set of two volumes on the phenomena of wave propagation in nonreacting and reacting media. The first, entitled Wave Propagation in Solids and Fluids (published by Springer-Verlag in 1988), deals with wave phenomena in nonreacting media (solids and fluids). This book is concerned with wave propagation in reacting media-specifically, in electro magnetic materials. Since these volumes were designed to be relatively self contained, we have taken the liberty of adapting some of the pertinent material, especially in the theory of hyperbolic partial differential equations (concerned with electromagnetic wave propagation), variational methods, and Hamilton-Jacobi theory, to the phenomena of electromagnetic waves. The purpose of this volume is similar to that of the first, except that here we are dealing with electromagnetic waves. We attempt to present a clear and systematic account of the mathematical methods of wave phenomena in electromagnetic materials that will be readily accessi...
Harmonic surface wave propagation in plasma
International Nuclear Information System (INIS)
Shivarova, A.; Stoychev, T.
1980-01-01
Second order harmonic surface waves generated by one fundamental high-frequency surface wave are investigated experimentally in gas discharge plasma. Two types of harmonic waves of equal frequency, associated with the linear dispersion relation and the synchronism conditions relatively propagate. The experimental conditions and the different space damping rates of the waves ensure the existence of different spatial regions (consecutively arranged along the plasma column) of a dominant propagation of each one of these two waves. Experimental data are obtained both for the wavenumbers and the space damping rates by relatively precise methods for wave investigations such as the methods of time-space diagrams and of phase shift measurements. The results are explained by the theoretical model for nonlinear mixing of dispersive waves. (author)
Nonlinear coupled Alfven and gravitational waves
International Nuclear Information System (INIS)
Kaellberg, Andreas; Brodin, Gert; Bradley, Michael
2004-01-01
In this paper we consider nonlinear interaction between gravitational and electromagnetic waves in a strongly magnetized plasma. More specifically, we investigate the propagation of gravitational waves with the direction of propagation perpendicular to a background magnetic field and the coupling to compressional Alfven waves. The gravitational waves are considered in the high-frequency limit and the plasma is modeled by a multifluid description. We make a self-consistent, weakly nonlinear analysis of the Einstein-Maxwell system and derive a wave equation for the coupled gravitational and electromagnetic wave modes. A WKB-approximation is then applied and as a result we obtain the nonlinear Schroedinger equation for the slowly varying wave amplitudes. The analysis is extended to 3D wave pulses, and we discuss the applications to radiation generated from pulsar binary mergers. It turns out that the electromagnetic radiation from a binary merger should experience a focusing effect, that in principle could be detected
Enhancing propagation characteristics of truncated localized waves in silica
Salem, Mohamed
2011-07-01
The spectral characteristics of truncated Localized Waves propagating in dispersive silica are analyzed. Numerical experiments show that the immunity of the truncated Localized Waves propagating in dispersive silica to decay and distortion is enhanced as the non-linearity of the relation between the transverse spatial spectral components and the wave vector gets stronger, in contrast to free-space propagating waves, which suffer from early decay and distortion. © 2011 IEEE.
Some considerations of wave propagation
Verdonk, P. L. F. M.
The meaning of group velocity and its relation to conserved quantities are demonstrated. The origin of wave dispersion in terms of nonlocal and relaxation phenomena are clarified. The character of a wave described by an equation with a general type of nonlinearity and general dispersion terms is explained. The steepening of a wave flank and the occurrence of stationary waves are discussed.
Li, Tatsien
2017-01-01
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
Solitons and Weakly Nonlinear Waves in Plasmas
DEFF Research Database (Denmark)
Pécseli, Hans
1985-01-01
Theoretical descriptions of solitons and weakly nonlinear waves propagating in plasma media are reviewed, with particular attention to the Korteweg-de Vries (KDV) equation and the Nonlinear Schrödinger equation (NLS). The modifications of these basic equations due to the effects of resonant...
Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium
Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying
2015-01-01
A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium. PMID:26073066
Directory of Open Access Journals (Sweden)
L. S. Konev
2015-09-01
Full Text Available Numerical method for calculation of forward and backward waves of intense few-cycle laser pulses propagating in an optical waveguide with dispersion and cubic nonlinearity of electronic and electronic-vibration nature is described. Simulations made with the implemented algorithm show that accounting for Raman nonlinearity does not lead to qualitative changes in behavior of the backward wave. Speaking about quantitative changes, the increase of efficiency of energy transfer from the forward wave to the backward wave is observed. Presented method can be also used to simulate interaction of counterpropagating pulses.
Rogue waves in nonlinear science
International Nuclear Information System (INIS)
Yan Zhenya
2012-01-01
Rogue waves, as a special type of solitary waves, play an important role in nonlinear optics, Bose-Einstein condensates, ocean, atmosphere, and even finance. In this report, we mainly review on the history of the rogue wave phenomenon and recent development of rogue wave solutions in some nonlinear physical models arising in the fields of nonlinear science.
Wave propagation in electromagnetic media
International Nuclear Information System (INIS)
Davis, J.L.
1990-01-01
This book is concerned with wave propagation in reacting media, specifically in electromagnetic materials. An account is presented of the mathematical methods of wave phenomena in electromagnetic materials. The author presents the theory of time-varying electromagnetic fields, which involves a discussion of Faraday's laws, Maxwell's equations and their application to electromagnetic wave propagation under a variety of conditions. The author gives a discussion of magnetohydrodynamics and plasma physics. Chapters are included on quantum mechanics and the theory of relativity. The mathematical foundation of electromagnetic waves vis a vis partial differential equations is discussed
Nonlinear waves in plasma with negative ion
International Nuclear Information System (INIS)
Saito, Maki; Watanabe, Shinsuke; Tanaca, Hiroshi.
1984-01-01
The propagation of nonlinear ion wave is investigated theoretically in a plasma with electron, positive ion and negative ion. The ion wave of long wavelength is described by a modified K-dV equation instead of a K-dV equation when the nonlinear coefficient of the K-dV equation vanishes at the critical density of negative ion. In the vicinity of the critical density, the ion wave is described by a coupled K-dV and modified K-dV equation. The transition from a compressional soliton to a rarefactive soliton and vice versa are examined by the coupled equation as a function of the negative ion density. The ion wave of short wavelength is described by a nonlinear Schroedinger equation. In the plasma with a negative ion, the nonlinear coefficient of the nonlinear Schroedinger equation changes the sign and the ion wave becomes modulationally unstable. (author)
Numerical simulation methods for wave propagation through optical waveguides
International Nuclear Information System (INIS)
Sharma, A.
1993-01-01
The simulation of the field propagation through waveguides requires numerical solutions of the Helmholtz equation. For this purpose a method based on the principle of orthogonal collocation was recently developed. The method is also applicable to nonlinear pulse propagation through optical fibers. Some of the salient features of this method and its application to both linear and nonlinear wave propagation through optical waveguides are discussed in this report. 51 refs, 8 figs, 2 tabs
Modeling the SAR Signature of Nonlinear Internal Waves
National Research Council Canada - National Science Library
Lettvin, Ellen E
2008-01-01
Nonlinear Internal Waves are pervasive globally, particularly in coastal waters. The currents and displacements associated with internal waves influence acoustic propagation and underwater navigation, as well as ocean transport and mixing...
Propagation of an ionizing surface electromagnetic wave
Energy Technology Data Exchange (ETDEWEB)
Boev, A.G.; Prokopov, A.V.
1976-11-01
The propagation of an rf surface wave in a plasma which is ionized by the wave itself is analyzed. The exact solution of the nonlinear Maxwell equations is discussed for the case in which the density of plasma electrons is an exponential function of the square of the electric field. The range over which the surface wave exists and the frequency dependence of the phase velocity are found. A detailed analysis is given for the case of a plasma whose initial density exceeds the critical density at the wave frequency. An increase in the wave amplitude is shown to expand the frequency range over which the plasma is transparent; The energy flux in the plasma tends toward a certain finite value which is governed by the effective ionization field.
Energy Technology Data Exchange (ETDEWEB)
Moreira, Roger Matsumoto; Mendes, Andre Avelino de Oliveira; Bacchi, Raphael David Aquilino [Universidade Federal Fluminense (UFF), Niteroi, RJ (Brazil). Escola de Engenharia. Lab. de Dinamica dos Fluidos Computacional (LabCFD)], e-mail: roger@vm.uff.br, e-mail: andreavelinoom@gmail.com, e-mail: raphael@esss.com.br
2006-07-01
The present work aims to model numerically the generation and propagation of waves in a reservoir, represented by a two-dimensional impermeable box, with a flat horizontal bottom and two vertical walls. The horizontal or vertical harmonic motion is imposed at the container, which is partially filled with water, with two possible initial conditions for the free surface: still water or a stationary sinusoidal wave. Two numerical methods are employed in the solution of the boundary value problem. The first is based on solving an integral equation that arises from Cauchy's integral theorem for functions of a complex variable. The transient nonlinear free surface flow is simulated using a boundary integral method. Numerical results are validated by comparing them with classical analytical solutions. The second method uses the commercial code ANSYS CFX with its homogeneous free surface model. In this case, results are compared with experiments done by Bredmose et al. (2003). In both models, interesting features at the free surface are obtained and discussed. (author)
Nonlinear diffuse scattering of the random-phased wave
International Nuclear Information System (INIS)
Kato, Yoshiaki; Arinaga, Shinji; Mima, Kunioki.
1983-01-01
First experimental observation of the nonlinear diffuse scattering is reported. This new effect was observed in the propagation of the random-phased wave through a nonlinear dielectric medium. This effect is ascribed to the diffusion of the wavevector of the electro-magnetic wave to the lateral direction due to the randomly distributed nonlinear increase in the refractive index. (author)
2016-01-01
This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest. Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and numerical simulations, classical and modern mathematical approaches can be used to gain insight into their dynamics. The book presents several avenues and offers a wide range of material of current interest. Due to the interdisciplinary nature of the subject, the book should be of interest to mathematicians (pure and applied), physicists and engineers. The lectures provide a useful source for those who want to begin to investigate how mathematics can be used to improve our understanding of water wave phenomena. In addition, some of the...
Analytical and Numerical Modeling of Tsunami Wave Propagation for double layer state in Bore
Yuvaraj, V.; Rajasekaran, S.; Nagarajan, D.
2018-04-01
Tsunami wave enters into the river bore in the landslide. Tsunami wave propagation are described in two-layer states. The velocity and amplitude of the tsunami wave propagation are calculated using the double layer. The numerical and analytical solutions are given for the nonlinear equation of motion of the wave propagation in a bore.
Linear and Nonlinear Electrostatic Waves in Unmagnetized Dusty Plasmas
International Nuclear Information System (INIS)
Mamun, A. A.; Shukla, P. K.
2010-01-01
A rigorous and systematic theoretical study has been made of linear and nonlinear electrostatic waves propagating in unmagnetized dusty plasmas. The basic features of linear and nonlinear electrostatic waves (particularly, dust-ion-acoustic and dust-acoustic waves) for different space and laboratory dusty plasma conditions are described. The experimental observations of such linear and nonlinear features of dust-ion-acoustic and dust-acoustic waves are briefly discussed.
Solitary waves on nonlinear elastic rods. II
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1987-01-01
In continuation of an earlier study of propagation of solitary waves on nonlinear elastic rods, numerical investigations of blowup, reflection, and fission at continuous and discontinuous variation of the cross section for the rod and reflection at the end of the rod are presented. The results ar...... are compared with predictions of conservation theorems for energy and momentum....
2015-05-31
welded as well as HAZ region. Nonlinear Ultrasonic (NLU) is also now used to characterise the creep damage. Sony Baby et al. used the NLU technique...Šohaj, R Foret, “Microstructural stability of 316TI/P92 and 17242/P91 weld joints”, METAL 2011, 18th – 20th May 2011, Brno, Czech Republic, EU. [60] P J...harmonic generation”, J. Appl. Phys., 81(7); 2957-2962 (1997). [63] G E Dieter, Mechanical Metallurgy , McGraw-Hill Book Co., 1988 [64] J H Cantrell, and W
Wave propagation in spatially modulated tubes
Energy Technology Data Exchange (ETDEWEB)
Ziepke, A., E-mail: ziepke@itp.tu-berlin.de; Martens, S.; Engel, H. [Institut für Theoretische Physik, Hardenbergstraße 36, EW 7-1, Technische Universität Berlin, 10623 Berlin (Germany)
2016-09-07
We investigate wave propagation in rotationally symmetric tubes with a periodic spatial modulation of cross section. Using an asymptotic perturbation analysis, the governing quasi-two-dimensional reaction-diffusion equation can be reduced into a one-dimensional reaction-diffusion-advection equation. Assuming a weak perturbation by the advection term and using projection method, in a second step, an equation of motion for traveling waves within such tubes can be derived. Both methods predict properly the nonlinear dependence of the propagation velocity on the ratio of the modulation period of the geometry to the intrinsic width of the front, or pulse. As a main feature, we observe finite intervals of propagation failure of waves induced by the tube’s modulation and derive an analytically tractable condition for their occurrence. For the highly diffusive limit, using the Fick-Jacobs approach, we show that wave velocities within modulated tubes are governed by an effective diffusion coefficient. Furthermore, we discuss the effects of a single bottleneck on the period of pulse trains. We observe period changes by integer fractions dependent on the bottleneck width and the period of the entering pulse train.
Nonlinear extraordinary wave in dense plasma
Energy Technology Data Exchange (ETDEWEB)
Krasovitskiy, V. B., E-mail: krasovit@mail.ru [Russian Academy of Sciences, Keldysh Institute of Applied Mathematics (Russian Federation); Turikov, V. A. [Russian University of Peoples’ Friendship (Russian Federation)
2013-10-15
Conditions for the propagation of a slow extraordinary wave in dense magnetized plasma are found. A solution to the set of relativistic hydrodynamic equations and Maxwell’s equations under the plasma resonance conditions, when the phase velocity of the nonlinear wave is equal to the speed of light, is obtained. The deviation of the wave frequency from the resonance frequency is accompanied by nonlinear longitudinal-transverse oscillations. It is shown that, in this case, the solution to the set of self-consistent equations obtained by averaging the initial equations over the period of high-frequency oscillations has the form of an envelope soliton. The possibility of excitation of a nonlinear wave in plasma by an external electromagnetic pulse is confirmed by numerical simulations.
Periodic waves in nonlinear metamaterials
International Nuclear Information System (INIS)
Liu, Wen-Jun; Xiao, Jing-Hua; Yan, Jie-Yun; Tian, Bo
2012-01-01
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. -- Highlights: ► Equations for the monochromatic waves in transverse magnetic polarization have been studied. ► Analytic periodic waves for the equations have been obtained. ► Periodic waves are theoretically presented and studied in the nonlinear metamaterials.
Nonlocal nonlinear coupling of kinetic sound waves
Directory of Open Access Journals (Sweden)
O. Lyubchyk
2014-11-01
Full Text Available We study three-wave resonant interactions among kinetic-scale oblique sound waves in the low-frequency range below the ion cyclotron frequency. The nonlinear eigenmode equation is derived in the framework of a two-fluid plasma model. Because of dispersive modifications at small wavelengths perpendicular to the background magnetic field, these waves become a decay-type mode. We found two decay channels, one into co-propagating product waves (forward decay, and another into counter-propagating product waves (reverse decay. All wavenumbers in the forward decay are similar and hence this decay is local in wavenumber space. On the contrary, the reverse decay generates waves with wavenumbers that are much larger than in the original pump waves and is therefore intrinsically nonlocal. In general, the reverse decay is significantly faster than the forward one, suggesting a nonlocal spectral transport induced by oblique sound waves. Even with low-amplitude sound waves the nonlinear interaction rate is larger than the collisionless dissipation rate. Possible applications regarding acoustic waves observed in the solar corona, solar wind, and topside ionosphere are briefly discussed.
On the propagation of truncated localized waves in dispersive silica
Salem, Mohamed
2010-01-01
Propagation characteristics of truncated Localized Waves propagating in dispersive silica and free space are numerically analyzed. It is shown that those characteristics are affected by the changes in the relation between the transverse spatial spectral components and the wave vector. Numerical experiments demonstrate that as the non-linearity of this relation gets stronger, the pulses propagating in silica become more immune to decay and distortion whereas the pulses propagating in free-space suffer from early decay and distortion. © 2010 Optical Society of America.
Nonlinear wave beams in a piezo semiconducting layer
International Nuclear Information System (INIS)
Bagdoev, A.G.; Shekoyan, A.V.; Danoyan, Z.N.
1997-01-01
The propagation of quasi-monochromatic nonlinear wave in a piezo semiconducting layer taking into account electron-concentration nonlinearity is considered. For such medium the evolution equations for incoming and reflected waves are derived. Nonlinear Schroedinger equations and solutions for narrow beams are obtained. It is shown that symmetry of incoming and reflected waves does not take place. The focusing of beams is investigated.18 refs
Collapse of nonlinear Langmuir waves
International Nuclear Information System (INIS)
Malkin, V.M.
1986-01-01
The dispersion of sufficiently intensive Langmuir waves is determined by intrinsic (electron) nonlinearity. During Langmuir collapse the wave energy density required for the appearance of electron nonlinearity is attained, generally speaking, prior to the development of dissipative processes. Up to now, the effect of electron nonlinearity on the collapse dynamics and spectrum of strong Langmuir turbulence ( which may be very appreciable ) has not been studied extensively because of the difficulty of describing nonlinear Langmuir waves. In the present paper the positive determinacy of the electron nonlinear hamiltonian is proven, the increment of modulation instability of a nonlinear Langmuir wave cluster localized in a cavity is calculated, and the universal law of their collapse is found
Wave Propagation in Bimodular Geomaterials
Kuznetsova, Maria; Pasternak, Elena; Dyskin, Arcady; Pelinovsky, Efim
2016-04-01
Observations and laboratory experiments show that fragmented or layered geomaterials have the mechanical response dependent on the sign of the load. The most adequate model accounting for this effect is the theory of bimodular (bilinear) elasticity - a hyperelastic model with different elastic moduli for tension and compression. For most of geo- and structural materials (cohesionless soils, rocks, concrete, etc.) the difference between elastic moduli is such that their modulus in compression is considerably higher than that in tension. This feature has a profound effect on oscillations [1]; however, its effect on wave propagation has not been comprehensively investigated. It is believed that incorporation of bilinear elastic constitutive equations within theory of wave dynamics will bring a deeper insight to the study of mechanical behaviour of many geomaterials. The aim of this paper is to construct a mathematical model and develop analytical methods and numerical algorithms for analysing wave propagation in bimodular materials. Geophysical and exploration applications and applications in structural engineering are envisaged. The FEM modelling of wave propagation in a 1D semi-infinite bimodular material has been performed with the use of Marlow potential [2]. In the case of the initial load expressed by a harmonic pulse loading strong dependence on the pulse sign is observed: when tension is applied before compression, the phenomenon of disappearance of negative (compressive) strains takes place. References 1. Dyskin, A., Pasternak, E., & Pelinovsky, E. (2012). Periodic motions and resonances of impact oscillators. Journal of Sound and Vibration, 331(12), 2856-2873. 2. Marlow, R. S. (2008). A Second-Invariant Extension of the Marlow Model: Representing Tension and Compression Data Exactly. In ABAQUS Users' Conference.
Propagation of sound waves in ducts
DEFF Research Database (Denmark)
Jacobsen, Finn
2000-01-01
Plane wave propagation in ducts with rigid walls, radiation from ducts, classical four-pole theory for composite duct systems, and three-dimentional waves in wave guides of various cross-sectional shape are described.......Plane wave propagation in ducts with rigid walls, radiation from ducts, classical four-pole theory for composite duct systems, and three-dimentional waves in wave guides of various cross-sectional shape are described....
Use of conformal mapping to describe MHD wave propagation
International Nuclear Information System (INIS)
Bulanov, S.V.; Pegoraro, F.
1993-01-01
A method is proposed for finding explicit exact solutions of the magnetohydrodynamic equations describing the propagation of magnetoacoustic waves in a plasma in a magnetic potential that depends on two spatial coordinates. This method is based on the use of conformal mappings to transform the wave equation into an equation describing the propagation of waves in a uniform magnetic field. The basic properties of magnetoacoustic and Alfven waves near the critical points, magnetic separatrices, and in configuration with magnetic islands are discussed. Expressions are found for the dimensionless parameters which determine the relative roles of the plasma pressure, nonlinearity, and dissipation near the critical points. 30 refs
Nonlinear wavenumber of an electron plasma wave
International Nuclear Information System (INIS)
Vidmar, P.J.; Malmberg, J.H.; Starke, T.P.
1976-01-01
The wavenumber of a large-amplitude electron plasma wave propagating on a collisionless plasma column is measured. The wavenumber is shifted from that of a small-amplitude wave of the same frequency. This nonlinear wavenumber shift, deltak/subr/, depends on position, frequency, and initial wave amplitude, Phi. The observed spatial oscillations of deltak/subr/ agree qualitatively with recent theories. Experimentally deltak/subr/proportionalk/subi/S (Phi) rootPhi where k/subi/ is the linear Landau damping coefficient, S (Phi) equivalentk/subi/(Phi)/k/subi/, and k/subi/(Phi) is the initial damping coefficient which depends on Phi
Optical rogue waves and soliton turbulence in nonlinear fibre optics
DEFF Research Database (Denmark)
Genty, G.; Dudley, J. M.; de Sterke, C. M.
2009-01-01
We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required.......We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required....
On Maximally Dissipative Shock Waves in Nonlinear Elasticity
Knowles, James K.
2010-01-01
Shock waves in nonlinearly elastic solids are, in general, dissipative. We study the following question: among all plane shock waves that can propagate with a given speed in a given one-dimensional nonlinearly elastic bar, which one—if any—maximizes the rate of dissipation? We find that the answer to this question depends strongly on the qualitative nature of the stress-strain relation characteristic of the given material. When maximally dissipative shocks do occur, they propagate according t...
Radio wave propagation and parabolic equation modeling
Apaydin, Gokhan
2018-01-01
A thorough understanding of electromagnetic wave propagation is fundamental to the development of sophisticated communication and detection technologies. The powerful numerical methods described in this book represent a major step forward in our ability to accurately model electromagnetic wave propagation in order to establish and maintain reliable communication links, to detect targets in radar systems, and to maintain robust mobile phone and broadcasting networks. The first new book on guided wave propagation modeling and simulation to appear in nearly two decades, Radio Wave Propagation and Parabolic Equation Modeling addresses the fundamentals of electromagnetic wave propagation generally, with a specific focus on radio wave propagation through various media. The authors explore an array of new applications, and detail various v rtual electromagnetic tools for solving several frequent electromagnetic propagation problems. All of the methods described are presented within the context of real-world scenari...
Nonlinear MHD Waves in a Prominence Foot
Ofman, L.; Knizhnik, K.; Kucera, T.; Schmieder, B.
2015-11-01
We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ˜ δn/n). The waves are evident as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5-11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5-14 G. For the typical prominence density the corresponding fast magnetosonic speed is ˜20 km s-1, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.
NONLINEAR MHD WAVES IN A PROMINENCE FOOT
Energy Technology Data Exchange (ETDEWEB)
Ofman, L. [Catholic University of America, Washington, DC 20064 (United States); Knizhnik, K.; Kucera, T. [NASA Goddard Space Flight Center, Code 671, Greenbelt, MD 20771 (United States); Schmieder, B. [LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris-Diderot, Sorbonne Paris Cit, 5 place Jules Janssen, F-92195 Meudon (France)
2015-11-10
We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ∼ δn/n). The waves are evident as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5–11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5–14 G. For the typical prominence density the corresponding fast magnetosonic speed is ∼20 km s{sup −1}, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations...
Studies of nonlinear femtosecond pulse propagation in bulk materials
Eaton, Hilary Kaye
2000-10-01
Femtosecond pulse lasers are finding widespread application in a variety of fields including medical research, optical switching and communications, plasma formation, high harmonic generation, and wavepacket formation and control. As the number of applications for femtosecond pulses increases, so does the need to fully understand the linear and nonlinear processes involved in propagating these pulses through materials under various conditions. Recent advances in pulse measurement techniques, such as frequency-resolved optical gating (FROG), allow measurement of the full electric field of the pulse and have made detailed investigations of short- pulse propagation effects feasible. In this thesis, I present detailed experimental studies of my work involving nonlinear propagation of femtosecond pulses in bulk media. Studies of plane-wave propagation in fused silica extend the SHG form of FROG from a simple pulse diagnostic to a useful method of interrogating the nonlinear response of a material. Studies of nonlinear propagation are also performed in a regime where temporal pulse splitting occurs. Experimental results are compared with a three- dimensional nonlinear Schrödinger equation. This comparison fuels the development of a more complete model for pulse splitting. Experiments are also performed at peak input powers above those at which pulse splitting is observed. At these higher intensities, a broadband continuum is generated. This work presents a detailed study of continuum behavior and power loss as well as the first near-field spatial- spectral measurements of the generated continuum light. Nonlinear plane-wave propagation of short pulses in liquids is also investigated, and a non-instantaneous nonlinearity with a surprisingly short response time of 10 fs is observed in methanol. Experiments in water confirm that this effect in methanol is indeed real. Possible explanations for the observed effect are discussed and several are experimentally rejected. This
Nonlinear propagation in fusion laser systems
International Nuclear Information System (INIS)
Bliss, E.S.; Glass, A.J.; Glaze, J.A.
1977-11-01
This report was assembled to provide a brief review of the historical development of the study of self-focusing and nonlinear light propagation and its impact on the design of large, Nd-glass lasers for fusion research. No claim to completeness is made, but we feel that the enclosed summary does not miss many of the major developments in the field
Nonlinear waves in waveguides with stratification
Leble, Sergei B
1991-01-01
S.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory.
Nonlinear evolution equations for waves in random media
International Nuclear Information System (INIS)
Pelinovsky, E.; Talipova, T.
1994-01-01
The scope of this paper is to highlight the main ideas of asymptotical methods applying in modern approaches of description of nonlinear wave propagation in random media. We start with the discussion of the classical conception of ''mean field''. Then an exactly solvable model describing nonlinear wave propagation in the medium with fluctuating parameters is considered in order to demonstrate that the ''mean field'' method is not correct. We develop new asymptotic procedures of obtaining the nonlinear evolution equations for the wave fields in random media. (author). 16 refs
Lamb wave propagation in monocrystalline silicon wafers
Fromme, P.; Pizzolato, M.; Robyr, J-L; Masserey, B.
2018-01-01
Monocrystalline silicon wafers are widely used in the photovoltaic industry for solar panels with high conversion efficiency. Guided ultrasonic waves offer the potential to efficiently detect micro-cracks in the thin wafers. Previous studies of ultrasonic wave propagation in silicon focused on effects of material anisotropy on bulk ultrasonic waves, but the dependence of the wave propagation characteristics on the material anisotropy is not well understood for Lamb waves. The phase slowness a...
Gurbatov, S N; Saichev, A I
2012-01-01
"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is...
Nonlinear Scattering of VLF Waves in the Radiation Belts
Crabtree, Chris; Rudakov, Leonid; Ganguli, Guru; Mithaiwala, Manish
2014-10-01
Electromagnetic VLF waves, such as whistler mode waves, control the lifetime of trapped electrons in the radiation belts by pitch-angle scattering. Since the pitch-angle scattering rate is a strong function of the wave properties, a solid understanding of VLF wave sources and propagation in the magnetosphere is critical to accurately calculate electron lifetimes. Nonlinear scattering (Nonlinear Landau Damping) is a mechanism that can strongly alter VLF wave propagation [Ganguli et al. 2010], primarily by altering the direction of propagation, and has not been accounted for in previous models of radiation belt dynamics. Laboratory results have confirmed the dramatic change in propagation direction when the pump wave has sufficient amplitude to exceed the nonlinear threshold [Tejero et al. 2014]. Recent results show that the threshold for nonlinear scattering can often be met by naturally occurring VLF waves in the magnetosphere, with wave magnetic fields of the order of 50-100 pT inside the plasmapause. Nonlinear scattering can then dramatically alter the macroscopic dynamics of waves in the radiation belts leading to the formation of a long-lasting wave-cavity [Crabtree et al. 2012] and, when amplification is present, a multi-pass amplifier [Ganguli et al. 2012]. By considering these effects, the lifetimes of electrons can be dramatically reduced. This work is supported by the Naval Research Laboratory base program.
On nonlinear periodic drift waves
International Nuclear Information System (INIS)
Kauschke, U.; Schlueter, H.
1990-09-01
Nonlinear periodic drift waves are investigated on the basis of a simple perturbation scheme for both the amplitude and inverse frequency. The coefficients for the generation of the forced harmonics are derived, a nonlinear dispersion relation is suggested and a criterion for the onset of the modulational instability is obtained. The results are compared with the ones obtained with the help of a standard KBM-treatment. Moreover cnoidal drift waves are suggested and compared to an experimental observation. (orig.)
Shock wave propagation in neutral and ionized gases
International Nuclear Information System (INIS)
Podder, N. K.; Wilson IV, R. B.; Bletzinger, P.
2008-01-01
Preliminary measurements on a recently built shock tube are presented. Planar shock waves are excited by the spark discharge of a capacitor, and launched into the neutral argon or nitrogen gas as well as its ionized glow discharge in the pressure region 1-17 Torr. For the shock wave propagation in the neutral argon at fixed capacitor charging voltage, the shock wave velocity is found to increase nonlinearly at the lower pressures, reach a maximum at an intermediate pressure, and then decrease almost linearly at the higher pressures, whereas the shock wave strength continues to increase at a nonlinear rate over the entire range of pressure. However, at fixed gas pressure the shock wave velocity increases almost monotonically as the capacitor charging voltage is increased. For the shock wave propagation in the ionized argon glow, the shock wave is found to be most influenced by the glow discharge plasma current. As the plasma current is increased, both the shock wave propagation velocity and the dispersion width are observed to increase nonlinearly
A theory of coherent propagation of light wave in semiconductors
International Nuclear Information System (INIS)
Zi-zhao, G.; Guo-zhen, Y.
1980-05-01
In this paper, we suggest a theory to describe the pheonmena of coherent propagation of light wave in semiconductors. Basing on two band system and considering the interband and intraband transitions induced by light wave and the interaction between electrons, we obtain the nonlinear equations for the description of interaction between carriers and coherent light wave. We have made use of the equations to analyse the phenomena which arise from the interaction between semiconductors and coherent light, for example, the multiphoton transitions, the saturation of light absorption of exciton, the shift of exciton line in intense light field, and the coherent propagation phenomena such as self-induced transparency, etc. (author)
Moderately nonlinear ultrasound propagation in blood-mimicking fluid.
Kharin, Nikolay A; Vince, D Geoffrey
2004-04-01
In medical diagnostic ultrasound (US), higher than-in-water nonlinearity of body fluids and tissue usually does not produce strong nonlinearly distorted waves because of the high absorption. The relative influence of absorption and nonlinearity can be characterized by the Gol'dberg number Gamma. There are two limiting cases in nonlinear acoustics: weak waves (Gamma 1). However, at diagnostic frequencies in tissue and body fluids, the nonlinear effects and effects of absorption more likely are comparable (Gol'dberg number Gamma approximately 1). The aim of this work was to study the nonlinear propagation of a moderately nonlinear US second harmonic signal in a blood-mimicking fluid. Quasilinear solutions to the KZK equation are presented, assuming radiation from a flat and geometrically focused circular Gaussian source. The solutions are expressed in a new simplified closed form and are in very good agreement with those of previous studies measuring and modeling Gaussian beams. The solutions also show good agreement with the measurements of the beams produced by commercially available transducers, even without special Gaussian shading.
Nonlinear effects in water waves
International Nuclear Information System (INIS)
Janssen, P.A.E.M.
1989-05-01
This set of lecture notes on nonlinear effects in water waves was written on the occasion of the first ICTP course on Ocean Waves and Tides held from 26 September until 28 October 1988 in Trieste, Italy. It presents a summary and unification of my knowledge on nonlinear effects of gravity waves on an incompressible fluid without vorticity. The starting point of the theory is the Hamiltonian for water waves. The evolution equations of both weakly nonlinear, shallow water and deep water gravity waves are derived by suitable approximation of the energy of the waves, resulting in the Korteweg-de Vries equation and the Zakharov equation, respectively. Next, interesting properties of the KdV equation (solitons) and the Zakharov equation (instability of a finite amplitude wave train) are discussed in some detail. Finally, the evolution of a homogeneous, random wave field due to resonant four wave processes is considered and the importance of this process for ocean wave prediction is pointed out. 38 refs, 21 figs
Laser beam propagation in nonlinear optical media
Guha, Shekhar
2013-01-01
""This is very unique and promises to be an extremely useful guide to a host of workers in the field. They have given a generalized presentation likely to cover most if not all situations to be encountered in the laboratory, yet also highlight several specific examples that clearly illustrate the methods. They have provided an admirable contribution to the community. If someone makes their living by designing lasers, optical parametric oscillators or other devices employing nonlinear crystals, or designing experiments incorporating laser beam propagation through linear or nonlinear media, then
International Nuclear Information System (INIS)
Jacquot, Jonathan
2013-01-01
A correct understanding of the interactions between the edge plasma and the ion cyclotron (IC) waves (40-80 MHz) is needed to inject reliably large amount of power required for self-sustainable fusion plasmas. These thesis objectives were to model separately, with Comsol Multiphysics, but in compatible approaches the wave coupling and the radio-frequency (RF) sheath formation to anticipate development of a single code combining both. Modelling of fast wave coupling requires a detailed description of the antenna (2D or 3D) and of the plasma environment by a full wave approach for a cold plasma. Absorption of outgoing waves is emulated by perfectly matched layers, rendered compatible with a plasma dielectric tensor. Experimental trends for the coupling resistance of the antennas of Tore Supra are qualitatively reproduced but the coupling efficiency is overestimated. In parallel a novel self-consistent description, including RF sheaths, of the interplay between the cold wave propagation and DC biasing of the magnetized edge plasma of a tokamak was developed with the minimum set of physics ingredients. For Tore Supra antenna cases, the code coupled with TOPICA allowed to unveil qualitatively some unexpected observations on the latest design of Tore Supra Faraday screens whose electrical design was supposed to minimize RF sheaths. From simulations, a DC (Direct Current) current transport appears necessary to explain the radial structures of measurements. Cantilevered bars have been identified as the design element in the antenna structure enhancing the plasma potential. (author) [fr
Wave Propagation of Coupled Modes in the DNA Double Helix
International Nuclear Information System (INIS)
Tabi, Conrad B.; Mohamadou, Alidou; Kofane, Timoleon C.
2010-06-01
The dynamics of waves propagating along the DNA molecule is described by the coupled nonlinear Schroedinger equations. We consider both the single and the coupled nonlinear excitation modes, and we discuss their biological implications. Furthermore, the characteristics of the coupled mode solution are discussed and we show that such a solution can describe the local opening observed within the transcription and the replication phenomena. (author)
Generalized dispersive wave emission in nonlinear fiber optics.
Webb, K E; Xu, Y Q; Erkintalo, M; Murdoch, S G
2013-01-15
We show that the emission of dispersive waves in nonlinear fiber optics is not limited to soliton-like pulses propagating in the anomalous dispersion regime. We demonstrate, both numerically and experimentally, that pulses propagating in the normal dispersion regime can excite resonant dispersive radiation across the zero-dispersion wavelength into the anomalous regime.
Topology optimization of wave-propagation problems
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard; Sigmund, Ole
2006-01-01
Topology optimization is demonstrated as a useful tool for systematic design of wave-propagation problems. We illustrate the applicability of the method for optical, acoustic and elastic devices and structures.......Topology optimization is demonstrated as a useful tool for systematic design of wave-propagation problems. We illustrate the applicability of the method for optical, acoustic and elastic devices and structures....
Wave propagation in thermoelastic saturated porous medium
Indian Academy of Sciences (India)
the existence and propagation of four waves in the medium. Three of the waves are ... predicted infinite speed for propagation of ther- mal signals. Lord and ..... saturated reservoir rock (North-sea Sandstone) is chosen for the numerical model ...
Terrestrial propagation of long electromagnetic waves
Galejs, Janis; Fock, V A
2013-01-01
Terrestrial Propagation of Long Electromagnetic Waves deals with the propagation of long electromagnetic waves confined principally to the shell between the earth and the ionosphere, known as the terrestrial waveguide. The discussion is limited to steady-state solutions in a waveguide that is uniform in the direction of propagation. Wave propagation is characterized almost exclusively by mode theory. The mathematics are developed only for sources at the ground surface or within the waveguide, including artificial sources as well as lightning discharges. This volume is comprised of nine chapte
Oscillating nonlinear acoustic shock waves
DEFF Research Database (Denmark)
Gaididei, Yuri; Rasmussen, Anders Rønne; Christiansen, Peter Leth
2016-01-01
We investigate oscillating shock waves in a tube using a higher order weakly nonlinear acoustic model. The model includes thermoviscous effects and is non isentropic. The oscillating shock waves are generated at one end of the tube by a sinusoidal driver. Numerical simulations show that at resona......We investigate oscillating shock waves in a tube using a higher order weakly nonlinear acoustic model. The model includes thermoviscous effects and is non isentropic. The oscillating shock waves are generated at one end of the tube by a sinusoidal driver. Numerical simulations show...... polynomial in the space and time variables, we find analytical approximations to the observed single shock waves in an infinitely long tube. Using perturbation theory for the driven acoustic system approximative analytical solutions for the off resonant case are determined....
Rogue and shock waves in nonlinear dispersive media
Resitori, Stefania; Baronio, Fabio
2016-01-01
This self-contained set of lectures addresses a gap in the literature by providing a systematic link between the theoretical foundations of the subject matter and cutting-edge applications in both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values. Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together here in terms of their underlying theoretical treatment. This book offers a self-contained graduate-level text intended as both an introduction and reference guide for a new generation of scientists ...
Nonlinear propagation of ultrashort laser pulses in transparent media
International Nuclear Information System (INIS)
Vincotte, A.
2006-10-01
We present different aspects of the propagation of ultrashort laser pulses in transparent media. First, we derive the propagation equations starting from the Maxwell equations. We remind of the main physical phenomena undergone by ultrashort and powerful laser pulses. First self-focusing occurs, owing to the Kerr response of the medium. This self-focusing is stopped by plasma generation from the laser-induced ionization of the ambient atoms. The propagation of the wave generates a super-continuum through self-phase modulation. We recall the main results concerning the simple and multiple filamentation of an intense wave, induced by the beam inhomogeneities and which take place as soon as the beam power is above critical. In a second part, we investigate the influence of high-order nonlinearities on the propagation of the beam and especially on its filamentation pattern. To control the multi-filamentation process, we investigate in a third part the propagation of beams with special designs, namely; Gradient- and vortex-shaped beams. We justify the robustness of this latter kind of optical objects. Eventually, we investigate multi-filamentation patterns of femtosecond pulses in a fog tube and in cells of ethanol doped with coumarin, for different beam configurations. (author)
Nonlinear electrostatic solitary waves in electron-positron plasmas
Lazarus, I. J.; Bharuthram, R.; Moolla, S.; Singh, S. V.; Lakhina, G. S.
2016-02-01
The generation of nonlinear electrostatic solitary waves (ESWs) is explored in a magnetized four component two-temperature electron-positron plasma. Fluid theory is used to derive a set of nonlinear equations for the ESWs, which propagate obliquely to an external magnetic field. The electric field structures are examined for various plasma parameters and are shown to yield sinusoidal, sawtooth and bipolar waveforms. It is found that an increase in the densities of the electrons and positrons strengthen the nonlinearity while the periodicity and nonlinearity of the wave increases as the cool-to-hot temperature ratio increases. Our results could be useful in understanding nonlinear propagation of waves in astrophysical environments and related laboratory experiments.
New approaches to nonlinear waves
2016-01-01
The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems. The introductory chapter provides a general overview, thematically linking the objects described in the book. Two chapters are devoted to wave systems possessing resonances with linear frequencies (Chapter 2) and with nonlinear frequencies (Chapter 3). In the next two chapters modulation instability in the KdV-type of equations is studied using rigorous mathematical methods (Chapter 4) and its possible connection to freak waves is investigated (Chapter 5). The book goes on to demonstrate how the choice of the Hamiltonian (Chapter 6) or the Lagrangian (Chapter 7) framework allows us to gain a deeper insight into the properties of a specific wave system. The final chapter discusses problems encountered when attempting to verify the theoretical predictions using numerical or laboratory experiments. All the chapters are illustrated by ample constructive examples demonstrating the app...
Nonlinear VLF Wave Physics in the Radiation Belts
Crabtree, C. E.; Tejero, E. M.; Ganguli, G.; Mithaiwala, M.; Rudakov, L.; Hospodarsky, G. B.; Kletzing, C.
2014-12-01
Electromagnetic VLF waves, such as whistler mode waves, both control the lifetime of trapped electrons in the radiation belts by pitch-angle scattering and are responsible for the energization of electrons during storms. Traditional approaches to understanding the influence of waves on trapped electrons have assumed that the wave characteristics (frequency spectrum, wave-normal angle distribution, etc.) were both stationary in time and amplitude independent from event to event. In situ data from modern satellite missions, such as the Van Allen probes, are showing that this assumption may not be justified. In addition, recent theoretical results [Crabtree et al. 2012] show that the threshold for nonlinear wave scattering can often be met by naturally occurring VLF waves in the magnetosphere, with wave magnetic fields of the order of 50-100 pT inside the plasmapause. Nonlinear wave scattering (Nonlinear Landau Damping) is an amplitude dependent mechanism that can strongly alter VLF wave propagation [Ganguli et al. 2010], primarily by altering the direction of propagation. Laboratory results have confirmed the dramatic change in propagation direction when the pump wave has sufficient amplitude to exceed the nonlinear threshold [Tejero et al. 2014]. Nonlinear scattering can alter the macroscopic dynamics of waves in the radiation belts leading to the formation of a long-lasting wave-cavity [Crabtree et al. 2012] and, when amplification is present, a multi-pass amplifier [Ganguli et al., 2012]. Such nonlinear wave effects can dramatically reduce electron lifetimes. Nonlinear wave dynamics such as these occur when there are more than one wave present, such a condition necessarily violates the assumption of traditional wave-normal analysis [Santolik et al., 2003] which rely on the plane wave assumption. To investigate nonlinear wave dynamics using modern in situ data we apply the maximum entropy method [Skilling and Bryan, 1984] to solve for the wave distribution function
Nonlinear waves in solar plasmas - a review
International Nuclear Information System (INIS)
Ballai, I
2006-01-01
Nonlinearity is a direct consequence of large scale dynamics in the solar plasmas. When nonlinear steepening of waves is balanced by dispersion, solitary waves are generated. In the vicinity of resonances, waves can steepen into nonlinear waves influencing the efficiency of energy deposition. Here we review recent theoretical breakthroughs that have lead to a greater understanding of many aspects of nonlinear waves arising in homogeneous and inhomogeneous solar plasmas
Impact induced solitary wave propagation through a woodpile structure
International Nuclear Information System (INIS)
Kore, R; Waychal, A; Yadav, P; Shelke, A; Agarwal, S; Sahoo, N; Uddin, Ahsan
2016-01-01
In this paper, we investigate solitary wave propagation through a one-dimensional woodpile structure excited by low and high velocity impact. Woodpile structures are a sub-class of granular metamaterial, which supports propagation of nonlinear waves. Hertz contact law governs the behavior of the solitary wave propagation through the granular media. Towards an experimental study, a woodpile structure was fabricated by orthogonally stacking cylindrical rods. A shock tube facility has been developed to launch an impactor on the woodpile structure at a velocity of 30 m s −1 . Embedded granular chain sensors were fabricated to study the behavior of the solitary wave. The impact induced stress wave is studied to investigate solitary wave parameters, i.e. contact force, contact time, and solitary wave velocity. With the aid of the experimental setup, numerical simulations, and a theoretical solution based on the long wavelength approximation, formation of the solitary wave in the woodpile structure is validated to a reasonable degree of accuracy. The nondispersive and compact supported solitary waves traveling at sonic wave velocity offer unique properties that could be leveraged for application in nondestructive testing and structural health monitoring. (paper)
Wave propagation of spectral energy content in a granular chain
Shrivastava, Rohit Kumar; Luding, Stefan
2017-01-01
A mechanical wave is propagation of vibration with transfer of energy and momentum. Understanding the spectral energy characteristics of a propagating wave through disordered granular media can assist in understanding the overall properties of wave propagation through inhomogeneous materials like
Modelization of highly nonlinear waves in coastal regions
Gouin, Maïté; Ducrozet, Guillaume; Ferrant, Pierre
2015-04-01
The proposed work deals with the development of a highly non-linear model for water wave propagation in coastal regions. The accurate modelization of surface gravity waves is of major interest in ocean engineering, especially in the field of marine renewable energy. These marine structures are intended to be settled in coastal regions where the effect of variable bathymetry may be significant on local wave conditions. This study presents a numerical model for the wave propagation with complex bathymetry. It is based on High-Order Spectral (HOS) method, initially limited to the propagation of non-linear wave fields over flat bottom. Such a model has been developed and validated at the LHEEA Lab. (Ecole Centrale Nantes) over the past few years and the current developments will enlarge its application range. This new numerical model will keep the interesting numerical properties of the original pseudo-spectral approach (convergence, efficiency with the use of FFTs, …) and enable the possibility to propagate highly non-linear wave fields over long time and large distance. Different validations will be provided in addition to the presentation of the method. At first, Bragg reflection will be studied with the proposed approach. If the Bragg condition is satisfied, the reflected wave generated by a sinusoidal bottom patch should be amplified as a result of resonant quadratic interactions between incident wave and bottom. Comparisons will be provided with experiments and reference solutions. Then, the method will be used to consider the transformation of a non-linear monochromatic wave as it propagates up and over a submerged bar. As the waves travel up the front slope of the bar, it steepens and high harmonics are generated due to non-linear interactions. Comparisons with experimental data will be provided. The different test cases will assess the accuracy and efficiency of the method proposed.
Lamb Wave Technique for Ultrasonic Nonlinear Characterization in Elastic Plates
International Nuclear Information System (INIS)
Lee, Tae Hun; Kim, Chung Seok; Jhang, Kyung Young
2010-01-01
Since the acoustic nonlinearity is sensitive to the minute variation of material properties, the nonlinear ultrasonic technique(NUT) has been considered as a promising method to evaluate the material degradation or fatigue. However, there are certain limitations to apply the conventional NUT using the bulk wave to thin plates. In case of plates, the use of Lamb wave can be considered, however, the propagation characteristics of Lamb wave are completely different with the bulk wave, and thus the separate study for the nonlinearity of Lamb wave is required. For this work, this paper analyzed first the conditions of mode pair suitable for the practical application as well as for the cumulative propagation of quadratic harmonic frequency and summarized the result in for conditions: phase matching, non-zero power flux, group velocity matching, and non-zero out-of-plane displacement. Experimental results in aluminum plates showed that the amplitude of the secondary Lamb wave and nonlinear parameter grew up with increasing propagation distance at the mode pair satisfying the above all conditions and that the ration of nonlinear parameters measured in Al6061-T6 and Al1100-H15 was closed to the ratio of the absolute nonlinear parameters
Propagation of SLF/ELF electromagnetic waves
Pan, Weiyan
2014-01-01
This book deals with the SLF/ELF wave propagation, an important branch of electromagnetic theory. The SLF/ELF wave propagation theory is well applied in earthquake electromagnetic radiation, submarine communication, thunderstorm detection, and geophysical prospecting and diagnostics. The propagation of SLF/ELF electromagnetic waves is introduced in various media like the earth-ionospheric waveguide, ionospheric plasma, sea water, earth, and the boundary between two different media or the stratified media. Applications in the earthquake electromagnetic radiation and the submarine communications are also addressed. This book is intended for scientists and engineers in the fields of radio propagation and EM theory and applications. Prof. Pan is a professor at China Research Institute of Radiowave Propagation in Qingdao (China). Dr. Li is a professor at Zhejiang University in Hangzhou (China).
Wave propagation and scattering in random media
Ishimaru, Akira
1978-01-01
Wave Propagation and Scattering in Random Media, Volume 2, presents the fundamental formulations of wave propagation and scattering in random media in a unified and systematic manner. The topics covered in this book may be grouped into three categories: waves in random scatterers, waves in random continua, and rough surface scattering. Random scatterers are random distributions of many particles. Examples are rain, fog, smog, hail, ocean particles, red blood cells, polymers, and other particles in a state of Brownian motion. Random continua are the media whose characteristics vary randomly an
Coupled seismic and electromagnetic wave propagation
Schakel, M.D.
2011-01-01
Coupled seismic and electromagnetic wave propagation is studied theoretically and experimentally. This coupling arises because of the electrochemical double layer, which exists along the solid-grain/fluid-electrolyte boundaries of porous media. Within the double layer, charge is redistributed,
Reversed phase propagation for hyperbolic surface waves
DEFF Research Database (Denmark)
Repän, Taavi; Novitsky, Andrey; Willatzen, Morten
2018-01-01
Magnetic properties can be used to control phase propagation in hyperbolic metamaterials. However, in the visible spectrum magnetic properties are difficult to obtain. We discuss hyperbolic surface waves allowing for a similar control over phase, achieved without magnetic properties....
International Nuclear Information System (INIS)
Abe, H.; Okuda, H.
1994-06-01
Soliton propagation in the dielectric media has been simulated by using the nonlinear Lorentz computational model, which was recently developed to study the propagation of electromagnetic waves in a linear and a nonlinear dielectric. The model is constructed by combining a microscopic model used in the semi-classical approximation for dielectric media and the particle model developed for the plasma simulations. The carrier wave frequency is retained in the simulation so that not only the envelope of the soliton but also its phase can be followed in time. It is shown that the model may be useful for studying pulse propagation in the dielectric media
Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials
International Nuclear Information System (INIS)
Wen, Shuangchun; Xiang, Yuanjiang; Dai, Xiaoyu; Tang, Zhixiang; Su, Wenhua; Fan, Dianyuan
2007-01-01
A metamaterial (MM) differs from an ordinary optical material mainly in that it has a dispersive magnetic permeability and offers greatly enhanced design freedom to alter the linear and nonlinear properties. This makes it possible for us to control the propagation of ultrashort electromagnetic pulses at will. Here we report on generic features of ultrashort electromagnetic pulse propagation and demonstrate the controllability of both the linear and nonlinear parameters of models for pulse propagation in MMs. First, we derive a generalized system of coupled three-dimensional nonlinear Schroedinger equations (NLSEs) suitable for few-cycle pulse propagation in a MM with both nonlinear electric polarization and nonlinear magnetization. The coupled equations recover previous models for pulse propagation in both ordinary material and a MM under the same conditions. Second, by using the coupled NLSEs in the Drude dispersive model as an example, we identify the respective roles of the dispersive electric permittivity and magnetic permeability in ultrashort pulse propagation and disclose some additional features of pulse propagation in MMs. It is shown that, for linear propagation, the sign and magnitude of space-time focusing can be controlled through adjusting the linear dispersive permittivity and permeability. For nonlinear propagation, the linear dispersive permittivity and permeability are incorporated into the nonlinear magnetization and nonlinear polarization, respectively, resulting in controllable magnetic and electric self-steepening effects and higher-order dispersively nonlinear terms in the propagation models
Nonlinear spin wave coupling in adjacent magnonic crystals
Energy Technology Data Exchange (ETDEWEB)
Sadovnikov, A. V., E-mail: sadovnikovav@gmail.com; Nikitov, S. A. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation); Kotel' nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009 (Russian Federation); Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation)
2016-07-25
We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.
Nonlinear spin wave coupling in adjacent magnonic crystals
International Nuclear Information System (INIS)
Sadovnikov, A. V.; Nikitov, S. A.; Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E.
2016-01-01
We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.
DEFF Research Database (Denmark)
Guo, Hairun; Zeng, Xianglong; Zhou, Binbin
2013-01-01
We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...... nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due...
Inward propagating chemical waves in Taylor vortices.
Thompson, Barnaby W; Novak, Jan; Wilson, Mark C T; Britton, Melanie M; Taylor, Annette F
2010-04-01
Advection-reaction-diffusion (ARD) waves in the Belousov-Zhabotinsky reaction in steady Taylor-Couette vortices have been visualized using magnetic-resonance imaging and simulated using an adapted Oregonator model. We show how propagating wave behavior depends on the ratio of advective, chemical and diffusive time scales. In simulations, inward propagating spiral flamelets are observed at high Damköhler number (Da). At low Da, the reaction distributes itself over several vortices and then propagates inwards as contracting ring pulses--also observed experimentally.
Nonlinear periodic space-charge waves in plasma
International Nuclear Information System (INIS)
Kovalev, V. A.
2009-01-01
A solution is obtained in the form of coupled nonlinear periodic space-charge waves propagating in a magnetoactive plasma. The wave spectrum in the vicinity of the critical point, where the number of harmonics increases substantially, is found to fall with harmonic number as ∝ s -1/3 . Periodic space-charge waves are invoked to explain the zebra pattern in the radio emission from solar flares.
Nonlinear waves and pattern dynamics
Pelinovsky, Efim; Mutabazi, Innocent
2018-01-01
This book addresses the fascinating phenomena associated with nonlinear waves and spatio-temporal patterns. These appear almost everywhere in nature from sand bed forms to brain patterns, and yet their understanding still presents fundamental scientific challenges. The reader will learn here, in particular, about the current state-of-the art and new results in: Nonlinear water waves: resonance, solitons, focusing, Bose-Einstein condensation, as well as and their relevance for the sea environment (sea-wind interaction, sand bed forms, fiber clustering) Pattern formation in non-equilibrium media: soap films, chimera patterns in oscillating media, viscoelastic Couette-Taylor flow, flow in the wake behind a heated cylinder, other pattern formation. The editors and authors dedicate this book to the memory of Alexander Ezersky, Professor of Fluid Mechanics at the University of Caen Normandie (France) from September 2007 to July 2016. Before 2007, he had served as a Senior Scientist at the Institute of Applied Physi...
Nonlinear positron acoustic solitary waves
International Nuclear Information System (INIS)
Tribeche, Mouloud; Aoutou, Kamel; Younsi, Smain; Amour, Rabia
2009-01-01
The problem of nonlinear positron acoustic solitary waves involving the dynamics of mobile cold positrons is addressed. A theoretical work is presented to show their existence and possible realization in a simple four-component plasma model. The results should be useful for the understanding of the localized structures that may occur in space and laboratory plasmas as new sources of cold positrons are now well developed.
Radiation and propagation of electromagnetic waves
Tyras, George; Declaris, Nicholas
1969-01-01
Radiation and Propagation of Electromagnetic Waves serves as a text in electrical engineering or electrophysics. The book discusses the electromagnetic theory; plane electromagnetic waves in homogenous isotropic and anisotropic media; and plane electromagnetic waves in inhomogenous stratified media. The text also describes the spectral representation of elementary electromagnetic sources; the field of a dipole in a stratified medium; and radiation in anisotropic plasma. The properties and the procedures of Green's function method of solution, axial currents, as well as cylindrical boundaries a
Lamb wave propagation in monocrystalline silicon wafers.
Fromme, Paul; Pizzolato, Marco; Robyr, Jean-Luc; Masserey, Bernard
2018-01-01
Monocrystalline silicon wafers are widely used in the photovoltaic industry for solar panels with high conversion efficiency. Guided ultrasonic waves offer the potential to efficiently detect micro-cracks in the thin wafers. Previous studies of ultrasonic wave propagation in silicon focused on effects of material anisotropy on bulk ultrasonic waves, but the dependence of the wave propagation characteristics on the material anisotropy is not well understood for Lamb waves. The phase slowness and beam skewing of the two fundamental Lamb wave modes A 0 and S 0 were investigated. Experimental measurements using contact wedge transducer excitation and laser measurement were conducted. Good agreement was found between the theoretically calculated angular dependency of the phase slowness and measurements for different propagation directions relative to the crystal orientation. Significant wave skew and beam widening was observed experimentally due to the anisotropy, especially for the S 0 mode. Explicit finite element simulations were conducted to visualize and quantify the guided wave beam skew. Good agreement was found for the A 0 mode, but a systematic discrepancy was observed for the S 0 mode. These effects need to be considered for the non-destructive testing of wafers using guided waves.
Cumulative second-harmonic generation of Lamb waves propagating in a two-layered solid plate
International Nuclear Information System (INIS)
Xiang Yanxun; Deng Mingxi
2008-01-01
The physical process of cumulative second-harmonic generation of Lamb waves propagating in a two-layered solid plate is presented by using the second-order perturbation and the technique of nonlinear reflection of acoustic waves at an interface. In general, the cumulative second-harmonic generation of a dispersive guided wave propagation does not occur. However, the present paper shows that the second-harmonic of Lamb wave propagation arising from the nonlinear interaction of the partial bulk acoustic waves and the restriction of the three boundaries of the solid plates does have a cumulative growth effect if some conditions are satisfied. Through boundary condition and initial condition of excitation, the analytical expression of cumulative second-harmonic of Lamb waves propagation is determined. Numerical results show the cumulative effect of Lamb waves on second-harmonic field patterns. (classical areas of phenomenology)
Computational Modeling of Ultrafast Pulse Propagation in Nonlinear Optical Materials
Goorjian, Peter M.; Agrawal, Govind P.; Kwak, Dochan (Technical Monitor)
1996-01-01
There is an emerging technology of photonic (or optoelectronic) integrated circuits (PICs or OEICs). In PICs, optical and electronic components are grown together on the same chip. rib build such devices and subsystems, one needs to model the entire chip. Accurate computer modeling of electromagnetic wave propagation in semiconductors is necessary for the successful development of PICs. More specifically, these computer codes would enable the modeling of such devices, including their subsystems, such as semiconductor lasers and semiconductor amplifiers in which there is femtosecond pulse propagation. Here, the computer simulations are made by solving the full vector, nonlinear, Maxwell's equations, coupled with the semiconductor Bloch equations, without any approximations. The carrier is retained in the description of the optical pulse, (i.e. the envelope approximation is not made in the Maxwell's equations), and the rotating wave approximation is not made in the Bloch equations. These coupled equations are solved to simulate the propagation of femtosecond optical pulses in semiconductor materials. The simulations describe the dynamics of the optical pulses, as well as the interband and intraband.
Directory of Open Access Journals (Sweden)
S.-D. Zhang
2000-10-01
Full Text Available By analyzing the results of the numerical simulations of nonlinear propagation of three Gaussian gravity-wave packets in isothermal atmosphere individually, the nonlinear effects on the characteristics of gravity waves are studied quantitatively. The analyses show that during the nonlinear propagation of gravity wave packets the mean flows are accelerated and the vertical wavelengths show clear reduction due to nonlinearity. On the other hand, though nonlinear effects exist, the time variations of the frequencies of gravity wave packets are close to those derived from the dispersion relation and the amplitude and phase relations of wave-associated disturbance components are consistent with the predictions of the polarization relation of gravity waves. This indicates that the dispersion and polarization relations based on the linear gravity wave theory can be applied extensively in the nonlinear region.Key words: Meteorology and atmospheric dynamics (middle atmosphere dynamics; waves and tides
Nonlinear surface waves at ferrite-metamaterial waveguide structure
Hissi, Nour El Houda; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Shabat, Mohammed Musa; Atangana, Jacques
2016-09-01
A new ferrite slab made of a metamaterial (MTM), surrounded by a nonlinear cover cladding and a ferrite substrate, was shown to support unusual types of electromagnetic surface waves. We impose the boundary conditions to derive the dispersion relation and others necessary to formulate the proposed structure. We analyse the dispersion properties of the nonlinear surface waves and we calculate the associated propagation index and the film-cover interface nonlinearity. In the calculation, several sets of the permeability of the MTM are considered. Results show that the waves behaviour depends on the values of the permeability of the MTM, the thickness of the waveguide and the film-cover interface nonlinearity. It is also shown that the use of the singular solutions to the electric field equation allows to identify several new properties of surface waves which do not exist in conventional waveguide.
Excitation of coherent propagating spin waves by pure spin currents.
Demidov, Vladislav E; Urazhdin, Sergei; Liu, Ronghua; Divinskiy, Boris; Telegin, Andrey; Demokritov, Sergej O
2016-01-28
Utilization of pure spin currents not accompanied by the flow of electrical charge provides unprecedented opportunities for the emerging technologies based on the electron's spin degree of freedom, such as spintronics and magnonics. It was recently shown that pure spin currents can be used to excite coherent magnetization dynamics in magnetic nanostructures. However, because of the intrinsic nonlinear self-localization effects, magnetic auto-oscillations in the demonstrated devices were spatially confined, preventing their applications as sources of propagating spin waves in magnonic circuits using these waves as signal carriers. Here, we experimentally demonstrate efficient excitation and directional propagation of coherent spin waves generated by pure spin current. We show that this can be achieved by using the nonlocal spin injection mechanism, which enables flexible design of magnetic nanosystems and allows one to efficiently control their dynamic characteristics.
Linear and Nonlinear Infrasound Propagation to 1000 km
2015-12-15
AFRL-RV-PS- AFRL-RV-PS- TR-2016-0017 TR-2016-0017 LINEAR AND NONLINEAR INFRASOUND PROPAGATION TO 1000 KM Catherine de Groot-Hedlin Scripps...Nonlinear Infrasound Propagation to 1000 km 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 62601F 6. AUTHOR(S) Catherine de Groot
Statistical properties of nonlinear one-dimensional wave fields
Directory of Open Access Journals (Sweden)
D. Chalikov
2005-01-01
Full Text Available A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.
Statistical properties of nonlinear one-dimensional wave fields
Chalikov, D.
2005-06-01
A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.
Raju, Thokala Soloman; Pal, Ritu
2018-05-01
We derive the analytical rogue wave solutions for the generalized inhomogeneous nonlinear Schrödinger-Maxwell-Bloch (GINLS-MB) equation describing the pulse propagation in erbium-doped fibre system. Then by suitably choosing the inhomogeneous parameters, we delineate the tunneling properties of rogue waves through dispersion and nonlinearity barriers or wells. Finally, we demonstrate the propagating characteristics of optical solitons by considering their tunneling through periodic barriers by the proper choice of external potential.
Nonlinear propagation of ultra-low-frequency electronic modes in a magnetized dusty plasma
International Nuclear Information System (INIS)
Mamun, A.A.
1999-07-01
A theoretical investigation has been made of nonlinear propagation of ultra-low-frequency electromagnetic waves in a magnetized two fluid (negatively charged dust and positively charged ion fluids) dusty plasma. These are modified Alfven waves for small value of θ and are modified magnetosonic waves for large θ, where θ is the angle between the directions of the external magnetic field and the wave propagation. A nonlinear evolution equation for the wave magnetic field, which is known as Korteweg de Vries (K-dV) equation and which admits a stationary solitary wave solution, is derived by the reductive perturbation method. The effects of external magnetic field and dust characteristics on the amplitude and the width of these solitary structures are examined. The implications of these results to some space and astrophysical plasma systems, especially to planetary ring-systems, are briefly mentioned. (author)
Submillimeter wave propagation in tokamak plasmas
International Nuclear Information System (INIS)
Ma, C.H.; Hutchinson, D.P.; Staats, P.A.; Vander Sluis, K.L.; Mansfield, D.K.; Park, H.; Johnson, L.C.
1985-01-01
The propagation of submillimeter-waves (smm) in tokamak plasmas has been investigated both theoretically and experimentally to ensure successful measurements of electron density and plasma current distributions in tokamak devices. Theoretical analyses have been carried out to study the polarization of the smm waves in TFTR and ISX-B tokamaks. A multichord smm wave interferometer/polarimeter system has been employed to simultaneously measure the line electron density and poloidal field-induced Faraday rotation in the ISX-B tokamak. The experimental study on TFTR is under way. Computer codes have been developed and have been used to study the wave propagation and to reconstruct the distributions of plasma current and density from the measured data. The results are compared with other measurements
Submillimeter wave propagation in tokamak plasmas
International Nuclear Information System (INIS)
Ma, C.H.; Hutchinson, D.P.; Staats, P.A.; Vander Sluis, K.L.; Mansfield, D.K.; Park, H.; Johnson, L.C.
1986-01-01
Propagation of submillimeter waves (smm) in tokamak plasma was investigated both theoretically and experimentally to ensure successful measurements of electron density and plasma current distributions in tokamak devices. Theoretical analyses were carried out to study the polarization of the smm waves in TFTR and ISX-B tokamaks. A multichord smm wave interferometer/polarimeter system was employed to simultaneously measure the line electron density and poloidal field-induced Faraday rotation in the ISX-B tokamak. The experimental study on TFTR is under way. Computer codes were developed and have been used to study the wave propagation and to reconstruct the distributions of plasma current and density from the measured data. The results are compared with other measurements. 5 references, 2 figures
Counter-propagating wave interaction for contrast-enhanced ultrasound imaging
Renaud, G.; Bosch, J. G.; ten Kate, G. L.; Shamdasani, V.; Entrekin, R.; de Jong, N.; van der Steen, A. F. W.
2012-11-01
Most techniques for contrast-enhanced ultrasound imaging require linear propagation to detect nonlinear scattering of contrast agent microbubbles. Waveform distortion due to nonlinear propagation impairs their ability to distinguish microbubbles from tissue. As a result, tissue can be misclassified as microbubbles, and contrast agent concentration can be overestimated; therefore, these artifacts can significantly impair the quality of medical diagnoses. Contrary to biological tissue, lipid-coated gas microbubbles used as a contrast agent allow the interaction of two acoustic waves propagating in opposite directions (counter-propagation). Based on that principle, we describe a strategy to detect microbubbles that is free from nonlinear propagation artifacts. In vitro images were acquired with an ultrasound scanner in a phantom of tissue-mimicking material with a cavity containing a contrast agent. Unlike the default mode of the scanner using amplitude modulation to detect microbubbles, the pulse sequence exploiting counter-propagating wave interaction creates no pseudoenhancement behind the cavity in the contrast image.
Nonlinear lattice waves in heterogeneous media
International Nuclear Information System (INIS)
Laptyeva, T V; Ivanchenko, M V; Flach, S
2014-01-01
We discuss recent advances in the understanding of the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry–André localization for quasiperiodic potentials. Additional nonlinear terms in the wave equations can either preserve the phase-coherent localization of waves, or destroy it through nonintegrability and deterministic chaos. Spreading wave packets are observed to show universal features in their dynamics which are related to properties of nonlinear diffusion equations. (topical review)
On the propagation of low-hybrid waves of finite amplitude
International Nuclear Information System (INIS)
Kozyrev, A.N.; Piliya, A.D.; Fedorov, V.I.
1979-01-01
Propagation of low-hybrid waves of a finite amplitude with allowance for variation in plasma density caused by HF field pressure is studied. Considered is wave ''overturning'' which takes place in the absence of space dispersion. With taking account of dispersion the wave propagation is described by the third-order nonlinear equation which differs in shape from the complex modified Korteweg-de-Vries (Hirota) equation. Solutions of this equation of the space solution type are found
Alfven wave resonances and flow induced by nonlinear Alfven waves in a stratified atmosphere
International Nuclear Information System (INIS)
Stark, B. A.; Musielak, Z. E.; Suess, S. T.
1996-01-01
A nonlinear, time-dependent, ideal MHD code has been developed and used to compute the flow induced by nonlinear Alfven waves propagating in an isothermal, stratified, plane-parallel atmosphere. The code is based on characteristic equations solved in a Lagrangian frame. Results show that resonance behavior of Alfven waves exists in the presence of a continuous density gradient and that the waves with periods corresponding to resonant peaks exert considerably more force on the medium than off-resonance periods. If only off-peak periods are considered, the relationship between the wave period and induced longitudinal velocity shows that short period WKB waves push more on the background medium than longer period, non-WKB, waves. The results also show the development of the longitudinal waves induced by finite amplitude Alfven waves. Wave energy transferred to the longitudinal mode may provide a source of localized heating
Lagrangian analysis of nonlinear wave-wave interactions in bounded plasmas
International Nuclear Information System (INIS)
Carr, A.R.
1979-01-01
In a weakly turbulent nonlinear wave-supporting medium, one of the important nonlinear processes which may occur is resonant three-wave interaction. Whitham's averaged Lagrangian method provides a general formulation of wave evolution laws which is easily adapted to nonlinear dispersive media. In this thesis, the strength of nonlinear interactions between three coherent, axisymmetric, low frequency, magnetohydrodynamic (Alfven) waves propagating in resonance along a cold cylindrical magnetized plasma column is calculated. Both a uniform and a parabolic density distribution have been considered. To account for a non-zero plasma temperature, pressure effects have been included. Distinctive features of the work are the use of cylindrical geometry, the presence of a finite rather than an infinite axial magnetic field, the treatment of a parabolic density distribution, and the inclusion of both ion and electron contributions in all expressions. Two astrophysical applications of the presented theory have been considered. In the first, the possibility of resonant three-wave coupling between geomagnetic micropulsations, which propagate as Alfven or magnetosonic waves along the Earth's magnetic field lines, has been investigated. The second case is the theory of energy transport through the solar chromosphere by upward propagating magnetohydrodynamic waves, which may then couple to heavily damped waves in the corona, causing the observed excess heating in that region
Modeling of shock wave propagation in large amplitude ultrasound.
Pinton, Gianmarco F; Trahey, Gregg E
2008-01-01
The Rankine-Hugoniot relation for shock wave propagation describes the shock speed of a nonlinear wave. This paper investigates time-domain numerical methods that solve the nonlinear parabolic wave equation, or the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, and the conditions they require to satisfy the Rankine-Hugoniot relation. Two numerical methods commonly used in hyperbolic conservation laws are adapted to solve the KZK equation: Godunov's method and the monotonic upwind scheme for conservation laws (MUSCL). It is shown that they satisfy the Rankine-Hugoniot relation regardless of attenuation. These two methods are compared with the current implicit solution based method. When the attenuation is small, such as in water, the current method requires a degree of grid refinement that is computationally impractical. All three numerical methods are compared in simulations for lithotripters and high intensity focused ultrasound (HIFU) where the attenuation is small compared to the nonlinearity because much of the propagation occurs in water. The simulations are performed on grid sizes that are consistent with present-day computational resources but are not sufficiently refined for the current method to satisfy the Rankine-Hugoniot condition. It is shown that satisfying the Rankine-Hugoniot conditions has a significant impact on metrics relevant to lithotripsy (such as peak pressures) and HIFU (intensity). Because the Godunov and MUSCL schemes satisfy the Rankine-Hugoniot conditions on coarse grids, they are particularly advantageous for three-dimensional simulations.
Propagation of three-dimensional electron-acoustic solitary waves
International Nuclear Information System (INIS)
Shalaby, M.; El-Sherif, L. S.; El-Labany, S. K.; Sabry, R.
2011-01-01
Theoretical investigation is carried out for understanding the properties of three-dimensional electron-acoustic waves propagating in magnetized plasma whose constituents are cold magnetized electron fluid, hot electrons obeying nonthermal distribution, and stationary ions. For this purpose, the hydrodynamic equations for the cold magnetized electron fluid, nonthermal electron density distribution, and the Poisson equation are used to derive the corresponding nonlinear evolution equation, Zkharov-Kuznetsov (ZK) equation, in the small- but finite- amplitude regime. The ZK equation is solved analytically and it is found that it supports both solitary and blow-up solutions. It is found that rarefactive electron-acoustic solitary waves strongly depend on the density and temperature ratios of the hot-to-cold electron species as well as the nonthermal electron parameter. Furthermore, there is a critical value for the nonthermal electron parameter, which decides whether the electron-acoustic solitary wave's amplitude is decreased or increased by changing various plasma parameters. Importantly, the change of the propagation angles leads to miss the balance between the nonlinearity and dispersion; hence, the localized pulses convert to explosive/blow-up pulses. The relevance of this study to the nonlinear electron-acoustic structures in the dayside auroral zone in the light of Viking satellite observations is discussed.
Wave propagation retrieval method for chiral metamaterials
DEFF Research Database (Denmark)
Andryieuski, Andrei; Malureanu, Radu; Lavrinenko, Andrei
2010-01-01
In this paper we present the wave propagation method for the retrieving of effective properties of media with circularly polarized eigenwaves, in particularly for chiral metamaterials. The method is applied for thick slabs and provides bulk effective parameters. Its strong sides are the absence...
Wave propagation in complex structures with LEGO
Lancellotti, V.; Hon, de B.P.; Tijhuis, A.G.
2012-01-01
We present the extension of the linear embedding via Green's operators (LEGO) scheme to problems that involve elementary sources localized inside complex structures made of different dielectric media with inclusions. We show how this new feature allows solving problems of wave propagation within,
Electromagnetic Wave Propagation in Random Media
DEFF Research Database (Denmark)
Pécseli, Hans
1984-01-01
The propagation of a narrow frequency band beam of electromagnetic waves in a medium with randomly varying index of refraction is considered. A novel formulation of the governing equation is proposed. An equation for the average Green function (or transition probability) can then be derived...
Propagation of extensional waves in a piezoelectric semiconductor rod
Directory of Open Access Journals (Sweden)
C.L. Zhang
2016-04-01
Full Text Available We studied the propagation of extensional waves in a thin piezoelectric semiconductor rod of ZnO whose c-axis is along the axis of the rod. The macroscopic theory of piezoelectric semiconductors was used which consists of the coupled equations of piezoelectricity and the conservation of charge. The problem is nonlinear because the drift current is the product of the unknown electric field and the unknown carrier density. A perturbation procedure was used which resulted in two one-way coupled linear problems of piezoelectricity and the conservation of charge, respectively. The acoustic wave and the accompanying electric field were obtained from the equations of piezoelectricity. The motion of carriers was then determined from the conservation of charge using a trigonometric series. It was found that while the acoustic wave was approximated by a sinusoidal wave, the motion of carriers deviates from a sinusoidal wave qualitatively because of the contributions of higher harmonics arising from the originally nonlinear terms. The wave crests become higher and sharper while the troughs are shallower and wider. This deviation is more pronounced for acoustic waves with larger amplitudes.
Nonlinear Electron Waves in Strongly Magnetized Plasmas
DEFF Research Database (Denmark)
Pécseli, Hans; Juul Rasmussen, Jens
1980-01-01
Weakly nonlinear dispersive electron waves in strongly magnetized plasma are considered. A modified nonlinear Schrodinger equation is derived taking into account the effect of particles resonating with the group velocity of the waves (nonlinear Landau damping). The possibility of including the ion...... dynamics in the analysis is also demonstrated. As a particular case the authors investigate nonlinear waves in a strongly magnetized plasma filled wave-guide, where the effects of finite geometry are important. The relevance of this problem to laboratory experiments is discussed....
Thermoelastic wave propagation in laminated composites plates
Directory of Open Access Journals (Sweden)
Verma K. L.
2012-12-01
Full Text Available The dispersion of thermoelastic waves propagation in an arbitrary direction in laminated composites plates is studied in the framework of generalized thermoelasticity in this article. Three dimensional field equations of thermoelasticity with relaxation times are considered. Characteristic equation is obtained on employing the continuity of displacements, temperature, stresses and thermal gradient at the layers’ interfaces. Some important particular cases such as of free waves on reducing plates to single layer and the surface waves when thickness tends to infinity are also discussed. Uncoupled and coupled thermoelasticity are the particular cases of the obtained results. Numerical results are also obtained and represented graphically.
Wave propagation in elastic layers with damping
DEFF Research Database (Denmark)
Sorokin, Sergey; Darula, Radoslav
2016-01-01
The conventional concepts of a loss factor and complex-valued elastic moduli are used to study wave attenuation in a visco-elastic layer. The hierarchy of reduced-order models is employed to assess attenuation levels in various situations. For the forcing problem, the attenuation levels are found...... for alternative excitation cases. The differences between two regimes, the low frequency one, when a waveguide supports only one propagating wave, and the high frequency one, when several waves are supported, are demonstrated and explained....
Nonlinear transient waves in coupled phase oscillators with inertia.
Jörg, David J
2015-05-01
Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here, we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.
Wave propagation in embedded inhomogeneous nanoscale plates incorporating thermal effects
Ebrahimi, Farzad; Barati, Mohammad Reza; Dabbagh, Ali
2018-04-01
In this article, an analytical approach is developed to study the effects of thermal loading on the wave propagation characteristics of an embedded functionally graded (FG) nanoplate based on refined four-variable plate theory. The heat conduction equation is solved to derive the nonlinear temperature distribution across the thickness. Temperature-dependent material properties of nanoplate are graded using Mori-Tanaka model. The nonlocal elasticity theory of Eringen is introduced to consider small-scale effects. The governing equations are derived by the means of Hamilton's principle. Obtained frequencies are validated with those of previously published works. Effects of different parameters such as temperature distribution, foundation parameters, nonlocal parameter, and gradient index on the wave propagation response of size-dependent FG nanoplates have been investigated.
Counterstreaming magnetized plasmas. II. Perpendicular wave propagation
International Nuclear Information System (INIS)
Tautz, R.C.; Schlickeiser, R.
2006-01-01
The properties of longitudinal and transverse oscillations in magnetized symmetric counterstreaming Maxwellian plasmas with equal thermal velocities for waves propagating perpendicular to the stream direction are investigated on the basis of Maxwell equations and the nonrelativistic Vlasov equation. With the constraint of vanishing particle flux in the stream direction, three distinct dispersion relations are known, which are the ordinary-wave mode, the Bernstein wave mode, and the extraordinary electromagnetic wave mode, where the latter two are only approximations. In this article, all three dispersion relations are evaluated for a counterstreaming Maxwellian distribution function in terms of the hypergeometric function 2 F 2 . The growth rates for the ordinary-wave mode are compared to earlier results by Bornatici and Lee [Phys. Fluids 13, 3007 (1970)], who derived approximate results, whereas in this article the exact dispersion relation is solved numerically. The original results are therefore improved and show differences of up to 21% to the results obtained in this article
Variational structure of inverse problems in wave propagation and vibration
Energy Technology Data Exchange (ETDEWEB)
Berryman, J.G.
1995-03-01
Practical algorithms for solving realistic inverse problems may often be viewed as problems in nonlinear programming with the data serving as constraints. Such problems are most easily analyzed when it is possible to segment the solution space into regions that are feasible (satisfying all the known constraints) and infeasible (violating some of the constraints). Then, if the feasible set is convex or at least compact, the solution to the problem will normally lie on the boundary of the feasible set. A nonlinear program may seek the solution by systematically exploring the boundary while satisfying progressively more constraints. Examples of inverse problems in wave propagation (traveltime tomography) and vibration (modal analysis) will be presented to illustrate how the variational structure of these problems may be used to create nonlinear programs using implicit variational constraints.
On the interaction of small-scale linear waves with nonlinear solitary waves
Xu, Chengzhu; Stastna, Marek
2017-04-01
In the study of environmental and geophysical fluid flows, linear wave theory is well developed and its application has been considered for phenomena of various length and time scales. However, due to the nonlinear nature of fluid flows, in many cases results predicted by linear theory do not agree with observations. One of such cases is internal wave dynamics. While small-amplitude wave motion may be approximated by linear theory, large amplitude waves tend to be solitary-like. In some cases, when the wave is highly nonlinear, even weakly nonlinear theories fail to predict the wave properties correctly. We study the interaction of small-scale linear waves with nonlinear solitary waves using highly accurate pseudo spectral simulations that begin with a fully nonlinear solitary wave and a train of small-amplitude waves initialized from linear waves. The solitary wave then interacts with the linear waves through either an overtaking collision or a head-on collision. During the collision, there is a net energy transfer from the linear wave train to the solitary wave, resulting in an increase in the kinetic energy carried by the solitary wave and a phase shift of the solitary wave with respect to a freely propagating solitary wave. At the same time the linear waves are greatly reduced in amplitude. The percentage of energy transferred depends primarily on the wavelength of the linear waves. We found that after one full collision cycle, the longest waves may retain as much as 90% of the kinetic energy they had initially, while the shortest waves lose almost all of their initial energy. We also found that a head-on collision is more efficient in destroying the linear waves than an overtaking collision. On the other hand, the initial amplitude of the linear waves has very little impact on the percentage of energy that can be transferred to the solitary wave. Because of the nonlinearity of the solitary wave, these results provide us some insight into wave-mean flow
Fast and accurate modeling of nonlinear pulse propagation in graded-index multimode fibers.
Conforti, Matteo; Mas Arabi, Carlos; Mussot, Arnaud; Kudlinski, Alexandre
2017-10-01
We develop a model for the description of nonlinear pulse propagation in multimode optical fibers with a parabolic refractive index profile. It consists of a 1+1D generalized nonlinear Schrödinger equation with a periodic nonlinear coefficient, which can be solved in an extremely fast and efficient way. The model is able to quantitatively reproduce recently observed phenomena like geometric parametric instability and broadband dispersive wave emission. We envisage that our equation will represent a valuable tool for the study of spatiotemporal nonlinear dynamics in the growing field of multimode fiber optics.
Directory of Open Access Journals (Sweden)
N. N. Rosanov
2015-09-01
Full Text Available Problem statement ill-posedness in the paper by L.S. Konev et al. devoted to formation of backward wave at short laser pulse propagation in nonlinear media or fibers is specified. It is inconceivable in the correct problem statement to consider the radiation field at the medium entrance as a given function of time due to generation of backward wave in the medium, when the backward wave characteristics are target values. The proper evolution variable is time, and it is convenient to use the adopted finite-difference time-domain (FDTD method for backward wave calculation.
Energy Technology Data Exchange (ETDEWEB)
Zuo, Peng; Fan, Zheng, E-mail: ZFAN@ntu.edu.sg [School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 (Singapore); Zhou, Yu [Advanced Remanufacturing and Technology Center (ARTC), 3 Clean Tech Loop, CleanTech Two, Singapore 637143 (Singapore)
2016-07-15
Nonlinear guided waves have been investigated widely in simple geometries, such as plates, pipe and shells, where analytical solutions have been developed. This paper extends the application of nonlinear guided waves to waveguides with arbitrary cross sections. The criteria for the existence of nonlinear guided waves were summarized based on the finite deformation theory and nonlinear material properties. Numerical models were developed for the analysis of nonlinear guided waves in complex geometries, including nonlinear Semi-Analytical Finite Element (SAFE) method to identify internal resonant modes in complex waveguides, and Finite Element (FE) models to simulate the nonlinear wave propagation at resonant frequencies. Two examples, an aluminum plate and a steel rectangular bar, were studied using the proposed numerical model, demonstrating the existence of nonlinear guided waves in such structures and the energy transfer from primary to secondary modes.
Surface acoustic wave propagation in graphene film
International Nuclear Information System (INIS)
Roshchupkin, Dmitry; Plotitcyna, Olga; Matveev, Viktor; Kononenko, Oleg; Emelin, Evgenii; Irzhak, Dmitry; Ortega, Luc; Zizak, Ivo; Erko, Alexei; Tynyshtykbayev, Kurbangali; Insepov, Zinetula
2015-01-01
Surface acoustic wave (SAW) propagation in a graphene film on the surface of piezoelectric crystals was studied at the BESSY II synchrotron radiation source. Talbot effect enabled the visualization of the SAW propagation on the crystal surface with the graphene film in a real time mode, and high-resolution x-ray diffraction permitted the determination of the SAW amplitude in the graphene/piezoelectric crystal system. The influence of the SAW on the electrical properties of the graphene film was examined. It was shown that the changing of the SAW amplitude enables controlling the magnitude and direction of current in graphene film on the surface of piezoelectric crystals
The effect of lower-hybrid waves on the propagation of hydromagnetic waves
International Nuclear Information System (INIS)
Hamabata, Hiromitsu; Namikawa, Tomikazu; Mori, Kazuhiro
1988-01-01
Propagation characteristics of hydromagnetic waves in a magnetic plasma are investigated using the two-plasma fluid equations including the effect of lower-hybrid waves propagating perpendicularly to the magnetic field. The effect of lower-hybrid waves on the propagation of hydromagnetic waves is analysed in terms of phase speed, growth rate, refractive index, polarization and the amplitude relation between the density perturbation and the magnetic-field perturbation for the cases when hydromagnetic waves propagate in the plane whose normal is perpendicular to both the magnetic field and the propagation direction of lower-hybrid waves and in the plane perpendicular to the propagation direction of lower-hybrid waves. It is shown that hydromagnetic waves propagating at small angles to the propagation direction of lower-hybrid waves can be excited by the effect of lower-hybrid waves and the energy of excited waves propagates nearly parallel to the propagation direction of lower-hybrid waves. (author)
Energy Technology Data Exchange (ETDEWEB)
Torello, David [GW Woodruff School of Mechanical Engineering, Georgia Tech (United States); Kim, Jin-Yeon [School of Civil and Environmental Engineering, Georgia Tech (United States); Qu, Jianmin [Department of Civil and Environmental Engineering, Northwestern University (United States); Jacobs, Laurence J. [School of Civil and Environmental Engineering, Georgia Tech and GW Woodruff School of Mechanical Engineering, Georgia Tech (United States)
2015-03-31
This research considers the effects of diffraction, attenuation, and the nonlinearity of generating sources on measurements of nonlinear ultrasonic Rayleigh wave propagation. A new theoretical framework for correcting measurements made with air-coupled and contact piezoelectric receivers for the aforementioned effects is provided based on analytical models and experimental considerations. A method for extracting the nonlinearity parameter β{sub 11} is proposed based on a nonlinear least squares curve-fitting algorithm that is tailored for Rayleigh wave measurements. Quantitative experiments are conducted to confirm the predictions for the nonlinearity of the piezoelectric source and to demonstrate the effectiveness of the curve-fitting procedure. These experiments are conducted on aluminum 2024 and 7075 specimens and a β{sub 11}{sup 7075}/β{sub 11}{sup 2024} measure of 1.363 agrees well with previous literature and earlier work.
SPP propagation in nonlinear glass-metal interface
Sagor, Rakibul Hasan; Alsunaidi, Mohammad A.; Ooi, Boon S.
2011-01-01
The non-linear propagation of Surface-Plasmon-Polaritons (SPP) in single interface of metal and chalcogenide glass (ChG) is considered. A time domain simulation algorithm is developed using the Finite Difference Time Domain (FDTD) method
Nonlinear optical beam manipulation, beam combining, and atmospheric propagation
International Nuclear Information System (INIS)
Fischer, R.A.
1988-01-01
These proceedings collect papers on optics: Topics include: diffraction properties of laser speckle, coherent beam combination by plasma modes, nonlinear responses, deformable mirrors, imaging radiometers, electron beam propagation in inhomogeneous media, and stability of laser beams in a structured environment
Diaz, Manuel A.; Solovchuk, Maxim A.; Sheu, Tony W. H.
2018-06-01
A nonlinear system of partial differential equations capable of describing the nonlinear propagation and attenuation of finite amplitude perturbations in thermoviscous media is presented. This system constitutes a full nonlinear wave model that has been formulated in the conservation form. Initially, this model is investigated analytically in the inviscid limit where it has been found that the resulting flux function fulfills the Lax-Wendroff theorem, and the scheme can match the solutions of the Westervelt and Burgers equations numerically. Here, high-order numerical descriptions of strongly nonlinear wave propagations become of great interest. For that matter we consider finite difference formulations of the weighted essentially non-oscillatory (WENO) schemes associated with explicit strong stability preserving Runge-Kutta (SSP-RK) time integration methods. Although this strategy is known to be computationally demanding, it is found to be effective when implemented to be solved in graphical processing units (GPUs). As we consider wave propagations in unbounded domains, perfectly matching layers (PML) have been also considered in this work. The proposed system model is validated and illustrated by using one- and two-dimensional benchmark test cases proposed in the literature for nonlinear acoustic propagation in homogeneous thermoviscous media.
Nonlinear evolution of astrophysical Alfven waves
Spangler, S. R.
1984-01-01
Nonlinear Alfven waves were studied using the derivative nonlinear Schrodinger equation as a model. The evolution of initial conditions, such as envelope solitons, amplitude-modulated waves, and band-limited noise was investigated. The last two furnish models for naturally occurring Alfven waves in an astrophysical plasma. A collapse instability in which a wave packet becomes more intense and of smaller spatial extent was analyzed. It is argued that this instability leads to enhanced plasma heating. In studies in which the waves are amplified by an electron beam, the instability tends to modestly inhibit wave growth.
Propagating wave correlations in complex systems
International Nuclear Information System (INIS)
Creagh, Stephen C; Gradoni, Gabriele; Hartmann, Timo; Tanner, Gregor
2017-01-01
We describe a novel approach for computing wave correlation functions inside finite spatial domains driven by complex and statistical sources. By exploiting semiclassical approximations, we provide explicit algorithms to calculate the local mean of these correlation functions in terms of the underlying classical dynamics. By defining appropriate ensemble averages, we show that fluctuations about the mean can be characterised in terms of classical correlations. We give in particular an explicit expression relating fluctuations of diagonal contributions to those of the full wave correlation function. The methods have a wide range of applications both in quantum mechanics and for classical wave problems such as in vibro-acoustics and electromagnetism. We apply the methods here to simple quantum systems, so-called quantum maps, which model the behaviour of generic problems on Poincaré sections. Although low-dimensional, these models exhibit a chaotic classical limit and share common characteristics with wave propagation in complex structures. (paper)
Pressure wave propagation in sodium loop
International Nuclear Information System (INIS)
Botelho, D.A.
1989-01-01
A study was done on the pressure wave propagation within the pipes and mixture vessel of a termohydraulic loop for thermal shock with sodium. It was used the characteristic method to solve the one-dimensional continuity and momentum equations. The numerical model includes the pipes and the effects of valves and other accidents on pressure losses. The study was based on designer informations and engineering tables. It was evaluated the pressure wave sizes, parametrically as a function of the draining valve closure times. (author) [pt
Electromagnetic wave propagating along a space curve
Lai, Meng-Yun; Wang, Yong-Long; Liang, Guo-Hua; Wang, Fan; Zong, Hong-Shi
2018-03-01
By using the thin-layer approach, we derive the effective equation for the electromagnetic wave propagating along a space curve. We find intrinsic spin-orbit, extrinsic spin-orbit, and extrinsic orbital angular-momentum and intrinsic orbital angular-momentum couplings induced by torsion, which can lead to geometric phase, spin, and orbital Hall effects. And we show the helicity inversion induced by curvature that can convert a right-handed circularly polarized electromagnetic wave into a left-handed polarized one, vice versa. Finally, we demonstrate that the gauge invariance of the effective dynamics is protected by the geometrically induced gauge potential.
Nonlinear acoustic waves in partially ionized collisional plasmas
International Nuclear Information System (INIS)
Rao, N.N.; Kaup, D.J.; Shukla, P.K.
1991-01-01
Nonlinear propagation of acoustic-type waves in a partially ionized three-component collisional plasma consisting of electrons, ions and neutral particles is investigated. For bidirectional propagation, it is shown that the small- but finite-amplitude waves are governed by the Boussinesq equation, which for unidirectional propagation near the acoustic speed reduces to the usual Korteweg-de Vries equation. For large-amplitude waves, it is demonstrated that the relevant fluid equations are integrable in a stationary frame, and the parameter values for the existence of finite-amplitude solutions are explicitly obtained. In both cases, the different temperatures of the individual species, are taken into account. The relevance of the results to the earth's ionospheric plasma in the lower altitude ranges is pointed out. (author)
Obliquely propagating dust-density waves
International Nuclear Information System (INIS)
Piel, A.; Arp, O.; Klindworth, M.; Melzer, A.
2008-01-01
Self-excited dust-density waves are experimentally studied in a dusty plasma under microgravity. Two types of waves are observed: a mode inside the dust volume propagating in the direction of the ion flow and another mode propagating obliquely at the boundary between the dusty plasma and the space charge sheath. The dominance of oblique modes can be described in the frame of a fluid model. It is shown that the results fom the fluid model agree remarkably well with a kinetic electrostatic model of Rosenberg [J. Vac. Sci. Technol. A 14, 631 (1996)]. In the experiment, the instability is quenched by increasing the gas pressure or decreasing the dust density. The critical pressure and dust density are well described by the models
Seismic Wave Propagation in Layered Viscoelastic Media
Borcherdt, R. D.
2008-12-01
Advances in the general theory of wave propagation in layered viscoelastic media reveal new insights regarding seismic waves in the Earth. For example, the theory predicts: 1) P and S waves are predominantly inhomogeneous in a layered anelastic Earth with seismic travel times, particle-motion orbits, energy speeds, Q, and amplitude characteristics that vary with angle of incidence and hence, travel path through the layers, 2) two types of shear waves exist, one with linear and the other with elliptical particle motions each with different absorption coefficients, and 3) surface waves with amplitude and particle motion characteristics not predicted by elasticity, such as Rayleigh-Type waves with tilted elliptical particle motion orbits and Love-Type waves with superimposed sinusoidal amplitude dependencies that decay exponentially with depth. The general theory provides closed-form analytic solutions for body waves, reflection-refraction problems, response of multiple layers, and surface wave problems valid for any material with a viscoelastic response, including the infinite number of models, derivable from various configurations of springs and dashpots, such as elastic, Voight, Maxwell, and Standard Linear. The theory provides solutions independent of the amount of intrinsic absorption and explicit analytic expressions for physical characteristics of body waves in low-loss media such as the deep Earth. The results explain laboratory and seismic observations, such as travel-time and wide-angle reflection amplitude anomalies, not explained by elasticity or one dimensional Q models. They have important implications for some forward modeling and inverse problems. Theoretical advances and corresponding numerical results as recently compiled (Borcherdt, 2008, Viscoelastic Waves in Layered Media, Cambridge University Press) will be reviewed.
Rapid assessment of nonlinear optical propagation effects in dielectrics
Hoyo, J. Del; de La Cruz, A. Ruiz; Grace, E.; Ferrer, A.; Siegel, J.; Pasquazi, A.; Assanto, G.; Solis, J.
2015-01-01
Ultrafast laser processing applications need fast approaches to assess the nonlinear propagation of the laser beam in order to predict the optimal range of processing parameters in a wide variety of cases. We develop here a method based on the simple monitoring of the nonlinear beam shaping against numerical prediction. The numerical code solves the nonlinear Schrödinger equation with nonlinear absorption under simplified conditions by employing a state-of-the art computationally efficient approach. By comparing with experimental results we can rapidly estimate the nonlinear refractive index and nonlinear absorption coefficients of the material. The validity of this approach has been tested in a variety of experiments where nonlinearities play a key role, like spatial soliton shaping or fs-laser waveguide writing. The approach provides excellent results for propagated power densities for which free carrier generation effects can be neglected. Above such a threshold, the peculiarities of the nonlinear propagation of elliptical beams enable acquiring an instantaneous picture of the deposition of energy inside the material realistic enough to estimate the effective nonlinear refractive index and nonlinear absorption coefficients that can be used for predicting the spatial distribution of energy deposition inside the material and controlling the beam in the writing process.
Laser beam propagation in non-linearly absorbing media
CSIR Research Space (South Africa)
Forbes, A
2006-08-01
Full Text Available Many analytical techniques exist to explore the propagation of certain laser beams in free space, or in a linearly absorbing medium. When the medium is nonlinearly absorbing the propagation must be described by an iterative process using the well...
Solitary waves on nonlinear elastic rods. I
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1984-01-01
Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction betwe...... nonlinearity. The balance between dispersion and nonlinearity in the equation is investigated.......Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction between...... the solitary waves numerically. It is demonstrated that the waves behave almost like solitons in agreement with the fact that the improved Boussinesq equations are nearly integrable. Thus three conservation theorems can be derived from the equations. A new subsonic quasibreather is found in the case of a cubic...
Wave Propagation in Jointed Geologic Media
Energy Technology Data Exchange (ETDEWEB)
Antoun, T
2009-12-17
Predictive modeling capabilities for wave propagation in a jointed geologic media remain a modern day scientific frontier. In part this is due to a lack of comprehensive understanding of the complex physical processes associated with the transient response of geologic material, and in part it is due to numerical challenges that prohibit accurate representation of the heterogeneities that influence the material response. Constitutive models whose properties are determined from laboratory experiments on intact samples have been shown to over-predict the free field environment in large scale field experiments. Current methodologies for deriving in situ properties from laboratory measured properties are based on empirical equations derived for static geomechanical applications involving loads of lower intensity and much longer durations than those encountered in applications of interest involving wave propagation. These methodologies are not validated for dynamic applications, and they do not account for anisotropic behavior stemming from direcitonal effects associated with the orientation of joint sets in realistic geologies. Recent advances in modeling capabilities coupled with modern high performance computing platforms enable physics-based simulations of jointed geologic media with unprecedented details, offering a prospect for significant advances in the state of the art. This report provides a brief overview of these modern computational approaches, discusses their advantages and limitations, and attempts to formulate an integrated framework leading to the development of predictive modeling capabilities for wave propagation in jointed and fractured geologic materials.
Wave propagation in the magnetosphere of Jupiter
Liemohn, H. B.
1972-01-01
A systematic procedure is developed for identifying the spatial regimes of various modes of wave propagation in the Jupiter magnetosphere that may be encountered by flyby missions. The Clemmow-Mullaly-Allis (CMA) diagram of plasma physics is utilized to identify the frequency regimes in which different modes of propagation occur in the magnetoplasma. The Gledhill model and the Ioannidis and Brice model of the magnetoplasma are summarized, and configuration-space CMA diagrams are constructed for each model for frequencies from 10 Hz to 1 MHz. The distinctive propagation features, the radio noise regimes, and the wave-particle interactions are discussed. It is concluded that the concentration of plasma in the equatorial plane makes this region of vital importance for radio observations with flyby missions. Local radio noise around the electron cyclotron frequency will probably differ appreciably from its terrestrial counterpart due to the lack of field-line guidance. Hydromagnetic wave properties at frequencies near the ion cyclotron frequency and below will probably be similar to the terrestrial case.
Nonlinear modulation of torsional waves in elastic rod. [Instability
Energy Technology Data Exchange (ETDEWEB)
Hirao, M; Sugimoto, N [Osaka Univ., Toyonaka (Japan). Faculty of Engineering Science
1977-06-01
Nonlinear Schroedinger equation, which describes the nonlinear modulation of dispersive torsional waves in an elastic rod of circular cross-section, is derived by the derivative expansion method. It is found, for the lowest dispersive mode, that the modulational instability occurs except in the range of the carrier wavenumber, 2.799
Nonlinear Displacement Discontinuity Model for Generalized Rayleigh Wave in Contact Interface
Energy Technology Data Exchange (ETDEWEB)
Kim, No Hyu; Yang, Seung Yong [Korea University of Technology and Education, Cheonan (Korea, Republic of)
2007-12-15
Imperfectly jointed interface serves as mechanical waveguide for elastic waves and gives rise to two distinct kinds of guided wave propagating along the interface. Contact acoustic nonlinearity (CAN) is known to plays major role in the generation of these interface waves called generalized Rayleigh waves in non-welded interface. Closed crack is modeled as non-welded interface that has nonlinear discontinuity condition in displacement across its boundary. Mathematical analysis of boundary conditions and wave equation is conducted to investigate the dispersive characteristics of the interface waves. Existence of the generalized Rayleigh wave(interface wave) in nonlinear contact interface is verified in theory where the dispersion equation for the interface wave is formulated and analyzed. It reveals that the interface waves have two distinct modes and that the phase velocity of anti-symmetric wave mode is highly dependent on contact conditions represented by linear and nonlinear dimensionless specific stiffness
Nonlinear Displacement Discontinuity Model for Generalized Rayleigh Wave in Contact Interface
International Nuclear Information System (INIS)
Kim, No Hyu; Yang, Seung Yong
2007-01-01
Imperfectly jointed interface serves as mechanical waveguide for elastic waves and gives rise to two distinct kinds of guided wave propagating along the interface. Contact acoustic nonlinearity (CAN) is known to plays major role in the generation of these interface waves called generalized Rayleigh waves in non-welded interface. Closed crack is modeled as non-welded interface that has nonlinear discontinuity condition in displacement across its boundary. Mathematical analysis of boundary conditions and wave equation is conducted to investigate the dispersive characteristics of the interface waves. Existence of the generalized Rayleigh wave(interface wave) in nonlinear contact interface is verified in theory where the dispersion equation for the interface wave is formulated and analyzed. It reveals that the interface waves have two distinct modes and that the phase velocity of anti-symmetric wave mode is highly dependent on contact conditions represented by linear and nonlinear dimensionless specific stiffness
Nonlinear wave collapse and strong turbulence
International Nuclear Information System (INIS)
Robinson, P.A.
1997-01-01
The theory and applications of wave self-focusing, collapse, and strongly nonlinear wave turbulence are reviewed. In the last decade, the theory of these phenomena and experimental realizations have progressed rapidly. Various nonlinear wave systems are discussed, but the simplest case of collapse and strong turbulence of Langmuir waves in an unmagnetized plasma is primarily used in explaining the theory and illustrating the main ideas. First, an overview of the basic physics of linear waves and nonlinear wave-wave interactions is given from an introductory perspective. Wave-wave processes are then considered in more detail. Next, an introductory overview of the physics of wave collapse and strong turbulence is provided, followed by a more detailed theoretical treatment. Later sections cover numerical simulations of Langmuir collapse and strong turbulence and experimental applications to space, ionospheric, and laboratory plasmas, including laser-plasma and beam-plasma interactions. Generalizations to self-focusing, collapse, and strong turbulence of waves in other systems are also discussed, including nonlinear optics, solid-state systems, magnetized auroral and astrophysical plasmas, and deep-water waves. The review ends with a summary of the main ideas of wave collapse and strong-turbulence theory, a collection of open questions in the field, and a brief discussion of possible future research directions. copyright 1997 The American Physical Society
Yoshioka, Masahiro; Sato, Sojun; Kikuchi, Tsuneo; Matsuda, Yoichi
2006-05-01
In this study, the influence of ultrasonic nonlinear propagation on hydrophone calibration by the two-transducer reciprocity method is investigated quantitatively using the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation. It is proposed that the correction for the diffraction and attenuation of ultrasonic waves used in two-transducer reciprocity calibration can be derived using the KZK equation to remove the influence of nonlinear propagation. The validity of the correction is confirmed by comparing the sensitivities calibrated by the two-transducer reciprocity method and laser interferometry.
Dispersive shock waves in nonlinear and atomic optics
Directory of Open Access Journals (Sweden)
Kamchatnov Anatoly
2017-01-01
Full Text Available A brief review is given of dispersive shock waves observed in nonlinear optics and dynamics of Bose-Einstein condensates. The theory of dispersive shock waves is developed on the basis of Whitham modulation theory for various situations taking place in these two fields. In particular, the full classification is established for types of wave structures evolving from initial discontinuities for propagation of long light pulses in fibers with account of steepening effect and for dynamics of the polarization mode in two-component Bose-Einstein condensates.
Kharin, Nikolay A.
2000-04-01
In nonlinear ultrasound imaging the images are formed using the second harmonic energy generated due to the nonlinear nature of finite amplitude propagation. This propagation can be modeled using the KZK wave equation. This paper presents further development of nonlinear diffractive field theory based on the KZK equation and its solution by means of the slowly changing profile method for moderate nonlinearity. The analytical expression for amplitudes and phases of sum frequency wave are obtained in addition to the second harmonic wave. Also, the analytical expression for the relative curvature of the wave fronts of fundamental and second harmonic signals are derived. The media with different nonlinear properties and absorption coefficients were investigated to characterize the diffractive field of the transducer at medical frequencies. All expressions demonstrate good agreement with experimental results. The expressions are novel and provide an easy way for prediction of amplitude and phase structure of nonlinearly distorted field of a transducer. The sum frequency signal technique could be implemented as well as second harmonic technique to improve the quality of biomedical images. The results obtained are of importance for medical diagnostic ultrasound equipment design.
Linear superposition solutions to nonlinear wave equations
International Nuclear Information System (INIS)
Liu Yu
2012-01-01
The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed
SPP propagation in nonlinear glass-metal interface
Sagor, Rakibul Hasan
2011-12-01
The non-linear propagation of Surface-Plasmon-Polaritons (SPP) in single interface of metal and chalcogenide glass (ChG) is considered. A time domain simulation algorithm is developed using the Finite Difference Time Domain (FDTD) method. The general polarization algorithm incorporated in the auxiliary differential equation (ADE) is used to model frequency-dependent dispersion relation and third-order nonlinearity of ChG. The main objective is to observe the nonlinear behavior of SPP propagation and study the dynamics of the whole structure. © 2011 IEEE.
Third harmonic generation of shear horizontal guided waves propagation in plate-like structures
Energy Technology Data Exchange (ETDEWEB)
Li, Wei Bin [School of Aerospace Engineering, Xiamen University, Xiamen (China); Xu, Chun Guang [School of Mechanical Engineering, Beijing Institute of Technology, Beijing (China); Cho, Youn Ho [School of Mechanical Engineering, Pusan National University, Busan (Korea, Republic of)
2016-04-15
The use of nonlinear ultrasonics wave has been accepted as a promising tool for monitoring material states related to microstructural changes, as it has improved sensitivity compared to conventional non-destructive testing approaches. In this paper, third harmonic generation of shear horizontal guided waves propagating in an isotropic plate is investigated using the perturbation method and modal analysis approach. An experimental procedure is proposed to detect the third harmonics of shear horizontal guided waves by electromagnetic transducers. The strongly nonlinear response of shear horizontal guided waves is measured. The accumulative growth of relative acoustic nonlinear response with an increase of propagation distance is detected in this investigation. The experimental results agree with the theoretical prediction, and thus providing another indication of the feasibility of using higher harmonic generation of electromagnetic shear horizontal guided waves for material characterization.
Experimental observation of azimuthal shock waves on nonlinear acoustical vortices
International Nuclear Information System (INIS)
Brunet, Thomas; Thomas, Jean-Louis; Marchiano, Regis; Coulouvrat, Francois
2009-01-01
Thanks to a new focused array of piezoelectric transducers, experimental results are reported here to evidence helical acoustical shock waves resulting from the nonlinear propagation of acoustical vortices (AVs). These shock waves have a three-dimensional spiral shape, from which both the longitudinal and azimuthal components are studied. The inverse filter technique used to synthesize AVs allows various parameters to be varied, especially the topological charge which is the key parameter describing screw dislocations. Firstly, an analysis of the longitudinal modes in the frequency domain reveals a wide cascade of harmonics (up to the 60th order) leading to the formation of the shock waves. Then, an original measurement in the transverse plane exhibits azimuthal behaviour which has never been observed until now for acoustical shock waves. Finally, these new experimental results suggest interesting potential applications of nonlinear effects in terms of acoustics spanners in order to manipulate small objects.
Propagation of internal gravity waves in the inhomogeneous atmosphere
International Nuclear Information System (INIS)
Deminov, M.G.; Ponomareva, L.I.
1988-01-01
Equations for disturbances of the density, temperature and speed of large-scale horizontally propagating internal gravity wave (IGM) wind are presented with regard to non-linearity, dispersion, molecular viscosity, thermal conductivity and background horizontal density and wind speed gradients. It is shown that values of wind speed and background atmosphere density decrease, typical of night conditions, provide for IGV amplitude increase near 250 km above the equator about 1.5 times, which with regard to the both hemispheres, fully compensates the effect of viscosity and thermal conductivity under increased solar activity. Speed and density decrease along IGW propagation can be provided both by background distribution of thermosphere parameters and by the front of a large-scale IGW on the background of which isolated IGW amplitude can grow
Nonlinear dynamics of resistive electrostatic drift waves
DEFF Research Database (Denmark)
Korsholm, Søren Bang; Michelsen, Poul; Pécseli, H.L.
1999-01-01
The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which is pertur......The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which...... polarity, i.e. a pair of electrostatic convective cells....
Modulated Langmuir waves and nonlinear Landau damping
International Nuclear Information System (INIS)
Yajima, Nobuo; Oikawa, Masayuki; Satsuma, Junkichi; Namba, Chusei.
1975-01-01
The nonlinear Schroedinger euqation with an integral term, iusub(t)+P/2.usub(xx)+Q/u/ 2 u+RP∫sub(-infinity)sup(infinity)[/u(x',t)/ 2 /(x-x')]dx'u=0, which describes modulated Langmuir waves with the nonlinear Landau damping effect, is solved by numerical calculations. Especially, the effects of nonlinear Landau damping on solitary wave solutions are studied. For both cases, PQ>0 and PQ<0, the results show that the solitary waves deform in an asymmetric way changing its velocity. (auth.)
Computational study of nonlinear plasma waves. I. Simulation model and monochromatic wave propagtion
International Nuclear Information System (INIS)
Matda, Y.; Crawford, F.W.
1974-12-01
An economical low noise plasma simulation model is applied to a series of problems associated with electrostatic wave propagation in a one-dimensional, collisionless, Maxwellian plasma, in the absence of magnetic field. The model is described and tested, first in the absence of an applied signal, and then with a small amplitude perturbation, to establish the low noise features and to verify the theoretical linear dispersion relation at wave energy levels as low as 0.000,001 of the plasma thermal energy. The method is then used to study propagation of an essentially monochromatic plane wave. Results on amplitude oscillation and nonlinear frequency shift are compared with available theories. The additional phenomena of sideband instability and satellite growth, stimulated by large amplitude wave propagation and the resulting particle trapping, are described. (auth)
Typology of nonlinear activity waves in a layered neural continuum.
Koch, Paul; Leisman, Gerry
2006-04-01
Neural tissue, a medium containing electro-chemical energy, can amplify small increments in cellular activity. The growing disturbance, measured as the fraction of active cells, manifests as propagating waves. In a layered geometry with a time delay in synaptic signals between the layers, the delay is instrumental in determining the amplified wavelengths. The growth of the waves is limited by the finite number of neural cells in a given region of the continuum. As wave growth saturates, the resulting activity patterns in space and time show a variety of forms, ranging from regular monochromatic waves to highly irregular mixtures of different spatial frequencies. The type of wave configuration is determined by a number of parameters, including alertness and synaptic conditioning as well as delay. For all cases studied, using numerical solution of the nonlinear Wilson-Cowan (1973) equations, there is an interval in delay in which the wave mixing occurs. As delay increases through this interval, during a series of consecutive waves propagating through a continuum region, the activity within that region changes from a single-frequency to a multiple-frequency pattern and back again. The diverse spatio-temporal patterns give a more concrete form to several metaphors advanced over the years to attempt an explanation of cognitive phenomena: Activity waves embody the "holographic memory" (Pribram, 1991); wave mixing provides a plausible cause of the competition called "neural Darwinism" (Edelman, 1988); finally the consecutive generation of growing neural waves can explain the discontinuousness of "psychological time" (Stroud, 1955).
Nonlinear low-frequency wave aspect of foreshock density holes
Directory of Open Access Journals (Sweden)
N. Lin
2008-11-01
Full Text Available Recent observations have uncovered short-duration density holes in the Earth's foreshock region. There is evidence that the formation of density holes involves non-linear growth of fluctuations in the magnetic field and plasma density, which results in shock-like boundaries followed by a decrease in both density and magnetic field. In this study we examine in detail a few such events focusing on their low frequency wave characteristics. The propagation properties of the waves are studied using Cluster's four point observations. We found that while these density hole-structures were convected with the solar wind, in the plasma rest frame they propagated obliquely and mostly sunward. The wave amplitude grows non-linearly in the process, and the waves are circularly or elliptically polarized in the left hand sense. The phase velocities calculated from four spacecraft timing analysis are compared with the velocity estimated from δE/δB. Their agreement justifies the plane electromagnetic wave nature of the structures. Plasma conditions are found to favor firehose instabilities. Oblique Alfvén firehose instability is suggested as a possible energy source for the wave growth. Resonant interaction between ions at certain energy and the waves could reduce the ion temperature anisotropy and thus the free energy, thereby playing a stabilizing role.
Nonlinear low-frequency wave aspect of foreshock density holes
Directory of Open Access Journals (Sweden)
N. Lin
2008-11-01
Full Text Available Recent observations have uncovered short-duration density holes in the Earth's foreshock region. There is evidence that the formation of density holes involves non-linear growth of fluctuations in the magnetic field and plasma density, which results in shock-like boundaries followed by a decrease in both density and magnetic field. In this study we examine in detail a few such events focusing on their low frequency wave characteristics. The propagation properties of the waves are studied using Cluster's four point observations. We found that while these density hole-structures were convected with the solar wind, in the plasma rest frame they propagated obliquely and mostly sunward. The wave amplitude grows non-linearly in the process, and the waves are circularly or elliptically polarized in the left hand sense. The phase velocities calculated from four spacecraft timing analysis are compared with the velocity estimated from δE/δB. Their agreement justifies the plane electromagnetic wave nature of the structures. Plasma conditions are found to favor firehose instabilities. Oblique Alfvén firehose instability is suggested as a possible energy source for the wave growth. Resonant interaction between ions at certain energy and the waves could reduce the ion temperature anisotropy and thus the free energy, thereby playing a stabilizing role.
International Nuclear Information System (INIS)
Mahalingam, A; Porsezian, K; Mani Rajan, M S; Uthayakumar, A
2009-01-01
In this paper, a generalized nonlinear Schroedinger-Maxwell-Bloch model with variable dispersion and nonlinearity management functions, which describes the propagation of optical pulses in an inhomogeneous erbium-doped fiber system under certain restrictive conditions, is under investigation. We derive the Lax pair with a variable spectral parameter and the exact soliton solution is generated from the Baecklund transformation. It is observed that stable solitons are possible only under a very restrictive condition for the spectral parameter and other inhomogeneous functions. For various forms of the inhomogeneous dispersion, nonlinearity and gain/loss functions, construction of different types of solitary waves like classical solitons, breathers, etc is discussed
Optical rogue waves generation in a nonlinear metamaterial
Onana Essama, Bedel Giscard; Atangana, Jacques; Biya-Motto, Frederick; Mokhtari, Bouchra; Cherkaoui Eddeqaqi, Noureddine; Kofane, Timoleon Crepin
2014-11-01
We investigate the behavior of electromagnetic wave which propagates in a metamaterial for negative index regime. The optical pulse propagation is described by the nonlinear Schrödinger equation with cubic-quintic nonlinearities, second- and third-order dispersion effects. The behavior obtained for negative index regime is compared to that observed for positive index regime. The characterization of electromagnetic wave uses some pulse parameters obtained analytically and called collective coordinates such as amplitude, temporal position, width, chirp, frequency shift and phase. Six frequency ranges have been pointed out where a numerical evolution of collective coordinates and their stability are studied under a typical example to verify our analysis. It appears that a robust soliton due to a perfect compensation process between second-order dispersion and cubic-nonlinearity is presented at each frequency range for both negative and positive index regimes. Thereafter, the stability of the soliton pulse and physical conditions leading to optical rogue waves generation are discussed at each frequency range for both regimes, when third-order dispersion and quintic-nonlinearity come into play. We have demonstrated that collective coordinates give much useful information on external and internal behavior of rogue events. Firstly, we determine at what distance begins the internal excitation leading to rogue waves. Secondly, what kind of internal modification and how it modifies the system in order to build-up rogue events. These results lead to a best comprehension of the mechanism of rogue waves generation. So, it clearly appears that the rogue wave behavior strongly depends on nonlinearity strength of distortion, frequency and regime considered.
Nonlinear plasma waves excited near resonance
International Nuclear Information System (INIS)
Cohen, B.I.; Kaufman, A.N.
1977-01-01
The nonlinear resonant response of a uniform plasma to an external plane-wave field is formulated in terms of the mismatch Δ/sub n l/ between the driving frequency and the time-dependent, complex, nonlinear normal mode frequency at the driving wavenumber. This formalism is applied to computer simulations of this process, yielding a deduced nonlinear frequency shift. The time dependence of the nonlinear phenomena, at frequency Δ/sub n l/ and at the bounce frequency of the resonant particles, is analyzed. The interdependence of the nonlinear features is described by means of energy and momentum relations
Wu, Z.; Zheng, Y.; Wang, K. W.
2018-02-01
We present an approach to achieve adaptable band structures and nonreciprocal wave propagation by exploring and exploiting the concept of metastable modular metastructures. Through studying the dynamics of wave propagation in a chain composed of finite metastable modules, we provide experimental and analytical results on nonreciprocal wave propagation and unveil the underlying mechanisms that facilitate such unidirectional energy transmission. In addition, we demonstrate that via transitioning among the numerous metastable states, the proposed metastructure is endowed with a large number of bandgap reconfiguration possibilities. As a result, we illustrate that unprecedented adaptable nonreciprocal wave propagation can be realized using the metastable modular metastructure. Overall, this research elucidates the rich dynamics attainable through the combinations of periodicity, nonlinearity, spatial asymmetry, and metastability and creates a class of adaptive structural and material systems capable of realizing tunable bandgaps and nonreciprocal wave transmissions.
Strongly nonlinear evolution of low-frequency wave packets in a dispersive plasma
Vasquez, Bernard J.
1993-01-01
The evolution of strongly nonlinear, strongly modulated wave packets is investigated in a dispersive plasma using a hybrid numerical code. These wave packets have amplitudes exceeding the strength of the external magnetic field, along which they propagate. Alfven (left helicity) wave packets show strong steepening for p Schrodinger (DNLS) equation.
Nonlinear interactions of counter-travelling waves
International Nuclear Information System (INIS)
Matsuuchi, Kazuo
1980-01-01
Nonlinear interactions between two waves travelling in opposite directions are investigated. When a nonlinear Klein-Gordon equation is adopted as a model equation, it is shown that such a wave system is governed by a simple set of equations for their complex amplitudes. Steady progressive waves governed by this set are investigated for various cases classified according to the signs of the coefficients. It is then found that one wave travelling in one direction appears from a certain point and the other travelling in the opposite direction has a constant amplitude from that point. This phenomenon may be regarded as a sort of reflection in spite of no rigid boundary. (author)
Evolution Of Nonlinear Waves in Compressing Plasma
International Nuclear Information System (INIS)
Schmit, P.F.; Dodin, I.Y.; Fisch, N.J.
2011-01-01
Through particle-in-cell simulations, the evolution of nonlinear plasma waves is examined in one-dimensional collisionless plasma undergoing mechanical compression. Unlike linear waves, whose wavelength decreases proportionally to the system length L(t), nonlinear waves, such as solitary electron holes, conserve their characteristic size Δ during slow compression. This leads to a substantially stronger adiabatic amplification as well as rapid collisionless damping when L approaches Δ. On the other hand, cessation of compression halts the wave evolution, yielding a stable mode.
Evolution Of Nonlinear Waves in Compressing Plasma
Energy Technology Data Exchange (ETDEWEB)
P.F. Schmit, I.Y. Dodin, and N.J. Fisch
2011-05-27
Through particle-in-cell simulations, the evolution of nonlinear plasma waves is examined in one-dimensional collisionless plasma undergoing mechanical compression. Unlike linear waves, whose wavelength decreases proportionally to the system length L(t), nonlinear waves, such as solitary electron holes, conserve their characteristic size {Delta} during slow compression. This leads to a substantially stronger adiabatic amplification as well as rapid collisionless damping when L approaches {Delta}. On the other hand, cessation of compression halts the wave evolution, yielding a stable mode.
Full wave simulations of lower hybrid wave propagation in tokamaks
International Nuclear Information System (INIS)
Wright, J. C.; Bonoli, P. T.; Phillips, C. K.; Valeo, E.; Harvey, R. W.
2009-01-01
Lower hybrid (LH) waves have the attractive property of damping strongly via electron Landau resonance on relatively fast tail electrons at (2.5-3)xv te , where v te ≡ (2T e /m e ) 1/2 is the electron thermal speed. Consequently these waves are well-suited to driving current in the plasma periphery where the electron temperature is lower, making LH current drive (LHCD) a promising technique for off-axis (r/a≥0.60) current profile control in reactor grade plasmas. Established techniques for computing wave propagation and absorption use WKB expansions with non-Maxwellian self-consistent distributions.In typical plasma conditions with electron densities of several 10 19 m -3 and toroidal magnetic fields strengths of 4 Telsa, the perpendicular wavelength is of the order of 1 mm and the parallel wavelength is of the order of 1 cm. Even in a relatively small device such as Alcator C-Mod with a minor radius of 22 cm, the number of wavelengths that must be resolved requires large amounts of computational resources for the full wave treatment. These requirements are met with a massively parallel version of the TORIC full wave code that has been adapted specifically for the simulation of LH waves [J. C. Wright, et al., Commun. Comput. Phys., 4, 545 (2008), J. C. Wright, et al., Phys. Plasmas 16 July (2009)]. This model accurately represents the effects of focusing and diffraction that occur in LH propagation. It is also coupled with a Fokker-Planck solver, CQL3D, to provide self-consistent distribution functions for the plasma dielectric as well as a synthetic hard X-ray (HXR) diagnostic for direct comparisons with experimental measurements of LH waves.The wave solutions from the TORIC-LH zero FLR model will be compared to the results from ray tracing from the GENRAY/CQL3D code via the synthetic HXR diagnostic and power deposition.
Field experiments and laboratory study of plasma turbulence and effects on EM wave propagation
International Nuclear Information System (INIS)
Lee, M.C.; Kuo, S.P.
1990-01-01
Both active experiments in space and laboratory experiments with plasma chambers have been planned to investigate plasma turbulence and effects on electromagnetic wave propagation. Plasma turbulence can be generated by intense waves or occur inherently with the production of plasmas. The turbulence effects to be singled out for investigation include nonlinear mode conversion process and turbulence scattering of electromagnetic waves by plasma density fluctuations. The authors have shown theoretically that plasma density fluctuations can render the nonlinear mode conversion of electromagnetic waves into lower hybrid waves, leading to anomalous absorption of waves in magnetoplasmas. The observed spectral broadening of VLF waves is the evidence of the occurrence of this process. Since the density fluctuations may have a broad range of scale lengths, this process is effective in weakening the electromagnetic waves in a wideband. In addition, plasma density fluctuations can scatter waves and diversify the electromagnetic energy. Schemes of generating plasma turbulence and the diagnoses of plasma effects are discussed
Investigation into stress wave propagation in metal foams
Directory of Open Access Journals (Sweden)
Li Lang
2015-01-01
Full Text Available The aim of this study is to investigate stress wave propagation in metal foams under high-speed impact loading. Three-dimensional Voronoi model is established to represent real closed-cell foam. Based on the one-dimensional stress wave theory and Voronoi model, a numerical model is developed to calculate the velocity of elastic wave and shock wave in metal foam. The effects of impact velocity and relative density of metal foam on the stress wave propagation in metal foams are explored respectively. The results show that both elastic wave and shock wave propagate faster in metal foams with larger relative density; with increasing the impact velocity, the shock wave propagation velocity increase, but the elastic wave propagation is not sensitive to the impact velocity.
Nonlinear Electrostatic Wave Equations for Magnetized Plasmas
DEFF Research Database (Denmark)
Dysthe, K.B.; Mjølhus, E.; Pécseli, Hans
1984-01-01
The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed.......The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed....
Topology Optimization for Transient Wave Propagation Problems
DEFF Research Database (Denmark)
Matzen, René
The study of elastic and optical waves together with intensive material research has revolutionized everyday as well as cutting edge technology in very tangible ways within the last century. Therefore it is important to continue the investigative work towards improving existing as well as innovate...... new technology, by designing new materials and their layout. The thesis presents a general framework for applying topology optimization in the design of material layouts for transient wave propagation problems. In contrast to the high level of modeling in the frequency domain, time domain topology...... optimization is still in its infancy. A generic optimization problem is formulated with an objective function that can be field, velocity, and acceleration dependent, as well as it can accommodate the dependency of filtered signals essential in signal shape optimization [P3]. The analytical design gradients...
Nonlinear propagation in ultrasonic fields: measurements, modelling and harmonic imaging.
Humphrey, V F
2000-03-01
In high amplitude ultrasonic fields, such as those used in medical ultrasound, nonlinear propagation can result in waveform distortion and the generation of harmonics of the initial frequency. In the nearfield of a transducer this process is complicated by diffraction effects associated with the source. The results of a programme to study the nonlinear propagation in the fields of circular, focused and rectangular transducers are described, and comparisons made with numerical predictions obtained using a finite difference solution to the Khokhlov-Zabolotskaya-Kuznetsov (or KZK) equation. These results are extended to consider nonlinear propagation in tissue-like media and the implications for ultrasonic measurements and ultrasonic heating are discussed. The narrower beamwidths and reduced side-lobe levels of the harmonic beams are illustrated and the use of harmonics to form diagnostic images with improved resolution is described.
Numerical Simulations of Upstream Propagating Solitary Waves and Wave Breaking In A Stratified Fjord
Stastna, M.; Peltier, W. R.
In this talk we will discuss ongoing numerical modeling of the flow of a stratified fluid over large scale topography motivated by observations in Knight Inlet, a fjord in British Columbia, Canada. After briefly surveying the work done on the topic in the past we will discuss our latest set of simulations in which we have observed the gener- ation and breaking of three different types of nonlinear internal waves in the lee of the sill topography. The first type of wave observed is a large lee wave in the weakly strat- ified main portion of the water column, The second is an upward propagating internal wave forced by topography that breaks in the strong, near-surface pycnocline. The third is a train of upstream propagating solitary waves that, in certain circumstances, form as breaking waves consisting of a nearly solitary wave envelope and a highly unsteady core near the surface. Time premitting, we will comment on the implications of these results for our long term goal of quantifying tidally driven mixing in Knight Inlet.
Propagation of sech2-type solitary waves in higher-order KdV-type systems
International Nuclear Information System (INIS)
Ilison, O.; Salupere, A.
2005-01-01
Wave propagation in microstructured media is essentially influenced by nonlinear and dispersive effects. The simplest model governing these effects results in the Korteweg-de Vries (KdV) equation. In the present paper a KdV-type evolution equation, including the third- and fifth-order dispersive and the fourth-order nonlinear terms, is used for modelling the wave propagation in microstructured solids like martensitic-austenitic alloys. The model equation is solved numerically under localised initial conditions. Possible solution types are defined and discussed. The existence of a threshold is established. Below the threshold, the relatively small solitary waves decay in time. However, if the amplitude exceeds a certain threshold, i.e., the critical value, then such a solitary wave can propagate with nearly a constant speed and amplitude and consequently conserve the energy
Seismic wave propagation in granular media
Tancredi, Gonzalo; López, Francisco; Gallot, Thomas; Ginares, Alejandro; Ortega, Henry; Sanchís, Johnny; Agriela, Adrián; Weatherley, Dion
2016-10-01
Asteroids and small bodies of the Solar System are thought to be agglomerates of irregular boulders, therefore cataloged as granular media. It is a consensus that many asteroids might be considered as rubble or gravel piles.Impacts on their surface could produce seismic waves which propagate in the interior of these bodies, thus causing modifications in the internal distribution of rocks and ejections of particles and dust, resulting in a cometary-type comma.We present experimental and numerical results on the study of propagation of impact-induced seismic waves in granular media, with special focus on behavior changes by increasing compression.For the experiment, we use an acrylic box filled with granular materials such as sand, gravel and glass spheres. Pressure inside the box is controlled by a movable side wall and measured with sensors. Impacts are created on the upper face of the box through a hole, ranging from free-falling spheres to gunshots. We put high-speed cameras outside the box to record the impact as well as piezoelectic sensors and accelerometers placed at several depths in the granular material to detect the seismic wave.Numerical simulations are performed with ESyS-Particle, a software that implements the Discrete Element Method. The experimental setting is reproduced in the numerical simulations using both individual spherical particles and agglomerates of spherical particles shaped as irregular boulders, according to rock models obtained with a 3D scanner. The numerical experiments also reproduces the force loading on one of the wall to vary the pressure inside the box.We are interested in the velocity, attenuation and energy transmission of the waves. These quantities are measured in the experiments and in the simulations. We study the dependance of these three parameters with characteristics like: impact speed, properties of the target material and the pressure in the media.These results are relevant to understand the outcomes of impacts in
International Nuclear Information System (INIS)
Elmer, Christopher E.; Vleck, Erik S. van
2003-01-01
This article is concerned with effect of spatial and temporal discretizations on traveling wave solutions to parabolic PDEs (Nagumo type) possessing piecewise linear bistable nonlinearities. Solution behavior is compared in terms of waveforms and in terms of the so-called (a,c) relationship where a is a parameter controlling the bistable nonlinearity by varying the potential energy difference of the two phases and c is the wave speed of the traveling wave. Uniform spatial discretizations and A(α) stable linear multistep methods in time are considered. Results obtained show that although the traveling wave solutions to parabolic PDEs are stationary for only one value of the parameter a,a 0 , spatial discretization of these PDEs produce traveling waves which are stationary for a nontrivial interval of a values which include a 0 , i.e., failure of the solution to propagate in the presence of a driving force. This is true no matter how wide the interface is with respect to the discretization. For temporal discretizations at large wave speeds the set of parameter a values for which there are traveling wave solutions is constrained. An analysis of a complete discretization points out the potential for nonuniqueness in the (a,c) relationship
Nonlinear reflection of shock shear waves in soft elastic media.
Pinton, Gianmarco; Coulouvrat, François; Gennisson, Jean-Luc; Tanter, Mickaël
2010-02-01
For fluids, the theoretical investigation of shock wave reflection has a good agreement with experiments when the incident shock Mach number is large. But when it is small, theory predicts that Mach reflections are physically unrealistic, which contradicts experimental evidence. This von Neumann paradox is investigated for shear shock waves in soft elastic solids with theory and simulations. The nonlinear elastic wave equation is approximated by a paraxial wave equation with a cubic nonlinear term. This equation is solved numerically with finite differences and the Godunov scheme. Three reflection regimes are observed. Theory is developed for shock propagation by applying the Rankine-Hugoniot relations and entropic constraints. A characteristic parameter relating diffraction and non-linearity is introduced and its theoretical values are shown to match numerical observations. The numerical solution is then applied to von Neumann reflection, where curved reflected and Mach shocks are observed. Finally, the case of weak von Neumann reflection, where there is no reflected shock, is examined. The smooth but non-monotonic transition between these three reflection regimes, from linear Snell-Descartes to perfect grazing case, provides a solution to the acoustical von Neumann paradox for the shear wave equation. This transition is similar to the quadratic non-linearity in fluids.
Propagation of transition fronts in nonlinear chains with non-degenerate on-site potentials
Shiroky, I. B.; Gendelman, O. V.
2018-02-01
We address the problem of transition front propagation in chains with a bi-stable nondegenerate on-site potential and a nonlinear gradient coupling. For generic nonlinear coupling, one encounters a special regime of transitions, characterized by extremely narrow fronts, far supersonic velocities of the front propagation, and long waves in the oscillatory tail. This regime can be qualitatively associated with a shock wave. The front propagation can be described with the help of a simple reduced-order model; the latter delivers a kinetic law, which is almost not sensitive to the fine details of the on-site potential. Besides, it is possible to predict all main characteristics of the transition front, including its velocity, as well as the frequency and the amplitude of the oscillatory tail. Numerical results are in good agreement with the analytical predictions. The suggested approach allows one to consider the effects of an external pre-load, the next-nearest-neighbor coupling and the on-site damping. When the damping is moderate, it is possible to consider the shock propagation in the damped chain as a perturbation of the undamped dynamics. This approach yields reasonable predictions. When the damping is high, the transition front enters a completely different asymptotic regime of a subsonic kink. The gradient nonlinearity generically turns negligible, and the propagating front converges to the regime described by a simple exact solution for a continuous model with linear coupling.
WAVE: Interactive Wave-based Sound Propagation for Virtual Environments.
Mehra, Ravish; Rungta, Atul; Golas, Abhinav; Ming Lin; Manocha, Dinesh
2015-04-01
We present an interactive wave-based sound propagation system that generates accurate, realistic sound in virtual environments for dynamic (moving) sources and listeners. We propose a novel algorithm to accurately solve the wave equation for dynamic sources and listeners using a combination of precomputation techniques and GPU-based runtime evaluation. Our system can handle large environments typically used in VR applications, compute spatial sound corresponding to listener's motion (including head tracking) and handle both omnidirectional and directional sources, all at interactive rates. As compared to prior wave-based techniques applied to large scenes with moving sources, we observe significant improvement in runtime memory. The overall sound-propagation and rendering system has been integrated with the Half-Life 2 game engine, Oculus-Rift head-mounted display, and the Xbox game controller to enable users to experience high-quality acoustic effects (e.g., amplification, diffraction low-passing, high-order scattering) and spatial audio, based on their interactions in the VR application. We provide the results of preliminary user evaluations, conducted to study the impact of wave-based acoustic effects and spatial audio on users' navigation performance in virtual environments.
Radiation from nonlinear coupling of plasma waves
International Nuclear Information System (INIS)
Fung, S.F.
1986-01-01
The author examines the generation of electromagnetic radiation by nonlinear resonant interactions of plasma waves in a cold, uniformly magnetized plasma. In particular, he considers the up-conversion of two electrostatic wave packets colliding to produce high frequency electromagnetic radiation. Efficient conversion of electrostatic to electromagnetic wave energy occurs when the pump amplitudes approach and exceed the pump depletion threshold. Results from the inverse scattering transform analysis of the three-wave interaction equations are applied. When the wave packets are initially separated, the fully nonlinear set of coupling equations, which describe the evolution of the wave packets, can be reduced to three separate eigenvalue problems; each can be considered as a scattering problem, analogous to eh Schroedinger equation. In the scattering space, the wave packet profiles act as the scattering potentials. When the wavepacket areas approach (or exceed) π/2, the wave functions are localized (bound states) and the scattering potentials are said to contain solitons. Exchange of solitons occurs during the interaction. The transfer of solitons from the pump waves to the electromagnetic wave leads to pump depletion and the production of strong radiation. The emission of radio waves is considered by the coupling of two upper-hybrid branch wave packets, and an upper-hybrid and a lower hybrid branch wave packet
Nonlinear Evolution of Alfvenic Wave Packets
Buti, B.; Jayanti, V.; Vinas, A. F.; Ghosh, S.; Goldstein, M. L.; Roberts, D. A.; Lakhina, G. S.; Tsurutani, B. T.
1998-01-01
Alfven waves are a ubiquitous feature of the solar wind. One approach to studying the evolution of such waves has been to study exact solutions to approximate evolution equations. Here we compare soliton solutions of the Derivative Nonlinear Schrodinger evolution equation (DNLS) to solutions of the compressible MHD equations.
On the propagation of truncated localized waves in dispersive silica
Salem, Mohamed; Bagci, Hakan
2010-01-01
Propagation characteristics of truncated Localized Waves propagating in dispersive silica and free space are numerically analyzed. It is shown that those characteristics are affected by the changes in the relation between the transverse spatial
Interpretation of nonlinearity in wind generated ocean surface waves
Digital Repository Service at National Institute of Oceanography (India)
Varkey, M.J.
of sinusoidal component waves; a consequent idea arising out of Fourier analysis. It is hypothesised that a sea state which is always nonlinear to various degrees is a result of interaction, both linear and nonlinear, between nonlinear component waves...
Nonlinear Waves in the Terrestrial Quasiparallel Foreshock.
Hnat, B; Kolotkov, D Y; O'Connell, D; Nakariakov, V M; Rowlands, G
2016-12-02
We provide strongly conclusive evidence that the cubic nonlinearity plays an important part in the evolution of the large amplitude magnetic structures in the terrestrial foreshock. Large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency are identified after nonharmonic slow variations are filtered out by applying the empirical mode decomposition. Numerical solutions of the derivative nonlinear Schrödinger equation, predicted analytically by the use of a pseudopotential approach, are found to be consistent with the observed wave forms. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfvén speed. We suggest that the feedback of the large amplitude fluctuations on background plasma is reflected in the evolution of the pseudopotential.
Non-Reciprocal Geometric Wave Diode by Engineering Asymmetric Shapes of Nonlinear Materials
Energy Technology Data Exchange (ETDEWEB)
Ren, Jie [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Li, Nianbei [Tongji Univ., Shanghai Shi (China)
2014-02-18
Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study how to design the novel wave diode devices to realize the non-reciprocal wave propagations. Analytical results reveal that such non-reciprocal wave propagation can be purely induced by asymmetric geometry in nonlinear materials. The detailed numerical simulations are performed for a more realistic geometric wave diode model with typical asymmetric shape, where good non-reciprocal wave diode effect has been demonstrated. The results open a way for making wave diodes efficiently simply through shape engineering.
Periodic solutions for one dimensional wave equation with bounded nonlinearity
Ji, Shuguan
2018-05-01
This paper is concerned with the periodic solutions for the one dimensional nonlinear wave equation with either constant or variable coefficients. The constant coefficient model corresponds to the classical wave equation, while the variable coefficient model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. For finding the periodic solutions of variable coefficient wave equation, it is usually required that the coefficient u (x) satisfies ess infηu (x) > 0 with ηu (x) = 1/2 u″/u - 1/4 (u‧/u)2, which actually excludes the classical constant coefficient model. For the case ηu (x) = 0, it is indicated to remain an open problem by Barbu and Pavel (1997) [6]. In this work, for the periods having the form T = 2p-1/q (p , q are positive integers) and some types of boundary value conditions, we find some fundamental properties for the wave operator with either constant or variable coefficients. Based on these properties, we obtain the existence of periodic solutions when the nonlinearity is monotone and bounded. Such nonlinearity may cross multiple eigenvalues of the corresponding wave operator. In particular, we do not require the condition ess infηu (x) > 0.
Nonlinear theory of localized standing waves
Denardo, Bruce; Larraza, Andrés; Putterman, Seth; Roberts, Paul
1992-01-01
An investigation of the nonlinear dispersive equations of continuum mechanics reveals localized standing-wave solutions that are domain walls between regions of different wave number. These states can appear even when the dispersion law is a single-valued function of the wave number. In addition, we calculate solutions for kinks in cutoff and noncutoff modes, as well as cutoff breather solitons. Division of Engineering and Geophysics of the Office of Basic Energy Science of U.S. DOE for su...
Analytical and numerical investigation of nonlinear internal gravity waves
Directory of Open Access Journals (Sweden)
S. P. Kshevetskii
2001-01-01
Full Text Available The propagation of long, weakly nonlinear internal waves in a stratified gas is studied. Hydrodynamic equations for an ideal fluid with the perfect gas law describe the atmospheric gas behaviour. If we neglect the term Ͽ dw/dt (product of the density and vertical acceleration, we come to a so-called quasistatic model, while we name the full hydro-dynamic model as a nonquasistatic one. Both quasistatic and nonquasistatic models are used for wave simulation and the models are compared among themselves. It is shown that a smooth classical solution of a nonlinear quasistatic problem does not exist for all t because a gradient catastrophe of non-linear internal waves occurs. To overcome this difficulty, we search for the solution of the quasistatic problem in terms of a generalised function theory as a limit of special regularised equations containing some additional dissipation term when the dissipation factor vanishes. It is shown that such solutions of the quasistatic problem qualitatively differ from solutions of a nonquasistatic nature. It is explained by the fact that in a nonquasistatic model the vertical acceleration term plays the role of a regularizator with respect to a quasistatic model, while the solution qualitatively depends on the regularizator used. The numerical models are compared with some analytical results. Within the framework of the analytical model, any internal wave is described as a system of wave modes; each wave mode interacts with others due to equation non-linearity. In the principal order of a perturbation theory, each wave mode is described by some equation of a KdV type. The analytical model reveals that, in a nonquasistatic model, an internal wave should disintegrate into solitons. The time of wave disintegration into solitons, the scales and amount of solitons generated are important characteristics of the non-linear process; they are found with the help of analytical and numerical investigations. Satisfactory
Nonlinear ultrasonic imaging with X wave
Du, Hongwei; Lu, Wei; Feng, Huanqing
2009-10-01
X wave has a large depth of field and may have important application in ultrasonic imaging to provide high frame rate (HFR). However, the HFR system suffers from lower spatial resolution. In this paper, a study of nonlinear imaging with X wave is presented to improve the resolution. A theoretical description of realizable nonlinear X wave is reported. The nonlinear field is simulated by solving the KZK nonlinear wave equation with a time-domain difference method. The results show that the second harmonic field of X wave has narrower mainlobe and lower sidelobes than the fundamental field. In order to evaluate the imaging effect with X wave, an imaging model involving numerical calculation of the KZK equation, Rayleigh-Sommerfeld integral, band-pass filtering and envelope detection is constructed to obtain 2D fundamental and second harmonic images of scatters in tissue-like medium. The results indicate that if X wave is used, the harmonic image has higher spatial resolution throughout the entire imaging region than the fundamental image, but higher sidelobes occur as compared to conventional focus imaging. A HFR imaging method with higher spatial resolution is thus feasible provided an apodization method is used to suppress sidelobes.
Wave propagation in a magnetically structured atmosphere. Pt. 2
International Nuclear Information System (INIS)
Roberts, B.
1981-01-01
Magnetic fields may introduce structure (inhomogeneity) into an otherwise uniform medium and thus change the nature of wave propagation in that medium. As an example of such structuring, wave propagation in an isolated magnetic slab is considered. It is supposed that disturbances outside the slab are laterally non-propagating. The effect of gravity is ignored. The field can support the propagation of both body and surface waves. The existence and nature of these waves depends upon the relative magnitudes of the sound speed c 0 and Alfven speed upsilonsub(A) inside the slab, and the sound speed csub(e) in the field-free environment. (orig./WL)
Nonlinear Waves on Stochastic Support: Calcium Waves in Astrocyte Syncytia
Jung, P.; Cornell-Bell, A. H.
Astrocyte-signaling has been observed in cell cultures and brain slices in the form of Calcium waves. Their functional relevance for neuronal communication, brain functions and diseases is, however, not understood. In this paper, the propagation of intercellular calcium waves is modeled in terms of waves in excitable media on a stochastic support. We utilize a novel method to decompose the spatiotemporal patterns into space-time clusters (wave fragments). Based on this cluster decomposition, a statistical description of wave patterns is developed.
International Nuclear Information System (INIS)
Zhang, Shan; Hong, Xue-Ren; Wang, Hong-Yu; Xie, Bai-Song
2011-01-01
Nonparaxial and nonlinear propagation of a short intense laser beam in a parabolic plasma channel is analyzed by means of the variational method and nonlinear dynamics. The beam propagation properties are classified by five kinds of behaviors. In particularly, the electromagnetic solitary wave for finite pulse laser is found beside the other four propagation cases including beam periodically oscillating with defocussing and focusing amplitude, constant spot size, beam catastrophic focusing. It is also found that the laser pulse can be allowed to propagate in the plasma channel only when a certain relation for laser parameters and plasma channel parameters is satisfied. For the solitary wave, it may provide an effective way to obtain ultra-short laser pulse.
Topological horseshoes in travelling waves of discretized nonlinear wave equations
International Nuclear Information System (INIS)
Chen, Yi-Chiuan; Chen, Shyan-Shiou; Yuan, Juan-Ming
2014-01-01
Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes
Topological horseshoes in travelling waves of discretized nonlinear wave equations
Energy Technology Data Exchange (ETDEWEB)
Chen, Yi-Chiuan, E-mail: YCChen@math.sinica.edu.tw [Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan (China); Chen, Shyan-Shiou, E-mail: sschen@ntnu.edu.tw [Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan (China); Yuan, Juan-Ming, E-mail: jmyuan@pu.edu.tw [Department of Financial and Computational Mathematics, Providence University, Shalu, Taichung 43301, Taiwan (China)
2014-04-15
Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes.
Electromagnetic wave propagation in relativistic magnetized plasmas
International Nuclear Information System (INIS)
Weiss, I.
1985-01-01
An improved mathematical technique and a new code for deriving the conductivity tensor for collisionless plasmas have been developed. The method is applicable to a very general case, including both hot (relativistic) and cold magnetized plasmas, with only isotropic equilibrium distributions being considered here. The usual derivation starts from the relativistic Vlasov equation and leads to an integration over an infinite sum of Bessel functions which has to be done numerically. In the new solution the integration is carried out over a product of two Bessel functions only. This reduces the computing time very significantly. An added advantage over existing codes is our capability to perform the computations for waves propagating obliquely to the magnetic field. Both improvements greatly facilitate investigations of properties of the plasma under conditions hitherto unexplored
Propagation of hypergeometric Gaussian beams in strongly nonlocal nonlinear media
Tang, Bin; Bian, Lirong; Zhou, Xin; Chen, Kai
2018-01-01
Optical vortex beams have attracted lots of interest due to its potential application in image processing, optical trapping and optical communications, etc. In this work, we theoretically and numerically investigated the propagation properties of hypergeometric Gaussian (HyGG) beams in strongly nonlocal nonlinear media. Based on the Snyder-Mitchell model, analytical expressions for propagation of the HyGG beams in strongly nonlocal nonlinear media were obtained. The influence of input power and optical parameters on the evolutions of the beam width and radius of curvature is illustrated, respectively. The results show that the beam width and radius of curvature of the HyGG beams remain invariant, like a soliton when the input power is equal to the critical power. Otherwise, it varies periodically like a breather, which is the result of competition between the beam diffraction and nonlinearity of the medium.
Statistical Characterization of Electromagnetic Wave Propagation in Mine Environments
Yucel, Abdulkadir C.; Liu, Yang; Bagci, Hakan; Michielssen, Eric
2013-01-01
A computational framework for statistically characterizing electromagnetic (EM) wave propagation through mine tunnels and galleries is presented. The framework combines a multi-element probabilistic collocation method with a full-wave fast Fourier
Bulk nonlinear elastic strain waves in a bar with nanosize inclusions
DEFF Research Database (Denmark)
Gula, Igor A.; Samsonov (†), Alexander M.
2018-01-01
We propose a mathematical model for propagation of the long nonlinearly elastic longitudinal strain waves in a bar, which contains nanoscale structural inclusions. The model is governed by a nonlinear doubly dispersive equation (DDE) with respect to the one unknown longitudinal strain function. We...
Obliquely propagating large amplitude solitary waves in charge neutral plasmas
Directory of Open Access Journals (Sweden)
F. Verheest
2007-01-01
Full Text Available This paper deals in a consistent way with the implications, for the existence of large amplitude stationary structures in general plasmas, of assuming strict charge neutrality between electrons and ions. With the limit of pair plasmas in mind, electron inertia is retained. Combining in a fluid dynamic treatment the conservation of mass, momentum and energy with strict charge neutrality has indicated that nonlinear solitary waves (as e.g. oscillitons cannot exist in electron-ion plasmas, at no angle of propagation with respect to the static magnetic field. Specifically for oblique propagation, the proof has turned out to be more involved than for parallel or perpendicular modes. The only exception is pair plasmas that are able to support large charge neutral solitons, owing to the high degree of symmetry naturally inherent in such plasmas. The nonexistence, in particular, of oscillitons is attributed to the breakdown of the plasma approximation in dealing with Poisson's law, rather than to relativistic effects. It is hoped that future space observations will allow to discriminate between oscillitons and large wave packets, by focusing on the time variability (or not of the phase, since the amplitude or envelope graphs look very similar.
E3D, 3-D Elastic Seismic Wave Propagation Code
International Nuclear Information System (INIS)
Larsen, S.; Harris, D.; Schultz, C.; Maddix, D.; Bakowsky, T.; Bent, L.
2004-01-01
1 - Description of program or function: E3D is capable of simulating seismic wave propagation in a 3D heterogeneous earth. Seismic waves are initiated by earthquake, explosive, and/or other sources. These waves propagate through a 3D geologic model, and are simulated as synthetic seismograms or other graphical output. 2 - Methods: The software simulates wave propagation by solving the elasto-dynamic formulation of the full wave equation on a staggered grid. The solution scheme is 4-order accurate in space, 2-order accurate in time
Nonlinear damping of oblique whistler mode waves through Landau resonance
Hsieh, Y.; Omura, Y.
2017-12-01
Nonlinear trapping of electrons through Landau resonance is a characteristic dynamics in oblique whistler-mode wave particle interactions. The resonance velocity of the Landau resonance at quasi-parallel propagation becomes very close to the parallel group velocity of whistler-mode wave at frequency around 0.5 Ωe, causing a long distance of resonant interaction and strong acceleration of resonant electrons [1]. We demonstrate these effective accelerations for electrons with high equatorial pitch angle ( > 60°) by test particle simulations with parameters for the Earth's inner magnetosphere at L=5. In the simulations, we focus on slightly oblique whistler mode waves with wave normal angle 10.1002/2016JA023255.
Wave propagation on a plasma media
International Nuclear Information System (INIS)
Torres-Silva, H.; Villarroel-Gonzalez, C.; Reggiani, N.; Sakanaka, P.H.
1995-01-01
Chiral-media and ferrite media have been studied over the last decade for many applications. Chiral-media have been examined as coating for reducing radar cross section, for antennas and arrays, for antenna radomes in waveguides and for microstrip substrate. Here, we examine a chiral-plasma medium, where the plasma part of the composite medium is non-reciprocal due to the external magnetic field, to find the general dispersion relation giving the ω against K behavior, vector phasor Helmholtz based equations are derived. We determine the modal eigenvalue properties in the chiral-plasma medium, which is doubly anisotropic. For the case of waves which propagate parallel to the magnetic field is a cold magnetized chiro-plasma. We compare our results with the typical results obtained for a cold plasma. Also we obtain the chiral-Faraday rotation which can be compared with the typical Faraday rotation for a pair of right-and left-handed circularly polarized waves. (author). 5 refs., 2 figs
Mathematical problems in wave propagation theory
1970-01-01
The papers comprising this collection are directly or indirectly related to an important branch of mathematical physics - the mathematical theory of wave propagation and diffraction. The paper by V. M. Babich is concerned with the application of the parabolic-equation method (of Academician V. A. Fok and M. A, Leontovich) to the problem of the asymptotic behavior of eigenfunc tions concentrated in a neighborhood of a closed geodesie in a Riemannian space. The techniques used in this paper have been föund useful in solving certain problems in the theory of open resonators. The topic of G. P. Astrakhantsev's paper is similar to that of the paper by V. M. Babich. Here also the parabolic-equation method is used to find the asymptotic solution of the elasticity equations which describes Love waves concentrated in a neighborhood of some surface ray. The paper of T. F. Pankratova is concerned with finding the asymptotic behavior of th~ eigenfunc tions of the Laplace operator from the exact solution for the surf...
Simulations of nonlinear continuous wave pressure fields in FOCUS
Zhao, Xiaofeng; Hamilton, Mark F.; McGough, Robert J.
2017-03-01
The Khokhlov - Zabolotskaya - Kuznetsov (KZK) equation is a parabolic approximation to the Westervelt equation that models the effects of diffraction, attenuation, and nonlinearity. Although the KZK equation is only valid in the far field of the paraxial region for mildly focused or unfocused transducers, the KZK equation is widely applied in medical ultrasound simulations. For a continuous wave input, the KZK equation is effectively modeled by the Bergen Code [J. Berntsen, Numerical Calculations of Finite Amplitude Sound Beams, in M. F. Hamilton and D. T. Blackstock, editors, Frontiers of Nonlinear Acoustics: Proceedings of 12th ISNA, Elsevier, 1990], which is a finite difference model that utilizes operator splitting. Similar C++ routines have been developed for FOCUS, the `Fast Object-Oriented C++ Ultrasound Simulator' (http://www.egr.msu.edu/˜fultras-web) to calculate nonlinear pressure fields generated by axisymmetric flat circular and spherically focused ultrasound transducers. This new routine complements an existing FOCUS program that models nonlinear ultrasound propagation with the angular spectrum approach [P. T. Christopher and K. J. Parker, J. Acoust. Soc. Am. 90, 488-499 (1991)]. Results obtained from these two nonlinear ultrasound simulation approaches are evaluated and compared for continuous wave linear simulations. The simulation results match closely in the farfield of the paraxial region, but the results differ in the nearfield. The nonlinear pressure field generated by a spherically focused transducer with a peak surface pressure of 0.2MPa radiating in a lossy medium with β = 3.5 is simulated, and the computation times are also evaluated. The nonlinear simulation results demonstrate acceptable agreement in the focal zone. These two related nonlinear simulation approaches are now included with FOCUS to enable convenient simulations of nonlinear pressure fields on desktop and laptop computers.
International Nuclear Information System (INIS)
Egerton, B.; Barnett, S.; Vella, G.
1994-01-01
Diagnostic ultrasound is an established imaging modality without any documented harmful effects. New developments such as pulsed Doppler and intracavity investigations may result in increases in ultrasound exposures which could cause harm. Thermal mechanisms and cavitation may become relevant sources of bioeffects. The preliminary study described here investigates the distribution and amplitude of harmonics generated through nonlinear propagation of ultrasound in water. Knowledge of harmonic attenuation will help predict sites of enhanced heating and enable accurate modelling of clinical situations. This presentation is concerned with thermal safety guidelines, their relationship to a typical ultrasound beam profile for a single, medium focussed, transducer operating in water and possible sites of enhanced heating due to nonlinear propagation effects. Measurements were made of the amplitudes of the harmonics generated by the nonlinear propagation of ultrasound in water. The amplitudes of the harmonics were detected up to frequencies of 35 MHz and displayed using Fast Fourier Transform facilities within the oscilloscope. The nonlinearity parameter of the ultrasonic waveforms has been identified as an important factor in thermal effects of ultrasound interactions. The appearance of nonlinear distortion is shown to be dependant on the peak compressional pressure and distance from the ultrasound source. 20 refs., 2 figs
Nonlinear effects in the propagation of shortwave transverse sound in pure superconductors
International Nuclear Information System (INIS)
Gal'perin, Y.
1982-01-01
Various mechanisms are analyzed which lead to nonlinear phenomena (e.g., the dependence of the absorption coefficient and of the velocity of sound on its intensity) in the propagation of transverse shortwave sound in pure superconductors (the wavelength of the sound being much less than the mean free path of the quasiparticles). It is shown that the basic mechanism, over a wide range of superconductor parameters and of the sound intensity, is the so-called momentum nonlinearity. The latter is due to the distortion (induced by the sound wave) of the quasimomentum distribution of resonant electrons interacting with the wave. The dependences of the absorption coefficient and of the sound velocity on its intensity and on the temperature are analyzed in the vicinity of the superconducting transition point. The feasibility of an experimental study of nonlinear acoustic phenomena in the case of transverse sound is considered
Cumulative Second Harmonic Generation in Lamb Waves for the Detection of Material Nonlinearities
International Nuclear Information System (INIS)
Bermes, Christian; Jacobs, Laurence J.; Kim, Jin-Yeon; Qu, Jianmin
2007-01-01
An understanding of the generation of higher harmonics in Lamb waves is of critical importance for applications such as remaining life prediction of plate-like structural components. The objective of this work is to use nonlinear Lamb waves to experimentally investigate inherent material nonlinearities in aluminum plates. These nonlinearities, e.g. lattice anharmonicities, precipitates or vacancies, cause higher harmonics to form in propagating Lamb waves. The amplitudes of the higher harmonics increase with increasing propagation distance due to the accumulation of nonlinearity while the Lamb wave travels along its path. Special focus is laid on the second harmonic, and a relative nonlinearity parameter is defined as a function of the fundamental and second harmonic amplitude. The experimental setup uses an ultrasonic transducer and a wedge for the Lamb wave generation, and laser interferometry for detection. The experimentally measured Lamb wave signals are processed with a short-time Fourier transformation (STFT), which yields the amplitudes at different frequencies as functions of time, allowing the observation of the nonlinear behavior of the material. The increase of the relative nonlinearity parameter with propagation distance as an indicator of cumulative second harmonic generation is shown in the results for the alloy aluminum 1100-H14
Nonlocal wave propagation in an embedded DWBNNT conveying fluid via strain gradient theory
International Nuclear Information System (INIS)
Ghorbanpour Arani, A.; Kolahchi, R.; Vossough, H.
2012-01-01
Based on the strain gradient and Eringen’s piezoelasticity theories, wave propagation of an embedded double-walled boron nitride nanotube (DWBNNT) conveying fluid is investigated using Euler-Bernoulli beam model. The elastic medium is simulated by the Pasternak foundation. The van der Waals (vdW) forces between the inner and outer nanotubes are taken into account. Since, considering electro-mechanical coupling made the nonlinear motion equations, a numerical procedure is proposed to evaluate the upstream and downstream phase velocities. The results indicate that the effect of nonlinear terms in motion equations on the phase velocity cannot be neglected at lower wave numbers. Furthermore, the effect of fluid-conveying on wave propagation of the DWBNNT is significant at lower wave numbers.
Solitons and nonlinear waves in space plasmas
International Nuclear Information System (INIS)
Stasiewicz, K.
2005-01-01
Recent measurements made on the ESA/NASA Cluster mission to the Earth's magnetosphere have provided first detailed measurements of magnetosonic solitons in space. The solitons represent localized enhancements of the magnetic field by a factor of 2-10, or depressions down to 10% of the ambient field. The magnetic field signatures are associated with density depressions/enhancements A two-fluid model of nonlinear electron and ion inertial waves in anisotropic plasmas explains the main properties of these structures. It is shown that warm plasmas support four types of nonlinear waves, which correspond to four linear modes: Alfvenic, magnetosonic, sound, and electron inertial waves. Each of these nonlinear modes has slow and fast versions. It is shown by direct integration that the exponential growth rate of nonlinear modes is balanced by the ion and electron dispersion leading to solutions in the form of trains of solitons or cnoidal waves. By using a novel technique of phase portraits it is shown how the dispersive properties of electron and ion inertial waves change at the transition between warm and hot plasmas, and how trains of solitons ('' mirror modes '') are produced in a hot, anisotropic plasma. The applicability of the model is illustrated with data from Cluster spacecraft. (author)
Models for seismic wave propagation in periodically layered porous media
Kudarova, A.; Van Dalen, K.N.; Drijkoningen, G.G.
2014-01-01
Several models are discussed for seismic wave propagation in periodically layered poroelastic media where layers represent mesoscopic-scale heterogeneities that are larger than the pore and grain sizes but smaller than the wavelength. The layers behave according to Biot’s theory. Wave propagation
New exact travelling wave solutions of nonlinear physical models
International Nuclear Information System (INIS)
Bekir, Ahmet; Cevikel, Adem C.
2009-01-01
In this work, we established abundant travelling wave solutions for some nonlinear evolution equations. This method was used to construct travelling wave solutions of nonlinear evolution equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The ((G ' )/G )-expansion method presents a wider applicability for handling nonlinear wave equations.
Propagation of ionization waves during ignition of fluorescent lamps
International Nuclear Information System (INIS)
Langer, R; Tidecks, R; Horn, S; Garner, R; Hilscher, A
2008-01-01
The propagation of the first ionization wave in a compact fluorescent lamp (T4 tube with standard electrodes) during ignition was investigated for various initial dc-voltages (both polarities measured against ground) and gas compositions (with and without mercury). In addition the effect of the presence of a fluorescent powder coating was studied. The propagation velocity of the initial wave was measured by an assembly of photomultipliers installed along the tube, which detected the light emitted by the wave head. The propagation was found to be faster for positive than for negative polarity. This effect is explained involving processes in the electrode region as well as in the wave head. Waves propagate faster in the presence of a fluorescent powder coating than without it and gases of lighter mass show a faster propagation than gases with higher mass
Nonlinear wave equation with intrinsic wave particle dualism
International Nuclear Information System (INIS)
Klein, J.J.
1976-01-01
A nonlinear wave equation derived from the sine-Gordon equation is shown to possess a variety of solutions, the most interesting of which is a solution that describes a wave packet travelling with velocity usub(e) modulating a carrier wave travelling with velocity usub(c). The envelop and carrier wave speeds agree precisely with the group and phase velocities found by de Broglie for matter waves. No spreading is exhibited by the soliton, so that it behaves exactly like a particle in classical mechanics. Moreover, the classically computed energy E of the disturbance turns out to be exactly equal to the frequency ω of the carrier wave, so that the Planck relation is automatically satisfied without postulating a particle-wave dualism. (author)
Propagation of Tsunami-like Surface Long Waves in the Bays of a Variable Depth
Directory of Open Access Journals (Sweden)
A.Yu. Bazykina
2016-08-01
Full Text Available Within the framework of the nonlinear long wave theory the regularities of solitary long wave propagation in the semi-closed bays of model and real geometry are numerically studied. In the present article the zones of wave amplification in the bay are found. The first one is located near the wave running-up on the beach (in front of the bay entrance and the other one – in the middle part of the sea basin. Wave propagation in these zones is accompanied both by significant rise and considerable fall of the sea level. Narrowing of the bay entrance and increase of the entering wave length result in decrease of the sea level maximum rises and falls. The Feodosiya Gulf in the Black Sea is considered as a real basin. In general the dynamics of the waves in the gulf is similar to wave dynamics in the model bay. Four zones of the strongest wave amplification in the Feodosiya Gulf are revealed in the article. The sea level maximum rises and extreme falls which tend to grow with decrease of the entering wave length are observed in these zones. The distance traveled by the wave before the collapse (due to non-linear effects, was found to reduce with decreasing wavelength of the entrance to the bay (gulf.
Energy Technology Data Exchange (ETDEWEB)
Matsumoto, H.; Kimura, T.
1986-01-01
Triggered by the experimental results of the MINIX, a computer simulation study was initiated on the nonlinear excitation of electrostatic electron cyclotron waves by a monochromatic electromagnetic wave such as the transmitted microwave in the MINIX. The model used assumes that both of the excited waves and exciting (pumping) electromagnetic wave as well as the idler electromagnetic wave propagate in the direction perpendicular to the external magnetic field. The simulation code used for this study was the one-and-two-half dimensional electromagnetic particle code named KEMPO. The simulation result shows the high power electromagnetic wave produces both the backscattered electromagnetic wave and electrostatic electron cyclotron waves as a result of nonlinear parametric instability. Detailed nonlinear microphysics related to the wave excitation is discussed in terms of the nonlinear wave-wave couplings and associated ponderomotive force produced by the high power electromagnetic waves. 2 references, 4 figures.
International Nuclear Information System (INIS)
Matsumoto, H.; Kimura, T.
1986-01-01
Triggered by the experimental results of the MINIX, a computer simulation study was initiated on the nonlinear excitation of electrostatic electron cyclotron waves by a monochromatic electromagnetic wave such as the transmitted microwave in the MINIX. The model used assumes that both of the excited waves and exciting (pumping) electromagnetic wave as well as the idler electromagnetic wave propagate in the direction perpendicular to the external magnetic field. The simulation code used for this study was the one-and-two-half dimensional electromagnetic particle code named KEMPO. The simulation result shows the high power electromagnetic wave produces both the backscattered electromagnetic wave and electrostatic electron cyclotron waves as a result of nonlinear parametric instability. Detailed nonlinear microphysics related to the wave excitation is discussed in terms of the nonlinear wave-wave couplings and associated ponderomotive force produced by the high power electromagnetic waves. 2 references, 4 figures
Fukuhara, Keisuke; Morita, Nagayoshi
New FDTD algorithm is proposed for analyzing ultrasonic pulse propagation in the human body, the problem being connected with ESWL (Extracorporeal Shock Wave Lithotripsy). In this method, we do not use plane wave approximation but employ directly the original equations taking account of Lagrangian to derive new FDTD algorithms. This method is applied to an experimental setup and its numerical model that resemble actual treatment situation to compare sound pressure distributions obtained numerically with those obtained experimentally. It is shown that the present method gives clearly better results than the earlier method, in the viewpoint of numerical reappearance of strongly nonlinear waveform.
Wave propagation in plasma-filled wave-guide
International Nuclear Information System (INIS)
Leprince, Philippe
1966-01-01
This research thesis reports the study of wave propagation along a plasma column without external magnetic field. The author first present and comment various theoretical results, and dispersion curves plotted for the main modes (particularly, the bipolar mode). He tries to define fundamental magnitudes which characterise a plasma-filled wave-guide. He reports the comparison of some experimental results with the previous theoretical results. Based on the study of the bipolar mode, the author develops a method of measurement of plasma column density. In the last part, the author reports the study of the resonance of a plasma-containing cavity. Several resonances are highlighted and new dispersion curves are plotted by using a varying length cavity. He also addresses the coupling of plasma modes with guide modes, and thus indicates the shape of Brillouin diagrams for a plasma-filled wave-guide. Moreover, some phenomena highlighted during plasma column density measurements by using the cavity method could then be explained [fr
Nonlinear waves: some biomedical applications
International Nuclear Information System (INIS)
Rudenko, Oleg V
2007-01-01
The field of nonlinear physics, item No. 11 on Ginzburg's list of 'the most important and interesting problems', is reviewed. An example at the intersection of applied physics, medicine, and instrument engineering is discussed to illustrate the range and scope of the field and how deep the ideas and approaches it involves are incorporated in modern natural science and engineering. Results of relevant research and development, which has attracted much recent interest and financial support, are briefly examined. (oral issue of the journal 'uspekhi fizicheskikh nauk')
Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media
International Nuclear Information System (INIS)
Kartashov, Yaroslav V; Egorov, Alexey A; Vysloukh, Victor A; Torner, Lluis
2004-01-01
We review the latest progress and properties of the families of bright and dark one-dimensional periodic waves propagating in saturable Kerr-type and quadratic nonlinear media. We show how saturation of the nonlinear response results in the appearance of stability (instability) bands in a focusing (defocusing) medium, which is in sharp contrast with the properties of periodic waves in Kerr media. One of the key results discovered is the stabilization of multicolour periodic waves in quadratic media. In particular, dark-type waves are shown to be metastable, while bright-type waves are completely stable in a broad range of energy flows and material parameters. This yields the first known example of completely stable periodic wave patterns propagating in conservative uniform media supporting bright solitons. Such results open the way to the experimental observation of the corresponding self-sustained periodic wave patterns
The Green-function transform and wave propagation
Directory of Open Access Journals (Sweden)
Colin eSheppard
2014-11-01
Full Text Available Fourier methods well known in signal processing are applied to three-dimensional wave propagation problems. The Fourier transform of the Green function, when written explicitly in terms of a real-valued spatial frequency, consists of homogeneous and inhomogeneous components. Both parts are necessary to result in a pure out-going wave that satisfies causality. The homogeneous component consists only of propagating waves, but the inhomogeneous component contains both evanescent and propagating terms. Thus we make a distinction between inhomogeneous waves and evanescent waves. The evanescent component is completely contained in the region of the inhomogeneous component outside the k-space sphere. Further, propagating waves in the Weyl expansion contain both homogeneous and inhomogeneous components. The connection between the Whittaker and Weyl expansions is discussed. A list of relevant spherically symmetric Fourier transforms is given.
Wave propagation in nanostructures nonlocal continuum mechanics formulations
Gopalakrishnan, Srinivasan
2013-01-01
Wave Propagation in Nanostructures describes the fundamental and advanced concepts of waves propagating in structures that have dimensions of the order of nanometers. The book is fundamentally based on non-local elasticity theory, which includes scale effects in the continuum model. The book predominantly addresses wave behavior in carbon nanotubes and graphene structures, although the methods of analysis provided in this text are equally applicable to other nanostructures. The book takes the reader from the fundamentals of wave propagation in nanotubes to more advanced topics such as rotating nanotubes, coupled nanotubes, and nanotubes with magnetic field and surface effects. The first few chapters cover the basics of wave propagation, different modeling schemes for nanostructures and introduce non-local elasticity theories, which form the building blocks for understanding the material provided in later chapters. A number of interesting examples are provided to illustrate the important features of wave behav...
Rielly, Matthew Robert
An existing numerical model (known as the Bergen code) is used to investigate finite amplitude ultrasound propagation through multiple layers of tissue-like media. This model uses a finite difference method to solve the nonlinear parabolic KZK wave equation. The code is modified to include an arbitrary frequency dependence of absorption and transmission effects for wave propagation across a plane interface at normal incidence. In addition the code is adapted to calculate the total intensity loss associated with the absorption of the fundamental and nonlinearly generated harmonics. Measurements are also taken of the axial nonlinear pressure field generated from a circular focused, 2.25 MHz source, through single and multiple layered tissue mimicking fluids, for source pressures in the range from 13 kPa to 310 kPa. Two tissue mimicking fluids are developed to provide acoustic properties similar to amniotic fluid and a typical soft tissue. The values of the nonlinearity parameter, sound velocity and frequency dependence of attenuation for both fluids are presented, and the measurement procedures employed to obtain these characteristics are described in detail. These acoustic parameters, together with the measured source conditions are used as input to the numerical model, allowing the experimental conditions to be simulated. Extensive comparisons are made between the model's predictions and the axial pressure field measurements. Results are presented in the frequency domain showing the fundamental and three subsequent harmonic amplitudes on axis, as a function of axial distance. These show that significant nonlinear distortion can occur through media with characteristics typical of tissue. Time domain waveform comparisons are also made. An excellent agreement is found between theory and experiment indicating that the model can be used to predict nonlinear ultrasound propagation through multiple layers of tissue-like media. The numerical code is also used to model the
Topics in nonlinear wave theory with applications
International Nuclear Information System (INIS)
Tracy, E.R.
1984-01-01
Selected topics in nonlinear wave theory are discussed, and applications to the study of modulational instabilities are presented. A historical survey is given of topics relating to solitons and modulational problems. A method is then presented for generating exact periodic and quasi-periodic solutions to several nonlinear wave equations, which have important physical applications. The method is then specialized for the purposes of studying the modulational instability of a plane wave solution of the nonlinear Schroedinger equation, an equation with general applicability in one-dimensional modulational problems. Some numerical results obtained in conjunction with the analytic study are presented. The analytic approach explains the recurrence phenomena seen in the numerical studies, and the numerical work of other authors. The method of solution (related to the inverse scattering method) is then analyzed within the context of Hamiltonian dynamics where it is shown that the method can be viewed as simply a pair of canonical transformations. The Abel Transformation, which appears here and in the work of other authors, is shown to be a special form of Liouville's transformation to action-angle variables. The construction of closed form solutions of these nonlinear wave equations, via the solution of Jacobi's inversion problem, is surveyed briefly
Four Wave Mixing using Intermodal Nonlinearities
DEFF Research Database (Denmark)
Rishøj, Lars Søgaard
The nonlinear process of four-wave mixing (FWM) enables coupling of energy between wavelengths. This is useful for both optical amplification and wavelength conversion. A crucial prerequisite for the process is phase matching. This PhD project investigates how higher order modes (HOMs) in fibers...
Energy Technology Data Exchange (ETDEWEB)
Arevalo, Edward, E-mail: arevalo@temf.tu-darmstadt.d [Technische Universitaet Darmstadt, Institut fuer Theorie elektromagnetischer Felder, TEMF, Schlossgartenstr. 8, D-64289 Darmstadt (Germany)
2009-09-21
The effect of instability on the propagation of solitary waves along one-dimensional discrete nonlinear Schroedinger 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.
TWO-DIMENSIONAL MODELLING OF ACCIDENTAL FLOOD WAVES PROPAGATION
Lorand Catalin STOENESCU
2011-01-01
The study presented in this article describes a modern modeling methodology of the propagation of accidental flood waves in case a dam break; this methodology is applied in Romania for the first time for the pilot project „Breaking scenarios of Poiana Uzului dam”. The calculation programs used help us obtain a bidimensional calculation (2D) of the propagation of flood waves, taking into consideration the diminishing of the flood wave on a normal direction to the main direction; this diminishi...
A wave propagation matrix method in semiclassical theory
International Nuclear Information System (INIS)
Lee, S.Y.; Takigawa, N.
1977-05-01
A wave propagation matrix method is used to derive the semiclassical formulae of the multiturning point problem. A phase shift matrix and a barrier transformation matrix are introduced to describe the processes of a particle travelling through a potential well and crossing a potential barrier respectively. The wave propagation matrix is given by the products of phase shift matrices and barrier transformation matrices. The method to study scattering by surface transparent potentials and the Bloch wave in solids is then applied
Propagation of Axially Symmetric Detonation Waves
Energy Technology Data Exchange (ETDEWEB)
Druce, R L; Roeske, F; Souers, P C; Tarver, C M; Chow, C T S; Lee, R S; McGuire, E M; Overturf, G E; Vitello, P A
2002-06-26
We have studied the non-ideal propagation of detonation waves in LX-10 and in the insensitive explosive TATB. Explosively-driven, 5.8-mm-diameter, 0.125-mm-thick aluminum flyer plates were used to initiate 38-mm-diameter, hemispherical samples of LX-10 pressed to a density of 1.86 g/cm{sup 3} and of TATB at a density of 1.80 g/cm{sup 3}. The TATB powder was a grade called ultrafine (UFTATB), having an arithmetic mean particle diameter of about 8-10 {micro}m and a specific surface area of about 4.5 m{sup 2}/g. Using PMMA as a transducer, output pressure was measured at 5 discrete points on the booster using a Fabry-Perot velocimeter. Breakout time was measured on a line across the booster with a streak camera. Each of the experimental geometries was calculated using the Ignition and Growth Reactive Flow Model, the JWL++ Model and the Programmed Burn Model. Boosters at both ambient and cold (-20 C and -54 C) temperatures have been experimentally and computationally studied. A comparison of experimental and modeling results is presented.
Nonlinear electromagnetic waves in a degenerate electron-positron plasma
Energy Technology Data Exchange (ETDEWEB)
El-Labany, S.K., E-mail: skellabany@hotmail.com [Department of Physics, Faculty of Science, Damietta University, New Damietta (Egypt); El-Taibany, W.F., E-mail: eltaibany@hotmail.com [Department of Physics, College of Science for Girls in Abha, King Khalid University, Abha (Saudi Arabia); El-Samahy, A.E.; Hafez, A.M.; Atteya, A., E-mail: ahmedsamahy@yahoo.com, E-mail: am.hafez@sci.alex.edu.eg, E-mail: ahmed_ateya2002@yahoo.com [Department of Physics, Faculty of Science, Alexandria University, Alexandria (Egypt)
2015-08-15
Using the reductive perturbation technique (RPT), the nonlinear propagation of magnetosonic solitary waves in an ultracold, degenerate (extremely dense) electron-positron (EP) plasma (containing ultracold, degenerate electron, and positron fluids) is investigated. The set of basic equations is reduced to a Korteweg-de Vries (KdV) equation for the lowest-order perturbed magnetic field and to a KdV type equation for the higher-order perturbed magnetic field. The solutions of these evolution equations are obtained. For better accuracy and searching on new features, the new solutions are analyzed numerically based on compact objects (white dwarf) parameters. It is found that including the higher-order corrections results as a reduction (increment) of the fast (slow) electromagnetic wave amplitude but the wave width is increased in both cases. The ranges where the RPT can describe adequately the total magnetic field including different conditions are discussed. (author)
International Nuclear Information System (INIS)
Kavitha, L.; Saravanan, M.; Srividya, B.; Gopi, D.
2011-01-01
We investigate the nature of propagation of electromagnetic waves (EMWs) in an antiferromagnetic medium with Dzyaloshinsky-Moriya (DM) interaction environment. The interplay of bilinear and DM exchange spin coupling with the magnetic field component of the EMW has been studied by solving Maxwell's equations coupled with a nonlinear spin equation for the magnetization of the medium. We made a nonuniform expansion of the magnetization and magnetic field along the direction of propagation of EMW, in the framework of reductive perturbation method, and the dynamics of the system is found to be governed by a generalized derivative nonlinear Schroedinger (DNLS) equation. We employ the Jacobi-elliptic function method to solve the DNLS equation, and the electromagnetic wave propagation in an antiferromagnetic medium is governed by the breatherlike spatially and temporally coherent localized modes under the influence of DM interaction parameter.
Counter-propagating wave interaction for contrast-enhanced ultrasound imaging
International Nuclear Information System (INIS)
Renaud, G; Bosch, J G; Ten Kate, G L; De Jong, N; Van der Steen, A F W; Shamdasani, V; Entrekin, R
2012-01-01
Most techniques for contrast-enhanced ultrasound imaging require linear propagation to detect nonlinear scattering of contrast agent microbubbles. Waveform distortion due to nonlinear propagation impairs their ability to distinguish microbubbles from tissue. As a result, tissue can be misclassified as microbubbles, and contrast agent concentration can be overestimated; therefore, these artifacts can significantly impair the quality of medical diagnoses. Contrary to biological tissue, lipid-coated gas microbubbles used as a contrast agent allow the interaction of two acoustic waves propagating in opposite directions (counter-propagation). Based on that principle, we describe a strategy to detect microbubbles that is free from nonlinear propagation artifacts. In vitro images were acquired with an ultrasound scanner in a phantom of tissue-mimicking material with a cavity containing a contrast agent. Unlike the default mode of the scanner using amplitude modulation to detect microbubbles, the pulse sequence exploiting counter-propagating wave interaction creates no pseudoenhancement behind the cavity in the contrast image. (fast track communication)
Wave Propagation From Electrons to Photonic Crystals and Left-Handed Materials
Markos, Peter
2010-01-01
This textbook offers the first unified treatment of wave propagation in electronic and electromagnetic systems and introduces readers to the essentials of the transfer matrix method, a powerful analytical tool that can be used to model and study an array of problems pertaining to wave propagation in electrons and photons. It is aimed at graduate and advanced undergraduate students in physics, materials science, electrical and computer engineering, and mathematics, and is ideal for researchers in photonic crystals, negative index materials, left-handed materials, plasmonics, nonlinear effects,
Unidirectional Wave Propagation in Low-Symmetric Colloidal Photonic-Crystal Heterostructures
Directory of Open Access Journals (Sweden)
Vassilios Yannopapas
2015-03-01
Full Text Available We show theoretically that photonic crystals consisting of colloidal spheres exhibit unidirectional wave propagation and one-way frequency band gaps without breaking time-reversal symmetry via, e.g., the application of an external magnetic field or the use of nonlinear materials. Namely, photonic crystals with low symmetry such as the monoclinic crystal type considered here as well as with unit cells formed by the heterostructure of different photonic crystals show significant unidirectional electromagnetic response. In particular, we show that the use of scatterers with low refractive-index contrast favors the formation of unidirectional frequency gaps which is the optimal route for achieving unidirectional wave propagation.
Unidirectional Wave Propagation in Low-Symmetric Colloidal Photonic-Crystal Heterostructures.
Yannopapas, Vassilios
2015-03-19
We show theoretically that photonic crystals consisting of colloidal spheres exhibit unidirectional wave propagation and one-way frequency band gaps without breaking time-reversal symmetry via, e.g., the application of an external magnetic field or the use of nonlinear materials. Namely, photonic crystals with low symmetry such as the monoclinic crystal type considered here as well as with unit cells formed by the heterostructure of different photonic crystals show significant unidirectional electromagnetic response. In particular, we show that the use of scatterers with low refractive-index contrast favors the formation of unidirectional frequency gaps which is the optimal route for achieving unidirectional wave propagation.
Time-Frequency (Wigner Analysis of Linear and Nonlinear Pulse Propagation in Optical Fibers
Directory of Open Access Journals (Sweden)
José Azaña
2005-06-01
Full Text Available Time-frequency analysis, and, in particular, Wigner analysis, is applied to the study of picosecond pulse propagation through optical fibers in both the linear and nonlinear regimes. The effects of first- and second-order group velocity dispersion (GVD and self-phase modulation (SPM are first analyzed separately. The phenomena resulting from the interplay between GVD and SPM in fibers (e.g., soliton formation or optical wave breaking are also investigated in detail. Wigner analysis is demonstrated to be an extremely powerful tool for investigating pulse propagation dynamics in nonlinear dispersive systems (e.g., optical fibers, providing a clearer and deeper insight into the physical phenomena that determine the behavior of these systems.
Propagation law of impact elastic wave based on specific materials
Directory of Open Access Journals (Sweden)
Chunmin CHEN
2017-02-01
Full Text Available In order to explore the propagation law of the impact elastic wave on the platform, the experimental platform is built by using the specific isotropic materials and anisotropic materials. The glass cloth epoxy laminated plate is used for anisotropic material, and an organic glass plate is used for isotropic material. The PVDF sensors adhered on the specific materials are utilized to collect data, and the elastic wave propagation law of different thick plates and laminated plates under impact conditions is analyzed. The Experimental results show that in anisotropic material, transverse wave propagation speed along the fiber arrangement direction is the fastest, while longitudinal wave propagation speed is the slowest. The longitudinal wave propagation speed in anisotropic laminates is much slower than that in the laminated thick plates. In the test channel arranged along a particular angle away from the central region of the material, transverse wave propagation speed is larger. Based on the experimental results, this paper proposes a material combination mode which is advantageous to elastic wave propagation and diffusion in shock-isolating materials. It is proposed to design a composite material with high acoustic velocity by adding regularly arranged fibrous materials. The overall design of the barrier material is a layered structure and a certain number of 90°zigzag structure.
Ion stochastic heating by obliquely propagating magnetosonic waves
International Nuclear Information System (INIS)
Gao Xinliang; Lu Quanming; Wu Mingyu; Wang Shui
2012-01-01
The ion motions in obliquely propagating Alfven waves with sufficiently large amplitudes have already been studied by Chen et al.[Phys. Plasmas 8, 4713 (2001)], and it was found that the ion motions are stochastic when the wave frequency is at a fraction of the ion gyro-frequency. In this paper, with test particle simulations, we investigate the ion motions in obliquely propagating magnetosonic waves and find that the ion motions also become stochastic when the amplitude of the magnetosonic waves is sufficiently large due to the resonance at sub-cyclotron frequencies. Similar to the Alfven wave, the increase of the propagating angle, wave frequency, and the number of the wave modes can lower the stochastic threshold of the ion motions. However, because the magnetosonic waves become more and more compressive with the increase of the propagating angle, the decrease of the stochastic threshold with the increase of the propagating angle is more obvious in the magnetosonic waves than that in the Alfven waves.
Nonlinear whistler wave model for lion roars in the Earth’s magnetosheath
DEFF Research Database (Denmark)
Dwivedi, N. K.; Singh, S.
2017-01-01
In the present study, we construct a nonlinear whistler wave model to explain the magnetic field spectra observed for lion roars in the Earth’s magnetosheath region. We use two-fluid theory and semi-analytical approach to derive the dynamical equation of whistler wave propagating along the ambient...... magnetic field. We examine the magnetic field localization of parallel propagating whistler wave in the intermediate beta plasma applicable to the Earth’s magnetosheath. In addition, we investigate spectral features of the magnetic field fluctuations and the spectral slope value. The magnetic field...... semi-analytical model provides exposure to the whistler wave turbulence in the Earth’s magnetosheath....
Langmuir wave-packet generation from an electron beam propagating in the inhomogeneous solar wind
International Nuclear Information System (INIS)
Zaslavsky, A.; Maksimovic, M.; Volokitin, A. S.; Krasnoselskikh, V. V.; Bale, S. D.
2010-01-01
Recent in-situ observations by the TDS instrument equipping the STEREO spacecraft revealed that large amplitude spatially localized Langmuir waves are frequent in the solar wind, and correlated with the presence of suprathermal electron beams during type III events or close to the electron foreshock. We briefly present the new theoretical model used to perform the study of these localized electrostatic waves, and show first results of simulations of the destabilization of Langmuir waves by a beam propagating in the inhomogeneous solar wind. The main results are that the destabilized waves are mainly focalized near the minima of the density profiles, and that the nonlinear interaction of the waves with the resonant particles enhances this focalization compared to a situation in which the only propagation effects are taken into account.
Ma, Li-Yuan; Ji, Jia-Liang; Xu, Zong-Wei; Zhu, Zuo-Nong
2018-03-01
We study a nonintegrable discrete nonlinear Schrödinger (dNLS) equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformation, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation. The analysis of stability of stationary solitary waves is performed. It is shown that the nonlinear nearest-neighbor interaction term has great influence on the form of solitary wave. The shape of solitary wave is important in the electric field propagating. If we neglect the nonlinear nearest-neighbor interaction term, much important information in the electric field propagating may be missed. Our numerical simulation also demonstrates the difference of chaos phenomenon between the nonintegrable dNLS equation with nonlinear nearest-neighbor interaction and another nonintegrable dNLS equation without the term. Project supported by the National Natural Science Foundation of China (Grant Nos. 11671255 and 11701510), the Ministry of Economy and Competitiveness of Spain (Grant No. MTM2016-80276-P (AEI/FEDER, EU)), and the China Postdoctoral Science Foundation (Grant No. 2017M621964).
Creep Damage Evaluation of Titanium Alloy Using Nonlinear Ultrasonic Lamb Waves
International Nuclear Information System (INIS)
Xiang Yan-Xun; Xuan Fu-Zhen; Deng Ming-Xi; Chen Hu; Chen Ding-Yue
2012-01-01
The creep damage in high temperature resistant titanium alloys Ti60 is measured using the nonlinear effect of an ultrasonic Lamb wave. The results show that the normalised acoustic nonlinearity of a Lamb wave exhibits a variation of the 'increase-decrease' tendency as a function of the creep damage. The influence of microstructure evolution on the nonlinear Lamb wave propagation has been analyzed based on metallographic studies, which reveal that the normalised acoustic nonlinearity increases due to a rising of the precipitation volume fraction and the dislocation density in the early stage, and it decreases as a combined result of dislocation change and micro-void initiation in the material. The nonlinear Lamb wave exhibits the potential for the assessment of the remaining creep life in metals
Parametric instabilities of parallel propagating incoherent Alfven waves in a finite ion beta plasma
International Nuclear Information System (INIS)
Nariyuki, Y.; Hada, T.; Tsubouchi, K.
2007-01-01
Large amplitude, low-frequency Alfven waves constitute one of the most essential elements of magnetohydrodynamic (MHD) turbulence in the fast solar wind. Due to small collisionless dissipation rates, the waves can propagate long distances and efficiently convey such macroscopic quantities as momentum, energy, and helicity. Since loading of such quantities is completed when the waves damp away, it is important to examine how the waves can dissipate in the solar wind. Among various possible dissipation processes of the Alfven waves, parametric instabilities have been believed to be important. In this paper, we numerically discuss the parametric instabilities of coherent/incoherent Alfven waves in a finite ion beta plasma using a one-dimensional hybrid (superparticle ions plus an electron massless fluid) simulation, in order to explain local production of sunward propagating Alfven waves, as suggested by Helios/Ulysses observation results. Parameter studies clarify the dependence of parametric instabilities of coherent/incoherent Alfven waves on the ion and electron beta ratio. Parametric instabilities of coherent Alfven waves in a finite ion beta plasma are vastly different from those in the cold ions (i.e., MHD and/or Hall-MHD systems), even if the collisionless damping of the Alfven waves are neglected. Further, ''nonlinearly driven'' modulational instability is important for the dissipation of incoherent Alfven waves in a finite ion beta plasma regardless of their polarization, since the ion kinetic effects let both the right-hand and left-hand polarized waves become unstable to the modulational instability. The present results suggest that, although the antisunward propagating dispersive Alfven waves are efficiently dissipated through the parametric instabilities in a finite ion beta plasma, these instabilities hardly produce the sunward propagating waves
Nonlinear waves in reaction-diffusion systems: The effect of transport memory
International Nuclear Information System (INIS)
Manne, K. K.; Hurd, A. J.; Kenkre, V. M.
2000-01-01
Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wave fronts in reaction-diffusion systems. We obtain results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-front speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piecewise linear representation of the nonlinearity. (c) 2000 The American Physical Society
Collisionless damping of nonlinear dust ion acoustic wave due to dust charge fluctuation
International Nuclear Information System (INIS)
Ghosh, Samiran; Chaudhuri, Tushar K.; Sarkar, Susmita; Khan, Manoranjan; Gupta, M.R.
2002-01-01
A dissipation mechanism for the damping of the nonlinear dust ion acoustic wave in a collisionless dusty plasma consisting of nonthermal electrons, ions, and variable charge dust grains has been investigated. It is shown that the collisionless damping due to dust charge fluctuation causes the nonlinear dust ion acoustic wave propagation to be described by the damped Korteweg-de Vries equation. Due to the presence of nonthermal electrons, the dust ion acoustic wave admits both positive and negative potential and it suffers less damping than the dust acoustic wave, which admits only negative potential
Nonlinear waves in reaction-diffusion systems: The effect of transport memory
Manne, K. K.; Hurd, A. J.; Kenkre, V. M.
2000-04-01
Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wave fronts in reaction-diffusion systems. We obtain results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-front speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piecewise linear representation of the nonlinearity.
Nonlinear water waves: introduction and overview
Constantin, A.
2017-12-01
For more than two centuries progress in the study of water waves proved to be interdependent with innovative and deep developments in theoretical and experimental directions of investigation. In recent years, considerable progress has been achieved towards the understanding of waves of large amplitude. Within this setting one cannot rely on linear theory as nonlinearity becomes an essential feature. Various analytic methods have been developed and adapted to come to terms with the challenges encountered in settings where approximations (such as those provided by linear or weakly nonlinear theory) are ineffective. Without relying on simpler models, progress becomes contingent upon the discovery of structural properties, the exploitation of which requires a combination of creative ideas and state-of-the-art technical tools. The successful quest for structure often reveals unexpected patterns and confers aesthetic value on some of these studies. The topics covered in this issue are both multi-disciplinary and interdisciplinary: there is a strong interplay between mathematical analysis, numerical computation and experimental/field data, interacting with each other via mutual stimulation and feedback. This theme issue reflects some of the new important developments that were discussed during the programme `Nonlinear water waves' that took place at the Isaac Newton Institute for Mathematical Sciences (Cambridge, UK) from 31st July to 25th August 2017. A cross-section of the experts in the study of water waves who participated in the programme authored the collected papers. These papers illustrate the diversity, intensity and interconnectivity of the current research activity in this area. They offer new insight, present emerging theoretical methodologies and computational approaches, and describe sophisticated experimental results. This article is part of the theme issue 'Nonlinear water waves'.
Propagation and dispersion of shock waves in magnetoelastic materials
Crum, R. S.; Domann, J. P.; Carman, G. P.; Gupta, V.
2017-12-01
Previous studies examining the response of magnetoelastic materials to shock waves have predominantly focused on applications involving pulsed power generation, with limited attention given to the actual wave propagation characteristics. This study provides detailed magnetic and mechanical measurements of magnetoelastic shock wave propagation and dispersion. Laser generated rarefacted shock waves exceeding 3 GPa with rise times of 10 ns were introduced to samples of the magnetoelastic material Galfenol. The resulting mechanical measurements reveal the evolution of the shock into a compressive acoustic front with lateral release waves. Importantly, the wave continues to disperse even after it has decayed into an acoustic wave, due in large part to magnetoelastic coupling. The magnetic data reveal predominantly shear wave mediated magnetoelastic coupling, and were also used to noninvasively measure the wave speed. The external magnetic field controlled a 30% increase in wave propagation speed, attributed to a 70% increase in average stiffness. Finally, magnetic signals propagating along the sample over 20× faster than the mechanical wave were measured, indicating these materials can act as passive antennas that transmit information in response to mechanical stimuli.
Relativistic effects on large amplitude nonlinear Langmuir waves in a two-fluid plasma
International Nuclear Information System (INIS)
Nejoh, Yasunori
1994-07-01
Large amplitude relativistic nonlinear Langmuir waves are analyzed by the pseudo-potential method. The existence conditions for nonlinear Langmuir waves are confirmed by considering relativistic high-speed electrons in a two-fluid plasma. The significant feature of this investigation is that the propagation of nonlinear Langmuir waves depends on the ratio of the electron streaming velocity to the velocity of light, the normalized potential and the ion mass to electron mass ratio. The constant energy is determined by the specific range of the relativistic effect. In the non-relativistic limit, large amplitude relativistic Langmuir waves do not exist. The present investigation predicts new findings of large amplitude nonlinear Langmuir waves in space plasma phenomena in which relativistic electrons are important. (author)
Some models of propagation of extremely short electromagnetic pulses in a nonlinear medium
International Nuclear Information System (INIS)
Maimistov, Andrei I
2000-01-01
Some cases of model media considered in this paper allow analytical solutions to nonlinear wave equations to be found and the time dependence of the electric field strength to be determined in the explicit form for arbitrarily short electromagnetic pulses. Our analysis does not employ any assumptions concerning a harmonic carrier wave or the variation rate of the field in such pulses. The class of models considered includes two-level resonance and quasi-resonance systems. Nonresonance media are analysed in terms of models of anharmonic oscillators - the Duffing and Lorentz models. In most cases, only particular solutions describing the stationary propagation of a video pulse (a unipolar transient of the electric field or a pulse including a small number of oscillations of the electric field around zero) can be found. These solutions correspond to sufficiently strong electromagnetic fields when the dispersion inherent in the medium is suppressed by nonlinear processes. (invited paper)
Controlling nonlinear waves in excitable media
International Nuclear Information System (INIS)
Puebla, Hector; Martin, Roland; Alvarez-Ramirez, Jose; Aguilar-Lopez, Ricardo
2009-01-01
A new feedback control method is proposed to control the spatio-temporal dynamics in excitable media. Applying suitable external forcing to the system's slow variable, successful suppression and control of propagating pulses as well as spiral waves can be obtained. The proposed controller is composed by an observer to infer uncertain terms such as diffusive transport and kinetic rates, and an inverse-dynamics feedback function. Numerical simulations shown the effectiveness of the proposed feedback control approach.
Controlling nonlinear waves in excitable media
Energy Technology Data Exchange (ETDEWEB)
Puebla, Hector [Departamento de Energia, Universidad Autonoma Metropolitana, Av. San Pablo No. 180, Reynosa-Tamaulipas, Azcapotzalco 02200, DF, Mexico (Mexico)], E-mail: hpuebla@correo.azc.uam.mx; Martin, Roland [Laboratoire de Modelisation et d' Imagerie en Geosciences, CNRS UMR and INRIA Futurs Magique-3D, Universite de Pau (France); Alvarez-Ramirez, Jose [Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa (Mexico); Aguilar-Lopez, Ricardo [Departamento de Biotecnologia y Bioingenieria, CINVESTAV-IPN (Mexico)
2009-01-30
A new feedback control method is proposed to control the spatio-temporal dynamics in excitable media. Applying suitable external forcing to the system's slow variable, successful suppression and control of propagating pulses as well as spiral waves can be obtained. The proposed controller is composed by an observer to infer uncertain terms such as diffusive transport and kinetic rates, and an inverse-dynamics feedback function. Numerical simulations shown the effectiveness of the proposed feedback control approach.
Nonlinear wave forces on large ocean structures
Huang, Erick T.
1993-04-01
This study explores the significance of second-order wave excitations on a large pontoon and tests the feasibility of reducing a nonlinear free surface problem by perturbation expansions. A simulation model has been developed based on the perturbation expansion technique to estimate the wave forces. The model uses a versatile finite element procedure for the solution of the reduced linear boundary value problems. This procedure achieves a fair compromise between computation costs and physical details by using a combination of 2D and 3D elements. A simple hydraulic model test was conducted to observe the wave forces imposed on a rectangle box by Cnoidal waves in shallow water. The test measurements are consistent with the numerical predictions by the simulation model. This result shows favorable support to the perturbation approach for estimating the nonlinear wave forces on shallow draft vessels. However, more sophisticated model tests are required for a full justification. Both theoretical and experimental results show profound second-order forces that could substantially impact the design of ocean facilities.
Symmetry, phase modulation and nonlinear waves
Bridges, Thomas J
2017-01-01
Nonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such as Hamiltonian systems, symplectic geometry, conservation laws, Noether theory, Lagrangian field theory and analysis, all of which combine to generate the new theory of phase modulation. While the build-up of theory can be intensive, the resulting emergent partial differential equations are relatively simple. A key outcome of the theory is that the coefficients in the emergent modulation equations are universal and easy to calculate. This book gives several examples of the implications in the theory of fluid mechanics and points to a wide range of new applications.
Guided propagation of Alfven waves in a toroidal plasma
International Nuclear Information System (INIS)
Borg, G.G.; Brennan, M.H.; Cross, R.C.; Giannone, L.; Donnelly, I.J.
1985-01-01
Experimental results are presented which show that the Alfven wave is strongly guided by magnetic fields. The experiment was conducted in a Tokamak plasma using a small dipole loop antenna to generate a localised Alfven ray. The ray was observed, with magnetic probes, to propagate as a localised disturbance along the curved lines of the steady magnetic field without significant refraction due to the effects of finite frequency, resistivity or magnetic field gradients. These results agree with theoretical predictions and demonstrate that a localised Alfven wave may be excited, and may propagate, independently of the fast wave, as expected. The implication of these results for the Alfven wave heating scheme is discussed. (author)
Guided propagation of Alfven waves in a toroidal plasma
Energy Technology Data Exchange (ETDEWEB)
Borg, G G; Brennan, M H; Cross, R C; Giannone, L.; Donnelly, I J
1985-10-01
Experimental results are presented which show that the Alfven wave is strongly guided by magnetic fields. The experiment was conducted in a Tokamak plasma using a small dipole loop antenna to generate a localised Alfven ray. The ray was observed, with magnetic probes, to propagate as a localised disturbance along the curved lines of the steady magnetic field without significant refraction due to the effects of finite frequency, resistivity or magnetic field gradients. These results agree with theoretical predictions and demonstrate that a localised Alfven wave may be excited, and may propagate, independently of the fast wave, as expected. The implication of these results for the Alfven wave heating scheme is discussed.
The propagation of travelling waves for stochastic generalized KPP equations
International Nuclear Information System (INIS)
Elworthy, K.D.; Zhao, H.Z.
1993-09-01
We study the existence and propagation of approximate travelling waves of generalized KPP equations with seasonal multiplicative white noise perturbations of Ito type. Three regimes of perturbation are considered: weak, milk, and strong. We show that weak perturbations have little effect on the wave like solutions of the unperturbed equations while strong perturbations essentially destroy the wave and force the solutions to die down. For mild perturbations we show that there is a residual wave form but propagating at a different speed to that of the unperturbed equation. In the appendix J.G. Gaines illustrates these different regimes by computer simulations. (author). 27 refs, 13 figs
Propagation and scattering of waves in dusty plasmas
International Nuclear Information System (INIS)
Vladimirov, S.V.
1994-01-01
Wave propagation and scattering in dusty plasmas with variable charges on dust particles are considered. New kinetic theory including instant charge of a dust particle as a new independent variable is further developed. (author). 9 refs
Topics in Computational Modeling of Shock and Wave Propagation
National Research Council Canada - National Science Library
Gazonas, George A; Main, Joseph A; Laverty, Rich; Su, Dan; Santare, Michael H; Raghupathy, R; Molinari, J. F; Zhou, F
2006-01-01
This report contains reprints of four papers that focus on various aspects of shock and wave propagation in cellular, viscoelastic, microcracked, and fragmented media that appear in the Proceedings...
Topology optimization of vibration and wave propagation problems
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
2007-01-01
The method of topology optimization is a versatile method to determine optimal material layouts in mechanical structures. The method relies on, in principle, unlimited design freedom that can be used to design materials, structures and devices with significantly improved performance and sometimes...... novel functionality. This paper addresses basic issues in simulation and topology design of vibration and wave propagation problems. Steady-state and transient wave propagation problems are addressed and application examples for both cases are presented....
Free wave propagation in continuous pipes carrying a flowing fluid
International Nuclear Information System (INIS)
Espindola, J.J. de; Silva, J.B. da
1982-01-01
The propagation constants of a periodically supported pipe are computed. Use is made of a general free wave-propagation theory, based on transfer matrices. Comparison is made with previously published results, computed through a simpler, limited scope theory. (Author) [pt
The linear potential propagator via wave function expansion
International Nuclear Information System (INIS)
Nassar, Antonio B.; Cattani, Mauro S.D.
2002-01-01
We evaluate the quantum propagator for the motion of a particle in a linear potential via a recently developed formalism [A.B. Nassar et al., Phys. Rev. E56, 1230, (1997)]. In this formalism, the propagator comes about as a type of expansion of the wave function over the space of the initial velocities. (author)
Wave propagation of spectral energy content in a granular chain
Directory of Open Access Journals (Sweden)
Shrivastava Rohit Kumar
2017-01-01
Full Text Available A mechanical wave is propagation of vibration with transfer of energy and momentum. Understanding the spectral energy characteristics of a propagating wave through disordered granular media can assist in understanding the overall properties of wave propagation through inhomogeneous materials like soil. The study of these properties is aimed at modeling wave propagation for oil, mineral or gas exploration (seismic prospecting or non-destructive testing of the internal structure of solids. The focus is on the total energy content of a pulse propagating through an idealized one-dimensional discrete particle system like a mass disordered granular chain, which allows understanding the energy attenuation due to disorder since it isolates the longitudinal P-wave from shear or rotational modes. It is observed from the signal that stronger disorder leads to faster attenuation of the signal. An ordered granular chain exhibits ballistic propagation of energy whereas, a disordered granular chain exhibits more diffusive like propagation, which eventually becomes localized at long time periods. For obtaining mean-field macroscopic/continuum properties, ensemble averaging has been used, however, such an ensemble averaged spectral energy response does not resolve multiple scattering, leading to loss of information, indicating the need for a different framework for micro-macro averaging.
Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation
Semper, Sean R.; Crassidis, John L.; George, Jemin; Mukherjee, Siddharth; Singla, Puneet
2015-01-01
When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating
International Nuclear Information System (INIS)
Deng Mingxi; Wang Ping; Lv Xiafu
2006-01-01
This paper describes influences of interfacial properties on second-harmonic generation of Lamb waves propagating in layered planar structures. The nonlinearity in the elastic wave propagation is treated as a second-order perturbation of the linear elastic response. Due to the kinematic nonlinearity and the elastic nonlinearity of materials, there are second-order bulk and surface/interface driving sources in layered planar structures through which Lamb waves propagate. These driving sources can be thought of as forcing functions of a series of double frequency lamb waves (DFLWs) in terms of the approach of modal expansion analysis for waveguide excitation. The total second-harmonic fields consist of a summation of DFLWs in the corresponding stress-free layered planar structures. The interfacial properties of layered planar structures can be described by the well-known finite interfacial stiffness technique. The normal and tangential interfacial stiffness constants can be coupled with the equation governing the expansion coefficient of each DFLW component. On the other hand, the normal and tangential interfacial stiffness constants are associated with the degree of dispersion between Lamb waves and DFLWs. Theoretical analyses and numerical simulations indicate that the efficiency of second-harmonic generation by Lamb wave propagation is closely dependent on the interfacial properties of layered structures. The potential of using the effect of second-harmonic generation by Lamb wave propagation to characterize the interfacial properties of layered structures are considered. Some experimental results are presented
Nonlinear Theory of Nonparaxial Laser Pulse Propagation in Plasma Channels
International Nuclear Information System (INIS)
Esarey, E.; Schroeder, C. B.; Shadwick, B. A.; Wurtele, J. S.; Leemans, W. P.
2000-01-01
Nonparaxial propagation of ultrashort, high-power laser pulses in plasma channels is examined. In the adiabatic limit, pulse energy conservation, nonlinear group velocity, damped betatron oscillations, self-steepening, self-phase modulation, and shock formation are analyzed. In the nonadiabatic limit, the coupling of forward Raman scattering (FRS) and the self-modulation instability (SMI) is analyzed and growth rates are derived, including regimes of reduced growth. The SMI is found to dominate FRS in most regimes of interest. (c) 2000 The American Physical Society
Wave propagation through a dielectric layer containing densely packed fibers
International Nuclear Information System (INIS)
Lee, Siu-Chun
2011-01-01
This paper presents the theoretical formulation for the propagation of electromagnetic wave through a dielectric layer containing a random dense distribution of fibers. The diameter of the fibers is comparable to the inter-fiber spacing and wavelength of the incident radiation, but is much smaller than the thickness of the layer. Discontinuity of refractive index across the boundaries of the dielectric layer resulted in multiple internal reflection of both the primary source wave and the scattered waves. As a result the incident waves on the fibers consist of the multiply-reflected primary waves, scattered waves from other fibers, and scattered-reflected waves from the boundaries. The effective propagation constant of the dielectric fiber layer was developed by utilizing the Effective field-Quasicrystalline approximation. The influence of the refractive index of the dielectric medium on the radiative properties of a dense fiber layer was examined by means of numerical analyses.
Influence of Plasma Pressure Fluctuation on RF Wave Propagation
International Nuclear Information System (INIS)
Liu Zhiwei; Bao Weimin; Li Xiaoping; Liu Donglin; Zhou Hui
2016-01-01
Pressure fluctuations in the plasma sheath from spacecraft reentry affect radio-frequency (RF) wave propagation. The influence of these fluctuations on wave propagation and wave properties is studied using methods derived by synthesizing the compressible turbulent flow theory, plasma theory, and electromagnetic wave theory. We study these influences on wave propagation at GPS and Ka frequencies during typical reentry by adopting stratified modeling. We analyzed the variations in reflection and transmission properties induced by pressure fluctuations. Our results show that, at the GPS frequency, if the waves are not totally reflected then the pressure fluctuations can remarkably affect reflection, transmission, and absorption properties. In extreme situations, the fluctuations can even cause blackout. At the Ka frequency, the influences are obvious when the waves are not totally transmitted. The influences are more pronounced at the GPS frequency than at the Ka frequency. This suggests that the latter can mitigate blackout by reducing both the reflection and the absorption of waves, as well as the influences of plasma fluctuations on wave propagation. Given that communication links with the reentry vehicles are susceptible to plasma pressure fluctuations, the influences on link budgets should be taken into consideration. (paper)
Laser-based linear and nonlinear guided elastic waves at surfaces (2D) and wedges (1D).
Hess, Peter; Lomonosov, Alexey M; Mayer, Andreas P
2014-01-01
The characteristic features and applications of linear and nonlinear guided elastic waves propagating along surfaces (2D) and wedges (1D) are discussed. Laser-based excitation, detection, or contact-free analysis of these guided waves with pump-probe methods are reviewed. Determination of material parameters by broadband surface acoustic waves (SAWs) and other applications in nondestructive evaluation (NDE) are considered. The realization of nonlinear SAWs in the form of solitary waves and as shock waves, used for the determination of the fracture strength, is described. The unique properties of dispersion-free wedge waves (WWs) propagating along homogeneous wedges and of dispersive wedge waves observed in the presence of wedge modifications such as tip truncation or coatings are outlined. Theoretical and experimental results on nonlinear wedge waves in isotropic and anisotropic solids are presented. Copyright © 2013 Elsevier B.V. All rights reserved.
Non-Linear Excitation of Ion Acoustic Waves
DEFF Research Database (Denmark)
Michelsen, Poul; Hirsfield, J. L.
1974-01-01
The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation.......The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation....
Thermal Aging Evaluation of Mod. 9Cr-1Mo Steel using Nonlinear Rayleigh Waves
Energy Technology Data Exchange (ETDEWEB)
Joo, Young-Sang; Kim, Hoe-Woong; Kim, Jong-Bum [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Marino, Daniel; Kim, Jin-Yeon; Jacobs, L.J [Georgia Institute of Technology, Atlanta (United States); Ruiz, Alberto [UMSNH, Morelia (Mexico)
2014-10-15
Thermal aging can pose a high risk to decreases in the mechanical properties such as strength or creep resistance. This can lead to an unexpected failure during long term operation. Nonlinear NDE techniques are preferred over conventional NDE techniques (linear ultrasonic measurements) because nonlinear ultrasonic techniques have shown their capability to detect a microstructural damage in the structures undergoing fatigue and creep. These nonlinear ultrasonic techniques make use of the fact that the dislocation density increases, which will create a nonlinear distortion of an ultrasonic wave; this damage causes the generation of measurable higher harmonic components in an initially mono-chromatic ultrasonic signal. This study investigates the recently developed non-contact nonlinear ultrasonic technique to detect the microstructural damage of mod. 9Cr-1Mo steel based on nonlinear Rayleigh wave with varying propagation distances. Nonlinear Rayleigh surface wave measurements using a non-contact, air-coupled ultrasonic transducer have been applied for the thermal aging evaluation of modified 9Cr-1Mo ferritic-martensitic steel. Thermal aging for various heat treatment times of mod.. 9Cr-1Mo steel specimens is performed to obtain the nucleation and growth of precipitated particles in specimens. The amplitudes of the first and second harmonics are measured along the propagation distance and the relative nonlinearity parameter is obtained from these amplitudes. The relative nonlinearity parameter shows a similar trend with the Rockwell C hardness.
Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves
DEFF Research Database (Denmark)
Eldeberky, Y.; Madsen, Per A.
1999-01-01
and stochastic formulations are solved numerically for the case of cross shore motion of unidirectional waves and the results are verified against laboratory data for wave propagation over submerged bars and over a plane slope. Outside the surf zone the two model predictions are generally in good agreement......This paper presents a new and more accurate set of deterministic evolution equations for the propagation of fully dispersive, weakly nonlinear, irregular, multidirectional waves. The equations are derived directly from the Laplace equation with leading order nonlinearity in the surface boundary...... is significantly underestimated for larger wave numbers. In the present work we correct this inconsistency. In addition to the improved deterministic formulation, we present improved stochastic evolution equations in terms of the energy spectrum and the bispectrum for multidirectional waves. The deterministic...
The evolution of a localized nonlinear wave of the Kelvin-Helmholtz instability with gravity
Orazzo, Annagrazia; Hoepffner, Jérôme
2012-11-01
At the interface between two fluids of different density and in the presence of gravity, there are well known periodic surface waves which can propagate for long distances with little attenuation, as it is for instance the case at the surface of the sea. If wind is present, these waves progressively accumulate energy as they propagate and grow to large sizes—this is the Kelvin-Helmholtz instability. On the other hand, we show in this paper that for a given wind strength, there is potential for the growth of a localized nonlinear wave. This wave can reach a size such that the hydrostatic pressure drop from top to bottom equals the stagnation pressure of the wind. This process for the disruption of the flat interface is localized and nonlinear. We study the properties of this wave using numerical simulations of the Navier-Stokes equations.
International Nuclear Information System (INIS)
Sokolow, Adam; Sen, Surajit
2007-01-01
An energy pulse refers to a spatially compact energy bundle. In nonlinear pulse propagation, the nonlinearity of the relevant dynamical equations could lead to pulse propagation that is nondispersive or weakly dispersive in space and time. Nonlinear pulse propagation through layered media with widely varying pulse transmission properties is not wave-like and a problem of broad interest in many areas such as optics, geophysics, atmospheric physics and ocean sciences. We study nonlinear pulse propagation through a semi-infinite sequence of layers where the layers can have arbitrary energy transmission properties. By assuming that the layers are rigid, we are able to develop exact expressions for the backscattered energy received at the surface layer. The present study is likely to be relevant in the context of energy transport through soil and similar complex media. Our study reveals a surprising connection between the problem of pulse propagation and the number patterns in the well known Pascal's and Catalan's triangles and hence provides an analytic benchmark in a challenging problem of broad interest. We close with comments on the relationship between this study and the vast body of literature on the problem of wave localization in disordered systems
Nonlinear attenuation of S-waves and Love waves within ambient rock
Sleep, Norman H.; Erickson, Brittany A.
2014-04-01
obtain scaling relationships for nonlinear attenuation of S-waves and Love waves within sedimentary basins to assist numerical modeling. These relationships constrain the past peak ground velocity (PGV) of strong 3-4 s Love waves from San Andreas events within Greater Los Angeles, as well as the maximum PGV of future waves that can propagate without strong nonlinear attenuation. During each event, the shaking episode cracks the stiff, shallow rock. Over multiple events, this repeated damage in the upper few hundred meters leads to self-organization of the shear modulus. Dynamic strain is PGV divided by phase velocity, and dynamic stress is strain times the shear modulus. The frictional yield stress is proportional to depth times the effective coefficient of friction. At the eventual quasi-steady self-organized state, the shear modulus increases linearly with depth allowing inference of past typical PGV where rock over the damaged depth range barely reaches frictional failure. Still greater future PGV would cause frictional failure throughout the damaged zone, nonlinearly attenuating the wave. Assuming self-organization has taken place, estimated maximum past PGV within Greater Los Angeles Basins is 0.4-2.6 m s-1. The upper part of this range includes regions of accumulating sediments with low S-wave velocity that may have not yet compacted, rather than having been damaged by strong shaking. Published numerical models indicate that strong Love waves from the San Andreas Fault pass through Whittier Narrows. Within this corridor, deep drawdown of the water table from its currently shallow and preindustrial levels would nearly double PGV of Love waves reaching Downtown Los Angeles.
Efficient simulation of multimodal nonlinear propagation in step-index fibers
DEFF Research Database (Denmark)
Lægsgaard, Jesper
2017-01-01
A numerical approach to nonlinear propagation in waveguides based on real-space Gaussian quadrature integration of the nonlinear polarization during propagation is investigated and compared with the more conventional approach based on expressing the nonlinear polarization by a sum of mode overlap...
Zhao, J. S.; Voitenko, Y.; De Keyser, J.; Wu, D. J.
2018-04-01
We study the decay of Alfvén waves in the solar wind, accounting for the joint operation of two-dimensional (2D) scalar and three-dimensional (3D) vector nonlinear interactions between Alfvén and slow waves. These interactions have previously been studied separately in long- and short-wavelength limits where they lead to 2D scalar and 3D vector decays, correspondingly. The joined action of the scalar and vector interactions shifts the transition between 2D and 3D decays to significantly smaller wavenumbers than was predicted by Zhao et al. who compared separate scalar and vector decays. In application to the broadband Alfvén waves in the solar wind, this means that the vector nonlinear coupling dominates in the extended wavenumber range 5 × 10‑4 ≲ ρ i k 0⊥ ≲ 1, where the decay is essentially 3D and nonlocal, generating product Alfvén and slow waves around the ion gyroscale. Here ρ i is the ion gyroradius, and k 0⊥ is the pump Alfvén wavenumber. It appears that, except for the smallest wavenumbers at and below {ρ }i{k}0\\perp ∼ {10}-4 in Channel I, the nonlinear decay of magnetohydrodynamic Alfvén waves propagating from the Sun is nonlocal and cannot generate counter-propagating Alfvén waves with similar scales needed for the turbulent cascade. Evaluation of the nonlinear frequency shift shows that product Alfvén waves can still be approximately described as normal Alfvénic eigenmodes. On the contrary, nonlinearly driven slow waves deviate considerably from normal modes and are therefore difficult to identify on the basis of their phase velocities and/or polarization.
Nonlinear ion-acoustic cnoidal waves in a dense relativistic degenerate magnetoplasma.
El-Shamy, E F
2015-03-01
The complex pattern and propagation characteristics of nonlinear periodic ion-acoustic waves, namely, ion-acoustic cnoidal waves, in a dense relativistic degenerate magnetoplasma consisting of relativistic degenerate electrons and nondegenerate cold ions are investigated. By means of the reductive perturbation method and appropriate boundary conditions for nonlinear periodic waves, a nonlinear modified Korteweg-de Vries (KdV) equation is derived and its cnoidal wave is analyzed. The various solutions of nonlinear ion-acoustic cnoidal and solitary waves are presented numerically with the Sagdeev potential approach. The analytical solution and numerical simulation of nonlinear ion-acoustic cnoidal waves of the nonlinear modified KdV equation are studied. Clearly, it is found that the features (amplitude and width) of nonlinear ion-acoustic cnoidal waves are proportional to plasma number density, ion cyclotron frequency, and direction cosines. The numerical results are applied to high density astrophysical situations, such as in superdense white dwarfs. This research will be helpful in understanding the properties of compact astrophysical objects containing cold ions with relativistic degenerate electrons.
Weakly nonlinear electromagnetic waves in an electron-ion positron plasma
International Nuclear Information System (INIS)
Rizzato, F.B.; Schneider, R.S.; Dillenburg, D.
1987-01-01
The modulation of a high-frequency electromagnetic wave which is circulary polarized and propagates in a plasma made up of electrons, ions and positrons is investigated. The coefficient of the cubic nonlinear term in the Schroedinger equation may change sign as the relative particle concentrations vary, and consequently a marginal state of modulation instability may exist. To described the system in the neighbourhood of this state an appropriate equation is derived. Particular stationary solutions of this equation are envelope solitary waves, envelope Kinks and envelope hole solitary waves. The dependence of the amplitude of the solutions on the propagation velocity and the particle concentrations is discussed. (author) [pt
Propagation-invariant waves in acoustic, optical, and radio-wave fields
Salo, Janne
2003-01-01
The physical phenomena considered in this thesis are associated with electromagnetic and acoustic waves that propagate in free space or in homogeneous media without diffraction. The concept of rotationally periodic wave propagation is introduced in the first journal article included in the thesis and it is subsequently used to analyse waves that avoid diffractive deterioration by repeatedly returning to their initial shape, possibly rotated around the optical axis. Such waves constitute an es...
Stress Wave Propagation Through Heterogeneous Media
National Research Council Canada - National Science Library
2002-01-01
.... In this work the influence of interface scattering on finite-amplitude shock waves was experimentally investigated by impacting flyer plates onto periodically layered polycarbonate/6061 aluminum...
Stress Wave Propagation in Larch Plantation Trees-Numerical Simulation
Fenglu Liu; Fang Jiang; Xiping Wang; Houjiang Zhang; Wenhua Yu
2015-01-01
In this paper, we attempted to simulate stress wave propagation in virtual tree trunks and construct two dimensional (2D) wave-front maps in the longitudinal-radial section of the trunk. A tree trunk was modeled as an orthotropic cylinder in which wood properties along the fiber and in each of the two perpendicular directions were different. We used the COMSOL...
Statistical Characterization of Electromagnetic Wave Propagation in Mine Environments
Yucel, Abdulkadir C.
2013-01-01
A computational framework for statistically characterizing electromagnetic (EM) wave propagation through mine tunnels and galleries is presented. The framework combines a multi-element probabilistic collocation method with a full-wave fast Fourier transform and fast multipole method accelerated surface integral equation-based EM simulator to statistically characterize fields from wireless transmitters in complex mine environments. 1536-1225 © 2013 IEEE.
Effect of surface conditions on blast wave propagation
International Nuclear Information System (INIS)
Song, Seung Ho; Li, Yi Bao; Lee, Chang Hoon; Choi, Jung Il
2016-01-01
We performed numerical simulations of blast wave propagations on surfaces by solving axisymmetric two-dimensional Euler equations. Assuming the initial stage of fireball at the breakaway point after an explosion, we investigated the effect of surface conditions considering surface convex or concave elements and thermal conditions on blast wave propagations near the ground surface. Parametric studies were performed by varying the geometrical factors of the surface element as well as thermal layer characteristics. We found that the peak overpressure near the ground zero was increased due to the surface elements, while modulations of the blast wave propagations were limited within a region for the surface elements. Because of the thermal layer, the precursor was formed in the propagations, which led to the attenuation of the peak overpressure on the ground surface
Characteristics of coupled acoustic wave propagation in metal pipe
International Nuclear Information System (INIS)
Kim, Ho Wuk; Kim, Min Soo; Lee, Sang Kwon
2008-01-01
The circular cylinder pipes are used in the many industrial areas. In this paper, the acoustic wave propagation in the pipe containing gas is researched. First of all, the theory for the coupled acoustic wave propagation in a pipe is investigated. Acoustic wave propagation in pipe can not be occurred independently between the wave of the fluid and the shell. It requires complicated analysis. However, as a special case, the coupled wave in a high density pipe containing a light density medium is corresponded closely to the uncoupled in-vacuo shell waves and to the rigid-walled duct fluid waves. The coincidence frequencies of acoustic and shell modes contribute to the predominant energy transmission. The coincidence frequency means the frequency corresponding to the coincidence of the wavenumber in both acoustic and shell. In this paper, it is assumed that the internal medium is much lighter than the pipe shell. After the uncoupled acoustic wave in the internal medium and uncoupled shell wave are considered, the coincidence frequencies are found. The analysis is successfully confirmed by the verification of the experiment using the real long steel pipe. This work verifies that the coupled wave characteristic of the shell and the fluid is occurred as predominant energy transmission at the coincidence frequencies
Relativistic harmonic content of nonlinear electromagnetic waves in underdense plasmas
International Nuclear Information System (INIS)
Mori, W.B.; Decker, C.D.; Leemans, W.P.
1993-01-01
The relativistic harmonic content of large amplitude electromagnetic waves propagating in underdense plasmas is investigated. The steady state harmonic content of nonlinear linearly polarized waves is calculated for both the very underdense (w p /w o ) much-lt 1 and critical density (w p /w o ) ≅ 1 limits. For weak nonlinearities, eE o /mcw o p /w o . Arguments are given for extending these results for arbitrary wave amplitudes. The authors also show that the use of the variable x-ct and the quasi-static approximation leads to errors in both magnitude and sign when calculating the third harmonic. In the absence of damping or density gradients the third harmonic's amplitude is found to oscillate between zero and twice the steady state value. Preliminary PIC simulation results are presented. The simulation results are in basic agreement with the uniform plasma predictions for the third harmonic amplitude. However, the higher harmonics are orders of magnitude larger than expected and the presence of density ramps significantly modifies the results
Nonlinear instability and chaos in plasma wave-wave interactions
International Nuclear Information System (INIS)
Kueny, C.S.
1993-01-01
Conventional linear stability analysis may fail for fluid systems with an indefinite free energy functional. When such a system is linearly stable, it is said to possess negative energy modes. Instability may then occur either via dissipation of the negative energy modes. Instability may then occur either via dissipation of the negative energy modes. Instability may then occur either via dissipitation of the negative energy modes, or nonlinearly via resonant wave-wave coupling, which leads to explosive growth. In the dissipationaless case, it is conjectured that intrinsic chaotic behavior may allow initially non-resonant systems to reach resonance by diffusion in phase space. This is illustrated for a simple equilibrium involving cold counter-streaming ions. The system is described in the fluid approximation by a Hamilitonian functional and associated noncanonical Poisson bracket. By Fourier decomposition and appropriate coordinate transformations, the Hamilitonian for the perturbed energy is expressed in action-angle form. The normal modes correspond to Doppler-shifted ion-acoustic waves of positive and negative energy. Nonlinear coupling leads to decay instability via two-wave interactions, which occur generically for long enough wavelengths. Three-wave interactions which occur in isolated, but numerous, regions of parameter space can drive either decay instability or explosive instability. When the resonance for explosive growth is detuned, a stable region exists around the equilibrium point in phase space, while explosive growth occurs outside of a separatrix. These interactions may be described exactly if only one resonance is considered, while multiple nonlinear terms make the Hamiltonian nonintegradable. Simple Hamiltonians of two and three degrees of freedom are studied numerically using symplectic integration algorithms, including an explicit algorithm derived using Lie algebraic methods
Dispersive Evolution of Nonlinear Fast Magnetoacoustic Wave Trains
Energy Technology Data Exchange (ETDEWEB)
Pascoe, D. J.; Goddard, C. R.; Nakariakov, V. M., E-mail: D.J.Pascoe@warwick.ac.uk [Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, Coventry CV4 7AL (United Kingdom)
2017-10-01
Quasi-periodic rapidly propagating wave trains are frequently observed in extreme ultraviolet observations of the solar corona, or are inferred by the quasi-periodic modulation of radio emission. The dispersive nature of fast magnetohydrodynamic waves in coronal structures provides a robust mechanism to explain the detected quasi-periodic patterns. We perform 2D numerical simulations of impulsively generated wave trains in coronal plasma slabs and investigate how the behavior of the trapped and leaky components depend on the properties of the initial perturbation. For large amplitude compressive perturbations, the geometrical dispersion associated with the waveguide suppresses the nonlinear steepening for the trapped wave train. The wave train formed by the leaky components does not experience dispersion once it leaves the waveguide and so can steepen and form shocks. The mechanism we consider can lead to the formation of multiple shock fronts by a single, large amplitude, impulsive event and so can account for quasi-periodic features observed in radio spectra.
Nonlinear Electron Acoustic Waves in Dissipative Plasma with Superthermal Electrons
El-Hanbaly, A. M.; El-Shewy, E. K.; Kassem, A. I.; Darweesh, H. F.
2016-01-01
The nonlinear properties of small amplitude electron-acoustic ( EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and superthermal hot electrons obeying superthermal distribution, and stationary ions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili-Burgers (KP-Brugers) equation. Some solutions of physical interest are obtained. These solutions are related to soliton, monotonic and oscillatory shock waves and their behaviour are shown graphically. The formation of these solutions depends crucially on the value of the Burgers term and the plasma parameters as well. By using the tangent hyperbolic (tanh) method, another interesting type of solution which is a combination between shock and soliton waves is obtained. The topology of phase portrait and potential diagram of the KP-Brugers equation is investigated.The advantage of using this method is that one can predict different classes of the travelling wave solutions according to different phase orbits. The obtained results may be helpful in better understanding of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.
Directional bending wave propagation in periodically perforated plates
DEFF Research Database (Denmark)
Andreassen, Erik; Manktelow, Kevin; Ruzzene, Massimo
2015-01-01
We report on the investigation of wave propagation in a periodically perforated plate. A unit cell with double-C perforations is selected as a test article suitable to investigate two-dimensional dispersion characteristics, group velocities, and internal resonances. A numerical model, formulated...... using Mindlin plate elements, is developed to predict relevant wave characteristics such as dispersion, and group velocity variation as a function of frequency and direction of propagation. Experimental tests are conducted through a scanning laser vibrometer, which provides full wave field information...... for the design of phononic waveguides with directional and internal resonant characteristics....
Ion acoustic waves in pair-ion plasma: Linear and nonlinear analyses
International Nuclear Information System (INIS)
Saeed, R.; Mushtaq, A.
2009-01-01
Linear and nonlinear properties of low frequency ion acoustic wave (IAW) in pair-ion plasma in the presence of electrons are investigated. The dispersion relation and Kadomtsev-Petviashvili equation for linear/nonlinear IAW are derived from sets of hydrodynamic equations where the ion pairs are inertial while electrons are Boltzmannian. The dispersion curves for various concentrations of electrons are discussed and compared with experimental results. The predicted linear IAW propagates at the same frequencies as those of the experimentally observed IAW if n e0 ∼10 4 cm -3 . It is found that nonlinear profile of the ion acoustic solitary waves is significantly affected by the percentage ratio of electron number density and temperature. It is also determined that rarefactive solitary waves can propagate in this system. It is hoped that the results presented in this study would be helpful in understanding the salient features of the finite amplitude localized ion acoustic solitary pulses in a laboratory fullerene plasma.
Unidirectional Wave Propagation in Low-Symmetric Colloidal Photonic-Crystal Heterostructures
Yannopapas, Vassilios
2015-01-01
We show theoretically that photonic crystals consisting of colloidal spheres exhibit unidirectional wave propagation and one-way frequency band gaps without breaking time-reversal symmetry via, e.g., the application of an external magnetic field or the use of nonlinear materials. Namely, photonic crystals with low symmetry such as the monoclinic crystal type considered here as well as with unit cells formed by the heterostructure of different photonic crystals show significant unidirectional ...
Propagation of ionizing waves in glow discharge
International Nuclear Information System (INIS)
Suzuki, T.
1977-01-01
Ionizing waves were produced along the positive column of a glow discharge in air by applying an impulse voltage to an electrode at one end of the column. Five photomultipliers and three current-sensing coils were used to observe how the waves were affected by the rise time and the magnitude of the applied impulses and by the electron density in the positive column of the glow discharge. It is shown that the speed of the ionizing waves increases with the slope of the applied impulses and with the preexisting electron density. The electron density is augmented about 100--200 times due to the buildup of ionization at the front of the waves. The theory was developed to explain the property of ionizing waves
2D full wave simulation on electromagnetic wave propagation in toroidal plasma
International Nuclear Information System (INIS)
Hojo, Hitoshi; Uruta, Go; Nakayama, Kazunori; Mase, Atsushi
2002-01-01
Global full-wave simulation on electromagnetic wave propagation in toroidal plasma with an external magnetic field imaging a tokamak configuration is performed in two dimensions. The temporal behavior of an electromagnetic wave launched into plasma from a wave-guiding region is obtained. (author)
Nonlinear effects on mode-converted lower-hybrid waves
International Nuclear Information System (INIS)
Kuehl, H.H.
1976-01-01
Nonlinear ponderomotive force effects on mode-converted lower-hybrid waves are considered. The nonlinear distortion of these waves is shown to be governed by the cubic nonlinear Schroedinger equation. The threshold condition for self-focusing and filamentation is derived
Shear wave propagation in piezoelectric-piezoelectric composite layered structure
Directory of Open Access Journals (Sweden)
Anshu Mli Gaur
Full Text Available The propagation behavior of shear wave in piezoelectric composite structure is investigated by two layer model presented in this approach. The composite structure comprises of piezoelectric layers of two different materials bonded alternatively. Dispersion equations are derived for propagation along the direction normal to the layering and in direction of layering. It has been revealed that thickness and elastic constants have significant influence on propagation behavior of shear wave. The phase velocity and wave number is numerically calculated for alternative layer of Polyvinylidene Difluoride (PVDF and Lead Zirconate Titanate (PZT-5H in composite layered structure. The analysis carried out in this paper evaluates the effect of volume fraction on the phase velocity of shear wave.
Computer modeling of inelastic wave propagation in porous rock
International Nuclear Information System (INIS)
Cheney, J.A.; Schatz, J.F.; Snell, C.
1979-01-01
Computer modeling of wave propagation in porous rock has several important applications. Among them are prediction of fragmentation and permeability changes to be caused by chemical explosions used for in situ resource recovery, and the understanding of nuclear explosion effects such as seismic wave generation, containment, and site hardness. Of interest in all these applications are the distance from the source to which inelastic effects persist and the amount of porosity change within the inelastic region. In order to study phenomena related to these applications, the Cam Clay family of models developed at Cambridge University was used to develop a similar model that is applicable to wave propagation in porous rock. That model was incorporated into a finite-difference wave propagation computer code SOC. 10 figures, 1 table
Optimization of nonlinear wave function parameters
International Nuclear Information System (INIS)
Shepard, R.; Minkoff, M.; Chemistry
2006-01-01
An energy-based optimization method is presented for our recently developed nonlinear wave function expansion form for electronic wave functions. This expansion form is based on spin eigenfunctions, using the graphical unitary group approach (GUGA). The wave function is expanded in a basis of product functions, allowing application to closed-shell and open-shell systems and to ground and excited electronic states. Each product basis function is itself a multiconfigurational function that depends on a relatively small number of nonlinear parameters called arc factors. The energy-based optimization is formulated in terms of analytic arc factor gradients and orbital-level Hamiltonian matrices that correspond to a specific kind of uncontraction of each of the product basis functions. These orbital-level Hamiltonian matrices give an intuitive representation of the energy in terms of disjoint subsets of the arc factors, they provide for an efficient computation of gradients of the energy with respect to the arc factors, and they allow optimal arc factors to be determined in closed form for subspaces of the full variation problem. Timings for energy and arc factor gradient computations involving expansion spaces of > 10 24 configuration state functions are reported. Preliminary convergence studies and molecular dissociation curves are presented for some small molecules
Integrability and Linear Stability of Nonlinear Waves
Degasperis, Antonio; Lombardo, Sara; Sommacal, Matteo
2018-03-01
It is well known that the linear stability of solutions of 1+1 partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the linearized equation which makes use only of the associated Lax pair with no reference to spectral data and boundary conditions. This local construction is given in the general N× N matrix scheme so as to be applicable to a large class of integrable equations, including the multicomponent nonlinear Schrödinger system and the multiwave resonant interaction system. The analytical and numerical computations involved in this general approach are detailed as an example for N=3 for the particular system of two coupled nonlinear Schrödinger equations in the defocusing, focusing and mixed regimes. The instabilities of the continuous wave solutions are fully discussed in the entire parameter space of their amplitudes and wave numbers. By defining and computing the spectrum in the complex plane of the spectral variable, the eigenfrequencies are explicitly expressed. According to their topological properties, the complete classification of these spectra in the parameter space is presented and graphically displayed. The continuous wave solutions are linearly unstable for a generic choice of the coupling constants.
Propagation of waves in shear flows
Fabrikant, A L
1998-01-01
The state of the art in a theory of oscillatory and wave phenomena in hydrodynamical flows is presented in this book. A unified approach is used for waves of different physical origins. A characteristic feature of this approach is that hydrodynamical phenomena are considered in terms of physics; that is, the complement of the conventionally employed formal mathematical approach. Some physical concepts such as wave energy and momentum in a moving fluid are analysed, taking into account induced mean flow. The physical mechanisms responsible for hydrodynamic instability of shear flows are conside
Current structure of strongly nonlinear interfacial solitary waves
Semin, Sergey; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim; Churaev, Egor
2015-04-01
The characteristics of highly nonlinear solitary internal waves (solitons) in two-layer flow are computed within the fully nonlinear Navier-Stokes equations with use of numerical model of the Massachusetts Institute of Technology (MITgcm). The verification and adaptation of the model is based on the data from laboratory experiments [Carr & Davies, 2006]. The present paper also compares the results of our calculations with the computations performed in the framework of the fully nonlinear Bergen Ocean Model [Thiem et al, 2011]. The comparison of the computed soliton parameters with the predictions of the weakly nonlinear theory based on the Gardner equation is given. The occurrence of reverse flow in the bottom layer directly behind the soliton is confirmed in numerical simulations. The trajectories of Lagrangian particles in the internal soliton on the surface, on the interface and near the bottom are computed. The results demonstrated completely different trajectories at different depths of the model area. Thus, in the surface layer is observed the largest displacement of Lagrangian particles, which can be more than two and a half times larger than the characteristic width of the soliton. Located at the initial moment along the middle pycnocline fluid particles move along the elongated vertical loop at a distance of not more than one third of the width of the solitary wave. In the bottom layer of the fluid moves in the opposite direction of propagation of the internal wave, but under the influence of the reverse flow, when the bulk of the velocity field of the soliton ceases to influence the trajectory, it moves in the opposite direction. The magnitude of displacement of fluid particles in the bottom layer is not more than the half-width of the solitary wave. 1. Carr, M., and Davies, P.A. The motion of an internal solitary wave of depression over a fixed bottom boundary in a shallow, two-layer fluid. Phys. Fluids, 2006, vol. 18, No. 1, 1 - 10. 2. Thiem, O., Carr
Waves in nonlinear pre-stressed materials
Schneider, Wilhelm; Saccomandi, G
2007-01-01
The papers in this book provide a unique state-of-the-art multidisciplinary overview on the subject of waves in pre-stressed materials through the interaction of several topics, ranging from the mathematical modelling of incremental material response (elastic and inelastic), to the analysis of the governing differential equations and boundary-value problems, and to computational methods for the solution to these problems, with particular reference to industrial, geophysical, and biomechanical applications. A complete view on the title subject is proposed, including: The basic and fundamental theoretical issues (mechanical modelling, exact solutions, asymptotic methods, numerical treatment); A unified introduction to wave propagation (small on large and large on large); A look toward classical (such as geophysics and the mechanics of rubber-like solids) and emergent (such as biomechanics) applications.
International Nuclear Information System (INIS)
Macia, R.; Correig, A.M.
1987-01-01
Seismic wave propagation is described by a second order differential equation for medium displacement. By Fourier transforming with respect to time and space, wave equation transforms into a system of first order linear differential equations for the Fourier transform of displacement and stress. This system of differential equations is solved by means of Matrix Propagator and applied to the propagation of body waves in stratified media. The matrix propagators corresponding to P-SV and SH waves in homogeneous medium are found as an intermediate step to obtain the spectral response of body waves propagating through a stratified medium with homogeneous layers. (author) 14 refs
Nonlocal description of X waves in quadratic nonlinear materials
DEFF Research Database (Denmark)
Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole
2006-01-01
We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...
Ferroics and Multiferroics for Dynamically Controlled Terahertz Wave Propagation
Dutta, Moumita
The terahertz (THz) region of electromagnetic spectra, referred roughly to the frequency range of 100 GHz (0.1 THz) to 10 THz, is the bridging gap between the microwave and infrared spectral bands. Previously confined only to astronomy and analytical sciences due to the unavailability of technology, with the recent advancements in non-linear optics, this novel field has now started emerging as a promising area of research and study. Considerable efforts are underway to fill this 'THz gap' by developing efficient THz sources, detectors, switches, modulators etc. Be it any field, to realize this regime as one of the active frontiers, it is essential to have an efficient control over the wave propagation. In this research, functional materials (ferroics/multiferroics) have been explored to attain dynamic control over the THz beam propagation. The objective is to expand the horizon by enabling different family of materials to be incorporated in the design of THz modulators, exploiting the novel properties they exhibit. To reach that goal, following a comprehensive but selective (to dielectrics) review on the current-status of this research field, some preliminary studies on ferroic materials have been performed to understand the crux of ferroism and the novel functionalities they have to offer. An analytical study on microstructural and nanoscale properties of solid-solution ferroelectric Pb(Zr0.52Ti 0.48)O3 (PZT) and composite bio-ferroic seashells have been performed to elucidate the significance of structure-property relationship in intrinsic ferroelectrics. Moving forward, engineered ferroelectricity has been demonstrated. A precise control over fabrication parameters has been exploited to introduce oxygen-vacancy defined nanoscale polar-domains in centrosymmetric BaZrO3. Realizing that structure-property relationship can significantly influence the material properties and therefore the device performance, models for figure of merit analysis have been developed for
Wave propagation in the Lorenz-96 model
van Kekem, Dirk L.; Sterk, Alef E.
2018-04-01
In this paper we study the spatiotemporal properties of waves in the Lorenz-96 model and their dependence on the dimension parameter n and the forcing parameter F. For F > 0 the first bifurcation is either a supercritical Hopf or a double-Hopf bifurcation and the periodic attractor born at these bifurcations represents a traveling wave. Its spatial wave number increases linearly with n, but its period tends to a finite limit as n → ∞. For F traveling wave also grows linearly with n. For F < 0 and even n, however, a Hopf bifurcation is preceded by either one or two pitchfork bifurcations, where the number of the latter bifurcations depends on whether n has remainder 2 or 0 upon division by 4. This bifurcation sequence leads to stationary waves and their spatiotemporal properties also depend on the remainder after dividing n by 4. Finally, we explain how the double-Hopf bifurcation can generate two or more stable waves with different spatiotemporal properties that coexist for the same parameter values n and F.
Wave propagation in the Lorenz-96 model
Directory of Open Access Journals (Sweden)
D. L. van Kekem
2018-04-01
Full Text Available In this paper we study the spatiotemporal properties of waves in the Lorenz-96 model and their dependence on the dimension parameter n and the forcing parameter F. For F > 0 the first bifurcation is either a supercritical Hopf or a double-Hopf bifurcation and the periodic attractor born at these bifurcations represents a traveling wave. Its spatial wave number increases linearly with n, but its period tends to a finite limit as n → ∞. For F < 0 and odd n, the first bifurcation is again a supercritical Hopf bifurcation, but in this case the period of the traveling wave also grows linearly with n. For F < 0 and even n, however, a Hopf bifurcation is preceded by either one or two pitchfork bifurcations, where the number of the latter bifurcations depends on whether n has remainder 2 or 0 upon division by 4. This bifurcation sequence leads to stationary waves and their spatiotemporal properties also depend on the remainder after dividing n by 4. Finally, we explain how the double-Hopf bifurcation can generate two or more stable waves with different spatiotemporal properties that coexist for the same parameter values n and F.
Energy Technology Data Exchange (ETDEWEB)
He, Jiansen; Tu, Chuanyi; Wang, Linghua; Pei, Zhongtian [School of Earth and Space Sciences, Peking University, Beijing, 100871 (China); Marsch, Eckart [Institute for Experimental and Applied Physics, Christian-Albrechts-Universität zu Kiel, D-24118 Kiel (Germany); Chen, Christopher H. K. [Department of Physics, Imperial College London, London SW7 2AZ (United Kingdom); Zhang, Lei [Sate Key Laboratory of Space Weather, Chinese Academy of Sciences, Beijing 100190 (China); Salem, Chadi S.; Bale, Stuart D., E-mail: jshept@gmail.com [Space Sciences Laboratory, University of California, Berkeley, CA 94720 (United States)
2015-11-10
Magnetohydronamic turbulence is believed to play a crucial role in heating laboratory, space, and astrophysical plasmas. However, the precise connection between the turbulent fluctuations and the particle kinetics has not yet been established. Here we present clear evidence of plasma turbulence heating based on diagnosed wave features and proton velocity distributions from solar wind measurements by the Wind spacecraft. For the first time, we can report the simultaneous observation of counter-propagating magnetohydrodynamic waves in the solar wind turbulence. As opposed to the traditional paradigm with counter-propagating Alfvén waves (AWs), anti-sunward AWs are encountered by sunward slow magnetosonic waves (SMWs) in this new type of solar wind compressible turbulence. The counter-propagating AWs and SWs correspond, respectively, to the dominant and sub-dominant populations of the imbalanced Elsässer variables. Nonlinear interactions between the AWs and SMWs are inferred from the non-orthogonality between the possible oscillation direction of one wave and the possible propagation direction of the other. The associated protons are revealed to exhibit bi-directional asymmetric beams in their velocity distributions: sunward beams appear in short, narrow patterns and anti-sunward in broad extended tails. It is suggested that multiple types of wave–particle interactions, i.e., cyclotron and Landau resonances with AWs and SMWs at kinetic scales, are taking place to jointly heat the protons perpendicular and in parallel.
Excitation of Accelerating Plasma Waves by Counter-propagating Laser Beams
International Nuclear Information System (INIS)
Gennady Shvets; Nathaniel J. Fisch; Alexander Pukhov
2001-01-01
Generation of accelerating plasma waves using two counter-propagating laser beams is considered. Colliding-beam accelerator requires two laser pulses: the long pump and the short timing beam. We emphasize the similarities and differences between the conventional laser wakefield accelerator and the colliding-beam accelerator (CBA). The highly nonlinear nature of the wake excitation is explained using both nonlinear optics and plasma physics concepts. Two regimes of CBA are considered: (i) the short-pulse regime, where the timing beam is shorter than the plasma period, and (ii) the parametric excitation regime, where the timing beam is longer than the plasma period. Possible future experiments are also outlined
Weakly nonlinear electron plasma waves in collisional plasmas
DEFF Research Database (Denmark)
Pecseli, H. L.; Rasmussen, J. Juul; Tagare, S. G.
1986-01-01
The nonlinear evolution of a high frequency plasma wave in a weakly magnetized, collisional plasma is considered. In addition to the ponderomotive-force-nonlinearity the nonlinearity due to the heating of the electrons is taken into account. A set of nonlinear equations including the effect...
Engineering equations for characterizing non-linear laser intensity propagation in air with loss.
Karr, Thomas; Stotts, Larry B; Tellez, Jason A; Schmidt, Jason D; Mansell, Justin D
2018-02-19
The propagation of high peak-power laser beams in real atmospheres will be affected at long range by both linear and nonlinear effects contained therein. Arguably, J. H. Marburger is associated with the mathematical characterization of this phenomenon. This paper provides a validated set of engineering equations for characterizing the self-focusing distance from a laser beam propagating through non-turbulent air with, and without, loss as well as three source configurations: (1) no lens, (2) converging lens and (3) diverging lens. The validation was done against wave-optics simulation results. Some validated equations follow Marburger completely, but others do not, requiring modification of the original theory. Our results can provide a guide for numerical simulations and field experiments.
Numerical study of propagation properties of surface plasmon polaritons in nonlinear media
Sagor, Rakibul Hasan; Ghulam Saber, Md.; Alsunaidi, Mohammad
2016-01-01
We present a time-domain algorithm for simulating nonlinear propagation of surface plasmon polaritons (SPPs) in chalcogenide glass. Due to the high non-linearity property and strong dispersion and confinement chalcogenide glasses are widely known
Propagation of inertial-gravity waves on an island shelf
Bondur, V. G.; Sabinin, K. D.; Grebenyuk, Yu. V.
2015-09-01
The propagation of inertial-gravity waves (IGV) at the boundary of the Pacific shelf near the island of Oahu (Hawaii), whose generation was studied in the first part of this work [1], is analyzed. It is shown that a significant role there is played by the plane oblique waves; whose characteristics were identified by the method of estimating 3D wave parameters for the cases when the measurements are available only for two verticals. It is established that along with the descending propagation of energy that is typical of IGVs, wave packets ascend from the bottom to the upper layers, which is caused by the emission of waves from intense jets of discharged waters flowing out of a diffusor located at the bottom.
Periodic and solitary wave solutions of cubic–quintic nonlinear ...
Indian Academy of Sciences (India)
Hence, most of the real nonlinear physical equations possess variable ... evolution of the system with time and second term represents the convective flux term. The ... Travelling wave solutions of nonlinear reaction-diffusion equations are.
Propagation of electromagnetic waves in a weakly ionized dusty plasma
International Nuclear Information System (INIS)
Jia, Jieshu; Yuan, Chengxun; Gao, Ruilin; Wang, Ying; Liu, Yaoze; Gao, Junying; Zhou, Zhongxiang; Sun, Xiudong; Li, Hui; Wu, Jian; Pu, Shaozhi
2015-01-01
Propagation properties of electromagnetic (EM) waves in weakly ionized dusty plasmas are the subject of this study. Dielectric relation for EM waves propagating at a weakly ionized dusty plasma is derived based on the Boltzmann distribution law while considering the collision and charging effects of dust grains. The propagation properties of EM energy in dusty plasma of rocket exhaust are numerically calculated and studied, utilizing the parameters of rocket exhaust plasma. Results indicate that increase of dust radius and density enhance the reflection and absorption coefficient. High dust radius and density make the wave hardly transmit through the dusty plasmas. Interaction enhancements between wave and dusty plasmas are developed through effective collision frequency improvements. Numerical results coincide with observed results by indicating that GHz band wave communication is effected by dusty plasma as the presence of dust grains significantly affect propagation of EM waves in the dusty plasmas. The results are helpful to analyze the effect of dust in plasmas and also provide a theoretical basis for the experiments. (paper)
Energy Technology Data Exchange (ETDEWEB)
Han, Jiu-Ning, E-mail: hanjiuning@126.com; He, Yong-Lin; Luo, Jun-Hua; Nan, Ya-Gong; Han, Zhen-Hai; Dong, Guang-Xing [College of Physics and Electromechanical Engineering, Hexi University, Zhangye 734000 (China); Duan, Wen-Shan [College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070 (China); Li, Jun-Xiu [College of Civil Engineering, Hexi University, Zhangye 734000 (China)
2014-01-15
With the consideration of the superthermal electron distribution, we present a theoretical investigation about the nonlinear propagation of electron-acoustic solitary and shock waves in a dissipative, nonplanar non-Maxwellian plasma comprised of cold electrons, superthermal hot electrons, and stationary ions. The reductive perturbation technique is used to obtain a modified Korteweg-de Vries Burgers equation for nonlinear waves in this plasma. We discuss the effects of various plasma parameters on the time evolution of nonplanar solitary waves, the profile of shock waves, and the nonlinear structure induced by the collision between planar solitary waves. It is found that these parameters have significant effects on the properties of nonlinear waves and collision-induced nonlinear structure.
Carcione, José M
2014-01-01
Authored by the internationally renowned José M. Carcione, Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media examines the differences between an ideal and a real description of wave propagation, starting with the introduction of relevant stress-strain relations. The combination of this relation and the equations of momentum conservation lead to the equation of motion. The differential formulation is written in terms of memory variables, and Biot's theory is used to describe wave propagation in porous media. For each rheology, a plane-wave analysis is performed in order to understand the physics of wave propagation. This book contains a review of the main direct numerical methods for solving the equation of motion in the time and space domains. The emphasis is on geophysical applications for seismic exploration, but researchers in the fields of earthquake seismology, rock acoustics, and material science - including many branches of acoustics of fluids and ...
Li, Mingliang; Deng, Mingxi; Gao, Guangjian; Xiang, Yanxun
2018-05-01
This paper investigated modeling of second-harmonic generation (SHG) of circumferential guided wave (CGW) propagation in a composite circular tube, and then analyzed the influences of interfacial properties on the SHG effect of primary CGW. Here the effect of SHG of primary CGW propagation is treated as a second-order perturbation to its linear wave response. Due to the convective nonlinearity and the inherent elastic nonlinearity of material, there are second-order bulk driving forces and surface/interface driving stresses in the interior and at the surface/interface of a composite circular tube, when a primary CGW mode propagates along its circumference. Based on the approach of modal expansion analysis for waveguide excitation, the said second-order driving forces/stresses are regarded as the excitation sources to generate a series of double-frequency CGW modes that constitute the second-harmonic field of the primary CGW propagation. It is found that the modal expansion coefficient of each double-frequency CGW mode is closely related to the interfacial stiffness constants that are used to describe the interfacial properties between the inner and outer circular parts of the composite tube. Furthermore, changes in the interfacial stiffness constants essentially influence the dispersion relation of CGW propagation. This will remarkably affect the efficiency of cumulative SHG of primary CGW propagation. Some finite element simulations have been implemented of response characteristics of cumulative SHG to the interfacial properties. Both the theoretical analyses and numerical simulations indicate that the effect of cumulative SHG is found to be much more sensitive to changes in the interfacial properties than primary CGW propagation. The potential of using the effect of cumulative SHG by primary CGW propagation to characterize a minor change in the interfacial properties is considered.
Nonlinear acoustic waves in the viscous thermosphere and ionosphere above earthquake
Czech Academy of Sciences Publication Activity Database
Chum, Jaroslav; Cabrera, M. A.; Mošna, Zbyšek; Fagre, M.; Baše, Jiří; Fišer, Jiří
2016-01-01
Roč. 121, č. 12 (2016), s. 12126-12137 ISSN 2169-9380 R&D Projects: GA ČR(CZ) GC15-07281J Institutional support: RVO:68378289 Keywords : infrasound * seismic waves * ionosphere * nonlinear wave propagation * viscosity * dissipation * remote sensing Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 2.733, year: 2016 http://onlinelibrary.wiley.com/doi/10.1002/2016JA023450/full
Nonlinear drift waves in a dusty plasma with sheared flows
Energy Technology Data Exchange (ETDEWEB)
Vranjes, J. [K.U. Leuven (Belgium). Center for Plasma Astrophysics; Shukla, R.K. [Ruhr-Univ. Bochum (Germany). Inst. fuer Theoretische Physik IV
2002-01-01
Nonlinear properties of dust-modified drift waves and dust-drift waves in a dusty magnetoplasma with equilibrium sheared flows are examined. For this purpose, the relevant nonlinear equations for drift waves are analyzed for various profiles of the perpendicular and parallel plasma flows, and a variety of nonlinear solutions (viz. single and double vortex chains accompanied with zonal flows, tripolar and global vortices), which are driven by nommiform shear flows and nommiform dust density, is presented.
Nonlinear drift waves in a dusty plasma with sheared flows
International Nuclear Information System (INIS)
Vranjes, J.; Shukla, R.K.
2002-01-01
Nonlinear properties of dust-modified drift waves and dust-drift waves in a dusty magnetoplasma with equilibrium sheared flows are examined. For this purpose, the relevant nonlinear equations for drift waves are analyzed for various profiles of the perpendicular and parallel plasma flows, and a variety of nonlinear solutions (viz. single and double vortex chains accompanied with zonal flows, tripolar and global vortices), which are driven by nommiform shear flows and nommiform dust density, is presented
Pressure wave propagation in the discharge piping with water pool
International Nuclear Information System (INIS)
Bang, Young S.; Seul, Kwang W.; Kim, In Goo
2004-01-01
Pressure wave propagation in the discharge piping with a sparger submerged in a water pool, following the opening of a safety relief valve, is analyzed. To predict the pressure transient behavior, a RELAP5/MOD3 code is used. The applicability of the RELAP5 code and the adequacy of the present modeling scheme are confirmed by simulating the applicable experiment on a water hammer with voiding. As a base case, the modeling scheme was used to calculate the wave propagation inside a vertical pipe with sparger holes and submerged within a water pool. In addition, the effects on wave propagation of geometric factors, such as the loss coefficient, the pipe configuration, and the subdivision of sparger pipe, are investigated. The effects of inflow conditions, such as water slug inflow and the slow opening of a safety relief valve are also examined
Detecting electromagnetic cloaks using backward-propagating waves
Salem, Mohamed
2011-08-01
A novel approach for detecting transformation-optics invisibility cloaks is proposed. The detection method takes advantage of the unusual backward-propagation characteristics of recently reported beams and pulses to induce electromagnetic scattering from the cloak. Even though waves with backward-propagating energy flux cannot penetrate the cloaking shell and interact with the cloaked objects (i.e., they do not make the cloaked object visible), they provide a mechanism for detecting the presence of cloaks. © 2011 IEEE.
Detecting electromagnetic cloaks using backward-propagating waves
Salem, Mohamed; Bagci, Hakan
2011-01-01
A novel approach for detecting transformation-optics invisibility cloaks is proposed. The detection method takes advantage of the unusual backward-propagation characteristics of recently reported beams and pulses to induce electromagnetic scattering from the cloak. Even though waves with backward-propagating energy flux cannot penetrate the cloaking shell and interact with the cloaked objects (i.e., they do not make the cloaked object visible), they provide a mechanism for detecting the presence of cloaks. © 2011 IEEE.
Wave propagation model of heat conduction and group speed
Zhang, Long; Zhang, Xiaomin; Peng, Song
2018-03-01
In view of the finite relaxation model of non-Fourier's law, the Cattaneo and Vernotte (CV) model and Fourier's law are presented in this work for comparing wave propagation modes. Independent variable translation is applied to solve the partial differential equation. Results show that the general form of the time spatial distribution of temperature for the three media comprises two solutions: those corresponding to the positive and negative logarithmic heating rates. The former shows that a group of heat waves whose spatial distribution follows the exponential function law propagates at a group speed; the speed of propagation is related to the logarithmic heating rate. The total speed of all the possible heat waves can be combined to form the group speed of the wave propagation. The latter indicates that the spatial distribution of temperature, which follows the exponential function law, decays with time. These features show that propagation accelerates when heated and decelerates when cooled. For the model media that follow Fourier's law and correspond to the positive heat rate of heat conduction, the propagation mode is also considered the propagation of a group of heat waves because the group speed has no upper bound. For the finite relaxation model with non-Fourier media, the interval of group speed is bounded and the maximum speed can be obtained when the logarithmic heating rate is exactly the reciprocal of relaxation time. And for the CV model with a non-Fourier medium, the interval of group speed is also bounded and the maximum value can be obtained when the logarithmic heating rate is infinite.
Excitation of nonlinear wave patterns in flowing complex plasmas
Jaiswal, S.; Bandyopadhyay, P.; Sen, A.
2018-01-01
We describe experimental observations of nonlinear wave structures excited by a supersonic mass flow of dust particles over an electrostatic potential hill in a dusty plasma medium. The experiments have been carried out in a Π- shaped experimental (DPEx) device in which micron sized Kaolin particles are embedded in a DC glow discharge Argon plasma. An equilibrium dust cloud is formed by maintaining the pumping speed and gas flow rate and the dust flow is induced either by suddenly reducing the height of a potential hill or by suddenly reducing the gas flow rate. For a supersonic flow of the dust fluid precursor solitons are seen to propagate in the upstream direction while wake structures propagate in the downstream direction. For flow speeds with a Mach number greater than 2 the dust particles flowing over the potential hill give rise to dispersive dust acoustic shock waves. The experimental results compare favorably with model theories based on forced K-dV and K-dV Burger's equations.
Merkel, A; Tournat, V; Gusev, V
2014-08-01
We report the experimental observation of the gravity-induced asymmetry for the nonlinear transformation of acoustic waves in a noncohesive granular phononic crystal. Because of the gravity, the contact precompression increases with depth inducing space variations of not only the linear and nonlinear elastic moduli but also of the acoustic wave dissipation. We show experimentally and explain theoretically that, in contrast to symmetric propagation of linear waves, the amplitude of the nonlinearly self-demodulated wave depends on whether the propagation of the waves is in the direction of the gravity or in the opposite direction. Among the observed nonlinear processes, we report frequency mixing of the two transverse-rotational modes belonging to the optical band of vibrations and propagating with negative phase velocities, which results in the excitation of a longitudinal wave belonging to the acoustic band of vibrations and propagating with positive phase velocity. We show that the measurements of the gravity-induced asymmetry in the nonlinear acoustic phenomena can be used to compare the in-depth distributions of the contact nonlinearity and of acoustic absorption.
DEMETER observations of manmade waves that propagate in the ionosphere
Parrot, Michel
2018-01-01
This paper is a review of manmade waves observed by the ionospheric satellite DEMETER. It concerns waves emitted by the ground-based VLF and ELF transmitters, by broadcasting stations, by the power line harmonic radiation, by industrial noise, and by active experiments. Examples are shown including, for the first time, the record of a wave coming from an ELF transmitter. These waves propagate upwards in the magnetosphere and they can be observed in the magnetically conjugated region of emission. Depending on their frequencies, they perturb the ionosphere and the particles in the radiation belts, and additional emissions are triggered. xml:lang="fr"
Parabolic approximation method for fast magnetosonic wave propagation in tokamaks
International Nuclear Information System (INIS)
Phillips, C.K.; Perkins, F.W.; Hwang, D.Q.
1985-07-01
Fast magnetosonic wave propagation in a cylindrical tokamak model is studied using a parabolic approximation method in which poloidal variations of the wave field are considered weak in comparison to the radial variations. Diffraction effects, which are ignored by ray tracing mthods, are included self-consistently using the parabolic method since continuous representations for the wave electromagnetic fields are computed directly. Numerical results are presented which illustrate the cylindrical convergence of the launched waves into a diffraction-limited focal spot on the cyclotron absorption layer near the magnetic axis for a wide range of plasma confinement parameters
Transient Aspects of Wave Propagation Connected with Spatial Coherence
Directory of Open Access Journals (Sweden)
Ezzat G. Bakhoum
2013-01-01
Full Text Available This study presents transient aspects of light wave propagation connected with spatial coherence. It is shown that reflection and refraction phenomena involve spatial patterns which are created within a certain transient time interval. After this transient time interval, these patterns act like a memory, determining the wave vector for subsequent sets of reflected/refracted waves. The validity of this model is based on intuitive aspects regarding phase conservation of energy for waves reflected/refracted by multiple centers in a certain material medium.
Relativistic nonlinear waves of cyclotron in electron and electron-ion plasmas
International Nuclear Information System (INIS)
Bruno, R.
1981-12-01
Dispersion relations for electron-cyclotron and ion-cyclotron waves are examined in two models of plasmas, the first propagating in fluent electronic plasmas (''streaming'') as well as in fluent electron-ionic plasmas, and the last in fluent electron-ionic plasmas. The identification of the propagation modes is realized with the aid of a special technique of polinomial expantion of the dispersion relation in the limit of large frequencies and short wavelenghts. The analisys so developed on these dispersion relations for fluent plasmas show that: (i) the wave amplitudes are frequency dependent; (ii) the ''resonances'' frequencies of the respective estationary plasmas must be re-examined with the relations between wave amplitudes and the propagation frequencies near these frequencies; (iii) the electric field amplitudes for the non-linear waves of electron-cyclotron and ion-cyclotron go to zero in the limits of the respective cyclotron frequencies in both fluent plasma models. (M.W.O.) [pt
Wave propagation through an electron cyclotron resonance layer
International Nuclear Information System (INIS)
Westerhof, E.
1997-01-01
The propagation of a wave beam through an electron cyclotron resonance layer is analysed in two-dimensional slab geometry in order to assess the deviation from cold plasma propagation due to resonant, warm plasma changes in wave dispersion. For quasi-perpendicular propagation, N ' 'parallel to'' ≅ v t /c, an O-mode beam is shown to exhibit a strong wiggle in the trajectory of the centre of the beam when passing through the fundamental electron cyclotron resonance. The effects are largest for low temperatures and close to perpendicular propagation. Predictions from standard dielectric wave energy fluxes are inconsistent with the trajectory of the beam. Qualitatively identical results are obtained for the X-mode second harmonic. In contrast, the X-mode at the fundamental resonance shows significant deviations form cold plasma propagation only for strongly oblique propagation and/or high temperatures. On the basis of the obtained results a practical suggestion is made for ray tracing near electron cyclotron resonance. (Author)
Radio Wave Propagation Scene Partitioning for High-Speed Rails
Directory of Open Access Journals (Sweden)
Bo Ai
2012-01-01
Full Text Available Radio wave propagation scene partitioning is necessary for wireless channel modeling. As far as we know, there are no standards of scene partitioning for high-speed rail (HSR scenarios, and therefore we propose the radio wave propagation scene partitioning scheme for HSR scenarios in this paper. Based on our measurements along the Wuhan-Guangzhou HSR, Zhengzhou-Xian passenger-dedicated line, Shijiazhuang-Taiyuan passenger-dedicated line, and Beijing-Tianjin intercity line in China, whose operation speeds are above 300 km/h, and based on the investigations on Beijing South Railway Station, Zhengzhou Railway Station, Wuhan Railway Station, Changsha Railway Station, Xian North Railway Station, Shijiazhuang North Railway Station, Taiyuan Railway Station, and Tianjin Railway Station, we obtain an overview of HSR propagation channels and record many valuable measurement data for HSR scenarios. On the basis of these measurements and investigations, we partitioned the HSR scene into twelve scenarios. Further work on theoretical analysis based on radio wave propagation mechanisms, such as reflection and diffraction, may lead us to develop the standard of radio wave propagation scene partitioning for HSR. Our work can also be used as a basis for the wireless channel modeling and the selection of some key techniques for HSR systems.
Studying Electromechanical Wave Propagation and Transport Delays in Power Systems
Dasgupta, Kalyan; Kulkarni, A. M.; Soman, Shreevardhan
2013-05-01
Abstract: In this paper, we make an attempt to describe the phenomenon of wave propagation when a disturbance is introduced in an electromechanical system. The focus is mainly on generator trips in a power system. Ordering of the generators is first done using a sensitivity matrix. Thereafter, orthogonal decomposition of the ordered generators is done to group them based on their participation in different modes. Finally, we find the velocity of propagation of the wave and the transport delay associated with it using the ESPRIT method. The analysis done on generators from the eastern and western regions of India.1
24 GHz cmWave Radio Propagation Through Vegetation
DEFF Research Database (Denmark)
Rodriguez, Ignacio; Abreu, Renato Barbosa; Portela Lopes de Almeida, Erika
2016-01-01
This paper presents a measurement-based analysis of cm-wave radio propagation through vegetation at 24 GHz. A set of dedicated directional measurements were performed with horn antennas located close to street level inside a densely-vegetated area illuminated from above. The full azimuth was exam......This paper presents a measurement-based analysis of cm-wave radio propagation through vegetation at 24 GHz. A set of dedicated directional measurements were performed with horn antennas located close to street level inside a densely-vegetated area illuminated from above. The full azimuth...
Tripathi, B. B.; Espíndola, D.; Pinton, G. F.
2017-11-01
The recent discovery of shear shock wave generation and propagation in the porcine brain suggests that this new shock phenomenology may be responsible for a broad range of traumatic injuries. Blast-induced head movement can indirectly lead to shear wave generation in the brain, which could be a primary mechanism for injury. Shear shock waves amplify the local acceleration deep in the brain by up to a factor of 8.5, which may tear and damage neurons. Currently, there are numerical methods that can model compressional shock waves, such as comparatively well-studied blast waves, but there are no numerical full-wave solvers that can simulate nonlinear shear shock waves in soft solids. Unlike simplified representations, e.g., retarded time, full-wave representations describe fundamental physical behavior such as reflection and heterogeneities. Here we present a piecewise parabolic method-based solver for one-dimensional linearly polarized nonlinear shear wave in a homogeneous medium and with empirical frequency-dependent attenuation. This method has the advantage of being higher order and more directly extendable to multiple dimensions and heterogeneous media. The proposed numerical scheme is validated analytically and experimentally and compared to other shock capturing methods. A Riemann step-shock problem is used to characterize the numerical dissipation. This dissipation is then tuned to be negligible with respect to the physical attenuation by choosing an appropriate grid spacing. The numerical results are compared to ultrasound-based experiments that measure planar polarized shear shock wave propagation in a tissue-mimicking gelatin phantom. Good agreement is found between numerical results and experiment across a 40 mm propagation distance. We anticipate that the proposed method will be a starting point for the development of a two- and three-dimensional full-wave code for the propagation of nonlinear shear waves in heterogeneous media.
Slow Wave Propagation and Sheath Interaction for ICRF Waves in the Tokamak SOL
International Nuclear Information System (INIS)
Myra, J. R.; D'Ippolito, D. A.
2009-01-01
In previous work we studied the propagation of slow-wave resonance cones launched parasitically by a fast-wave antenna into a tenuous magnetized plasma. Here we extend the previous calculation to ''dense'' scrape-off-layer (SOL) plasmas where the usual slow wave is evanescent. Using the sheath boundary condition, it is shown that for sufficiently close limiters, the slow wave couples to a sheath plasma wave and is no longer evanescent, but radially propagating. A self-consistent calculation of the rf-sheath width yields the resulting sheath voltage in terms of the amplitude of the launched SW, plasma parameters and connection length.
New travelling wave solutions for nonlinear stochastic evolution ...
Indian Academy of Sciences (India)
expansion method to look for travelling wave solutions of nonlinear partial differential equations. It is interesting to mention that, in this method the sign of the parameters can be used to judge the numbers and types of travelling wave solutions.
Nonlinear modulation of ion acoustic waves in a magnetized plasma
International Nuclear Information System (INIS)
Bharuthram, R.; Shukla, P.K.
1987-01-01
The quasistatic plasma slow response to coherent ion acoustic waves in a magnetized plasma is considered. A multidimensional cubic nonlinear Schroedinger equation is derived. It is found that the ion acoustic waves remain modulationally stable against oblique perturbations
High frequency guided wave propagation in monocrystalline silicon wafers
Pizzolato, Marco; Masserey, Bernard; Robyr, Jean-Luc; Fromme, Paul
2017-04-01
Monocrystalline silicon wafers are widely used in the photovoltaic industry for solar panels with high conversion efficiency. The cutting process can introduce micro-cracks in the thin wafers and lead to varying thickness. High frequency guided ultrasonic waves are considered for the structural monitoring of the wafers. The anisotropy of the monocrystalline silicon leads to variations of the wave characteristics, depending on the propagation direction relative to the crystal orientation. Full three-dimensional Finite Element simulations of the guided wave propagation were conducted to visualize and quantify these effects for a line source. The phase velocity (slowness) and skew angle of the two fundamental Lamb wave modes (first anti-symmetric mode A0 and first symmetric mode S0) for varying propagation directions relative to the crystal orientation were measured experimentally. Selective mode excitation was achieved using a contact piezoelectric transducer with a custom-made wedge and holder to achieve a controlled contact pressure. The out-of-plane component of the guided wave propagation was measured using a noncontact laser interferometer. Good agreement was found with the simulation results and theoretical predictions based on nominal material properties of the silicon wafer.
Three-wave interaction in two-component quadratic nonlinear lattices
DEFF Research Database (Denmark)
Konotop, V. V.; Cunha, M. D.; Christiansen, Peter Leth
1999-01-01
We investigate a two-component lattice with a quadratic nonlinearity and find with the multiple scale technique that integrable three-wave interaction takes place between plane wave solutions when these fulfill resonance conditions. We demonstrate that. energy conversion and pulse propagation known...... from three-wave interaction is reproduced in the lattice and that exact phase matching of parametric processes can be obtained in non-phase-matched lattices by tilting the interacting plane waves with respect to each other. [S1063-651X(99)15110-9]....
Non-Linear Back-propagation: Doing Back-Propagation withoutDerivatives of the Activation Function
DEFF Research Database (Denmark)
Hertz, John; Krogh, Anders Stærmose; Lautrup, Benny
1997-01-01
The conventional linear back-propagation algorithm is replaced by a non-linear version, which avoids the necessity for calculating the derivative of the activation function. This may be exploited in hardware realizations of neural processors. In this paper we derive the non-linear back...
Mahmood, S.; Sadiq, Safeer; Haque, Q.; Ali, Munazza Z.
2016-06-01
The obliquely propagating arbitrary amplitude electrostatic wave is studied in a dense magnetized plasma having singly and doubly charged helium ions with nonrelativistic and ultrarelativistic degenerate electrons pressures. The Fermi temperature for ultrarelativistic degenerate electrons described by N. M. Vernet [(Cambridge University Press, Cambridge, 2007), p. 57] is used to define ion acoustic speed in ultra-dense plasmas. The pseudo-potential approach is used to solve the fully nonlinear set of dynamic equations for obliquely propagating electrostatic waves in a dense magnetized plasma containing helium ions. The upper and lower Mach number ranges for the existence of electrostatic solitons are found which depends on the obliqueness of the wave propagation with respect to applied magnetic field and charge number of the helium ions. It is found that only compressive (hump) soliton structures are formed in all the cases and only subsonic solitons are formed for a singly charged helium ions plasma case with nonrelativistic degenerate electrons. Both subsonic and supersonic soliton hump structures are formed for doubly charged helium ions with nonrelativistic degenerate electrons and ultrarelativistic degenerate electrons plasma case containing singly as well as doubly charged helium ions. The effect of propagation direction on the soliton amplitude and width of the electrostatic waves is also presented. The numerical plots are also shown for illustration using dense plasma parameters of a compact star (white dwarf) from literature.
Spherical shock-wave propagation in three-dimensional granular packings.
Xue, Kun; Bai, Chun-Hua
2011-02-01
We investigate numerically the spherical shock-wave propagation in an open dense granular packing perturbed by the sudden expansion of a spherical intruder in the interior of the pack, focusing on the correlation between geometrical fabrics and propagating properties. The measurements of the temporal and spatial variations in a variety of propagating properties define a consistent serrated wave substructure with characteristic length on the orders of particle diameters. Further inspection of particle packing reveals a well-defined particle layering that persists several particle diameters away from the intruder, although its dominant effects are only within one to two diameters. This interface-induced layering not only exactly coincides with the serrated wave profile, but also highlights the competition between two energy transmission mechanisms involving distinct transport speeds. The alternating dominances between these two mechanisms contribute to the nonlinear wave propagation on the particle scale. Moreover, the proliferation of intricate three-dimensional contact force networks suggests the anisotropic stress transmission, which is found to also arise from the localized packing structure in the vicinity of the intruder.
A two-step FEM-SEM approach for wave propagation analysis in cable structures
Zhang, Songhan; Shen, Ruili; Wang, Tao; De Roeck, Guido; Lombaert, Geert
2018-02-01
Vibration-based methods are among the most widely studied in structural health monitoring (SHM). It is well known, however, that the low-order modes, characterizing the global dynamic behaviour of structures, are relatively insensitive to local damage. Such local damage may be easier to detect by methods based on wave propagation which involve local high frequency behaviour. The present work considers the numerical analysis of wave propagation in cables. A two-step approach is proposed which allows taking into account the cable sag and the distribution of the axial forces in the wave propagation analysis. In the first step, the static deformation and internal forces are obtained by the finite element method (FEM), taking into account geometric nonlinear effects. In the second step, the results from the static analysis are used to define the initial state of the dynamic analysis which is performed by means of the spectral element method (SEM). The use of the SEM in the second step of the analysis allows for a significant reduction in computational costs as compared to a FE analysis. This methodology is first verified by means of a full FE analysis for a single stretched cable. Next, simulations are made to study the effects of damage in a single stretched cable and a cable-supported truss. The results of the simulations show how damage significantly affects the high frequency response, confirming the potential of wave propagation based methods for SHM.
Manipulating acoustic wave reflection by a nonlinear elastic metasurface
Guo, Xinxin; Gusev, Vitalyi E.; Bertoldi, Katia; Tournat, Vincent
2018-03-01
The acoustic wave reflection properties of a nonlinear elastic metasurface, derived from resonant nonlinear elastic elements, are theoretically and numerically studied. The metasurface is composed of a two degree-of-freedom mass-spring system with quadratic elastic nonlinearity. The possibility of converting, during the reflection process, most of the fundamental incoming wave energy into the second harmonic wave is shown, both theoretically and numerically, by means of a proper design of the nonlinear metasurface. The theoretical results from the harmonic balance method for a monochromatic source are compared with time domain simulations for a wave packet source. This protocol allows analyzing the dynamics of the nonlinear reflection process in the metasurface as well as exploring the limits of the operating frequency bandwidth. The reported methodology can be applied to a wide variety of nonlinear metasurfaces, thus possibly extending the family of exotic nonlinear reflection processes.
Nonlinear low frequency (LF) waves - Comets and foreshock phenomena
Tsurutani, Bruce T.
1991-01-01
A review is conducted of LF wave nonlinear properties at comets and in the earth's foreshock, engaging such compelling questions as why there are no cometary cyclotron waves, the physical mechanism responsible for 'dispersive whiskers', and the character of a general description of linear waves. Attention is given to the nonlinear properties of LF waves, whose development is illustrated by examples of waves and their features at different distances from the comet, as well as by computer simulation results. Also discussed is a curious wave mode detected from Comet Giacobini-Zinner, both at and upstream of the bow shock/wave.
International Nuclear Information System (INIS)
Bhattacharyya, B.; Chakraborty, B.
1979-01-01
Nonlinear corrections of a left and a right circularly polarized electromagnetic wave of the same frequency, propagating in the direction of a static and uniform magnetic field in a cold and collisionally damped two-component plasma, have been evaluated. The nonlinearly correct dispersion relation, self-generating nonlinear precessional rotation of the polarization ellipse of the wave and the shift in a wave parameter depend on linear combinations of products of the amplitude components taken two at a time and hence on the energies of the waves. Both in the low frequency resonance (that is when the ion cyclotron frequency equals the wave frequency) and in the high frequency resonance (that is when the electron cyclotron frequency equals the wave frequency), the self-precessional rate and wavenumber shift are found to be large and so have the possibility of detection in laboratory experiments. Moreover, for the limit leading to Alfven waves, these nonlinear effects have been found to have some interesting and significant properties. (Auth.)
TWO-DIMENSIONAL MODELLING OF ACCIDENTAL FLOOD WAVES PROPAGATION
Directory of Open Access Journals (Sweden)
Lorand Catalin STOENESCU
2011-05-01
Full Text Available The study presented in this article describes a modern modeling methodology of the propagation of accidental flood waves in case a dam break; this methodology is applied in Romania for the first time for the pilot project „Breaking scenarios of Poiana Uzului dam”. The calculation programs used help us obtain a bidimensional calculation (2D of the propagation of flood waves, taking into consideration the diminishing of the flood wave on a normal direction to the main direction; this diminishing of the flood wave is important in the case of sinuous courses of water or with urban settlements very close to the minor river bed. In the case of Poiana Uzului dam, 2 scenarios were simulated with the help of Ph.D. Eng. Dan Stematiu, plausible scenarios but with very little chances of actually producing. The results were presented as animations with flooded surfaces at certain time steps successively.
International Nuclear Information System (INIS)
Ohsawa, Yukiharu.
1984-12-01
A 2-1/2 dimensional fully relativistic, fully electromagnetic particle code is used to study a time evolution of nonlinear magnetosonic pulse propagating in the direction perpendicular to a magnetic field. The pulse is excited by an instantaneous piston acceleration, and evolves totally self-consistently. Large amplitude pulse traps some ions and accelerates them parallel to the wave front. They are detrapped when their velocities become of the order of the sum of the ExB drift velocity and the wave phase velocity, where E is the electric field in the direction of wave propagation. The pulse develops into a quasi-shock wave in a collisionless plasma by a dissipation due to the resonant ion acceleration. Simple nonlinear wave theory for a cold plasma well describes the shock properties observed in the simulation except for the effects of resonant ions. In particular, magnitude of an electric potential across the shock region is derived analytically and is found to be in good agreement with our simulations. The potential jump is proportional to B 2 , and hence the ExB drift velocity of the trapped ions is proportional to B. (author)
Stress wave propagation in linear viscoelasticity
International Nuclear Information System (INIS)
Asada, Kazuo; Fukuoka, Hidekazu.
1992-01-01
Decreasing characteristics of both stress and stress gradient with propagation distance at a 2-dimensional linear viscoelasticity wavefront are derived by using our 3-dimensional theoretical equation for particle velocity discontinuities. By finite-element method code DYNA3D, stress at a noncurvature dilatation wavefront of linear viscoelasticity is shown to decrease exponentially. This result is in good accordance with our theory. By dynamic photoelasticity experiment, stress gradients of urethane rubber plates at 3 types of wavefronts are shown to decrease exponentially at a noncurvature wavefront and are shown to be a decreasing function of (1/√R) exp (α 1 2 /(2α 0 3 ξ)) at a curvature wavefront. These experiment results are in good accordance with our theory. (author)
Estimating propagation velocity through a surface acoustic wave sensor
Xu, Wenyuan; Huizinga, John S.
2010-03-16
Techniques are described for estimating the propagation velocity through a surface acoustic wave sensor. In particular, techniques which measure and exploit a proper segment of phase frequency response of the surface acoustic wave sensor are described for use as a basis of bacterial detection by the sensor. As described, use of velocity estimation based on a proper segment of phase frequency response has advantages over conventional techniques that use phase shift as the basis for detection.
Observations of apparent superslow wave propagation in solar prominences
Raes, J. O.; Van Doorsselaere, T.; Baes, M.; Wright, A. N.
2017-06-01
Context. Phase mixing of standing continuum Alfvén waves and/or continuum slow waves in atmospheric magnetic structures such as coronal arcades can create the apparent effect of a wave propagating across the magnetic field. Aims: We observe a prominence with SDO/AIA on 2015 March 15 and find the presence of oscillatory motion. We aim to demonstrate that interpreting this motion as a magneto hydrodynamic (MHD) wave is faulty. We also connect the decrease of the apparent velocity over time with the phase mixing process, which depends on the curvature of the magnetic field lines. Methods: By measuring the displacement of the prominence at different heights to calculate the apparent velocity, we show that the propagation slows down over time, in accordance with the theoretical work of Kaneko et al. We also show that this propagation speed drops below what is to be expected for even slow MHD waves for those circumstances. We use a modified Kippenhahn-Schlüter prominence model to calculate the curvature of the magnetic field and fit our observations accordingly. Results: Measuring three of the apparent waves, we get apparent velocities of 14, 8, and 4 km s-1. Fitting a simple model for the magnetic field configuration, we obtain that the filament is located 103 Mm below the magnetic centre. We also obtain that the scale of the magnetic field strength in the vertical direction plays no role in the concept of apparent superslow waves and that the moment of excitation of the waves happened roughly one oscillation period before the end of the eruption that excited the oscillation. Conclusions: Some of the observed phase velocities are lower than expected for slow modes for the circumstances, showing that they rather fit with the concept of apparent superslow propagation. A fit with our magnetic field model allows for inferring the magnetic geometry of the prominence. The movie attached to Fig. 1 is available at http://www.aanda.org
High frequency guided wave propagation in monocrystalline silicon wafers
Pizzolato, M.; Masserey, B.; Robyr, J. L.; Fromme, P.
2017-01-01
Monocrystalline silicon wafers are widely used in the photovoltaic industry for solar panels with high conversion efficiency. The cutting process can introduce micro-cracks in the thin wafers and lead to varying thickness. High frequency guided ultrasonic waves are considered for the structural monitoring of the wafers. The anisotropy of the monocrystalline silicon leads to variations of the wave characteristics, depending on the propagation direction relative to the crystal orientation. Full...
On the rogue wave propagation in ion pair superthermal plasma
Energy Technology Data Exchange (ETDEWEB)
Abdelwahed, H. G., E-mail: hgomaa-eg@yahoo.com, E-mail: hgomaa-eg@mans.edu.eg; Zahran, M. A. [Physics Department, College of Sciences and Humanities Studies Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj (Saudi Arabia); Theoretical Physics Group, Physics Department, Faculty of Science, Mansoura University, Mansoura (Egypt); El-Shewy, E. K., E-mail: emadshewy@yahoo.com; Elwakil, S. A. [Theoretical Physics Group, Physics Department, Faculty of Science, Mansoura University, Mansoura (Egypt)
2016-02-15
Effects of superthermal electron on the features of nonlinear acoustic waves in unmagnetized collisionless ion pair plasma with superthermal electrons have been examined. The system equations are reduced in the form of the nonlinear Schrodinger equation. The rogue wave characteristics dependences on the ionic density ratio (ν = n{sub –0}/n{sub +0}), ionic mass ratio (Q = m{sub +}/m{sub −}), and superthermality index (κ) are investigated. It is worth mentioning that the results present in this work could be applicable in the Earth's ionosphere plasmas.
International Nuclear Information System (INIS)
Orlov, Sergei N; Polivanov, Yurii N
2007-01-01
Dispersion phase matching curves and spectral distributions of the efficiency of difference frequency generation in the terahertz range are calculated for collinear propagation of interacting waves in zinc blende semiconductor crystals (ZnTe, CdTe, GaP, GaAs). The effect of the pump wavelength, the nonlinear crystal length and absorption in the terahertz range on the spectral distribution of the efficiency of difference frequency generation is analysed. (nonlinear optical phenomena)
Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation
Karney, C. F. F.
1977-01-01
Equations describing the nonlinear propagation of waves in an anisotropic plasma are rarely exactly soluble. However it is often possible to make approximations that reduce the exact equations into a simpler equation. The use of MACSYMA to make such approximations, and so reduce the equation describing lower hybrid waves into the nonlinear Schrodinger equation which is soluble by the inverse scattering method is demonstrated. MACSYMA is used at several stages in the calculation only because there is a natural division between calculations that are easiest done by hand, and those that are easiest done by machine.
Seismic Wave Propagation in Icy Ocean Worlds
Stähler, Simon C.; Panning, Mark P.; Vance, Steven D.; Lorenz, Ralph D.; van Driel, Martin; Nissen-Meyer, Tarje; Kedar, Sharon
2018-01-01
Seismology was developed on Earth and shaped our model of the Earth's interior over the twentieth century. With the exception of the Philae lander, all in situ extraterrestrial seismological effort to date was limited to other terrestrial planets. All have in common a rigid crust above a solid mantle. The coming years may see the installation of seismometers on Europa, Titan, and Enceladus, so it is necessary to adapt seismological concepts to the setting of worlds with global oceans covered in ice. Here we use waveform analyses to identify and classify wave types, developing a lexicon for icy ocean world seismology intended to be useful to both seismologists and planetary scientists. We use results from spectral-element simulations of broadband seismic wavefields to adapt seismological concepts to icy ocean worlds. We present a concise naming scheme for seismic waves and an overview of the features of the seismic wavefield on Europa, Titan, Ganymede, and Enceladus. In close connection with geophysical interior models, we analyze simulated seismic measurements of Europa and Titan that might be used to constrain geochemical parameters governing the habitability of a sub-ice ocean.
Propagation of acoustic waves in a stratified atmosphere, 1
Kalkofen, W.; Rossi, P.; Bodo, G.; Massaglia, S.
1994-01-01
This work is motivated by the chromospheric 3 minute oscillations observed in the K(sub 2v) bright points. We study acoustic gravity waves in a one-dimensional, gravitationally stratified, isothermal atmosphere. The oscillations are excited either by a velocity pulse imparted to a layer in an atmosphere of infinite vertical extent, or by a piston forming the lower boundary of a semi-infinite medium. We consider both linear and non-linear waves.
Propagation of waves in a multicomponent plasma having charged ...
Indian Academy of Sciences (India)
Propagation of waves in a multicomponent plasma having charged dust particles has been investigated by various authors in recent times as the presence of charged dust grains give rise to a new kind of modes called dust modes and it has wide applications in magneto- sphere and space plasma [1–3]. In fact, Rao et al [4] ...
Chiral metamaterials characterisation using the wave propagation retrieval method
DEFF Research Database (Denmark)
Andryieuski, Andrei; Lavrinenko, Andrei; Malureanu, Radu
2010-01-01
In this presentation we extend the wave propagation method for the retrieval of the effective properties to the case of chiral metamaterials with circularly polarised eigenwaves. The method is unambiguous, simple and provides bulk effective parameters. Advantages and constraints are discussed...
Surface wave propagation in a fluid-saturated incompressible ...
Indian Academy of Sciences (India)
dilatational and one rotational elastic waves in fluid-saturated porous solids. Biot theory ..... If the pore liquid is absent or gas is filled in the pores, then ρF ..... Biot M A (1962) Mechanics of deformation and acoustic propagation in porous media.
Seismic wave propagation in fractured media: A discontinuous Galerkin approach
De Basabe, Jonás D.
2011-01-01
We formulate and implement a discontinuous Galekin method for elastic wave propagation that allows for discontinuities in the displacement field to simulate fractures or faults using the linear- slip model. We show numerical results using a 2D model with one linear- slip discontinuity and different frequencies. The results show a good agreement with analytic solutions. © 2011 Society of Exploration Geophysicists.
Statistical characterization of wave propagation in mine environments
Bakir, Onur
2012-07-01
A computational framework for statistically characterizing electromagnetic (EM) wave propagation through mine tunnels and galleries is presented. The framework combines a multi-element probabilistic collocation (ME-PC) method with a novel domain-decomposition (DD) integral equation-based EM simulator to obtain statistics of electric fields due to wireless transmitters in realistic mine environments. © 2012 IEEE.
Wave propagation in coated cylinders with reference to fretting fatigue
Indian Academy of Sciences (India)
is to study stress wave propagation in cylinders with reference to high frequency fretting. ... The motivation for studying of fretting fatigue at higher frequency is to investigate the ... Hence focus in this work is given to thin rods and cylinders. The.
International Nuclear Information System (INIS)
Adcock, T. A. A.; Taylor, P. H.
2016-01-01
The non-linear Schrödinger equation and its higher order extensions are routinely used for analysis of extreme ocean waves. This paper compares the evolution of individual wave-packets modelled using non-linear Schrödinger type equations with packets modelled using fully non-linear potential flow models. The modified non-linear Schrödinger Equation accurately models the relatively large scale non-linear changes to the shape of wave-groups, with a dramatic contraction of the group along the mean propagation direction and a corresponding extension of the width of the wave-crests. In addition, as extreme wave form, there is a local non-linear contraction of the wave-group around the crest which leads to a localised broadening of the wave spectrum which the bandwidth limited non-linear Schrödinger Equations struggle to capture. This limitation occurs for waves of moderate steepness and a narrow underlying spectrum
Obliquely propagating cnoidal waves in a magnetized dusty plasma with variable dust charge
International Nuclear Information System (INIS)
Yadav, L. L.; Sayal, V. K.
2009-01-01
We have studied obliquely propagating dust-acoustic nonlinear periodic waves, namely, dust-acoustic cnoidal waves, in a magnetized dusty plasma consisting of electrons, ions, and dust grains with variable dust charge. Using reductive perturbation method and appropriate boundary conditions for nonlinear periodic waves, we have derived Korteweg-de Vries (KdV) equation for the plasma. It is found that the contribution to the dispersion due to the deviation from plasma approximation is dominant for small angles of obliqueness, while for large angles of obliqueness, the dispersion due to magnetic force becomes important. The cnoidal wave solution of the KdV equation is obtained. It is found that the frequency of the cnoidal wave depends on its amplitude. The effects of the magnetic field, the angle of obliqueness, the density of electrons, the dust-charge variation and the ion-temperature on the characteristics of the dust-acoustic cnoidal wave are also discussed. It is found that in the limiting case the cnoidal wave solution reduces to dust-acoustic soliton solution.
On propagation of axisymmetric waves in pressurized functionally graded elastomeric hollow cylinders
Wu, Bin; Su, Yipin; Liu, Dongying; Chen, Weiqiu; Zhang, Chuanzeng
2018-05-01
Soft materials can be designed with a functionally graded (FG) property for specific applications. Such material inhomogeneity can also be found in many soft biological tissues whose functionality is only partly understood to date. In this paper, we analyze the axisymmetric guided wave propagation in a pressurized FG elastomeric hollow cylinder. The cylinder is subjected to a combined action of axial pre-stretch and pressure difference applied to the inner and outer cylindrical surfaces. We consider both torsional waves and longitudinal waves propagating in the FG cylinder made of incompressible isotropic elastomer, which is characterized by the Mooney-Rivlin strain energy function but with the material parameters varying with the radial coordinate in an affine way. The pressure difference generates an inhomogeneous deformation field in the FG cylinder, which dramatically complicates the superimposed wave problem described by the small-on-large theory. A particularly efficient approach is hence employed which combines the state-space formalism for the incremental wave motion with the approximate laminate or multi-layer technique. Dispersion relations for the two types of axisymmetric guided waves are then derived analytically. The accuracy and convergence of the proposed approach is validated numerically. The effects of the pressure difference, material gradient, and axial pre-stretch on both the torsional and the longitudinal wave propagation characteristics are discussed in detail through numerical examples. It is found that the frequency of axisymmetric waves depends nonlinearly on the pressure difference and the material gradient, and an increase in the material gradient enhances the capability of the pressure difference to adjust the wave behavior in the FG cylinder. This work provides a theoretical guidance for characterizing FG soft materials by in-situ ultrasonic nondestructive evaluation and for designing tunable waveguides via material tailoring along
Ion acoustic solitary waves in a dusty plasma obliquely propagating to an external magnetic field
International Nuclear Information System (INIS)
Choi, Cheong Rim; Ryu, Chang-Mo; Lee, Nam C.; Lee, D.-Y.
2005-01-01
The nonlinear ion acoustic solitary wave in a magnetized dusty plasma, obliquely propagating to the embedding external magnetic field, is revisited. It is found that when the charge density of dust particles is high, the Sagdeev potential needs to be expanded up to δn 4 near n=1. In this case, it is shown that there could exist rarefactive ion acoustic solitary waves as well as the kink-type double layer solutions, in addition to the conventional hump-type ones found in the δn 3 expansion. The amplitude variations of ion acoustic solitary waves in a magnetized dusty plasma are also examined with respect to the change of the dust charge density and the wave directional angle
Earthquake wave propagation in immiscibly compressible porous soil
International Nuclear Information System (INIS)
Xue, S.; Kurita, S.; Izumi, M.
1993-01-01
This paper utilizes the formalism of the theory of immiscible compressible mixtures to formulate the wave propagation equation for the soil where the soil has been assumed as a binary mixture consisting of one solid phase and one fluid phase. The method is developed to solve the one dimensional wave equation by the above theory. The relations between the wave attenuating characteristic value Q and the volume fraction, the relative motion of two phases have been shown. It is concluded that based on such theory we can solve more precisely the soil behaviors while considering the interaction of structure and soil of immiscible mixture. (author)
Effective constants for wave propagation through partially saturated porous media
International Nuclear Information System (INIS)
Berryman, J.G.; Thigpen, L.
1985-01-01
The multipole scattering coefficients for elastic wave scattering from a spherical inhomogeneity in a fluid-saturated porous medium have been calculated. These coefficients may be used to obtain estimates of the effective macroscopic constants for long-wavelength propagation of elastic waves through partially saturated media. If the volume average of the single scattering from spherical bubbles of gas and liquid is required to vanish, the resulting equations determine the effective bulk modulus, density, and viscosity of the multiphase fluid filling the pores. The formula for the effective viscosity during compressional wave excitation is apparently new
Variational Boussinesq model for strongly nonlinear dispersive waves
Lawrence, C.; Adytia, D.; van Groesen, E.
2018-01-01
For wave tank, coastal and oceanic applications, a fully nonlinear Variational Boussinesq model with optimized dispersion is derived and a simple Finite Element implementation is described. Improving a previous weakly nonlinear version, high waves over flat and varying bottom are shown to be
Two-dimensional linear and nonlinear Talbot effect from rogue waves.
Zhang, Yiqi; Belić, Milivoj R; Petrović, Milan S; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Lu, Keqing; Zhang, Yanpeng
2015-03-01
We introduce two-dimensional (2D) linear and nonlinear Talbot effects. They are produced by propagating periodic 2D diffraction patterns and can be visualized as 3D stacks of Talbot carpets. The nonlinear Talbot effect originates from 2D rogue waves and forms in a bulk 3D nonlinear medium. The recurrences of an input rogue wave are observed at the Talbot length and at the half-Talbot length, with a π phase shift; no other recurrences are observed. Differing from the nonlinear Talbot effect, the linear effect displays the usual fractional Talbot images as well. We also find that the smaller the period of incident rogue waves, the shorter the Talbot length. Increasing the beam intensity increases the Talbot length, but above a threshold this leads to a catastrophic self-focusing phenomenon which destroys the effect. We also find that the Talbot recurrence can be viewed as a self-Fourier transform of the initial periodic beam that is automatically performed during propagation. In particular, linear Talbot effect can be viewed as a fractional self-Fourier transform, whereas the nonlinear Talbot effect can be viewed as the regular self-Fourier transform. Numerical simulations demonstrate that the rogue-wave initial condition is sufficient but not necessary for the observation of the effect. It may also be observed from other periodic inputs, provided they are set on a finite background. The 2D effect may find utility in the production of 3D photonic crystals.
Linear and nonlinear dynamics of current-driven waves in dusty plasmas
Ahmad, Ali; Ali Shan, S.; Haque, Q.; Saleem, H.
2012-09-01
The linear and nonlinear dynamics of a recently proposed plasma mode of dusty plasma is studied using kappa distribution for electrons. This electrostatic wave can propagate in the plasma due to the sheared flow of electrons and ions parallel to the external magnetic field in the presence of stationary dust. The coupling of this wave with the usual drift wave and ion acoustic wave is investigated. D'Angelo's mode is also modified in the presence of superthermal electrons. In the nonlinear regime, the wave can give rise to dipolar vortex structures if the shear in flow is weaker and tripolar vortices if the flow has steeper gradient. The results have been applied to Saturn's magnetosphere corresponding to negatively charged dust grains. But the theoretical model is applicable for positively charged dust as well. This work will be useful for future observations and studies of dusty environments of planets and comets.
Linear and nonlinear dynamics of current-driven waves in dusty plasmas
Energy Technology Data Exchange (ETDEWEB)
Ahmad, Ali [National Centre for Physics (NCP), Shahdara Valley Road, 44000 Islamabad (Pakistan); Department of Physics, COMSATS Institute of Information Technology (CIIT), Islamabad (Pakistan); Theoretical Plasma Physics Division, PINSTECH, P. O. Nilore, Islamabad (Pakistan); Ali Shan, S.; Haque, Q. [National Centre for Physics (NCP), Shahdara Valley Road, 44000 Islamabad (Pakistan); Theoretical Plasma Physics Division, PINSTECH, P. O. Nilore, Islamabad (Pakistan); Saleem, H. [National Centre for Physics (NCP), Shahdara Valley Road, 44000 Islamabad (Pakistan); Department of Physics, COMSATS Institute of Information Technology (CIIT), Islamabad (Pakistan)
2012-09-15
The linear and nonlinear dynamics of a recently proposed plasma mode of dusty plasma is studied using kappa distribution for electrons. This electrostatic wave can propagate in the plasma due to the sheared flow of electrons and ions parallel to the external magnetic field in the presence of stationary dust. The coupling of this wave with the usual drift wave and ion acoustic wave is investigated. D'Angelo's mode is also modified in the presence of superthermal electrons. In the nonlinear regime, the wave can give rise to dipolar vortex structures if the shear in flow is weaker and tripolar vortices if the flow has steeper gradient. The results have been applied to Saturn's magnetosphere corresponding to negatively charged dust grains. But the theoretical model is applicable for positively charged dust as well. This work will be useful for future observations and studies of dusty environments of planets and comets.
International Nuclear Information System (INIS)
Yi Sumin; Ryu, C.-M.; Yoon, Peter H.
2003-01-01
The nonlinear frequency shift of a low-frequency, coherent dust-acoustic wave in the presence of higher frequency dust-acoustic turbulence is investigated in the framework of weak turbulence theory. It is found that the frequency shift of the dust-acoustic wave in an unmagnetized dusty plasma is always positive irrespective of the propagation direction of the coherent wave. It is also found that turbulent waves propagating in the same direction as the coherent wave are shown to give rise to a much higher frequency shift than the opposite case. Finally, it is shown that the nonlinear frequency shift of a dust-acoustic wave is more pronounced than in the case of the customary ion-acoustic waves in fully ionized plasmas
International Nuclear Information System (INIS)
Sugaya, Reiji
1989-01-01
General expressions of the matrix elements for nonlinear wave-particle scattering (nonlinear Landau and cyclotron damping) of electromagnetic and electrostatic waves in a homogeneous magnetized plasma are derived from the Vlasov-Maxwell equations. The kinetic wave equations obtained for electromagnetic waves are expressed by four-order tensors in the rotating and cartesian coordinates. No restrictions are imposed on the propagation angle to a uniform magnetic field, the Larmor radius, the frequencies, or the wave numbers. By electrostatic approximation of the dielectric tensor and the matrix elements the kinetic wave equations can be applied to the case in which two scattering waves are electrostatic or they are partially electrostatic. Further, the matrix elements in the limit of parallel or perpendicular propagation to the magnetic field are given. (author)
Nonlinear self-modulation of ion-acoustic waves
International Nuclear Information System (INIS)
Ikezi, H.; Schwarzenegger, K.; Simons, A.L.; Ohsawa, Y.; Kamimura, T.
1978-01-01
The nonlinear evolution of an ion-acoustic wave packet is studied. Experimentally, it is found that (i) nonlinear phase modulation develops in the wave packet; (ii) the phase modulation, together with the dispersion effect, causes expansion and breaking of the wave packet; (iii) the ions trapped in the troughs of the wave potential introduce self-phase modulation; and (iv) the ion-acoustic wave is stable with respect to the modulational instability. Computer simulations have reproduced the experimental results. The physical picture and the model equation describing the wave evolution are discussed
International Nuclear Information System (INIS)
Sen, S.; Roy Chowdhury, A.
1989-06-01
The nonlinear Alfven waves are governed by the Vector Derivative nonlinear Schroedinger (VDNLS) equation, which for parallel or quasi parallel propagation reduces to the Derivative Nonlinear Schroedinger (DNLS) equation for the circularly polarized waves. We have formulated the Quantum Inverse problem for a new type of Nonlinear Schroedinger Equation which has many properties similar to the usual NLS problem but the structure of classical and quantum R matrix are distinctly different. The commutation rules of the scattering data are obtained and the Algebraic Bethe Ansatz is formulated to derive the eigenvalue equation for the energy of the excited states. 10 refs
Mao, Hanling; Zhang, Yuhua; Mao, Hanying; Li, Xinxin; Huang, Zhenfeng
2018-06-01
This paper presents the study of applying the nonlinear ultrasonic wave to evaluate the stress state of metallic materials under steady state. The pre-stress loading method is applied to guarantee components with steady stress. Three kinds of nonlinear ultrasonic experiments based on critically refracted longitudinal wave are conducted on components which the critically refracted longitudinal wave propagates along x, x1 and x2 direction. Experimental results indicate the second and third order relative nonlinear coefficients monotonically increase with stress, and the normalized relationship is consistent with simplified dislocation models, which indicates the experimental result is logical. The combined ultrasonic nonlinear parameter is proposed, and three stress evaluation models at x direction are established based on three ultrasonic nonlinear parameters, which the estimation error is below 5%. Then two stress detection models at x1 and x2 direction are built based on combined ultrasonic nonlinear parameter, the stress synthesis method is applied to calculate the magnitude and direction of principal stress. The results show the prediction error is within 5% and the angle deviation is within 1.5°. Therefore the nonlinear ultrasonic technique based on LCR wave could be applied to nondestructively evaluate the stress of metallic materials under steady state which the magnitude and direction are included.
Alfven wave propagation in a partially ionized plasma
International Nuclear Information System (INIS)
Watts, Christopher; Hanna, Jeremy
2004-01-01
Results from a laboratory study of the dispersion relation of Alfven waves propagating through a partially ionized plasma are presented. The plasma is generated using a helicon source, creating a high density, current-free discharge, where the source can be adjusted to one of several modes with varying neutral fraction. Depending on the neutral fraction, the measured dispersion curve of shear Alfven waves can change significantly. Measurement results are compared with theoretical predictions of the effect of neutral particles on Alfven wave propagation. In fitting the theory, the neutral fraction is independently estimated using two simple particle transport models, one collisionless, the other collisional. The two models predict comparable neutral fractions, and agree well with the neutral fraction required for the Alfven dispersion theory
Propagation and application of waves in the ionosphere.
Yeh, K. C.; Liu, C. H.
1972-01-01
This review deals with the propagation of waves, especially radio waves in the ionosphere. In the macroscopic electromagnetic theory, the mathematical structure of wave propagation problems depends entirely on the properties of the dielectric operator in a magnetically nonpermeable medium. These properties can be deduced from general discussions of symmetry and considerations of physical principles. When the medium is specifically the ionosphere, various physical phenomena may occur. Because of a large number of parameters, it is desirable to define a parameter space. A point in the parameter space corresponds to a specific plasma. The parameter space is subdivided into regions whose boundaries correspond to conditions of resonance and cutoff. As the point crosses these boundaries, the refractive index surface transforms continuously.
Quasinormal modes and classical wave propagation in analogue black holes
International Nuclear Information System (INIS)
Berti, Emanuele; Cardoso, Vitor; Lemos, Jose P.S.
2004-01-01
Many properties of black holes can be studied using acoustic analogues in the laboratory through the propagation of sound waves. We investigate in detail sound wave propagation in a rotating acoustic (2+1)-dimensional black hole, which corresponds to the 'draining bathtub' fluid flow. We compute the quasinormal mode frequencies of this system and discuss late-time power-law tails. Because of the presence of an ergoregion, waves in a rotating acoustic black hole can be superradiantly amplified. We also compute superradiant reflection coefficients and instability time scales for the acoustic black hole bomb, the equivalent of the Press-Teukolsky black hole bomb. Finally we discuss quasinormal modes and late-time tails in a nonrotating canonical acoustic black hole, corresponding to an incompressible, spherically symmetric (3+1)-dimensional fluid flow
Nonlinear waves in bipolar complex viscous astroclouds
Karmakar, P. K.; Haloi, A.
2017-05-01
A theoretical evolutionary model to analyze the dynamics of strongly nonlinear waves in inhomogeneous complex astrophysical viscous clouds on the gravito-electrostatic scales of space and time is procedurally set up. It compositionally consists of warm lighter electrons and ions (Boltzmanian); and cold massive bi-polar dust grains (inertial fluids) alongside vigorous neutral dynamics in quasi-neutral hydrodynamic equilibrium. Application of the Sagdeev pseudo-potential method reduces the inter-coupled structure equations into a pair of intermixed forced Korteweg-de Vries-Burgers (f-KdVB) equations. The force-terms are self-consistently sourced by inhomogeneous gravito-electrostatic interplay. A numerical illustrative shape-analysis based on judicious astronomical parametric platform shows the electrostatic waves evolving as compressive dispersive shock-like eigen-modes. A unique transition from quasi-monotonic to non-monotonic oscillatory compressive shock-like patterns is found to exist. In contrast, the self-gravitational and effective perturbations grow purely as non-monotonic compressive oscillatory shock-like structures with no such transitory features. It is seen that the referral frame velocity acts as amplitude-reducing agent (stabilizing source) for the electrostatic fluctuations solely. A comparison in the prognostic light of various earlier satellite-based observations and in-situ measurements is presented. The paper ends up with synoptic highlights on the main implications and non-trivial applications in the interstellar space and cosmic plasma environments leading to bounded structure formation.
A Numerical Implementation of a Nonlinear Mild Slope Model for Shoaling Directional Waves
Directory of Open Access Journals (Sweden)
Justin R. Davis
2014-02-01
Full Text Available We describe the numerical implementation of a phase-resolving, nonlinear spectral model for shoaling directional waves over a mild sloping beach with straight parallel isobaths. The model accounts for non-linear, quadratic (triad wave interactions as well as shoaling and refraction. The model integrates the coupled, nonlinear hyperbolic evolution equations that describe the transformation of the complex Fourier amplitudes of the deep-water directional wave field. Because typical directional wave spectra (observed or produced by deep-water forecasting models such as WAVEWATCH III™ do not contain phase information, individual realizations are generated by associating a random phase to each Fourier mode. The approach provides a natural extension to the deep-water spectral wave models, and has the advantage of fully describing the shoaling wave stochastic process, i.e., the evolution of both the variance and higher order statistics (phase correlations, the latter related to the evolution of the wave shape. The numerical implementation (a Fortran 95/2003 code includes unidirectional (shore-perpendicular propagation as a special case. Interoperability, both with post-processing programs (e.g., MATLAB/Tecplot 360 and future model coupling (e.g., offshore wave conditions from WAVEWATCH III™, is promoted by using NetCDF-4/HD5 formatted output files. The capabilities of the model are demonstrated using a JONSWAP spectrum with a cos2s directional distribution, for shore-perpendicular and oblique propagation. The simulated wave transformation under combined shoaling, refraction and nonlinear interactions shows the expected generation of directional harmonics of the spectral peak and of infragravity (frequency <0.05 Hz waves. Current development efforts focus on analytic testing, development of additional physics modules essential for applications and validation with laboratory and field observations.
Modal analysis of wave propagation in dispersive media
Abdelrahman, M. Ismail; Gralak, B.
2018-01-01
Surveys on wave propagation in dispersive media have been limited since the pioneering work of Sommerfeld [Ann. Phys. 349, 177 (1914), 10.1002/andp.19143491002] by the presence of branches in the integral expression of the wave function. In this article a method is proposed to eliminate these critical branches and hence to establish a modal expansion of the time-dependent wave function. The different components of the transient waves are physically interpreted as the contributions of distinct sets of modes and characterized accordingly. Then, the modal expansion is used to derive a modified analytical expression of the Sommerfeld precursor improving significantly the description of the amplitude and the oscillating period up to the arrival of the Brillouin precursor. The proposed method and results apply to all waves governed by the Helmholtz equations.
Transfer and dissipation of energy during wave group propagation on a gentle beach slope
Padilla, Enrique M.; Alsina, José M.
2017-08-01
The propagation of bichromatic wave groups over a constant 1:100 beach slope and the influence of the group modulation is presented. The modulation is controlled by varying the group frequency, fg, which is shown to remarkably affect the energy transfer to high and low frequency components. The growth of the high frequency (hf) wave skewness increases when fg decreases. This is explained by nonlinear coupling between the primary frequencies, which results in a larger growth of hf components as fg decreases, causing the hf waves to break earlier. Due to high spatial resolution, wave tracking has provided an accurate measurement of the varying breakpoint. These breaking locations are very well described (R2>0.91) by the wave-height to effective-depth ratio (γ). However, for any given Iribarren number, this γ is shown to increase with fg. Therefore, a modified Iribarren number is proposed to include the grouping structure, leading to a considerable improvement in reproducing the measured γ-values. Within the surf zone, the behavior of the Incident Long Wave also depends on the group modulation. For low fg conditions, the lf wave decays only slightly by transferring energy back to the hf wave components. However, for high fg wave conditions, strong dissipation of low frequency (lf) components occurs close to the shoreline associated with lf wave breaking. This mechanism is explained by the growth of the lf wave height, induced partly by the self-self interaction of fg, and partly by the nonlinear coupling between the primary frequencies and fg.
Nonlinear Modeling and Analysis of Pressure Wave inside CEUP Fuel Pipeline
Directory of Open Access Journals (Sweden)
Qaisar Hayat
2014-01-01
Full Text Available Operating conditions dependent large pressure variations are one of the working characteristics of combination electronic unit pump (CEUP fuel injection system for diesel engines. We propose a precise and accurate nonlinear numerical model of pressure inside HP fuel pipeline of CEUP using wave equation (WE including both viscous and frequency dependent frictions. We have proved that developed hyperbolic approximation gives more realistic description of pressure wave as compared to classical viscous damped wave equation. Frictional effects of various frequencies on pressure wave have been averaged out across valid frequencies to represent the combined effect of all frequencies on pressure wave. Dynamic variations of key fuel properties including density, acoustic wave speed, and bulk modulus with varying pressures have also been incorporated. Based on developed model we present analysis on effect of fuel pipeline length on pressure wave propagation and variation of key fuel properties with both conventional diesel and alternate fuel rapeseed methyl ester (RME for CEUP pipeline.
A two dimension model of the uterine electrical wave propagation.
Rihana, S; Lefrançois, E; Marque, C
2007-01-01
The uterus, usually quiescent during pregnancy, exhibits forceful contractions at term leading to delivery. These contractions are caused by the synchronized propagation of electrical waves from the pacemaker cells to its neighbors inducing the whole coordinated contraction of the uterus wall leading to labor. In a previous work, we simulate the electrical activity of a single uterine cell by a set of ordinary differential equations. Then, this model has been used to simulate the electrical activity propagation. In the present work, the uterine cell tissue is assumed to have uniform and isotropic propagation, and constant electrical membrane properties. The stability of the numerical solution imposes the choice of a critical temporal step. A wave starts at a pacemaker cell; this electrical activity is initiated by the injection of an external stimulation current to the cell membrane. We observe synchronous wave propagation for axial resistance values around 0.5 GOmega or less and propoagation blocking for values greater than 0.7 GOmega. We compute the conduction velocity of the excitation, for different axial resistance values, and obtain a velocity about 10 cm/sec, approaching the one described by the literature for the rat at end of term.
New method for rekindling the nonlinear solitary waves in Maxwellian complex space plasma
Das, G. C.; Sarma, Ridip
2018-04-01
Our interest is to study the nonlinear wave phenomena in complex plasma constituents with Maxwellian electrons and ions. The main reason for this consideration is to exhibit the effects of dust charge fluctuations on acoustic modes evaluated by the use of a new method. A special method (G'/G) has been developed to yield the coherent features of nonlinear waves augmented through the derivation of a Korteweg-de Vries equation and found successfully the different nature of solitons recognized in space plasmas. Evolutions have shown with the input of appropriate typical plasma parameters to support our theoretical observations in space plasmas. All conclusions are in good accordance with the actual occurrences and could be of interest to further the investigations in experiments and satellite observations in space. In this paper, we present not only the model that exhibited nonlinear solitary wave propagation but also a new mathematical method to the execution.
Nonlinear interaction of waves in an inhomogeneous plasma
International Nuclear Information System (INIS)
Istomin, Ya.N.
1988-01-01
Nonlinear wave processes in a weakly inhomogeneous plasma are considered. A quasilinear equation is derived which takes into account the effect of the waves on resonance particles, provided that the inhomogeneity appreciably affects the nature of the resonance interaction. Three-wave interaction is investigated under the same conditions. As an example, the nonlinear interaction in a relativistic plasma moving along a strong curvilinear magnetic field is considered
Topics in the Analysis of Shear-Wave Propagation in Oblique-Plate Impact Tests
National Research Council Canada - National Science Library
Scheidler, Mike
2007-01-01
This report addresses several topics in the theoretical analysis of shock waves, acceleration waves, and centered simple waves, with emphasis on the propagation of shear waves generated in oblique-plate impact tests...
International Nuclear Information System (INIS)
Ryutova, M.
1990-08-01
Effects of strong and random inhomogeneities of the magnetic fields, plasma density, and temperature in the solar atmosphere on the properties of magnetoacoustic waves of arbitrary amplitudes are studied. The procedure which allows one to obtain the averaged equation containing the nonlinearity of a wave, dispersion properties of a system, and dissipative effects is described. It is shown that depending on the statistical properties of the medium, different scenarios of wave propagation arise: in the predominance of dissipative effects the primary wave is damped away in the linear stage and the efficiency of heating due to inhomogeneities is much greater than that in homogeneous medium. Depending on the interplay of nonlinear and dispersion effects, the process of heating can be afforded through the formation of shocks or through the storing of energy in a system of solitons which are later damped away. Our computer simulation supports and extends the above theoretical investigations. In particular the enhanced dissipation of waves due to the strong and random inhomogeneities is observed and this is more pronounced for shorter waves
Temporal Talbot effect in propagation of attosecond electron waves
International Nuclear Information System (INIS)
Varro, S.
2010-01-01
Complete text of publication follows. The rapid development in extreme strong-field and extreme short-pulse laser physics provide us with many potentials to explore the dynamics of fundamental processes taking place in light-matter interactions and in propagation of electromagnetic or matter waves. The present paper discusses the propagation of above-threshold electron waves generated by (not necessary ultra-short) strong laser fields. Recently we have shown that - in analogy with the formation of attosecond light pulses by interference of high-order harmonics - the wave components of photoelectrons are naturally assembled in attosecond spikes, through the Fourier synthesis of these de Broglie waves. We would like to emphasize that the proposed scheme does not presupposes an a priori ultrashort excitation. Owing to the inherent dispersion of electron waves even in vacuum, the clean attosecond structure (emanating perpendicularly from a metal target surface) is gradually spoiled due to destructive interference. Fortunately the collapsed fine structure recovers itself at certain distances from the source within well-defined 'revival layers'. This is a temporal analogon of the optical Talbot effect representing the self-imaging of a grating, which is illuminated by stationary plane waves, in the near field. The 'collaps bands' and the 'revival layers' introduced in ref. 3 have been found merely on the basis of some attosecond layers turned out to show certain regularities. In the meantime we have derived approximate analytic formulae for the propagation characteristics, with the help of which we can keep track of the locations of the 'collaps bands' and the 'revival layers' on a larger scale. We shall report on these semiclassical results, and also discuss their possible connection with the recently found entropy remnants in multiphoton Compton scattering by electronic wave packets. Acknowledgement. This work has been supported by the Hungarian National Scientific
Nonlinear physics of shear Alfvén waves
International Nuclear Information System (INIS)
Zonca, Fulvio; Chen, Liu
2014-01-01
Shear Alfvén waves (SAW) play fundamental roles in thermonuclear plasmas of fusion interest, since they are readily excited by energetic particles in the MeV range as well as by the thermal plasma components. Thus, understanding fluctuation induced transport in burning plasmas requires understanding nonlinear SAW physics. There exist two possible routes to nonlinear SAW physics: (i) wave-wave interactions and the resultant spectral energy transfer; (ii) nonlinear wave-particle interactions of SAW instabilities with energetic particles. Within the first route, it is advantageous to understand and describe nonlinear processes in term of proximity of the system to the Alfvénic state, where wave-wave interactions are minimized due to the cancellation of Reynolds and Maxwell stresses. Here, various wave-wave nonlinear dynamics are elucidated in terms of how they break the Alfvénic state. In particular, we discuss the qualitative and quantitative modification of the SAW parametric decay process due to finite ion compressibility and finite ion Larmor radius. We also show that toroidal geometry plays a crucial role in the nonlinear excitation of zonal structures by Alfvén eigenmodes. Within the second route, the coherent nonlinear dynamics of structures in the energetic particle phase space, by which secular resonant particle transport can occur on meso- and macro-scales, must be addressed and understood. These 'nonlinear equilibria' or 'phase-space zonal structures' dynamically evolve on characteristic (fluctuation induced) turbulent transport time scales, which are generally of the same order of the nonlinear time scale of the underlying fluctuations. In this work, we introduce the general structure of nonlinear Schrödinger equations with complex integro-differential nonlinear terms, which govern these physical processes. To elucidate all these aspects, theoretical analyses are presented together with numerical simulation results
Nonlinear physics of shear Alfvén waves
Zonca, Fulvio; Chen, Liu
2014-02-01
Shear Alfvén waves (SAW) play fundamental roles in thermonuclear plasmas of fusion interest, since they are readily excited by energetic particles in the MeV range as well as by the thermal plasma components. Thus, understanding fluctuation induced transport in burning plasmas requires understanding nonlinear SAW physics. There exist two possible routes to nonlinear SAW physics: (i) wave-wave interactions and the resultant spectral energy transfer; (ii) nonlinear wave-particle interactions of SAW instabilities with energetic particles. Within the first route, it is advantageous to understand and describe nonlinear processes in term of proximity of the system to the Alfvénic state, where wave-wave interactions are minimized due to the cancellation of Reynolds and Maxwell stresses. Here, various wave-wave nonlinear dynamics are elucidated in terms of how they break the Alfvénic state. In particular, we discuss the qualitative and quantitative modification of the SAW parametric decay process due to finite ion compressibility and finite ion Larmor radius. We also show that toroidal geometry plays a crucial role in the nonlinear excitation of zonal structures by Alfvén eigenmodes. Within the second route, the coherent nonlinear dynamics of structures in the energetic particle phase space, by which secular resonant particle transport can occur on meso- and macro-scales, must be addressed and understood. These "nonlinear equilibria" or "phase-space zonal structures" dynamically evolve on characteristic (fluctuation induced) turbulent transport time scales, which are generally of the same order of the nonlinear time scale of the underlying fluctuations. In this work, we introduce the general structure of nonlinear Schrödinger equations with complex integro-differential nonlinear terms, which govern these physical processes. To elucidate all these aspects, theoretical analyses are presented together with numerical simulation results.
Backscattering and Nonparaxiality Arrest Collapse of Damped Nonlinear Waves
Fibich, G.; Ilan, B.; Tsynkov, S.
2002-01-01
The critical nonlinear Schrodinger equation (NLS) models the propagation of intense laser light in Kerr media. This equation is derived from the more comprehensive nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. It is known that if the input power of the laser beam (i.e., L(sub 2) norm of the initial solution) is sufficiently high, then the NLS model predicts that the beam will self-focus to a point (i.e.. collapse) at a finite propagation distance. Mathematically, this behavior corresponds to the formation of a singularity in the solution of the NLS. A key question which has been open for many years is whether the solution to the NLH, i.e., the 'parent' equation, may nonetheless exist and remain regular everywhere, in particular for those initial conditions (input powers) that lead to blowup in the NLS. In the current study, we address this question by introducing linear damping into both models and subsequently comparing the numerical solutions of the damped NLH (boundary-value problem) with the corresponding solutions of the damped NLS (initial-value problem). Linear damping is introduced in much the same way as done when analyzing the classical constant-coefficient Helmholtz equation using the limiting absorption principle. Numerically, we have found that it provides a very efficient tool for controlling the solutions of both the NLH and NHS. In particular, we have been able to identify initial conditions for which the NLS solution does become singular. whereas the NLH solution still remains regular everywhere. We believe that our finding of a larger domain of existence for the NLH than that for the NLS is accounted for by precisely those mechanisms, that have been neglected when deriving the NLS from the NLH, i.e., nonparaxiality and backscattering.
Nonlinear Whistler Wave Physics in the Radiation Belts
Crabtree, Chris
2016-10-01
Wave particle interactions between electrons and whistler waves are a dominant mechanism for controlling the dynamics of energetic electrons in the radiation belts. They are responsible for loss, via pitch-angle scattering of electrons into the loss cone, and energization to millions of electron volts. It has previously been theorized that large amplitude waves on the whistler branch may scatter their wave-vector nonlinearly via nonlinear Landau damping leading to important consequences for the global distribution of whistler wave energy density and hence the energetic electrons. It can dramatically reduce the lifetime of energetic electrons in the radiation belts by increasing the pitch angle scattering rate. The fundamental building block of this theory has now been confirmed through laboratory experiments. Here we report on in situ observations of wave electro-magnetic fields from the EMFISIS instrument on board NASA's Van Allen Probes that show the signatures of nonlinear scattering of whistler waves in the inner radiation belts. In the outer radiation belts, whistler mode chorus is believed to be responsible for the energization of electrons from 10s of Kev to MeV energies. Chorus is characterized by bursty large amplitude whistler mode waves with frequencies that change as a function of time on timescales corresponding to their growth. Theories explaining the chirping have been developed for decades based on electron trapping dynamics in a coherent wave. New high time resolution wave data from the Van Allen probes and advanced spectral techniques are revealing that the wave dynamics is highly structured, with sub-elements consisting of multiple chirping waves with discrete frequency hops between sub-elements. Laboratory experiments with energetic electron beams are currently reproducing the complex frequency vs time dynamics of whistler waves and in addition revealing signatures of wave-wave and beat-wave nonlinear wave-particle interactions. These new data
Boussinesq Modeling of Wave Propagation and Runup over Fringing Coral Reefs, Model Evaluation Report
National Research Council Canada - National Science Library
Demirbilek, Zeki; Nwogu, Okey G
2007-01-01
..., for waves propagating over fringing reefs. The model evaluation had two goals: (a) investigate differences between laboratory and field characteristics of wave transformation processes over reefs, and (b...
Nonlinear density waves in a marginally stable gravitating disk
International Nuclear Information System (INIS)
Korchagin, V.I.
1986-01-01
The evolution of short nonlinear density waves in a disk at the stability limit is studied for arbitrary values of the radial wave number k/sub r/. For waves with wave numbers that do not lie at the minimum of the dispersion curve, the behavior of the amplitude is described by a nonlinear parabolic equation; however, stationary soliton solutions cannot exist in such a system since there is no dispersion spreading of a packet. For wave numbers lying at the minimum of the dispersion curve, soliton structures with determined amplitude are possible. In stable gravitating disks and in a disk at the stability limit, two physically different types of soliton can exist
Nonlinear Alfvén Waves in a Vlasov Plasma
DEFF Research Database (Denmark)
Bell, T.F.
1965-01-01
Stationary solutions to the nonlinear Vlasov—Boltzmann equations are considered which represent one-dimensional electromagnetic waves in a hot magnetoplasma. These solutions appear in arbitrary reference frames as circularly polarized, sinusoidal waves of unlimited amplitude, i.e., as nonlinear...... Alfvén waves. Solutions are found implicitly by deriving a set of integral dispersion relations which link the wave characteristics with the particle distribution functions. A physical discussion is given of the way in which the Alfvén waves can trap particles, and it is shown that the presence...
Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes
DEFF Research Database (Denmark)
Zhang, H.W.; Schäffer, Hemming Andreas
2007-01-01
An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....
The energy transport by the propagation of sound waves in wave guides with a moving medium
le Grand, P.
1977-01-01
The problem of the propagation of sound waves radiated by a source in a fluid moving with subsonic velocity between two parallel walls or inside a cylindrical tube is considered in [2], The most interesting thing of this problem is that waves may occur with constant amplitude coming from infinity.
Nonlinear interaction of the surface waves at a plasma boundary
International Nuclear Information System (INIS)
Dolgopolov, V.V.; El-Naggar, I.A.; Hussein, A.M.; Khalil, Sh.M.
1976-01-01
Amplitudes of electromagnetic waves with combination frequencies, radiating from the plasma boundary due to nonlinear interaction of the surface waves, have been found. Previous papers on this subject did not take into account that the tangential components of the electric field of waves with combination frequencies were discontinuous at the plasma boundary. (Auth.)
Energy Technology Data Exchange (ETDEWEB)
Sazonov, S. V., E-mail: sazonov.sergey@gmail.com [National Research Centre “Kurchatov Institute,” (Russian Federation); Ustinov, N. V., E-mail: n-ustinov@mail.ru [Moscow State University of Railways, Kaliningrad Branch (Russian Federation)
2017-02-15
The nonlinear propagation of extremely short electromagnetic pulses in a medium of symmetric and asymmetric molecules placed in static magnetic and electric fields is theoretically studied. Asymmetric molecules differ in that they have nonzero permanent dipole moments in stationary quantum states. A system of wave equations is derived for the ordinary and extraordinary components of pulses. It is shown that this system can be reduced in some cases to a system of coupled Ostrovsky equations and to the equation intagrable by the method for an inverse scattering transformation, including the vector version of the Ostrovsky–Vakhnenko equation. Different types of solutions of this system are considered. Only solutions representing the superposition of periodic solutions are single-valued, whereas soliton and breather solutions are multivalued.
Book Review: Wave propagation in materials and structures
Ferguson, Neil
2018-02-01
This book's remit is to provide a very extensive and detailed coverage of many one and two dimensional wave propagating behaviours primarily in structures such as rods, beams and plates of complexity covering laminated, sandwich plates, smart configurations and complex material compositions. This is potentially where the detailed presentation, including the derivation of the governing equations of motion from first principles, i.e. Hamilton's method, for example, distracts slightly from the subsequent wave solutions, the numerical simulations showing time responses, the wave speeds and importantly the dispersion characteristics. The author introduces a number of known analytical methodologies and means to obtain wave solutions, including the spectral finite element approach and also provides numerical examples showing the approach being applied to joints and framed structures.
Numerical study of propagation properties of surface plasmon polaritons in nonlinear media
Sagor, Rakibul Hasan
2016-03-29
We present a time-domain algorithm for simulating nonlinear propagation of surface plasmon polaritons (SPPs) in chalcogenide glass. Due to the high non-linearity property and strong dispersion and confinement chalcogenide glasses are widely known as ultrafast nonlinear materials. We have used the finite difference time domain (FDTD) method to develop the simulation algorithm for the current analysis. We have modeled the frequency dependent dispersion properties and third order nonlinearity property of chalcogenide glass utilizing the general polarization algorithm merged in the auxiliary differential equation (ADE) method. The propagation dynamics of the whole structure with and without third order nonlinearity property of chalcogenide glass have been simulated and the effect of nonlinearity on the propagation properties of SPP has been investigated. © 2016 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.
Generation of Caustics and Rogue Waves from Nonlinear Instability.
Safari, Akbar; Fickler, Robert; Padgett, Miles J; Boyd, Robert W
2017-11-17
Caustics are phenomena in which nature concentrates the energy of waves and may exhibit rogue-type behavior. Although they are known mostly in optics, caustics are intrinsic to all wave phenomena. As we demonstrate in this Letter, the formation of caustics and consequently rogue events in linear systems requires strong phase fluctuations. We show that nonlinear phase shifts can generate sharp caustics from even small fluctuations. Moreover, in that the wave amplitude increases dramatically in caustics, nonlinearity is usually inevitable. We perform an experiment in an optical system with Kerr nonlinearity, simulate the results based on the nonlinear Schrödinger equation, and achieve perfect agreement. As the same theoretical framework is used to describe other wave systems such as large-scale water waves, our results may also aid the understanding of ocean phenomena.
Nonlinear dynamics of resonant electrons interacting with coherent Langmuir waves
Tobita, Miwa; Omura, Yoshiharu
2018-03-01
We study the nonlinear dynamics of resonant particles interacting with coherent waves in space plasmas. Magnetospheric plasma waves such as whistler-mode chorus, electromagnetic ion cyclotron waves, and hiss emissions contain coherent wave structures with various discrete frequencies. Although these waves are electromagnetic, their interaction with resonant particles can be approximated by equations of motion for a charged particle in a one-dimensional electrostatic wave. The equations are expressed in the form of nonlinear pendulum equations. We perform test particle simulations of electrons in an electrostatic model with Langmuir waves and a non-oscillatory electric field. We solve equations of motion and study the dynamics of particles with different values of inhomogeneity factor S defined as a ratio of the non-oscillatory electric field intensity to the wave amplitude. The simulation results demonstrate deceleration/acceleration, thermalization, and trapping of particles through resonance with a single wave, two waves, and multiple waves. For two-wave and multiple-wave cases, we describe the wave-particle interaction as either coherent or incoherent based on the probability of nonlinear trapping.
Modelling Acoustic Wave Propagation in Axisymmetric Varying-Radius Waveguides
DEFF Research Database (Denmark)
Bæk, David; Willatzen, Morten
2008-01-01
A computationally fast and accurate model (a set of coupled ordinary differential equations) for fluid sound-wave propagation in infinite axisymmetric waveguides of varying radius is proposed. The model accounts for fluid heat conduction and fluid irrotational viscosity. The model problem is solved...... by expanding solutions in terms of cross-sectional eigenfunctions following Stevenson’s method. A transfer matrix can be easily constructed from simple model responses of a given waveguide and later used in computing the response to any complex wave input. Energy losses due to heat conduction and viscous...
On the lamb wave propagation in anisotropic laminated composite plates
International Nuclear Information System (INIS)
Park, Soo Keun; Jeong, Hyun Jo; Kim, Moon Saeng
1998-01-01
This paper examines the propagation of Lamb (or plate) waves in anisotropic laminated composite plates. The dispersion relations are explicitly derived using the classical plate theory (CLT), the first-order shear deformation theory (FSDT) and the exact solution (ES), Attention is paid to the lowest antisymmetric (flexural) and lowest symmetric(extensional) modes in the low frequency, long wavelength limit. Different values of shear correction factor were tested in FSDT and comparisons between flexural wave dispersion curves were made with exact results to asses the range of validity of approximate plate theories in the frequency domain.
Wave propagation in a quasi-chemical equilibrium plasma
Fang, T.-M.; Baum, H. R.
1975-01-01
Wave propagation in a quasi-chemical equilibrium plasma is studied. The plasma is infinite and without external fields. The chemical reactions are assumed to result from the ionization and recombination processes. When the gas is near equilibrium, the dominant role describing the evolution of a reacting plasma is played by the global conservation equations. These equations are first derived and then used to study the small amplitude wave motion for a near-equilibrium situation. Nontrivial damping effects have been obtained by including the conduction current terms.
Nonlinear acoustic waves in micro-inhomogeneous solids
Nazarov, Veniamin
2014-01-01
Nonlinear Acoustic Waves in Micro-inhomogeneous Solids covers the broad and dynamic branch of nonlinear acoustics, presenting a wide variety of different phenomena from both experimental and theoretical perspectives. The introductory chapters, written in the style of graduate-level textbook, present a review of the main achievements of classic nonlinear acoustics of homogeneous media. This enables readers to gain insight into nonlinear wave processes in homogeneous and micro-inhomogeneous solids and compare it within the framework of the book. The subsequent eight chapters covering: Physical m
Carcione, José M
2007-01-01
This book examines the differences between an ideal and a real description of wave propagation, where ideal means an elastic (lossless), isotropic and single-phase medium, and real means an anelastic, anisotropic and multi-phase medium. The analysis starts by introducing the relevant stress-strain relation. This relation and the equations of momentum conservation are combined to give the equation of motion. The differential formulation is written in terms of memory variables, and Biot's theory is used to describe wave propagation in porous media. For each rheology, a plane-wave analysis is performed in order to understand the physics of wave propagation. The book contains a review of the main direct numerical methods for solving the equation of motion in the time and space domains. The emphasis is on geophysical applications for seismic exploration, but researchers in the fields of earthquake seismology, rock acoustics, and material science - including many branches of acoustics of fluids and solids - may als...
Simulation of the acoustic wave propagation using a meshless method
Directory of Open Access Journals (Sweden)
Bajko J.
2017-01-01
Full Text Available This paper presents numerical simulations of the acoustic wave propagation phenomenon modelled via Linearized Euler equations. A meshless method based on collocation of the strong form of the equation system is adopted. Moreover, the Weighted least squares method is used for local approximation of derivatives as well as stabilization technique in a form of spatial ltering. The accuracy and robustness of the method is examined on several benchmark problems.
Singular value decomposition methods for wave propagation analysis
Czech Academy of Sciences Publication Activity Database
Santolík, Ondřej; Parrot, M.; Lefeuvre, F.
2003-01-01
Roč. 38, č. 1 (2003), s. 10-1-10-13 ISSN 0048-6604 R&D Projects: GA ČR GA205/01/1064 Grant - others:Barrande(CZ) 98039/98055 Institutional research plan: CEZ:AV0Z3042911; CEZ:MSM 113200004 Keywords : wave propagation * singular value decomposition Subject RIV: DG - Athmosphere Sciences, Meteorology Impact factor: 0.832, year: 2003
Wave propagation in layered anisotropic media with application to composites
Nayfeh, AH
1995-01-01
Recent advances in the study of the dynamic behavior of layered materials in general, and laminated fibrous composites in particular, are presented in this book. The need to understand the microstructural behavior of such classes of materials has brought a new challenge to existing analytical tools. This book explores the fundamental question of how mechanical waves propagate and interact with layered anisotropic media. The chapters are organized in a logical sequence depending upon the complexity of the physical model and its mathematical treatment.
Wave propagation in fluids models and numerical techniques
Guinot, Vincent
2012-01-01
This second edition with four additional chapters presents the physical principles and solution techniques for transient propagation in fluid mechanics and hydraulics. The application domains vary including contaminant transport with or without sorption, the motion of immiscible hydrocarbons in aquifers, pipe transients, open channel and shallow water flow, and compressible gas dynamics. The mathematical formulation is covered from the angle of conservation laws, with an emphasis on multidimensional problems and discontinuous flows, such as steep fronts and shock waves. Finite
Some remarks on coherent nonlinear coupling of waves in plasmas
International Nuclear Information System (INIS)
Wilhelmsson, H.
1976-01-01
The analysis of nonlinear processes in plasma physics has given rise to a basic set of coupled equations. These equations describe the coherent nonlinear evolution of plasma waves. In this paper various possibilities of analysing these equations are discussed and inherent difficulties in the description of nonlinear interactions between different types of waves are pointed out. Specific examples of stimulated excitation of waves are considered. These are the parametric excitation of hybrid resonances in hot magnetized multi-ion component plasma and laser-plasma interactions. (B.D.)
Radio Wave Propagation Handbook for Communication on and Around Mars
Ho, Christian; Golshan, Nasser; Kliore, Arvydas
2002-01-01
This handbook examines the effects of the Martian environment on radio wave propagation on Mars and in the space near the planet. The environmental effects include these from the Martian atmosphere, ionosphere, global dust storms, aerosols, clouds, and geomorphologic features. Relevant Martian environmental parameters were extracted from the measurements of Mars missions during the past 30 years, especially from Mars Pathfinder and Mars Global Surveyor. The results derived from measurements and analyses have been reviewed through an extensive literature search. The updated parameters have been theoretically analyzed to study their effects on radio propagation. This handbook also provides basic information about the entire telecommunications environment on and around Mars for propagation researchers, system engineers, and link analysts. Based on these original analyses, some important recommendations have been made, including the use of the Martian ionosphere as a reflector for Mars global or trans-horizon communication between future Martian colonies, reducing dust storm scattering effects, etc. These results have extended our wave propagation knowledge to a planet other than Earth; and the tables, models, and graphics included in this handbook will benefit telecommunication system engineers and scientific researchers.