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 transient wave propagation in homgeneous plasmas
International Nuclear Information System (INIS)
Thomsen, K.
1983-01-01
The transient phenomena associated with the propagation of nonlinear high frequency waves in homogeneous and isotropic or anisotropic plasma are considered. The basic equation for the different wave types included in this analysis are derived by using a two-fluid description of the plasma. Before discussing the importance of different nonlinearities the main results from a linear treatment are given. Generation of harmonic and local changes in the plasma frequency caused by ponderomotive forces are the nonlinear phenomena which are included in the nonlinear treatment. Generation of harmonics is only important for extraordinary waves and this case is discussed in detail. The density perturbations are described either as forced non-dispersive or as forced dispersive low frequency electrostatic waves. The differences between these two descriptions are first considered analytically then by a numerical analysis of the problem with the influence of the density variations on the propagation of the high frequency wave included. A one-dimensional description is used in all cases. (Auth.)
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 multi-frequency electromagnetic wave propagation phenomena
Valovik, Dmitry V.
2017-11-01
A generalisation of the concept of monochromatic electromagnetic waves guided by layered waveguide structures filled with non-linear medium is introduced. This generalisation leads to guided waves of a novel type: a non-linear multi-frequency guided wave. The existence of such waves, in particular guide structures, is proven using the perturbation method. Numerical experiments are presented for non-linear 1- and 2-frequency guided waves in plane and cylindrical (with a circular cross-section) waveguides. Numerically, a novel non-linear effect is found for particular cases of non-linear multi-frequency guided waves. The suggested generalisation gives not only a unified approach to treat various electromagnetic wave propagation problems but also paves the way to study non-linear interactions of guided waves.
Numerical modelling of nonlinear full-wave acoustic propagation
Energy Technology Data Exchange (ETDEWEB)
Velasco-Segura, Roberto, E-mail: roberto.velasco@ccadet.unam.mx; Rendón, Pablo L., E-mail: pablo.rendon@ccadet.unam.mx [Grupo de Acústica y Vibraciones, Centro de Ciencias Aplicadas y Desarrollo Tecnológico, Universidad Nacional Autónoma de México, Ciudad Universitaria, Apartado Postal 70-186, C.P. 04510, México D.F., México (Mexico)
2015-10-28
The various model equations of nonlinear acoustics are arrived at by making assumptions which permit the observation of the interaction with propagation of either single or joint effects. We present here a form of the conservation equations of fluid dynamics which are deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A two-dimensional, finite-volume method using Roe’s linearisation has been implemented to obtain numerically the solution of the proposed equations. This code, which has been written for parallel execution on a GPU, can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from models of diagnostic and therapeutic HIFU, to parametric acoustic arrays and nonlinear propagation in acoustic waveguides. Examples related to these applications are shown and discussed.
Nonlinear propagation of weakly relativistic ion-acoustic waves in ...
Indian Academy of Sciences (India)
2016-10-06
Oct 6, 2016 ... Abstract. This work presents theoretical and numerical discussion on the dynamics of ion-acoustic solitary wave for weakly relativistic regime in unmagnetized plasma comprising non-extensive electrons, Boltzmann positrons and relativistic ions. In order to analyse the nonlinear propagation phenomena, ...
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
Propagation of nonlinear waves in bi-inductance nonlinear transmission lines
Kengne, Emmanuel; Lakhssassi, Ahmed
2014-10-01
We consider a one-dimensional modified complex Ginzburg-Landau equation, which governs the dynamics of matter waves propagating in a discrete bi-inductance nonlinear transmission line containing a finite number of cells. Employing an extended Jacobi elliptic functions expansion method, we present new exact analytical solutions which describe the propagation of periodic and solitary waves in the considered network.
Highly Nonlinear Wave Propagation in Elastic Woodpile Periodic Structures
2016-08-03
Highly Nonlinear Wave Propagation in Elastic Woodpile Periodic Structures E. Kim,1 F. Li,1 C. Chong,2 G. Theocharis ,3 J. Yang,1 and P.G. Kevrekidis2...Kevrekidis, IMA J. Appl. Math. 76, 389 (2011). [4] G. Theocharis , N. Boechler, and C. Daraio, in Phononic Crystals and Metamaterials, Ch. 6, Springer...9] N. Boechler, G. Theocharis , and C. Daraio, Nature Ma- terials 10, 665 (2011). [10] F. Li, P. Anzel, J. Yang, P.G. Kevrekidis, and C. Daraio, Nat
Propagation of shear wave in nonlinear and dissipative medium
International Nuclear Information System (INIS)
Jeambrun, D.
1995-01-01
The civil engineering projects, like nuclear installations, submitted to vibrations or seismic motions, require the study of the soil behaviour underlying the site under intensive dynamic loading. In order to understand in depth the soil damping phenomenon, a propagation of a shear seismic wave in a dissipative medium has been numerically simulated. The computer code, based on a nonlinear hysteretic model using Newmark-Wilson and Newton-Raphson algorithms and variable spatial steps, passes through the difficulties related to acceleration discontinuities. The simulation should allow the identification of the soil parameters by comparison with in situ measures. (author)
Nonlinear internal wave effects on acoustic propagation and scattering
McMahon, Kara Grace
Experimental observations and theoretical studies show that nonlinear internal waves occur widely in shallow water and cause acoustic propagation effects including ducting and mode coupling. Horizontal ducting results when acoustic modes travel between internal wave fronts that form waveguide boundaries. For small grazing angles between a mode trajectory and a front, an interference pattern may arise that is a horizontal Lloyd mirror pattern. An analytic description for this feature is provided, along with comparisons between results from the formulated model predicting a horizontal Lloyd mirror pattern and an adiabatic mode parabolic equation. Different waveguide models are considered, including boxcar and jump sound speed profiles where change in sound speed is assumed 12 m/s. Modifications to the model are made to include multiple and moving fronts. The focus of this analysis is on different front locations relative to the source, as well as on the number of fronts and their curvatures and speeds. Curvature influences mode incidence angles and thereby changes the interference patterns. For sources oriented so that the front appears concave, the areas with interference patterns shrink as curvature increases, while convexly oriented fronts cause patterns to expand. Curvature also influence how energy is distributed in the internal wave duct. For certain curvatures and duct widths energy forms a whispering gallery or becomes fully ducted. Angular constraints which indicate when to expect these phenomena are presented. Results are compared to propagation calculations and were found to agree in most examples. In some cases trailing internal waves are present in the duct and disturb horizontal propagation. This type of propagation is characterized as a scattering process as a result of broken internal wave fronts between the lead waves. Traditionally this is handled in regimes where adiabatic normal modes are valid using sound speed perturbations to describe energy
International Nuclear Information System (INIS)
Romeo, Francesco; Rega, Giuseppe
2006-01-01
Free wave propagation properties in one-dimensional chains of nonlinear oscillators are investigated by means of nonlinear maps. In this realm, the governing difference equations are regarded as symplectic nonlinear transformations relating the amplitudes in adjacent chain sites (n, n + 1) thereby considering a dynamical system where the location index n plays the role of the discrete time. Thus, wave propagation becomes synonymous of stability: finding regions of propagating wave solutions is equivalent to finding regions of linearly stable map solutions. Mechanical models of chains of linearly coupled nonlinear oscillators are investigated. Pass- and stop-band regions of the mono-coupled periodic system are analytically determined for period-q orbits as they are governed by the eigenvalues of the linearized 2D map arising from linear stability analysis of periodic orbits. Then, equivalent chains of nonlinear oscillators in complex domain are tackled. Also in this case, where a 4D real map governs the wave transmission, the nonlinear pass- and stop-bands for periodic orbits are analytically determined by extending the 2D map analysis. The analytical findings concerning the propagation properties are then compared with numerical results obtained through nonlinear map iteration
Energy Technology Data Exchange (ETDEWEB)
Romeo, Francesco [Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma ' La Sapienza' , Via Gramsci 53, 00197 Rome (Italy)] e-mail: francesco.romeo@uniromal.it; Rega, Giuseppe [Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma ' La Sapienza' , Via Gramsci 53, 00197 Rome (Italy)] e-mail: giuseppe.rega@uniromal.it
2006-02-01
Free wave propagation properties in one-dimensional chains of nonlinear oscillators are investigated by means of nonlinear maps. In this realm, the governing difference equations are regarded as symplectic nonlinear transformations relating the amplitudes in adjacent chain sites (n, n + 1) thereby considering a dynamical system where the location index n plays the role of the discrete time. Thus, wave propagation becomes synonymous of stability: finding regions of propagating wave solutions is equivalent to finding regions of linearly stable map solutions. Mechanical models of chains of linearly coupled nonlinear oscillators are investigated. Pass- and stop-band regions of the mono-coupled periodic system are analytically determined for period-q orbits as they are governed by the eigenvalues of the linearized 2D map arising from linear stability analysis of periodic orbits. Then, equivalent chains of nonlinear oscillators in complex domain are tackled. Also in this case, where a 4D real map governs the wave transmission, the nonlinear pass- and stop-bands for periodic orbits are analytically determined by extending the 2D map analysis. The analytical findings concerning the propagation properties are then compared with numerical results obtained through nonlinear map iteration.
Asymmetric wave propagation through nonlinear PT-symmetric oligomers
D'Ambroise, J.; Kevrekidis, P. G.; Lepri, S.
2012-11-01
In the present paper, we consider nonlinear PT-symmetric dimers and trimers (more generally, oligomers) embedded within a linear Schrödinger lattice. We examine the stationary states of such chains in the form of plane waves, and analytically compute their reflection and transmission coefficients through the nonlinear PT symmetric oligomer, as well as the corresponding rectification factors which clearly illustrate the asymmetry between left and right propagation in such systems. We examine not only the existence but also the dynamical stability of the plane wave states and interestingly find them to be unstable except in the vicinity of the linear limit. Lastly, we generalize our numerical considerations to the more physically relevant case of Gaussian initial wavepackets and confirm that the asymmetry in the transmission properties persists in the case of such wavepackets, as well. The role of potential asymmetries in the nonlinearity or in the gain/loss pattern is also considered. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.
Introduction to Wave Propagation in Nonlinear Fluids and Solids
Drumheller, Douglas S.
1998-02-01
Waves occur widely in nature and have innumerable commercial uses. Waves are responsible for the sound of speech, meteors igniting the atmosphere, radio and television broadcasting, medical diagnosis using ultrasound. This book provides a thorough, modern introduction to the study of linear and nonlinear waves. Beginning with fundamental concepts of motion, the book goes on to discuss linear and nonlinear mechanical waves, thermodynamics, and constitutive models for a variety of gases, liquids, and solids. Among the important areas of research and application are impact analysis, shock wave research, explosive detonation, nonlinear acoustics, and hypersonic aerodynamics. Students at an advanced undergraduate/graduate level will find this text a clear and comprehensive introduction to the study of nonlinear wave phenomena, and it will also be valuable as a professional reference in engineering and applied physics.
Ferrarese, Giorgio
2011-01-01
Lectures: A. Jeffrey: Lectures on nonlinear wave propagation.- Y. Choquet-Bruhat: Ondes asymptotiques.- G. Boillat: Urti.- Seminars: D. Graffi: Sulla teoria dell'ottica non-lineare.- G. Grioli: Sulla propagazione del calore nei mezzi continui.- T. Manacorda: Onde nei solidi con vincoli interni.- T. Ruggeri: "Entropy principle" and main field for a non linear covariant system.- B. Straughan: Singular surfaces in dipolar materials and possible consequences for continuum mechanics
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 wave propagation through a ferromagnet with damping in ...
Indian Academy of Sciences (India)
wavelength in (2+1) dimensions. The purpose of the present work is to study the property of electromagnetic waves of long wavelength propagating through an isotropic ferromagnet in the classical continuum limit in (2+1) dimensions taking into account the dissipative effect. By using the long wave approximation of the ...
Relativistic nonlinearity and wave-guide propagation of rippled laser ...
Indian Academy of Sciences (India)
In the present paper we have investigated the self-focusing behaviour of radially symmetrical rippled Gaussian laser beam propagating in a plasma. Considering the nonlinearity to arise ... ripple as well as on the beam width. Values of critical power has been calculated for different values of the position parameter of ripple.
Relativistic nonlinearity and wave-guide propagation of rippled laser ...
Indian Academy of Sciences (India)
Abstract. In the present paper we have investigated the self-focusing behaviour of radially sym- metrical rippled Gaussian laser beam propagating in a plasma. Considering the nonlinearity to arise from relativistic phenomena and following the approach of Akhmanov et al, which is based on the. WKB and paraxial-ray ...
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...
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.
Linear and nonlinear wave propagation in rarefied plasmas
International Nuclear Information System (INIS)
Ballai, I.; Erdelyi, R.; Voitenko, Y.; Goossens, M.
2002-01-01
Small-amplitude magnetohydrodynamic waves are studied in a dilute collisionless plasma with an anisotropic plasma pressure. The parallel and perpendicular pressure components are defined by two polytropic pressure laws. Previous results obtained within the framework of the Chew-Goldberger-Low double-adiabatic and double-isothermal models are recovered for specific values of the polytropic indices. The double-polytropic model can be considered as an extension of its single-polytropic counterpart model. Dispersion relations for the linear waves are derived and analyzed in the presence of pressure anisotropy. Particular cases of linear and nonlinear waves in a magnetic slab with double-polytropic plasma are investigated. The presence of the effective parallel and perpendicular sound speeds in the slab gives rise to a complicated interplay between kink and sausage modes supported by the slab. The behavior of weakly nonlinear waves in the slab are governed by the Benjamin-Ono equation. The soliton-like solution of this equation may be accelerated or retarded depending on the values of parallel and perpendicular sound speeds. The solitons are always accelerated in the magnetically dominated slab
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
Ruderman, M. S.
1993-04-01
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.
Finite-element based perturbation analysis of wave propagation in nonlinear periodic structures
Manktelow, Kevin; Narisetti, Raj K.; Leamy, Michael J.; Ruzzene, Massimo
2013-08-01
Wave propagation in continuous, periodic structures subject to weak nonlinearities is studied using a finite-element discretization of a single unit cell followed by a perturbation analysis. The dispersion analysis is integrated with commercial finite-element analysis (FEA) software to expedite nonlinear analysis of geometrically-complex unit cells. A simple continuous multilayer system is used to illustrate the principle aspects of the procedure. A periodic structure formed by membrane elements on nonlinear elastic supports is used to demonstrate the versatility of the procedure. Weakly nonlinear band diagrams are generated in which amplitude-dependent bandgaps and group velocities are identified. The nonlinear dispersion analysis procedure described, coupled with commercial FEA software, should facilitate the study of wave propagation in a wide-variety of geometrically-complex, nonlinear periodic structures.
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 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.
Nonlinear propagation of dust-acoustic solitary waves in a dusty ...
Indian Academy of Sciences (India)
... Lecture Workshops · Refresher Courses · Symposia · Live Streaming. Home; Journals; Pramana – Journal of Physics; Volume 80; Issue 6. Nonlinear propagation of dust-acoustic solitary waves in a dusty plasma with arbitrarily charged dust and trapped electrons. O Rahman A A Mamun. Volume 80 Issue 6 June 2013 pp ...
PetClaw: A scalable parallel nonlinear wave propagation solver for Python
Alghamdi, Amal
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.
A nodal discontinuous Galerkin finite element method for nonlinear elastic wave propagation.
Bou Matar, Olivier; Guerder, Pierre-Yves; Li, YiFeng; Vandewoestyne, Bart; Van Den Abeele, Koen
2012-05-01
A nodal discontinuous Galerkin finite element method (DG-FEM) to solve the linear and nonlinear elastic wave equation in heterogeneous media with arbitrary high order accuracy in space on unstructured triangular or quadrilateral meshes is presented. This DG-FEM method combines the geometrical flexibility of the finite element method, and the high parallelization potentiality and strongly nonlinear wave phenomena simulation capability of the finite volume method, required for nonlinear elastodynamics simulations. In order to facilitate the implementation based on a numerical scheme developed for electromagnetic applications, the equations of nonlinear elastodynamics have been written in a conservative form. The adopted formalism allows the introduction of different kinds of elastic nonlinearities, such as the classical quadratic and cubic nonlinearities, or the quadratic hysteretic nonlinearities. Absorbing layers perfectly matched to the calculation domain of the nearly perfectly matched layers type have been introduced to simulate, when needed, semi-infinite or infinite media. The developed DG-FEM scheme has been verified by means of a comparison with analytical solutions and numerical results already published in the literature for simple geometrical configurations: Lamb's problem and plane wave nonlinear propagation.
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.
Nonlinear Propagation of Mag Waves Through the Transition Region
Jatenco-Pereira, V.; Steinolfson, R. S.; Mahajan, S.; Tajima, T.
1990-11-01
RESUMEN. Una onda de gravitaci5n magneto acustica (GMA), se inicia en el regimen de alta beta cerca de la basa de fot5sfera solar y es segui- da, usando simulaciones numericas, mientras viaja radialmente a traves de la cromosfera, la regi5n de transici6n y dentro de la corona. Se ha' seleccionado parametros iniciales de manera que la beta resulte menor que uno cerca de la parte alta de la regi6n de transici6n. Nuestro interes maximo se concentra en la cantidad y forma del flujo de energia que puede ser llevada por la onda hasta la corona dados una atm6sfera inicial y amplitud de onda especificas. Segun los estudios a la fecha, el flujo de energ1a termico domina, aumentando linealmente con la ampli tud deonda y resulta de aproximadamente i05 ergs/cm2-s en una amplitud de 0.5. El flujo de energia cinetica siempre permanece despreciable, mientras que el flujo de energia magnetica depende de la orientaci5n inicial del campo. Un modo GMA rapido y casi paralelo, el cual es esen- cialmente un modo MHD en la corona se convierte a un modo rapido modificado y a uno lento, cuando la beta atmosferica disminuye a uno. ABSTRACT: A magneto-acoustic-gravity (MAG) wave is initiated in the high-beta regime near the base of the solar photosphere and followed, using numerical siriiulations, as it travels radially through the chromosphere, the transition region, and into the corona. Initial parameters are selected such that beta becomes less than one near the top of the transition region. Our primary interest is in the amount and form of energy flux that can be carried by the wave train into the corona for a specified initial atmosphere and wave amplitude. For the studies conducted to date, the thermal energy flux dominates, it about linearly with wave amplitude and becomes approximately 10 ergs/cm2-s at an amplitude of 0.5. The kinetic energy flux always remains negligible, while the magnetic energy flux depends on the inLtial field orientation. A nearly parallel fast MAG mode, which
Alberucci, Alessandro; Laudyn, Urszula A; Piccardi, Armando; Kwasny, Michał; Klus, Bartlomiej; Karpierz, Mirosław A; Assanto, Gaetano
2017-07-01
We investigate nonlinear optical propagation of continuous-wave (CW) beams in bulk nematic liquid crystals. We thoroughly analyze the competing roles of reorientational and thermal nonlinearity with reference to self-focusing/defocusing and, eventually, the formation of nonlinear diffraction-free wavepackets, the so-called spatial optical solitons. To this extent we refer to dye-doped nematic liquid crystals in planar cells excited by a single CW beam in the highly nonlocal limit. To adjust the relative weight between the two nonlinear responses, we employ two distinct wavelengths, inside and outside the absorption band of the dye, respectively. Different concentrations of the dye are considered in order to enhance the thermal effect. The theoretical analysis is complemented by numerical simulations in the highly nonlocal approximation based on a semi-analytic approach. Theoretical results are finally compared to experimental results in the Nematic Liquid Crystals (NLC) 4-trans-4'-n-hexylcyclohexylisothiocyanatobenzene (6CHBT) doped with Sudan Blue dye.
Nonlinear propagation of whistler wave and turbulent spectrum in reconnection region of magnetopause
Sharma, R. P.; Pathak, Neha; Yadav, Nitin; Sharma, Prachi
2017-09-01
Whistler waves have ample of observations in the magnetosphere near the dayside magnetopause. Also, the role of whistler waves is well established in the context of magnetic reconnection as well as turbulence generation. In the present work, we examine the combined effect of guide field and nonlinearity in the development of turbulence in magnetic reconnection sites. We have derived the dynamical equation of 3D whistler wave propagating through Harris sheet assuming that background number density and background field are perturbed. The nonlinear dynamical equation is then solved numerically using pseudo-spectral method and finite difference method. Simulation results represent the nonlinear evolution of X-O field line in the presence of nonlinearity, which causes the generation of turbulence. We have also investigated the formation of current sheet/coherent structures as a result of the proposed mechanism. These localized structures have transverse scale size of the order of electron inertial length. When the system reaches quasi steady state, we have evaluated power spectrum in magnetopause and it shows two different scaling having k-3 /2 for k λe1 .The obtained results are consistent with the THEMIS observations. Energy distribution at smaller scales leads to the formation of thermal tail of energetic particles. The energy of these electrons is also calculated and comes out to be in the order of 100 keV.
Van Gorder, Robert A
2010-11-01
We apply the δ-expansion method to nonlinear stochastic differential equations describing wave propagation in a random medium. In particular, we focus our attention on a model describing a nonlinear wave propagating in a turbulent atmosphere which has random variations in the refractive index (we take these variations to be stochastic). The method allows us to construct much more reasonable perturbation solutions with relatively few terms (compared to standard "small-parameter" perturbation methods) due to more accurate linearization used in constructing the initial approximation. We demonstrate that the method allows one to compute effective wave numbers more precisely than other methods applied to the problem in the literature. The method also picks up on the stochastic damping of the solutions quickly, holding all of the relevant data in the initial term. These properties allow for both a qualitative and a quantitative construction of physically meaningful solutions. In particular, we show that the method allows one to retain higher-order harmonics which are hard to capture with standard perturbation methods based on small parameters.
Chabot, S.; Glinsky, N.; Mercerat, E. D.; Bonilla Hidalgo, L. F.
2018-02-01
We propose a nodal high-order discontinuous Galerkin method for 1D wave propagation in nonlinear media. We solve the elastodynamic equations written in the velocity-strain formulation and apply an upwind flux adapted to heterogeneous media with nonlinear constitutive behavior coupling stress and strain. Accuracy, convergence and stability of the method are studied through several numerical applications. Hysteresis loops distinguishing loading and unloading-reloading paths are also taken into account. We investigate several effects of nonlinearity in wave propagation, such as the generation of high frequencies and the frequency shift of resonant peaks to lower frequencies. Finally, we compare the results for both nonlinear models, with and without hysteresis, and highlight the effects of the former on the stabilization of the numerical scheme.
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.
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)
Wave propagation scattering theory
Birman, M Sh
1993-01-01
The papers in this collection were written primarily by members of the St. Petersburg seminar in mathematical physics. The seminar, now run by O. A. Ladyzhenskaya, was initiated in 1947 by V. I. Smirnov, to whose memory this volume is dedicated. The papers in the collection are devoted mainly to wave propagation processes, scattering theory, integrability of nonlinear equations, and related problems of spectral theory of differential and integral operators. The book is of interest to mathematicians working in mathematical physics and differential equations, as well as to physicists studying va
Wave propagation in mechanical metamaterials
Zhou, Y.
2017-01-01
In mechanical metamaterials, large deformations can occur in systems which are topological from the point of view of linear waves. The interplay between such nonlinearities and topology affects wave propagation. Beyond perfectly periodic systems, defects provide a way to modify and control
Interlaced linear-nonlinear wave propagation in a warm multicomponent plasma
Energy Technology Data Exchange (ETDEWEB)
Dutta, Debjit [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India); Singha, Prasenjit [Department of Mathematics, Hooghly Mohsin College, Chinsurah, Hooghly 712101 (India); Sahu, Biswajit, E-mail: biswajit-sahu@yahoo.co.in [Department of Mathematics, West Bengal State University, Barasat, Kolkata 700126 (India)
2014-12-15
Linear and nonlinear propagations of arbitrary amplitude nonlinear structures, viz. solitons, double layers, and supersolitons are investigated in multicomponent plasma consisting of warm ions, two temperature nonthermal electrons and hot nonthermal positrons. The Sagdeev pseudopotential approach is employed to obtain the energy integral equation in such a multicomponent plasma using fluid theory. The effects of several plasma parameters on the ion acoustic solitons, double layers, and supersolitons are analyzed. It is found that the present system supports the coexistence of arbitrary amplitude positive and negative potential solitons in a certain region of parameter space in addition to compressive and rarefactive double layers. Furthermore, numerical calculations reveal that these structures may exist either in supersonic or subsonic regimes. Also, the present plasma system supports supersolitonic structure in supersonic regime.
Directory of Open Access Journals (Sweden)
Paul C. Rivera
2006-01-01
Full Text Available A common approach in modeling the generation and propagation of tsunami is based on the assumption of a kinematic vertical displacement of ocean water that is analogous to the ocean bottom displacement during a submarine earthquake and the use of a non-dispersive long-wave model to simulate its physical transformation as it radiates outward from the source region. In this study, a new generation mechanism and the use of a highly-dispersive wave model to simulate tsunami inception, propagation and transformation are proposed. The new generation model assumes that transient ground motion during the earthquake can accelerate horizontal currents with opposing directions near the fault line whose successive convergence and divergence generate a series of potentially destructive oceanic waves. The new dynamic model incorporates the effects of earthquake moment magnitude, ocean compressibility through the buoyancy frequency, the effects of focal and water depths, and the orientation of ruptured fault line in the tsunami magnitude and directivity.For tsunami wave simulation, the nonlinear momentum-based wave model includes important wave propagation and transformation mechanisms such as refraction, diffraction, shoaling, partial reflection and transmission, back-scattering, frequency dispersion, and resonant wave-wave interaction. Using this model and a coarse-resolution bathymetry, the new mechanism is tested for the Indian Ocean tsunami of December 26, 2004. A new flooding and drying algorithm that consider waves coming from every direction is also proposed for simulation of inundation of low-lying coastal regions.It is shown in the present study that with the proposed generation model, the observed features of the Asian tsunami such as the initial drying of areas east of the source region and the initial flooding of western coasts are correctly simulated. The formation of a series of tsunami waves with periods and lengths comparable to observations
Breathing as a low frequency wave propagation in nonlinear elastic permeable medium
International Nuclear Information System (INIS)
Kyriakou, Elizabeth; McKenzie, David R.; Suchowerska, Natalka; Fulton, Roger R.
2007-01-01
Breathing can be regarded as a type of low frequency wave propagation. Unlike sound propagation in open air, in breathing, the air compressibility is not as important as the flow of air, and to a first approximation the air can be regarded as incompressible. We have developed a one-dimensional analytical description of wave motion in a metamaterial consisting of a porous elastic medium contained within chambers, separated by plates with orifices representing the minor airways. The metamaterial is placed within a cylinder with impermeable sides representing the thorax, driven at one end by a piston representing the diaphragm. The incompressible air is able to escape from the top of the cylinder. The solutions to the wave equation have characteristics that depend on the values of permeability (defined by the size of the orifice in the plates), the Young's modulus of the elastic medium and the density of lung tissue. A 'normal' regime is identified in which the strain of the medium near the diaphragm is large and the strain at the top of the cylinder near the outlet is small. An 'abnormal' regime is also identified in which the opposite applies. A rapid transition between the two regimes can be caused by changing the parameters representing the lung tissue. This transition may represent the onset of a disease state such as asthma
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.
El-Labany, S. K.; Sabry, R.; El-Shamy, E. F.; Khedr, D. M.; Khedr
2013-10-01
Investigation of arbitrary amplitude nonlinear ion-acoustic solitary waves which accompany collisionless positive-negative ion plasmas with high-energy electrons (represented by kappa distribution) is presented. Arbitrary amplitude solitary waves are investigated by deriving an energy-integral equation involving a Sagdeev-like pseudopotential. The existence regions of solitary pulses are, defined precisely, modified by the superthermality of energetic electrons. Furthermore, numerical calculations reveal that both compressive and rarefactive pulses may exist for negative ion mass groups in Titan's atmosphere. The superthermality of energetic electrons are found to modify the existence domains of large amplitude ion-acoustic waves in Titan's atmosphere. The dependence of solitary excitation characteristics on the superthermal parameter, the negative ion concentration, the positive-to-negative ions mass ratio, and the Mach number have been investigated. The present study might be helpful to understand the excitation of fully nonlinear ion-acoustic solitary pulses that may appear in the interplanetary medium and/or in the astrophysical plasmas in general.
Directory of Open Access Journals (Sweden)
E. M. Dubinin
2002-01-01
Full Text Available We investigate the nature of nonlinear waves propagating transverse to the magnetic field in a bi-ion plasma including plasma pressure. By using the conservation laws derived from the multi-ion fluid equations the system may be described by a single order differential equation whose properties control the structure of the flow and the magnetic field. Compressive solitons exist in specific ranges of the characteristic Mach numbers. Various features of solitons differ in different existence "windows". For example, there are solitons that contain a strong proton rarefaction core embedded in the main compressional structure. Compressive solitons are found in a wide range of flow parameters. Finite ion pressure introduces critical Mach numbers. In contrast to a plasma consisting only of protons and electrons these singular points are reached where a specific combination of ion and electron speeds lies on particular locii, in multi-parameter space, which corresponds to the generalized "sonic point" of the compound system.
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.
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
Observation of sound focusing and defocusing due to propagating nonlinear internal waves.
Luo, J; Badiey, M; Karjadi, E A; Katsnelson, B; Tskhoidze, A; Lynch, J F; Moum, J N
2008-09-01
Fluctuations of the low frequency sound field in the presence of an internal solitary wave packet during the Shallow Water '06 experiment are analyzed. Acoustic, environmental, and on-board ship radar image data were collected simultaneously before, during, and after a strong internal solitary wave packet passed through the acoustic track. Preliminary analysis of the acoustic wave temporal intensity fluctuations agrees with previously observed phenomena and the existing theory of the horizontal refraction mechanism, which causes focusing and defocusing when the acoustic track is nearly parallel to the front of the internal waves [J. Acoust. Soc. Am., 122(2), pp. 747-760 (2007)].
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 ion-acoustic waves in a degenerate dense ...
Indian Academy of Sciences (India)
both non-relativistic and ultrarelativistic limits. Therefore, in this paper, we consider a degenerate dense plasma containing non-relativistic degenerate cold ion fluid and both non-relativistic and ultrarelativistic degenerate electrons for studying the basic features of solitary waves in such a degenerate dense plasma.
Front propagation in nonlinear parabolic equations
Czech Academy of Sciences Publication Activity Database
Feireisl, Eduard; Hilhorst, D.; Petzeltová, Hana; Takáč, P.
2014-01-01
Roč. 90, č. 2 (2014), s. 551-572 ISSN 0024-6107 R&D Projects: GA ČR GA13-00522S Institutional support: RVO:67985840 Keywords : nonlinear parabolic equations * front propagation * travelling wave Subject RIV: BA - General Mathematics Impact factor: 0.820, year: 2014 http://jlms.oxfordjournals.org/content/90/2/551
Nonlinear propagation of dust-acoustic solitary waves in a dusty ...
Indian Academy of Sciences (India)
Dust-acoustic solitary waves in a dusty plasma. Now, using eqs (13)–(15) one can easily eliminate (∂n(2) d /∂ξ), (∂u(2) d /∂ξ), and. (∂φ(2)/∂ξ), and obtain. ∂φ(1). ∂τ. + A. √ φ(1). ∂φ(1). ∂ξ. + B. ∂3φ(1). ∂ξ3. = 0,. (16) where. A = 3γ. 4 vp. (μe + αμi). ,. (17). B = vp. 2(μe + αμi) . (18). Equation (16) is a mKdV equation for ...
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 5. Flood Wave Propagation-The Saint Venant Equations. P P Mujumdar. General Article Volume 6 Issue 5 May 2001 pp 66-73. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/006/05/0066-0073 ...
Indian Academy of Sciences (India)
I available for forecasting the propagation of the flood wave. Introduction. Among all natural disasters, floods are the most frequently occurring phenomena that affect a large section of population all over the world, every year. Throughout the last century, flood- ing has been one of the most devastating disasters both in terms.
Solitary wave propagation in solar flux tubes
International Nuclear Information System (INIS)
Erdelyi, Robert; Fedun, Viktor
2006-01-01
The aim of the present work is to investigate the excitation, time-dependent dynamic evolution, and interaction of nonlinear propagating (i.e., solitary) waves on vertical cylindrical magnetic flux tubes in compressible solar atmospheric plasma. The axisymmetric flux tube has a field strength of 1000 G at its footpoint, which is typical for photospheric regions. Nonlinear waves that develop into solitary waves are excited by a footpoint driver. The propagation of the nonlinear signal is investigated by solving numerically a set of fully nonlinear 2.0D magnetohydrodynamic (MHD) equations in cylindrical coordinates. For the initial conditions, axisymmetric solutions of the linear dispersion relation for wave modes in a magnetic flux tube are applied. In the present case, we focus on the sausage mode only. The dispersion relation is solved numerically for a range of plasma parameters. The equilibrium state is perturbed by a Gaussian at the flux tube footpoint. Two solitary solutions are found by solving the full nonlinear MHD equations. First, the nonlinear wave propagation with external sound speed is investigated. Next, the solitary wave propagating close to the tube speed, also found in the numerical solution, is studied. In contrast to previous analytical and numerical works, here no approximations were made to find the solitary solutions. A natural application of the present study may be spicule formation in the low chromosphere. Future possible improvements in modeling and the relevance of the photospheric chromospheric transition region coupling by spicules is suggested
Wave equations for pulse propagation
Energy Technology Data Exchange (ETDEWEB)
Shore, B.W.
1987-06-24
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.
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
Wave Height Distribution for Nonlinear Swell Waves in Deep an Depth Limited Wave Conditions
DEFF Research Database (Denmark)
Nørgaard, Jørgen Harck; Andersen, Thomas Lykke; Knudsen, Jannie Elkær
2017-01-01
This paper presents initial results from an on-going study on the influence from wave nonlinearity on the wave height distribution in deep- and depth-limited nonlinear wave conditions. A fully nonlinear VOF model, IH-2VOF, is applied to model the propagation of irregular waves on a sloping sea bed...... from deep to shallow water, including the effects of wave breaking. Different wave nonlinearities are evaluated in the model and the effects of the wave nonlinearity, described by the so-called Ursell-number, on the wave height distributions along the sloping sea bed are evaluated. The widely used...
Czech Academy of Sciences Publication Activity Database
Kolman, Radek; Cho, S.; Park, K.C.
2014-01-01
Roč. 19, č. 12 (2014) ISSN 1435-4934. [European Conference on Non-Destructive Testing (ECNDT 2014) /11./. Praha, 06.10.2014-10.10.2014] R&D Projects: GA ČR(CZ) GAP101/11/0288; GA ČR(CZ) GAP101/12/2315 Institutional support: RVO:61388998 Keywords : elastic and non-linear wave propagation * contact problem * finite element method * explicit time integration * dispersion * spurious oscillations Subject RIV: JR - Other Machinery http://www.ndt.net/events/ECNDT2014/app/content/Paper/17_Kolman_Rev1.pdf
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
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...
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.
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.
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.
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.
Wave Height Distribution for Nonlinear Swell Waves in Deep an Depth-Limited Wave Conditions
DEFF Research Database (Denmark)
Nørgaard, Jørgen Harck; Andersen, Thomas Lykke; Knudsen, Jannie Elkær
2017-01-01
This paper presents initial results from an on-going study on the influence from wave nonlinearity on the wave height distribution in deep- and depth-limited nonlinear wave conditions. A fully nonlinear VOF model, IH-2VOF, is applied to model the propagation of irregular waves on a sloping sea bed...... Battjes & Groenendijk (2000) shallow water wave height distribution is concluded in the present study to significantly underpredict the low-exceedance wave heights in case of very nonlinear waves. A modification of the Battjess & Groenendijk (2000) distribution is suggested in order to include the effects...... from deep to shallow water, including the effects of wave breaking. Different wave nonlinearities are evaluated in the model and the effects of the wave nonlinearity, described by the so-called Ursell-number, on the wave height distributions along the sloping sea bed are evaluated. The widely used...
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
Control methods for localization of nonlinear waves.
Porubov, Alexey; Andrievsky, Boris
2017-03-06
A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).
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)
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...
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...
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.
Polarization Shaping for Control of Nonlinear Propagation.
Bouchard, Frédéric; Larocque, Hugo; Yao, Alison M; Travis, Christopher; De Leon, Israel; Rubano, Andrea; Karimi, Ebrahim; Oppo, Gian-Luca; Boyd, Robert W
2016-12-02
We study the nonlinear optical propagation of two different classes of light beams with space-varying polarization-radially symmetric vector beams and Poincaré beams with lemon and star topologies-in a rubidium vapor cell. Unlike Laguerre-Gauss and other types of beams that quickly experience instabilities, we observe that their propagation is not marked by beam breakup while still exhibiting traits such as nonlinear confinement and self-focusing. Our results suggest that, by tailoring the spatial structure of the polarization, the effects of nonlinear propagation can be effectively controlled. These findings provide a novel approach to transport high-power light beams in nonlinear media with controllable distortions to their spatial structure and polarization properties.
Polarization Shaping for Control of Nonlinear Propagation
Bouchard, Frédéric; Larocque, Hugo; Yao, Alison M.; Travis, Christopher; De Leon, Israel; Rubano, Andrea; Karimi, Ebrahim; Oppo, Gian-Luca; Boyd, Robert W.
2016-12-01
We study the nonlinear optical propagation of two different classes of light beams with space-varying polarization—radially symmetric vector beams and Poincaré beams with lemon and star topologies—in a rubidium vapor cell. Unlike Laguerre-Gauss and other types of beams that quickly experience instabilities, we observe that their propagation is not marked by beam breakup while still exhibiting traits such as nonlinear confinement and self-focusing. Our results suggest that, by tailoring the spatial structure of the polarization, the effects of nonlinear propagation can be effectively controlled. These findings provide a novel approach to transport high-power light beams in nonlinear media with controllable distortions to their spatial structure and polarization properties.
Wave propagation and group velocity
Brillouin, Léon
1960-01-01
Wave Propagation and Group Velocity contains papers on group velocity which were published during the First World War and are missing in many libraries. It introduces three different definitions of velocities: the group velocity of Lord Rayleigh, the signal velocity of Sommerfeld, and the velocity of energy transfer, which yields the rate of energy flow through a continuous wave and is strongly related to the characteristic impedance. These three velocities are identical for nonabsorbing media, but they differ considerably in an absorption band. Some examples are discussed in the last chapter
Boundary control of long waves in nonlinear dispersive systems
DEFF Research Database (Denmark)
Hasan, Agus; Foss, Bjarne; Aamo, Ole Morten
2011-01-01
orders of the nonlinearity, the equation may have unstable solitary wave solutions. Although it is a one dimensional problem, achieving a global result for this equation is not trivial due to the nonlinearity and the mixed partial derivative. In this paper, two sets of nonlinear boundary control laws......Unidirectional propagation of long waves in nonlinear dispersive systems may be modeled by the Benjamin-Bona-Mahony-Burgers equation, a third order partial differential equation incorporating linear dissipative and dispersive terms, as well as a term covering nonlinear wave phenomena. For higher...... that achieve global exponential stability and semi-global exponential stability are derived for both linear and nonlinear cases....
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.
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.
Toward a Nonlinear Acoustic Analogy: Turbulence as a Source of Sound and Nonlinear Propagation
Miller, Steven A. E.
2015-01-01
An acoustic analogy is proposed that directly includes nonlinear propagation effects. We examine the Lighthill acoustic analogy and replace the Green's function of the wave equation with numerical solutions of the generalized Burgers' equation. This is justified mathematically by using similar arguments that are the basis of the solution of the Lighthill acoustic analogy. This approach is superior to alternatives because propagation is accounted for directly from the source to the far-field observer instead of from an arbitrary intermediate point. Validation of a numerical solver for the generalized Burgers' equation is performed by comparing solutions with the Blackstock bridging function and measurement data. Most importantly, the mathematical relationship between the Navier-Stokes equations, the acoustic analogy that describes the source, and canonical nonlinear propagation equations is shown. Example predictions are presented for nonlinear propagation of jet mixing noise at the sideline angle.
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....
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....
Experiments on nonlinear cross waves
Lichter, S.; Shemer, L.
1986-12-01
Surface water waves are generated by a paddle-type wavemaker operating at one end of a long tank. In addition to a progressing wave field at the forcing frequency, a subharmonic cross wave is generated in the neighborhood of the wavemaker. At lower forcing amplitudes there is a Benjamin-Feir instability of the progressing wave. At large forcing amplitudes, the fundamental decays rapidly along the channel. The cross wave dominates the near field and is strongly modulated on a slow time scale. During each modulation period a soliton propagates away from the wavemaker. The near-field standing cross wave undergoes a transformation into a progressing wave in the far field.
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 MHD WAVES IN A PROMINENCE FOOT
International Nuclear Information System (INIS)
Ofman, L.; Knizhnik, K.; Kucera, T.; Schmieder, B.
2015-01-01
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
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 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.
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...
Traveling wave solutions of a highly nonlinear shallow water equation
Geyer, A.; Quirchmayr, Ronald
2018-01-01
Motivated by the question whether higher-order nonlinear model equations, which go beyond the Camassa-Holm regime of moderate amplitude waves, could point us to new types of waves profiles, we study the traveling wave solutions of a quasilinear evolution equation which models the propagation of
Bakirova, M. I.; Dorodnitsyn, V. A.; Kurdiumov, S. P.; Samarskii, A. A.; Dimova, S. N.
The directed propagation of heat and combustion in an anisotropic medium is analyzed numerically. It is shown that at the asymptotic stage this process is described by an invariant (self-similar) solution obtained by Dorodnitsyn et al. (1983). In the isotropic case, an invariant solution is indicated which can describe circular and spiral combustion waves. The invariant solutions are obtained on the basis of the group properties of the heat-conduction equation.
Energy Technology Data Exchange (ETDEWEB)
Bakirova, M.I.; Dorodnitsyn, V.A.; Kurdiumov, S.P.; Samarskii, A.A.; Dimova, S.N.
1988-01-01
The directed propagation of heat and combustion in an anisotropic medium is analyzed numerically. It is shown that at the asymptotic stage this process is described by an invariant (self-similar) solution obtained by Dorodnitsyn et al. (1983). In the isotropic case, an invariant solution is indicated which can describe circular and spiral combustion waves. The invariant solutions are obtained on the basis of the group properties of the heat-conduction equation. 15 references.
Acoustic field distribution of sawtooth wave with nonlinear SBE model
Energy Technology Data Exchange (ETDEWEB)
Liu, Xiaozhou, E-mail: xzliu@nju.edu.cn; Zhang, Lue; Wang, Xiangda; Gong, Xiufen [Key Laboratory of Modern Acoustics, Ministry of Education, Institute of Acoustics, Nanjing University, Nanjing 210093 (China)
2015-10-28
For precise prediction of the acoustic field distribution of extracorporeal shock wave lithotripsy with an ellipsoid transducer, the nonlinear spheroidal beam equations (SBE) are employed to model acoustic wave propagation in medium. To solve the SBE model with frequency domain algorithm, boundary conditions are obtained for monochromatic and sawtooth waves based on the phase compensation. In numerical analysis, the influence of sinusoidal wave and sawtooth wave on axial pressure distributions are investigated.
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)
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
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
Observations of Obliquely Propagating Electron Bernstein Waves
DEFF Research Database (Denmark)
Armstrong, R. J.; Juul Rasmussen, Jens; Stenzel, R. L.
1981-01-01
Plane electron Bernstein waves propagating obliquely to the magnetic field are investigated. The waves are excited by a plane grid antenna in a large volume magnetoplasma. The observations compare favorably with the predictions of the linear dispersion relation.......Plane electron Bernstein waves propagating obliquely to the magnetic field are investigated. The waves are excited by a plane grid antenna in a large volume magnetoplasma. The observations compare favorably with the predictions of the linear dispersion relation....
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
Nonlinear ambipolar diffusion waves
Energy Technology Data Exchange (ETDEWEB)
Mendonca, J.T.; Rowlands, G.
1985-07-01
The evolution of a plasma perturbation in a neutral gas is considered using the ambipolar diffusion approximation. A nonlinear diffusion equation is derived and, in the one-dimensional case, exact solutions of shock type are obtained.
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.
Neutron optical tests of nonlinear wave mechanics
International Nuclear Information System (INIS)
Gahler, R.; Klein, A.G.; Zeilinger, A.
1979-01-01
The free-space propagation of matter waves is analysed with a view to placing an upper limit on the strength of possible non-linear terms in the Schrodinger equation. Such additional terms of the form psiF(/psi/ 2 ) were introduced by Bialynicki-Birula and Mycielski in order to counteract the spreading of wave packets, thereby allowing solutions which behave macroscopically like classical particles. For the particularly interesting case of a logarithmic nonlinearity, of the form F=-b ln/psi/ 2 it is found that the free-space propagation of slow neutrons places a very stringent upper limit on the magnitude of b. Precise measurements of Fresnel diffraction with slow neutrons do not give any evidence for nonlinear effects and allows the deduction of an upper limit for b -15 eV about 3 orders of magnitude smaller than the lower bound proposed by the above authors, making such nonlinearities extremely unlikely in the real world
Nonlinear waves in electron–positron–ion plasmas including charge ...
Indian Academy of Sciences (India)
2017-01-04
Jan 4, 2017 ... Recently, it has been suggested that the nonlinear study of wave propagation can be helpful to under- stand nonlinear structures similar to the broadband electrostatic noise (BEN) observed in the Earth's mag- netosphere by numerous satellites (spacecrafts) such as. Geotail [8], Polar [9],Viking [10], FAST ...
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....
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
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 ...
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 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
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 resonance a stationary state arise consisting of multiple oscillating shock waves. Off resonance driving leads to a nearly linear oscillating ground state but superimposed by bursts of a fast oscillating shock wave. Based on a travelling wave ansatz for the fluid velocity potential with an added 2'nd order...... 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....
Theory of Nonlinear Guided Electromagnetic Waves in a Plane Two-Layered Dielectric Waveguide
Directory of Open Access Journals (Sweden)
Valeria Yu. Kurseeva
2017-01-01
Full Text Available Propagation of transverse electric electromagnetic waves in a homogeneous plane two-layered dielectric waveguide filled with a nonlinear medium is considered. The original wave propagation problem is reduced to a nonlinear eigenvalue problem for an equation with discontinuous coefficients. The eigenvalues are propagation constants (PCs of the guided waves that the waveguide supports. The existence of PCs that do not have linear counterparts and therefore cannot be found with any perturbation method is proven. PCs without linear counterparts correspond to a novel propagation regime that arises due to the nonlinearity. Numerical results are also presented; the comparison between linear and nonlinear cases is made.
Strongly nonlinear waves in a chain of Teflon beads
Daraio, C.; Nesterenko, V. F.; Herbold, E. B.; Jin, S.
2005-01-01
One-dimensional “sonic vacuum” type phononic crystals were assembled from a chain of polytetrafluoroethylene (PTFE,Teflon) spheres with different diameters in a Teflon holder. It was demonstrated that this polymer-based sonic vacuum, with exceptionally low elastic modulus of particles, supports propagation of strongly nonlinear solitary waves with a very low speed. These solitary waves can be described using the classical nonlinear Hertz law despite the viscoelastic nature of the polymer and ...
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......, it is the universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...... in Fourier space and equipartition, the role of inhomogeneities and complex geometry and the importance of coupled systems....
Making and Propagating Elastic Waves: Overview of the new wave propagation code WPP
Energy Technology Data Exchange (ETDEWEB)
McCandless, K P; Petersson, N A; Nilsson, S; Rodgers, A; Sjogreen, B; Blair, S C
2006-05-09
We are developing a new parallel 3D wave propagation code at LLNL called WPP (Wave Propagation Program). WPP is being designed to incorporate the latest developments in embedded boundary and mesh refinement technology for finite difference methods, as well as having an efficient portable implementation to run on the latest supercomputers at LLNL. We are currently exploring seismic wave applications, including a recent effort to compute ground motions for the 1906 Great San Francisco Earthquake. This paper will briefly describe the wave propagation problem, features of our numerical method to model it, implementation of the wave propagation code, and results from the 1906 Great San Francisco Earthquake simulation.
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).
Nonlinear acoustic wave equations with fractional loss operators.
Prieur, Fabrice; Holm, Sverre
2011-09-01
Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlinear wave equation which describes attenuation and dispersion laws that match observations. This wave equation is a generalization of the Westervelt equation, and also leads to a fractional version of the Khokhlov-Zabolotskaya-Kuznetsov and Burgers' equations. © 2011 Acoustical Society of America
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,
DBEM crack propagation for nonlinear fracture problems
Directory of Open Access Journals (Sweden)
R. Citarella
2015-10-01
Full Text Available A three-dimensional crack propagation simulation is performed by the Dual Boundary Element Method (DBEM. The Stress Intensity Factors (SIFs along the front of a semi elliptical crack, initiated from the external surface of a hollow axle, are calculated for bending and press fit loading separately and for a combination of them. In correspondence of the latter loading condition, a crack propagation is also simulated, with the crack growth rates calculated using the NASGRO3 formula, calibrated for the material under analysis (steel ASTM A469. The J-integral and COD approaches are selected for SIFs calculation in DBEM environment, where the crack path is assessed by the minimum strain energy density criterion (MSED. In correspondence of the initial crack scenario, SIFs along the crack front are also calculated by the Finite Element (FE code ZENCRACK, using COD, in order to provide, by a cross comparison with DBEM, an assessment on the level of accuracy obtained. Due to the symmetry of the bending problem a pure mode I crack propagation is realised with no kinking of the propagating crack whereas for press fit loading the crack propagation becomes mixed mode. The crack growth analysis is nonlinear because of normal gap elements used to model the press fit condition with added friction, and is developed in an iterative-incremental procedure. From the analysis of the SIFs results related to the initial cracked configuration, it is possible to assess the impact of the press fit condition when superimposed to the bending load case.
Nonlinear Trivelpiece--Gould waves: Recurrence, harmonic cascade, and sidebands
Energy Technology Data Exchange (ETDEWEB)
Cabral, J.A.C.; Lapao, L.M.; Mendonca, J.T. (Centro de Electrodinamica, Instituto Superior Tecnico, 1096 Lisboa Codex (Portugal))
1993-03-01
A theoretical and experimental study of Trivelpiece--Gould waves propagating in a magnetized plasma column is presented in this paper. In the experiments, these waves are excited by a radio frequency (rf) source, which also serves to create the plasma. Observation of nonlinear effects includes space and time recurrence effects, a wave spectrum containing a large number (up to 25) harmonics, and low-frequency sidebands. The theoretical model explains the recurrence effects as a consequence of multiple nonlinear interactions between the fundamental wave and its harmonics. A good agreement is found between theory and the experiments.
Propagating waves in human motor cortex
Directory of Open Access Journals (Sweden)
Kazutaka eTakahashi
2011-04-01
Full Text Available Previous studies in non-human primates have shown that beta oscillations (15-30Hz of local field potentials (LFPs in the arm/hand areas of primary motor cortex (MI propagate as traveling waves across the cortex. These waves exhibited two stereotypical features across animals and tasks: 1 The waves propagated in two dominant modal directions roughly 180 degrees apart, and 2 their propagation speed ranged from 10 ~ 35 cm/s. It is, however, unknown if such cortical waves occur in the human motor cortex. This study shows that the two properties of propagating beta waves are present in MI of a tetraplegic human patient while he was instructed to perform an instruction delay center out task using a cursor controlled by the chin. Moreover, we show that beta waves are sustained and have similar properties whether the subject was engaged in the task or at rest. The directions of the successive sustained waves both in the human subject and a nonhuman primate (NHP subject tended to switch from one dominant mode to the other, and at least in the NHP subject the estimated distance travelled between successive waves traveling into and out of the central sulcus is consistent with the hypothesis of wave reflection between the border of motor and somatosensory cortices. Further, we show that the occurrence of the beta waves is not uniquely tied to periods of increased power in the beta frequency band. These results demonstrate that traveling beta waves in MI are a general phenomenon occurring in human as well as non-human primates. Consistent with the non-human primate data, the dominant directions of the beta LFP waves in human aligned to the proximal to distal gradient of joint representations in MI somatotopy. This consistent finding of wave propagation may imply the existence of a hardwired organization of motor cortex that mediates this spatio-temporal pattern.
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 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.
Wave propagation in thermoelastic saturated porous medium
Indian Academy of Sciences (India)
tural engineering or to hydrocarbon/geothermal processes. References. Bear J, Sorek S, Ben-Dor G and Mazor G 1992 Displacement waves in saturated thermoelastic porous media, I. Basic equations; Fluid Dyn. Res. 9 155–164. Biot M A 1956a The theory of propagation of elastic waves in a fluid-saturated porous solid, ...
Nonlinear wave interactions of kinetic sound waves
Directory of Open Access Journals (Sweden)
G. Brodin
2015-08-01
Full Text Available We reconsider the nonlinear resonant interaction between three electrostatic waves in a magnetized plasma. The general coupling coefficients derived from kinetic theory are reduced here to the low-frequency limit. The main contribution to the coupling coefficient we find in this way agrees with the coefficient recently presented in Annales Geophysicae. But we also deduce another contribution which sometimes can be important, and which qualitatively agrees with that of an even more recent paper. We have thus demonstrated how results derived from fluid theory can be improved and generalized by means of kinetic theory. Possible extensions of our results are outlined.
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
Nonlinear Wave-Particle Interactions in Radiation Belt Physics
Summers, D.; Tang, R.; Omura, Y.; Miyashita, Y.
2010-12-01
Earth's radiation belts have undergone considerable theoretical and experimental investigation since their discovery in 1958 by James Van Allen and colleagues.Much of our understanding of wave-particle interactions in the radiation belts has been based on the linear theory of plasma waves and quasi-linear diffusion.There is recent evidence ,however,that fully nonlinear aspects of wave-particle interactions may play an essential role in radiation belt physics.This evidence is in the form of increasingly refined wave and particle data,and,in parallel,recently developed nonlinear wave growth theory supported by self-consistent particle simulations.We examine the nonlinear spatio-temporal evolution of whistler-mode chorus emissions in the Earth's inner magnetosphere.Chorus waves with rising frequency are generated at the magnetic equator,and propagate to higher latitudes.During propagation,nonlinear wave evolution occurs due to interaction with resonant electrons.From model equations we reproduce the time evolution of the chorus wave at the equator.By taking into account the adiabatic variation of the off-equatorial energetic particle distribution,we determine the resonant current.Then by solving general wave equations numerically we obtain the time evolution of the chorus wave frequency and amplitude along the static dipole magnetic field.Further,we incorporate the effects of nonlinear wave growth into the calculation of the Kennel-Petschek limit for the stably-trapped particle flux in a planetary magnetosphere.Using the model chorus equations we estimate nonlinear growth rates for a range of input parameters.By calculating the resulting total wave gain,we are able to estimate the self-limiting particle flux.We compare our new theoretical results for the limiting flux with particle observations at Earth and Saturn.
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.
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
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.
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...
Acoustical Wave Propagation in Sonic Composites
Directory of Open Access Journals (Sweden)
Iulian Girip
2015-09-01
Full Text Available The goal of this paper is to discuss the technique of controlling the mechanical properties of sonic composites. The idea is to architecture the scatterers and material from which they are made, their number and geometry in order to obtain special features in their response to external waves. We refer to perfectly reflecting of acoustical waves over a desired range of frequencies or to prohibit their propagation in certain directions, or confining the waves within specified volumes. The internal structure of the material has to be chosen in such a way that to avoid the scattering of acoustical waves inside the material. This is possible if certain band-gaps of frequencies can be generated for which the waves are forbidden to propagate in certain directions. These bandgaps can be extended to cover all possible directions of propagation by resulting a full band-gap. If the band-gaps are not wide enough, their frequency ranges do not overlap. These band-gaps can overlap due to reflections on the surface of thick scatterers, as well as due to wave propagation inside them. growth.
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)
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
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
Wave Propagation in Smart Materials
DEFF Research Database (Denmark)
Pedersen, Michael
1999-01-01
In this paper we deal with the behavior of solutions to hyperbolicequations such as the wave equation:\\begin{equation}\\label{waveeq1}\\frac{\\partial^2}{\\partial t^2}u-\\Delta u=f,\\end{equation}or the equations of linear elasticity for an isotropic medium:\\begin{equation}\\label{elasteq1}\\frac......{\\partial^2}{\\partial t^2}u -(\\lambda+\\mu){\\text{\\rm grad div}} u -\\mu\\Deltau=0,\\end{equation}where $u=u(t,x)$ denotes a 3-vector field on $\\Bbb R\\times\\Bbb R^3$,and $\\lambda$ and $\\mu$ are the Lame-constants....
Wave Propagation in Smart Materials
DEFF Research Database (Denmark)
Pedersen, Michael
1999-01-01
In this paper we deal with the behavior of solutions to hyperbolic equations such as the wave equation: \\begin{equation}\\label{waveeq1} \\frac{\\partial^2}{\\partial t^2}u-\\Delta u=f, \\end{equation} or the equations of linear elasticity for an isotropic medium: \\begin{equation}\\label{elasteq1} \\frac......{\\partial^2}{\\partial t^2}u -(\\lambda+\\mu){\\text{\\rm grad div}} u -\\mu\\Delta u=0, \\end{equation} where $u=u(t,x)$ denotes a 3-vector field on $\\Bbb R\\times\\Bbb R^3$, and $\\lambda$ and $\\mu$ are the Lame-constants....
Propagation of three-dimensional electron-acoustic solitary waves
Shalaby, M.; El-Labany, S. K.; Sabry, R.; El-Sherif, L. S.
2011-06-01
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.
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.
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.
Antenna Construction and Propagation of Radio Waves.
Marine Corps Inst., Washington, DC.
Developed as part of the Marine Corps Institute (MCI) correspondence training program, this course on antenna construction and propagation of radio waves is designed to provide communicators with instructions in the selection and/or construction of the proper antenna(s) for use with current field radio equipment. Introductory materials include…
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...
An optimal design problem in wave propagation
DEFF Research Database (Denmark)
Bellido, J.C.; Donoso, Alberto
2007-01-01
We consider an optimal design problem in wave propagation proposed in Sigmund and Jensen (Roy. Soc. Lond. Philos. Trans. Ser. A 361:1001-1019, 2003) in the one-dimensional situation: Given two materials at our disposal with different elastic Young modulus and different density, the problem consists...
Ionospheric Plasma Heating During Powerful Wave Propagation ...
African Journals Online (AJOL)
Ionospheric Plasma Heating During Powerful Wave Propagation. S Ram. Full Text: EMAIL FULL TEXT EMAIL FULL TEXT · DOWNLOAD FULL TEXT DOWNLOAD FULL TEXT · http://dx.doi.org/10.4314/dai.v12i1.15563 · AJOL African Journals Online. HOW TO USE AJOL... for Researchers · for Librarians · for Authors · FAQ's ...
Four Wave Mixing using Intermodal Nonlinearities
DEFF Research Database (Denmark)
Rishøj, Lars Søgaard
99.8 % of the power from the fundamental mode to a specific HOM in the custom designed fiber. Furthermore, it is demonstrated that stable propagation in the considered fiber is possible, without deterioration from mode coupling. Finally, modulation instability and multiple FWM signal and idler lines......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...... can be used as an additional degree of freedom to fulfill this phase matching requirement. The design of a specialty few moded fiber is discussed. This fiber allows for FWM between a pump in the Ytterbium gain region with a signal at telecommunication wavelengths, hereby generating a new wavelength...
MIMO nonlinear ultrasonic tomography by propagation and backpropagation method.
Dong, Chengdong; Jin, Yuanwei
2013-03-01
This paper develops a fast ultrasonic tomographic imaging method in a multiple-input multiple-output (MIMO) configuration using the propagation and backpropagation (PBP) method. By this method, ultrasonic excitation signals from multiple sources are transmitted simultaneously to probe the objects immersed in the medium. The scattering signals are recorded by multiple receivers. Utilizing the nonlinear ultrasonic wave propagation equation and the received time domain scattered signals, the objects are to be reconstructed iteratively in three steps. First, the propagation step calculates the predicted acoustic potential data at the receivers using an initial guess. Second, the difference signal between the predicted value and the measured data is calculated. Third, the backpropagation step computes updated acoustical potential data by backpropagating the difference signal to the same medium computationally. Unlike the conventional PBP method for tomographic imaging where each source takes turns to excite the acoustical field until all the sources are used, the developed MIMO-PBP method achieves faster image reconstruction by utilizing multiple source simultaneous excitation. Furthermore, we develop an orthogonal waveform signaling method using a waveform delay scheme to reduce the impact of speckle patterns in the reconstructed images. By numerical experiments we demonstrate that the proposed MIMO-PBP tomographic imaging method results in faster convergence and achieves superior imaging quality.
Shallow water sound propagation with surface waves.
Tindle, Chris T; Deane, Grant B
2005-05-01
The theory of wavefront modeling in underwater acoustics is extended to allow rapid range dependence of the boundaries such as occurs in shallow water with surface waves. The theory allows for multiple reflections at surface and bottom as well as focusing and defocusing due to reflection from surface waves. The phase and amplitude of the field are calculated directly and used to model pulse propagation in the time domain. Pulse waveforms are obtained directly for all wavefront arrivals including both insonified and shadow regions near caustics. Calculated waveforms agree well with a reference solution and data obtained in a near-shore shallow water experiment with surface waves over a sloping bottom.
Topology Optimization for Transient Wave Propagation Problems
DEFF Research Database (Denmark)
Matzen, René
as for vectorial elastic wave propagation problems using finite element analysis [P2], [P4]. The concept is implemented in a parallel computing code that includes efficient techniques for performing gradient based topology optimization. Using the developed computational framework the thesis considers four...... are derived by use of the adjoint variable method. Many wave propagation problems are open-region problems, i.e. the outer boundaries of the modeling domain must be re ection-less. The thesis contains new and independent developments within perfectly matched layer techniques for scalar as well......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...
Gravitational wave propagation in isotropic cosmologies
International Nuclear Information System (INIS)
Hogan, P.A.; O'Shea, E.M.
2002-01-01
We study the propagation of gravitational waves carrying arbitrary information through isotropic cosmologies. The waves are modeled as small perturbations of the background Robertson-Walker geometry. The perfect fluid matter distribution of the isotropic background is, in general, modified by small anisotropic stresses. For pure gravity waves, in which the perturbed Weyl tensor is radiative (i.e. type N in the Petrov classification), we construct explicit examples for which the presence of the anisotropic stress is shown to be essential and the histories of the wave fronts in the background Robertson-Walker geometry are shear-free null hypersurfaces. The examples derived in this case are analogous to the Bateman waves of electromagnetic theory
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.
Sources and propagation of atmospherical acoustic shock waves
Coulouvrat, François
2012-09-01
Sources of aerial shock waves are numerous and produce acoustical signals that propagate in the atmosphere over long ranges, with a wide frequency spectrum ranging from infrasonic to audible, and with a complex human response. They can be of natural origin, like meteors, lightning or volcanoes, or human-made as for explosions, so-called "buzz-saw noise" (BSN) from aircraft engines or sonic booms. Their description, modeling and data analysis within the viewpoint of nonlinear acoustics will be the topic of the present lecture, with focus on two main points: the challenges of the source description, and the main features of nonlinear atmospheric propagation. Inter-disciplinary aspects, with links to atmospheric and geo-sciences will be outlined. Detailed description of the source is very dependent on its nature. Mobile supersonic sources can be rotating (fan blades of aircraft engines) or in translation (meteors, sonic boom). Mach numbers range from transonic to hypersonic. Detailed knowledge of geometry is critical for the processes of boom minimization and audible frequency spectrum of BSN. Sources of geophysical nature are poorly known, and various mechanisms for explaining infrasound recorded from meteors or thunderstorms have been proposed. Comparison between recorded data and modeling may be one way to discriminate between them. Moreover, the nearfield of these sources is frequently beyond the limits of acoustical approximation, or too complex for simple modeling. A proper numerical description hence requires specific matching procedures between nearfield behavior and farfield propagation. Nonlinear propagation in the atmosphere is dominated by temperature and wind stratification. Ray theory is an efficient way to analyze observations, but is invalid in various situations. Nonlinear effects are enhanced locally at caustics, or in case of grazing propagation over a rigid surface. Absorption, which controls mostly the high frequency part of the spectrum contained
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.
Nonlinear coseismic infrasound waves in the upper atmosphere and ionosphere
Chum, J.; Liu, J. Y.; Cabrera, M. A.
2017-12-01
Vertical motion of the ground surface caused by seismic waves generates acoustic waves that propagate nearly vertically upward because of supersonic speed of seismic waves. As the air density decreases with height, the amplitude of acoustic waves increases to conserve the energy flux. If the initial perturbation is large enough (larger than 10 mm/s) and the period of waves is long (>10 s), then the amplitude reaches significant values in the upper atmosphere (e.g. oscillation velocities of the air particles become comparable with sound speed) and the nonlinear phenomena start to play an important role before the wave is dissipated. The nonlinear phenomena lead to changes of spectral content of the wave packet. The energy is transferred to lower frequencies, which can cause the formation of roughly bipolar N-shaped pulse in the vicinity of the epicenters (up to distance about 1000-1500 km) of strong, M>7, earthquakes. The nonlinear propagation is studied on the basis of numerical solution of continuity, momentum and heat equations in 1D (along vertical axis) for viscous compressible atmosphere. Boundary conditions on the ground are determined by real measurements of the vertical motion of the ground surface. The results of numerical simulations are in a good agreement with atmospheric fluctuations observed by continuous Doppler sounding at heights of about 200 km and epicenter distance around 800 km. In addition, the expected fluctuations of GSP-TEC are calculated.
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)
Directory of Open Access Journals (Sweden)
Rasolofosaon P.
2006-12-01
non-linéarité sous fort confinement, et qui pourraient engendrer un signal résultant d'une interaction onde-onde . Tempérant ce pessimisme, il faut noter qu'un éventuel signal d'interaction non linéaire présenterait l'avantage, quant à sa détection, d'être dans une bande de fréquence différente de celle des ondes utilisées pour l'engendrer. Bien que nous n'ayons pas connaissance d'essais d'application actuels, les perspectives paraissent plus encourageantes dans le domaine du génie civil ou minier. C'est dans le domaine diagraphique, où des distances de propagation sont très faibles, que des applications semblent possibles à moyen terme. Si l'on en juge par le dépôt très récent de plusieurs brevets, les compagnies de logging poursuivraient des recherches dans cette voie. A general and important characteristic of rocks is their elastically nonlinear behavior resulting in significant effects on wave propagation. The nonlinear response of rock is a direct consequence of the compliant nature of rock : the macro-and micro-structure of the material (microcracks, grain-to-grain contacts, etc. . As a result, the material modulus varies as a function of the applied pressure. Interest has grown significantly in the last several years, as illustrated by the increasing number of publications regarding this topic. Here we present a summary of the fundamentals of theory and of experimental observations characteristic of rock, and we address possible applications in geophysics. Two disciplines regarding the nonlinear elasticity of rock have been developed over recent years in tandem :- Acoustoelasticity where wave propagation in statically, prestressed materials is studied. Here one relates the variation in applied pressure to the elastic wavespeed in order to extract the nonlinear coefficients. This area of study includes the topic of stress-induced anisotropy. - Acoustic nonlinearity where we are interested in the temporary and local variation in the elastic
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.
Wave propagation in axially moving periodic strings
DEFF Research Database (Denmark)
Sorokin, Vladislav S.; Thomsen, Jon Juel
2017-01-01
The paper deals with analytically studying transverse waves propagation in an axially moving string with periodically modulated cross section. The structure effectively models various relevant technological systems, e.g. belts, thread lines, band saws, etc., and, in particular, roller chain drives...... for diesel engines by capturing both their spatial periodicity and axial motion. The Method of Varying Amplitudes is employed in the analysis. It is shown that the compound wave traveling in the axially moving periodic string comprises many components with different frequencies and wavenumbers....... This is in contrast to non-moving periodic structures, for which all components of the corresponding compound wave feature the same frequency. Due to this "multi-frequency" character of the wave motion, the conventional notion of frequency band-gaps appears to be not applicable for the moving periodic strings. Thus...
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
Nonlinear wave time dependent dynamic evolution in solar flux tubes
Fedun, V.; Erdelyi, R.
2005-12-01
The aim of the present work is to investigate the excitation, time dependent dynamic evolution and interaction of weakly nonlinear propagating (i.e. solitary) waves on vertical cylindrical magnetic flux tubes in a compressible solar atmospheric plasma. The axisymmetric flux tube has a field strength of 1000 G at its footpoint what is typical for photospheric regions. Solitons are excited by a footpoint driver. The propagation of the nonlinear signal is investigated by solving numerically a set of fully nonlinear 2D MHD equations in cylindrical coordinates. For the initial conditions the solutions of the linear dispersion relation for wave modes (in the present case we focus on the sausage mode) in a magnetic flux tube is applied. This dispersion relation is solved numerically for a range of plasma parameters. We compare our results with the works of Roberts [1], Wilson [2] (dispersion relation), Molotovshchikov [3] (nonlinear slow sausage waves) and Weisshaar [4] (numerical solutions of the Leibovich-Prichard-Roberts equation). (1) We found solitary solutions and investigate solitary propagating with external sound speed by solving the full MHD equations. (2) We also found a solitary wave propagating with the tube speed. A natural application of our studies may be spicule formation in the chromosphere, as suggested by Roberts [5], where it was demonstrated theoretically, that a solar photospheric magnetic flux tube can support the propagation of solitons governed by the Benjamin-Ono (slow mode) equations. Future possible improvements in modeling and the relevance of the photospheric chromospheric transition region coupling by spicules is suggested. [1] B. Roberts and A. Webb, Sol. Phys., 1978, v. 56, p. 5 [2] P.R. Wilson, Astron. Astrophys., 1980, v. 87, p. 121 [3] A.L. Molotovshchikov and M.S. Ruderman, Sol. Phys., 1987, v. 109, p. 247 [4] E. Weisshaar, Phys. Fluids A, 1989, v. 1(8), p. 1406 [5] B. Roberts and A. Mangeney, Royal Astronomical Society, Monthly
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.
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...... of artificial branches of the refractive index and simplicity in implementation. We prove the validity of the method on three case studies of homogeneous magnetized plasma, bi-cross and U-shaped metamaterials....
Modeling of Electromagnetic Wave Propagation with Tapered Transmission Line
Lee, Kun-A.; Ko, Kwang-Cheol
2012-09-01
Tapered transmission line was used for impedance matching, for high voltage pulse, and atmospheric medium is applied to characteristic equation of tapered transmission line and reflection coefficient so that nonlinear load and circuit modeling of atmospheric medium was simulated by electromagnetic transient program (EMTP). A characteristic of atmospheric medium and Time delay are decided by inductance and capacitance of tapered transmission line. For electromagnetic wave propagation modeling, in this paper, tapered transmission line is implemented. It is difficult to model tapered transmission line directly. Other transmission line that can be expressed by the circuit is used. So object of this paper is efficient modeling of tapered transmission line.
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.
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.
Dispersive shock waves in nonlinear and atomic optics
Kamchatnov, Anatoly
2017-10-01
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.
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.
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
Simulations of Seismic Wave Propagation on Mars
Bozdağ, Ebru; Ruan, Youyi; Metthez, Nathan; Khan, Amir; Leng, Kuangdai; van Driel, Martin; Wieczorek, Mark; Rivoldini, Attilio; Larmat, Carène S.; Giardini, Domenico; Tromp, Jeroen; Lognonné, Philippe; Banerdt, Bruce W.
2017-10-01
We present global and regional synthetic seismograms computed for 1D and 3D Mars models based on the spectral-element method. For global simulations, we implemented a radially-symmetric Mars model with a 110 km thick crust (Sohl and Spohn in J. Geophys. Res., Planets 102(E1):1613-1635, 1997). For this 1D model, we successfully benchmarked the 3D seismic wave propagation solver SPECFEM3D_GLOBE (Komatitsch and Tromp in Geophys. J. Int. 149(2):390-412, 2002a; 150(1):303-318, 2002b) against the 2D axisymmetric wave propagation solver AxiSEM (Nissen-Meyer et al. in Solid Earth 5(1):425-445, 2014) at periods down to 10 s. We also present higher-resolution body-wave simulations with AxiSEM down to 1 s in a model with a more complex 1D crust, revealing wave propagation effects that would have been difficult to interpret based on ray theory. For 3D global simulations based on SPECFEM3D_GLOBE, we superimposed 3D crustal thickness variations capturing the distinct crustal dichotomy between Mars' northern and southern hemispheres, as well as topography, ellipticity, gravity, and rotation. The global simulations clearly indicate that the 3D crust speeds up body waves compared to the reference 1D model, whereas it significantly changes surface waveforms and their dispersive character depending on its thickness. We also perform regional simulations with the solver SES3D (Fichtner et al. Geophys. J. Int. 179:1703-1725, 2009) based on 3D crustal models derived from surface composition, thereby addressing the effects of various distinct crustal features down to 2 s. The regional simulations confirm the strong effects of crustal variations on waveforms. We conclude that the numerical tools are ready for examining more scenarios, including various other seismic models and sources.
Nonlinear pulse propagation in nanoscale waveguides
Wulf, Matthias
2015-01-01
The bottleneck of optical communication systems, which form the backbone of the internet, is formed by electronical signal processing. A promising approach to solve this issue is to route the data instead by all-optical means using nonlinear optical effects. To exploit the normally weak nonlinear
Seismic Wave Propagation on the Tablet Computer
Emoto, K.
2015-12-01
Tablet computers widely used in recent years. The performance of the tablet computer is improving year by year. Some of them have performance comparable to the personal computer of a few years ago with respect to the calculation speed and the memory size. The convenience and the intuitive operation are the advantage of the tablet computer compared to the desktop PC. I developed the iPad application of the numerical simulation of the seismic wave propagation. The numerical simulation is based on the 2D finite difference method with the staggered-grid scheme. The number of the grid points is 512 x 384 = 196,608. The grid space is 200m in both horizontal and vertical directions. That is the calculation area is 102km x 77km. The time step is 0.01s. In order to reduce the user waiting time, the image of the wave field is drawn simultaneously with the calculation rather than playing the movie after the whole calculation. P and S wave energies are plotted on the screen every 20 steps (0.2s). There is the trade-off between the smooth simulation and the resolution of the wave field image. In the current setting, it takes about 30s to calculate the 10s wave propagation (50 times image updates). The seismogram at the receiver is displayed below of the wave field updated in real time. The default medium structure consists of 3 layers. The layer boundary is defined by 10 movable points with linear interpolation. Users can intuitively change to the arbitrary boundary shape by moving the point. Also users can easily change the source and the receiver positions. The favorite structure can be saved and loaded. For the advance simulation, users can introduce the random velocity fluctuation whose spectrum can be changed to the arbitrary shape. By using this application, everyone can simulate the seismic wave propagation without the special knowledge of the elastic wave equation. So far, the Japanese version of the application is released on the App Store. Now I am preparing the
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.
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....
2D wave-front shaping in optical superlattices using nonlinear volume holography.
Yang, Bo; Hong, Xu-Hao; Lu, Rong-Er; Yue, Yang-Yang; Zhang, Chao; Qin, Yi-Qiang; Zhu, Yong-Yuan
2016-07-01
Nonlinear volume holography is employed to realize arbitrary wave-front shaping during nonlinear processes with properly designed 2D optical superlattices. The concept of a nonlinear polarization wave in nonlinear volume holography is investigated. The holographic imaging of irregular patterns was performed using 2D LiTaO3 crystals with fundamental wave propagating along the spontaneous polarization direction, and the results agree well with the theoretical predictions. This Letter not only extends the application area of optical superlattices, but also offers an efficient method for wave-front shaping technology.
Modeling Propagation of Shock Waves in Metals
Howard, W. M.; Molitoris, J. D.
2006-07-01
We present modeling results for the propagation of strong shock waves in metals. In particular, we use an arbitrary Lagrange Eulerian (ALE3D) code to model the propagation of strong pressure waves (P ˜ 300 to 400 kbars) generated with high explosives in contact with aluminum cylinders. The aluminum cylinders are assumed to be both flat-topped and have large-amplitude curved surfaces. We use 3D Lagrange mechanics. For the aluminum we use a rate-independent Steinberg-Guinan model, where the yield strength and shear modulus depend on pressure, density and temperature. The calculation of the melt temperature is based on the Lindermann law. At melt the yield strength and shear modulus is set to zero. The pressure is represented as a seven-term polynomial as a function of density. For the HMX-based high explosive, we use a JWL, with a program burn model that give the correct detonation velocity and C-J pressure (P ˜ 390 kbars). For the case of the large-amplitude curved surface, we discuss the evolving shock structure in terms of the early shock propagation experiments by Sakharov.
Computations of Nonlinear Propagation of Sound Emitted from High Speed Mixing Layers
Punekar, J.; Avital, E. J.; Musafir, R. E.
2014-01-01
Non-linear sound propagation is investigated computationally by simulating compressible time-developing mixing layers using the Large Eddy Simulation (LES) approach and solving the viscous Burgers Equation. The mixing layers are of convective Mach numbers of 0.4, 0.8 and 1.2. The LES results agree qualitatively with known flow behavior. Mach waves are observed in the near sound field of the supersonic mixing layer computed by the LES. These waves show steepening typical to non-linear propagat...
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
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.
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
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.
Full wave simulations of lower hybrid wave propagation in tokamaks
Wright, J. C.; Bonoli, P. T.; Phillips, C. K.; Valeo, E.; Harvey, R. W.
2009-11-01
Lower hybrid (LH) waves have the attractive property of damping strongly via electron Landau resonance on relatively fast tail electrons at (2.5-3)×vte, where vte ≡ (2Te/me)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 1019 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.
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.
Nonlinear pulse propagation phenomena in 1D photonic crystals
Centini, Marco; D'Aguanno, Giuseppe; Scalora, Michael; Sibilia, Concita; Bloemer, Mark J.; Bowden, Charles M.; Bertolotti, Mario
2002-06-01
We numerically investigate nonlinear pulse propagation in finite, 1-d photonic crystals, and highlight novel properties that may help pave the way to a new class of high-efficiency nano-devices. We show that phase matching conditions for multiple wavelength generation and interactions can be achieved by judiciously combining material's index dispersions and geometrical features. We also show that enhanced nonlinear interactions can occur with efficiencies three orders of magnitude larger with respect to bulk materials having the same lengths and nonlinearity. Finally, we suggest potential applications as miniaturized second and third harmonic generators, nonlinear mirrors, parametric amplifiers, and optical switchers.
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....
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.
Self-similar propagation of Hermite-Gauss water-wave pulses.
Fu, Shenhe; Tsur, Yuval; Zhou, Jianying; Shemer, Lev; Arie, Ady
2016-01-01
We demonstrate both theoretically and experimentally propagation dynamics of surface gravity water-wave pulses, having Hermite-Gauss envelopes. We show that these waves propagate self-similarly along an 18-m wave tank, preserving their general Hermite-Gauss envelopes in both the linear and the nonlinear regimes. The measured surface elevation wave groups enable observing the envelope phase evolution of both nonchirped and linearly frequency chirped Hermite-Gauss pulses, hence allowing us to measure Gouy phase shifts of high-order Hermite-Gauss pulses for the first time. Finally, when increasing pulse amplitude, nonlinearity becomes essential and the second harmonic of Hermite-Gauss waves was observed. We further show that these generated second harmonic bound waves still exhibit self-similar Hermite-Gauss shapes along the tank.
Nonlinear waves from a localized vortex source in strongly correlated fluids
Gupta, Akanksha; Ganesh, Rajaraman; Joy, Ashwin
2017-11-01
Highly charged quasi two-dimensional grain medium (complex plasma) is a remarkable test-bed to study wave like phenomena. Understanding of such wave propagation has many important applications in geophysics, petroleum engineering, and mining, earthquakes, and seismology. In the present study, for the first time, the propagation of nonlinear wave which originates from localized coherent vortex source has been studied using molecular dynamics simulation taking Yukawa liquids as a prototype for strongly correlated fluid. In this work, the coupling of transverse and longitudinal mode, effect of azimuthal speed of vortex source on the linear and nonlinear properties of generated wave will be presented as a function of strong correlation.
Propagation Dynamics of Nonspreading Cosine-Gauss Water-Wave Pulses.
Fu, Shenhe; Tsur, Yuval; Zhou, Jianying; Shemer, Lev; Arie, Ady
2015-12-18
Linear gravity water waves are highly dispersive; therefore, the spreading of initially short wave trains characterizes water surface waves, and is a universal property of a dispersive medium. Only if there is sufficient nonlinearity does this envelope admit solitary solutions which do not spread and remain in fixed forms. Here, in contrast to the nonlinear localized wave packets, we present both theoretically and experimentally a new type of linearly nondispersive water wave, having a cosine-Gauss envelope, as well as its higher-order Hermite cosine-Gauss variations. We show that these waves preserve their width despite the inherent dispersion while propagating in an 18-m wave tank, accompanied by a slowly varying carrier-envelope phase. These wave packets exhibit self-healing; i.e., they are restored after bypassing an obstacle. We further demonstrate that these nondispersive waves are robust to weakly nonlinear perturbations. In the strong nonlinear regime, symmetry breaking of these waves is observed, but their cosine-Gauss shapes are still approximately preserved during propagation.
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.
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.
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 between...
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.
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.
Non-Reciprocal Geometric Wave Diode by Engineering Asymmetric Shapes of Nonlinear Materials
Li, Nianbei; Ren, Jie
2014-01-01
Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study the novel design of wave diode devices by engineering asymmetric shapes of nonlinear materials to realize the function of non-reciprocal wave propagations. We first show analytical results revealing that both nonlinearity and asymmetry are necessary to induce such non-reciprocal (asymmetric) wave propagations. Detailed numerical simulations are further performed for a more realistic geometric wave diode model with typical asymmetric shape, where good non-reciprocal wave diode effect is demonstrated. Finally, we discuss the scalability of geometric wave diodes. The results open a flexible way for designing wave diodes efficiently simply through shape engineering of nonlinear materials, which may find broad implications in controlling energy, mass and information transports. PMID:25169668
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
Šantić, Neven; Fusaro, Adrien; Salem, Sabeur; Garnier, Josselin; Picozzi, Antonio; Kaiser, Robin
2018-02-01
The nonlinear Schrödinger equation, used to describe the dynamics of quantum fluids, is known to be valid not only for massive particles but also for the propagation of light in a nonlinear medium, predicting condensation of classical waves. Here we report on the initial evolution of random waves with Gaussian statistics using atomic vapors as an efficient two dimensional nonlinear medium. Experimental and theoretical analysis of near field images reveal a phenomenon of nonequilibrium precondensation, characterized by a fast relaxation towards a precondensate fraction of up to 75%. Such precondensation is in contrast to complete thermalization to the Rayleigh-Jeans equilibrium distribution, requiring prohibitive long interaction lengths.
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.
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
Nonlinear gravity-capillary water waves
Jiang, Lei
1997-11-01
Two-dimensional gravity-capillary water waves are analyzed using a fully-nonlinear Cauchy-integral method with spectral accuracy. Standing waves are generated in experiments by vertical oscillation and measured by a non-intrusive optical system along with a wave probe. Nonlinear resonance of standing waves with non-wetting contact line effects are discussed in detail. Amplitude- dependent wave frequency and damping in a glass rectangular tank suggest a new contact-line model. A new type of sideband resonance due to modulated forcing is discovered and explained by weakly-nonlinear analysis. This analytical solution is verified by our numerical simulations and physical experiments. New standing waveforms with dimpled or sharp crests are observed in experiments and computations. These new waveforms have strong symmetry breaking in time as a result of nonlinear harmonic interaction. With increasing wave steepness, steep standing waves experience period- tripling with three distinct forms: sharp crest, dimpled or flat crest, and round crest. Significant breaking occurs in the sharp-crest mode and the dimpled-crest mode. Using a complex-demodulation technique, I find that these breaking waves are related to the same 1:2 internal resonance (harmonic interaction) that causes the new steep waveforms. Novel approaches are used to estimate the (breaking and non-breaking) wave dissipation in steep and breaking standing waves. The breaking events (spray, air entrainment, and plunging) approximately double the wave dissipation. Weak capillarity significantly affects the limiting wave height and the form of standing waves, as demonstrated by both computations and small-scale Faraday-wave experiments. Capillary ripple generation on traveling waves is shown to be significant even at moderate wave steepness. The ubiquitous horizontal asymmetry of traveling waves is shown to be critical to capillary ripple generation. Two new asymmetric modes are identified and are shown to have an
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)
In Situ Observations of Seismic Wave Propagation
Hudson, Kenneth Stewart
Instrumented geotechnical field sites are designed to capture the infrequent but critically important in situ case histories of ground response, deformation, and liquefaction during significant earthquakes that generate high intensity ground shaking and large strains. The University of California at Santa Barbara has been monitoring densely instrumented geotechnical array field sites for almost three decades, with continuous recording now for more than a decade. When seismic waves travel into soil with sufficiently large ground motions, the soil behaves nonlinearly meaning the shear modulus of the material decreases from the linear value observed during weak ground motions. The degraded shear modulus can continue to affect a site for a period of time by changing the soil response during smaller ground motions after the large event. Decreased shear modulus is inferred when a decrease of shear wave velocity between two sensors in a vertical downhole array is observed. This velocity is calculated by measuring the difference in shear wave arrival times between the sensors using normalized cross correlation. The trend of decreasing shear wave velocity with increasing peak ground acceleration is observed at multiple geotechnical array field sites. The length of time the decreased velocity remains following stronger shaking is analyzed using more than 450 events over more than a decade at the Wildlife Liquefaction Array (WLA). Using both monthly and yearly velocity averages between sensors, there is evidence that suggests the shear wave velocity remains low over a period of months following larger significant shaking events at the site. In addition, at WLA there is evidence that the decrease in shear wave velocity can be detected at ground motion levels as low as 20 cm/s2. Additionally at the Garner Valley Downhole Array, a permanent cross-hole experiment is used to measure velocity changes in the soil with changing water table height. An underground hammer source swings
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
Wave propagation in heterogeneous excitable media
Schebesch, I.; Engel, H.
1998-04-01
Heterogeneities deeply affect pulse dynamics in excitable media. In one dimension, spatially periodic variation of the excitation threshold leads to a characteristic dependence of the propagation speed on the modulation period d with a maximum at a certain optimal value dopt. The maximum speed may be larger than the pulse velocity in an effective homogeneous medium. In two dimensions, the geometry and size of heterogeneities determine the wave dynamics. For example, an excitability distribution made of oblique stripes with different angles of inclination can result in a speedup or a slowdown of the pulse. The calculations are carried out with a modified Oregonator model for light-sensitive Belouzov-Zhabotinskii media where a heterogeneous distribution of excitability can be achieved by inhomogeneous illumination. Nevertheless, the results do not depend on the details of the local kinetics, but apply to the general case of excitable media.
Propagation of nonlinear reactive contaminants in porous media
Serrano, Sergio E.
2003-08-01
A study on the effect of nonlinear reactions on the space and time distribution of contaminant plumes governed by the advective-dispersive equation in porous media was conducted. Several models of nonlinear reactions were considered: the irreversible nonlinear first-order kinetic sorption model, the nonlinear Freundlich sorption isotherm model, the nonlinear Langmuir sorption isotherm model, and the reversible nonlinear kinetic sorption model. Each of these models was coupled with the advective-dispersive equation with dimensionless concentration and an approximate analytical series solutions was obtained. Comparison between linear and nonlinear plumes indicated that nonlinear reactions may have a significant effect on the shape and spatial distribution of a contaminant at a given time and in certain cases may explain quantitatively the occurrence of scaled (e.g., concentration change while preserving shape), retarded, and nonsymmetric plumes as well as the presence of back tails and sharp front ends usually observed in the field. By adopting a nonlinear model of contaminant migration a more realistic representation of contaminant propagation is possible than that obtained with a linear model.
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.
Bulk Nonlinear Elastic Strain Waves in a Bilayer Coaxial Cylindrical Rod
Gula, I. A.; Samsonov, A. M.
2017-12-01
The problem of the propagation of long nonlinear elastic strain waves in a bilayer coaxial cylindrical rod with an ideal contact between the layers has been considered. Expressions for transverse displacements through longitudinal displacements have been derived. The former satisfies free boundary conditions and continuity conditions for displacements and stresses at the interlayer interface with the desired accuracy. It has been shown how these expressions generalize the well-known plane-section and Love hypotheses for an isotropic homogeneous rod. An equation for the propagation of a nonlinearly elastic strain longitudinal wave has been derived, and its particular solution in the form of a solitary traveling wave has been studied.
Effect of Resolution on Propagating Detonation Wave
Energy Technology Data Exchange (ETDEWEB)
Menikoff, Ralph [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2014-07-10
Simulations of the cylinder test are used to illustrate the effect of mesh resolution on a propagating detonation wave. For this study we use the xRage code with the SURF burn model for PBX 9501. The adaptive mesh capability of xRage is used to vary the resolution of the reaction zone. We focus on two key properties: the detonation speed and the cylinder wall velocity. The latter is related to the release isentrope behind the detonation wave. As the reaction zone is refined (2 to 15 cells for cell size of 62 to 8μm), both the detonation speed and final wall velocity change by a small amount; less than 1 per cent. The detonation speed decreases with coarser resolution. Even when the reaction zone is grossly under-resolved (cell size twice the reaction-zone width of the burn model) the wall velocity is within a per cent and the detonation speed is low by only 2 per cent.
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...
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...... obtained the travelling wave solutions to DDE, and, in particular, the strain solitary wave solution, which was shown to be significantly affected by parameters of the inclusions. Moreover we found some critical inaccuracies, committed in papers by others in the derivation of a constitutive equation...... for the long strain waves in a microstructured medium, revised them, and showed an importance of improvements for correct estimation of wave parameters....
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
On the rogue waves propagation in non-Maxwellian complex space plasmas
Energy Technology Data Exchange (ETDEWEB)
El-Tantawy, S. A., E-mail: samireltantawy@yahoo.com; El-Awady, E. I., E-mail: eielawady@hotmail.com [Department of Physics, Faculty of Science, Port Said University, Port Said 42521 (Egypt); Tribeche, M., E-mail: mouloudtribeche@yahoo.fr, E-mail: mtribeche@usthb.dz [Plasma Physics Group, Theoretical Physics Laboratory, Faculty of Physics, University of Bab-Ezzouar, USTHB, BP 32, El Alia, Algiers 16111 (Algeria)
2015-11-15
The implications of the non-Maxwellian electron distributions (nonthermal/or suprathermal/or nonextensive distributions) are examined on the dust-ion acoustic (DIA) rogue/freak waves in a dusty warm plasma. Using a reductive perturbation technique, the basic set of fluid equations is reduced to a nonlinear Schrödinger equation. The latter is used to study the nonlinear evolution of modulationally unstable DIA wavepackets and to describe the rogue waves (RWs) propagation. Rogue waves are large-amplitude short-lived wave groups, routinely observed in space plasmas. The possible region for the rogue waves to exist is defined precisely for typical parameters of space plasmas. It is shown that the RWs strengthen for decreasing plasma nonthermality and increasing superthermality. For nonextensive electrons, the RWs amplitude exhibits a bit more complex behavior, depending on the entropic index q. Moreover, our numerical results reveal that the RWs exist with all values of the ion-to-electron temperature ratio σ for nonthermal and superthermal distributions and there is no limitation for the freak waves to propagate in both two distributions in the present plasma system. But, for nonextensive electron distribution, the bright- and dark-type waves can propagate in this case, which means that there is a limitation for the existence of freak waves. Our systematic investigation should be useful in understanding the properties of DIA solitary waves that may occur in non-Maxwellian space plasmas.
Surface wave propagation characteristics in atmospheric pressure plasma column
International Nuclear Information System (INIS)
Pencheva, M; Benova, E; Zhelyazkov, I
2007-01-01
In the typical experiments of surface wave sustained plasma columns at atmospheric pressure the ratio of collision to wave frequency (ν/ω) is much greater than unity. Therefore, one might expect that the usual analysis of the wave dispersion relation, performed under the assumption ν/ω = 0, cannot give adequate description of the wave propagation characteristics. In order to study these characteristics we have analyzed the wave dispersion relationship for arbitrary ν/ω. Our analysis includes phase and wave dispersion curves, attenuation coefficient, and wave phase and group velocities. The numerical results show that a turning back point appears in the phase diagram, after which a region of backward wave propagation exists. The experimentally observed plasma column is only in a region where wave propagation coefficient is higher than the attenuation coefficient. At the plasma column end the electron density is much higher than that corresponding to the turning back point and the resonance
Propagation of waves in a multicomponent plasma having charged ...
Indian Academy of Sciences (India)
Abstract. Propagation of both low and high frequency waves in a plasma consisting of electrons, ions, positrons and charged dust particles have been theoretically studied. The characteristics of dust acoustic wave propagating through the plasma has been analysed and the dispersion relation deduced is a generalization of ...
Topology Optimization in wave-propagation and flow problems
DEFF Research Database (Denmark)
Sigmund, Ole; Jensen, Jakob Søndergaard; Gersborg-Hansen, A.
2004-01-01
We discuss recent extensions of the topology optimization method to wave-propagation and flow problems. More specifically, we optimize material distribution in scalar wave propagation problems modelled by Helmholtz equation. Moreover, we investigate the influence of the inertia term on the optimal...
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
Sound wave propagation in weakly polydisperse granular materials
Mouraille, O.J.P.; Luding, Stefan
2008-01-01
Dynamic simulations of wave propagation are performed in dense granular media with a narrow polydisperse size-distribution and a linear contact-force law. A small perturbation is created on one side of a static packing and its propagation, for both P- and S-waves, is examined. A size variation
Wave Packet Propagation and Electric Conductivity of Nanowires
Maeda, Munehiko; Saito, Keiji; Miyashita, Seiji; Raedt, Hans De
2004-01-01
We compute the electric conductivity of nanowires in the presence of magnetic domain walls by the method of wave packet propagation. We demonstrate that the propagation through the wire depends on the initial state used in the wave packet simulation. We propose a procedure, based on the Landauer
Analysis of flexural wave propagation in poroelastic composite ...
African Journals Online (AJOL)
Wave propagation in an infinitely long poroelastic composite hollow cylinder in is examined by employing Biot's theory of wave propagation in poroelastic media. A poroelastic composite hollow cylinder consists of two concentric poroelastic cylindrical layers both of which are made of different poroelastic materials with each ...
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)
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
Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media
Energy Technology Data Exchange (ETDEWEB)
Kartashov, Yaroslav V [ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, E-08034 Barcelona (Spain); Egorov, Alexey A [Physics Department, M V Lomonosov Moscow State University, 119899, Moscow (Russian Federation); Vysloukh, Victor A [Departamento de Fisica y Matematicas, Universidad de las Americas-Puebla, Santa Catarina Martir, 72820, Puebla, Cholula (Mexico); Torner, Lluis [ICFO-Institut de Ciencies Fotoniques, and Department of Signal Theory and Communications, Universitat Politecnica de Catalunya, E-08034 Barcelona (Spain)
2004-05-01
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.
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
Wave propagation in damage assessment of ground anchors
Zima, B.; Rucka, M.
2015-07-01
The inspection possibilities of ground anchors are limited to destructive test such as pull-out test. Guided wave propagation gives an opportunity to develop an inspection system dedicated to determine the condition of inspected element without violation of their integrity. In this paper the experimental study on wave propagation in laboratory models of ground anchors are presented. Experiments were conducted for different bonding lengths and different frequencies of excitation. Waves were generated by a piezoelectric actuator and the laser vibrometry technique was used to register velocity signals. For all tested anchors it was possible to identify the boundary between steel and concrete based on the registered reflections in wave propagation signals.
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.
A propagation model of computer virus with nonlinear vaccination probability
Gan, Chenquan; Yang, Xiaofan; Liu, Wanping; Zhu, Qingyi
2014-01-01
This paper is intended to examine the effect of vaccination on the spread of computer viruses. For that purpose, a novel computer virus propagation model, which incorporates a nonlinear vaccination probability, is proposed. A qualitative analysis of this model reveals that, depending on the value of the basic reproduction number, either the virus-free equilibrium or the viral equilibrium is globally asymptotically stable. The results of simulation experiments not only demonstrate the validity of our model, but also show the effectiveness of nonlinear vaccination strategies. Through parameter analysis, some effective strategies for eradicating viruses are suggested.
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
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.
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.
Agapitov, O. V.; Krasnoselskikh, V; Mozer, F. S.; Artemyev, A.V.; Volokitin, A.S.
2015-01-01
International audience; Huge numbers of different nonlinear structures (double layers, electron holes, nonlinear whistlers, etc., referred to as Time Domain Structures, TDS) have been observed by the electric field experiment on the Van Allen Probes. Some of them are associated with whistler waves. Such TDS often emerge on the forward edges of the whistler wave packets and form chains. The parametric decay of a whistler wave into a whistler wave propagating in the opposite direction and an el...
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.
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.
Modeling Anisotropic Elastic Wave Propagation in Jointed Rock Masses
Hurley, R.; Vorobiev, O.; Ezzedine, S. M.; Antoun, T.
2016-12-01
We present a numerical approach for determining the anisotropic stiffness of materials with nonlinearly-compliant joints capable of sliding. The proposed method extends existing ones for upscaling the behavior of a medium with open cracks and inclusions to cases relevant to natural fractured and jointed rocks, where nonlinearly-compliant joints can undergo plastic slip. The method deviates from existing techniques by incorporating the friction and closure states of the joints, and recovers an anisotropic elastic form in the small-strain limit when joints are not sliding. We present the mathematical formulation of our method and use Representative Volume Element (RVE) simulations to evaluate its accuracy for joint sets with varying complexity. We then apply the formulation to determine anisotropic elastic constants of jointed granite found at the Nevada Nuclear Security Site (NNSS) where the Source Physics Experiments (SPE), a campaign of underground chemical explosions, are performed. Finally, we discuss the implementation of our numerical approach in a massively parallel Lagrangian code Geodyn-L and its use for studying wave propagation from underground explosions. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
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'.
Generation and propagation of shock waves in the exhaust pipe of a 4 cycle automobile engine
Sekine, N.; Matsumura, S.; Aoki, K.; Takayama, K.
1990-07-01
An experimental investigation was made of reduction of noise generated in the exhaust pipe of a half liter 4-cycle water-cooled automobile gasoline engine. The pressure measurement along the exhaust pipe showed the nonlinear transition of compression waves discharged from the exhaust port of the engine into shock waves. In order to obtain a direct evidence of shock waves in the exhaust pipe, a flow visualization study was also conducted using a double exposure holographic interferometry. Weak shock waves of Mach number 1.09 exist in the exhaust pipe. For the purpose of collecting the data for designing optimum muffler configurations, additional shock tube experiments were carried out. The results indicates that the study of the non-linear wave interaction and propagation is important for the design of muffler.
Nonlinear Evolution of Short-wavelength Torsional Alfvén Waves
Shestov, S. V.; Nakariakov, V. M.; Ulyanov, A. S.; Reva, A. A.; Kuzin, S. V.
2017-05-01
We analyze nonlinear evolution of torsional Alfvén waves in a straight magnetic flux tube filled in with a low-β plasma, and surrounded with a plasma of lower density. Such magnetic tubes model, in particular, a segment of a coronal loop or a polar plume. The wavelength is taken comparable to the tube radius. We perform a numerical simulation of the wave propagation using ideal magnetohydrodynamics. We find that a torsional wave nonlinearly induces three kinds of compressive flows: the parallel flow at the Alfvén speed, which constitutes a bulk plasma motion along the magnetic field, the tube wave, and also transverse flows in the radial direction, associated with sausage fast magnetoacoustic modes. In addition, the nonlinear torsional wave steepens and its propagation speed increases. The latter effect leads to the progressive distortion of the torsional wave front, I.e., nonlinear phase mixing. Because of the intrinsic non-uniformity of the torsional wave amplitude across the tube radius, the nonlinear effects are more pronounced in regions with higher wave amplitudes. They are always absent at the axes of the flux tube. In the case of a linear radial profile of the wave amplitude, the nonlinear effects are localized in an annulus region near the tube boundary. Thus, the parallel compressive flows driven by torsional Alfvén waves in the solar and stellar coronae, are essentially non-uniform in the perpendicular direction. The presence of additional sinks for the wave energy reduces the efficiency of the nonlinear parallel cascade in torsional Alfvén waves.
Kelvin-Helmholtz billows and their effects on mean state during gravity wave propagation
Directory of Open Access Journals (Sweden)
X. Liu
2009-07-01
Full Text Available The Kelvin-Helmholtz (KH billows which appear in the process of gravity wave (GW propagation are simulated directly by using a compressible nonlinear two-dimensional gravity wave model. The differences between our model and others include: the background field has no special initial configuration and there is no initial triggering mechanism needed in the mesosphere and lower thermosphere (MLT region to excite the KH billows. However, the initial triggering mechanism is performed in the lower atmosphere through GW, which then propagate into the MLT region and form billows. The braid structures and overturning of KH billows, caused by nonlinear interactions between GWs and mean flow, can be resolved precisely by the model. These results support the findings in airglow studies that GWs propagating from below into the MLT region are important sources of KH billows. The onset of small scale waves and the wave energy transfer induce the shallower vertical wave number power spectral densities (PSD. However, most of the slopes are steeper than the expected kz−3 power law, which indicates that GWs with 10 km vertical wavelength are still a dominant mode. The results also show that the evolution of mean wind vary substantially between the different processes of GWs propagation. Before the KH billows evolve, the mean wind is accelerated greatly by GWs. By contrast, as the KH billows evolve and mix with mean flow, the mean wind and its peak value decrease.
Propagation of Elastic Waves in Prestressed Media
Directory of Open Access Journals (Sweden)
Inder Singh
2010-01-01
Full Text Available 3D solutions of the dynamical equations in the presence of external forces are derived for a homogeneous, prestressed medium. 2D plane waves solutions are obtained from general solutions and show that there exist two types of plane waves, namely, quasi-P waves and quasi-SV waves. Expressions for slowness surfaces and apparent velocities for these waves are derived analytically as well as numerically and represented graphically.
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.
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)
Nonlinear waves in collisionless gravitating systems
Energy Technology Data Exchange (ETDEWEB)
Polyachenko, V.L.; Shukhman, I.G.
1979-09-01
Nonlinear equations are derived for the gravitational potential in collisionless systems modeling galaxies. Solutions in the form of solitary waves (solitons) are obtained and their stability is tested. Systems composed of both stars and gas are also discussed. The dependence of the critical wavelength on the perturbation amplitude is established for the classical Jeans problem (an infinite, homogeneous world model) and for its two- and one-dimensional analogs in the collisionless case.
Local principles of wave propagation in inhomogeneous media
Gingold, Harry; She, Jianming; Zorumski, William E.
1993-01-01
Four local principles are proven for waves propagating in a layered medium with a variable wave speed. These principles are (1) that inhomogeneities increase the amplitude of waves generated by a source of fixed strength, (2) that inhomogeneities reduce spatial oscillation, or increase the wavelength, (3) that inhomogeneities decrease transmission, or increase reflection, and (4) that transmission increases monotonically with frequency. Definitions of inhomogeneity, local wave function, and local reflection and transmission coefficients are made as a basis for stating these principles.
Whistler Wave Propagation Through the Ionosphere of Venus
Pérez-Invernón, F. J.; Lehtinen, N. G.; Gordillo-Vázquez, F. J.; Luque, A.
2017-11-01
We investigate the attenuation of whistler waves generated by hypotetical Venusian lightning occurring at the altitude of the cloud layer under different ionospheric conditions. We use the Stanford full-wave method for stratified media of Lehtinen and Inan (2008) to model wave propagation through the ionosphere of Venus. This method calculates the electromagnetic field created by an arbitrary source in a plane-stratified medium (i.e., uniform in the horizontal direction). We see that the existence of holes in electronic densities and the magnetic field configuration caused by solar wind play an important role in the propagation of electromagnetic waves through the Venusian ionosphere.
Surface wave propagation in a fluid-saturated incompressible ...
Indian Academy of Sciences (India)
saturated incompressible porous media. Many studies have discussed the surface wave propagation in elastic media and a com- prehensive review is available in the standard texts, e.g., Ewing et al (1957) and Achenbach. (1976). The surface ...
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...
Theoretical Studies of Stress Wave Propagation in Laterally Confined Soils
National Research Council Canada - National Science Library
Rohani, Behzad
1999-01-01
.... A considerable body of scientific literature on one-dimensional stress wave propagation for such models has been published in recent years by various researchers, both in the United States and abroad...
Evidence for Nonlinear VLF Wave Physics from Van Allen Probe Data
Crabtree, C. E.; Tejero, E. M.; Ganguli, G.; Hospodarsky, G. B.; Kletzing, C.
2015-12-01
VLF waves in the whistler mode branch in the Earth's radiation belts play a critical role in both the acceleration and loss of energetic electrons. VLF waves are often observed with magnetic field amplitudes that are a significant fraction of the background magnetic field suggesting that nonlinear effects may be important. We develop new Bayesian time-series analysis tools to investigate magnetic and electric field data from the EMFISIS instrument on board the Van Allen Probes. We also validate the analysis techniques through laboratory experiments. We apply these tools to Chorus waves to show that the picture of a single coherent plane wave is insufficient to explain EMFISIS data and that nonlinear collective wave interactions play an important role in moderating Chorus wave growth. We also apply these techniques to show that nonlinear induced scattering by thermal electrons can play a significant role in controlling the propagation of large amplitude lightning generated whistlers inside the plasmasphere.
On wave propagation in a random micropolar generalized thermoelastic medium
Mitra Manindra; Bhattacharyya Rabindra Kumar
2017-01-01
This paper endeavours to study aspects of wave propagation in a random generalized-thermal micropolar elastic medium. The smooth perturbation technique conformable to stochastic differential equations has been employed. Six different types of waves propagate in the random medium. The dispersion equations have been derived. The effects due to random variations of micropolar elastic and generalized thermal parameters have been computed. Randomness causes change of phase speed and attenuation of...
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
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.
Linear and Nonlinear Infrasound Propagation to 1000 km
2015-12-15
FOR PUBLIC RELEASE; DISTRIBUTION IS UNLIMITED. AIR FORCE RESEARCH LABORATORY Space Vehicles Directorate 3550 Aberdeen Ave. SE AIR FORCE MATERIEL...NUMBER 9. SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES) Air Force Research Laboratory Space Vehicles Directorate 3550 Aberdeen Avenue SE...the results of Castor et al. (2004), who found that the spectra of hydroacoustic waves also retain the nonlinear signature of a high amplitude source
Femtosecond Pulse Propagation in a Highly Nonlinear Photonic Crystal Fiber
J. F. Gabayno; C. A. Alonzo; W. O. Garcia
2004-01-01
Femtosecond pulses are launched into a highly nonlinear photonic crystal fiber (PCF). The input and output spectra were measured using a monochromator and streak camera. The spectrum of the output from a 50 cm PCF pumped at 794 nm for different pump powers features asymmetric side lobes due to intrapulse Raman scattering. Similar measurements on a 100 cm PCF pumped at 795 nm highlight the appearance of blueshifted peaks as a result of energy transfer of solitons to dispersive waves. Broadenin...
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....
A method for generating highly nonlinear periodic waves in physical wave basins
DEFF Research Database (Denmark)
Zhang, Haiwen; Schäffer, Hemming A.; Bingham, Harry B.
2006-01-01
This abstract describes a new method for generating nonlinear waves of constant form in physical wave basins. The idea is to combine fully dispersive linear wavemaker theory with nonlinear shallow water wave generation theory; and use an exact nonlinear theory as the target. We refer to the method...... as an ad-hoc unified wave generation theory, since there is no rigorous analysis behind the idea which is simply justified by the improved results obtained for the practical generation of steady nonlinear waves....
On wave propagation in a random micropolar generalized thermoelastic medium
Directory of Open Access Journals (Sweden)
Mitra Manindra
2017-06-01
Full Text Available This paper endeavours to study aspects of wave propagation in a random generalized-thermal micropolar elastic medium. The smooth perturbation technique conformable to stochastic differential equations has been employed. Six different types of waves propagate in the random medium. The dispersion equations have been derived. The effects due to random variations of micropolar elastic and generalized thermal parameters have been computed. Randomness causes change of phase speed and attenuation of waves. Attenuation coefficients for high frequency waves have been computed. Second moment properties have been briefly discussed with application to wave propagation in the random micropolar elastic medium. Integrals involving correlation functions have been transformed to radial forms. A special type of generalized thermo-mechanical auto-correlation functions has been used to approximately compute effects of random variations of parameters. Uncoupled problem has been briefly outlined.
Propagation of gravitational waves in the nonperturbative spinor vacuum
Energy Technology Data Exchange (ETDEWEB)
Dzhunushaliev, Vladimir [Al-Farabi Kazakh National University, Department of Theoretical and Nuclear Physics, Almaty (Kazakhstan); Al-Farabi Kazakh National University, Institute of Experimental and Theoretical Physics, Almaty (Kazakhstan); Eurasian National University, Institute for Basic Research, Astana (Kazakhstan); Institute of Physicotechnical Problems and Material Science of the NAS of the Kyrgyz Republic, Bishkek (Kyrgyzstan); Folomeev, Vladimir [Institute of Physicotechnical Problems and Material Science of the NAS of the Kyrgyz Republic, Bishkek (Kyrgyzstan)
2014-09-15
The propagation of gravitational waves on the background of a nonperturbative vacuum of a spinor field is considered. It is shown that there are several distinctive features in comparison with the propagation of plane gravitational waves through empty space: there exists a fixed phase difference between the h{sub yy,zz} and h{sub yz} components of the wave; the phase and group velocities of gravitational waves are not equal to the velocity of light; the group velocity is always less than the velocity of light; under some conditions the gravitational waves are either damped or absent; for given frequency, there exist two waves with different wave vectors. We also discuss the possibility of an experimental verification of the obtained effects as a tool to investigate nonperturbative quantum field theories. (orig.)
Badiey, M.; Lynch, J. F.
2012-11-01
In the past half-century numerous scientific research programs have been conducted which have advanced our understanding of shallow water acoustics far beyond the original and pioneering work by Ewing, Worzel, and Pekeris (1948). In particular, during the last three decades several major initiatives have focused on both observation and modeling of acoustic waves in shallow water region with extremely variable environmental properties. We now realize that the shallow water acoustic wave propagation problem is a complicated study of wave propagation in a 4D partially random media with anisotropic, time and space dependent physical properties. The nonlinear internal wave field, the shelf break front, and coastal eddies are good examples of oceanographic processes that cause this type of variability. A review of our progress, which focuses on the effects of the water column, is presented, as well as an assessment of what future questions will be of interest and importance.
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
Chirped self-similar waves for quadratic-cubic nonlinear Schrödinger equation
Pal, Ritu; Loomba, Shally; Kumar, C. N.
2017-12-01
We have constructed analytical self-similar wave solutions for quadratic-cubic Nonlinear Schrödinger equation (QC-NLSE) by means of similarity transformation method. Then, we have investigated the role of chirping on these self-similar waves as they propagate through the tapered graded index waveguide. We have revealed that the chirping leads to interesting features and allows us to control the propagation of self-similar waves. This has been demonstrated for two cases (i) periodically distributed system and (ii) constant choice of system parameters. We expect our results to be useful in designing high performance optical devices.
Remarks on the parallel propagation of small-amplitude dispersive Alfvénic waves
Directory of Open Access Journals (Sweden)
S. Champeaux
1999-01-01
Full Text Available The envelope formalism for the description of a small-amplitude parallel-propagating Alfvén wave train is tested against direct numerical simulations of the Hall-MHD equations in one space dimension where kinetic effects are neglected. It turns out that the magnetosonic-wave dynamics departs from the adiabatic approximation not only near the resonance between the speed of sound and the Alfvén wave group velocity, but also when the speed of sound lies between the group and phase velocities of the Alfvén wave. The modulational instability then does not anymore affect asymptotically large scales and strong nonlinear effects can develop even in the absence of the decay instability. When the Hall-MHD equations are considered in the long-wavelength limit, the weakly nonlinear dynamics is accurately reproduced by the derivative nonlinear Schrödinger equation on the expected time scale, provided no decay instabilities are present. The stronger nonlinear regime which develops at later time is captured by including the coupling to the nonlinear dynamics of the magnetosonic waves.
Nonlinear waves in Poynting-flux dominated outflows
Mochol, Iwona
2012-11-01
Rotating, compact objects power some of the most spectacular phenomena in astrophysics, e.g., gamma-ray bursts, active galactic nuclei and pulsar winds. The energy is carried by Poynting flux, and the system is usually modelled using relativistic magnetohydrodynamics (MHD). However, in the relatively low density medium expected around some of these objects, the MHD approximation breaks down, allowing new, large-amplitude waves to propagate. We discuss the role of these waves in two astrophysical contexts: In blazar jets, we show that a magnetic shear, launched together with a plasma from the black hole magnetosphere, begins to accelerate particles at a large distance from its source. The resulting non-thermal emission can, nevertheless, be modulated on very short timescales, which can explain the rapid variability of the TeV gamma-ray flux observed from some blazars. In pulsar winds, we analyze the radial propagation of superluminal modes, including their damping by radiation reaction and by interaction with an external photon field. We discuss their effect on the structure of the pulsar wind termination shock, presenting new solutions in which the nonlinear wave is asymptotically matched to the constant pressure surroundings. The observational implications of these solutions are discussed for both isolated pulsars, and pulsars in binary systems.
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...
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.
Rotation-induced nonlinear wavepackets in internal waves
Energy Technology Data Exchange (ETDEWEB)
Whitfield, A. J., E-mail: ashley.whitfield.12@ucl.ac.uk; Johnson, E. R., E-mail: e.johnson@ucl.ac.uk [Department of Mathematics, University College London, London WC1E 6BT (United Kingdom)
2014-05-15
The long time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual formation of a localised wavepacket. Here this initial value problem is considered within the context of the Ostrovsky, or the rotation-modified Korteweg-de Vries (KdV), equation and a numerical method for obtaining accurate wavepacket solutions is presented. The flow evolutions are described in the regimes of relatively-strong and relatively-weak rotational effects. When rotational effects are relatively strong a second-order soliton solution of the nonlinear Schrödinger equation accurately predicts the shape, and phase and group velocities of the numerically determined wavepackets. It is suggested that these solitons may form from a local Benjamin-Feir instability in the inertia-gravity wave-train radiated when a KdV solitary wave rapidly adjusts to the presence of strong rotation. When rotational effects are relatively weak the initial KdV solitary wave remains coherent longer, decaying only slowly due to weak radiation and modulational instability is no longer relevant. Wavepacket solutions in this regime appear to consist of a modulated KdV soliton wavetrain propagating on a slowly varying background of finite extent.
Nonlinear low-frequency electrostatic wave dynamics in a two-dimensional quantum plasma
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Samiran, E-mail: sran_g@yahoo.com [Department of Applied Mathematics, University of Calcutta, 92, Acharya Prafulla Chandra Road, Kolkata-700 009 (India); Chakrabarti, Nikhil, E-mail: nikhil.chakrabarti@saha.ac.in [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata-700064 (India)
2016-08-15
The problem of two-dimensional arbitrary amplitude low-frequency electrostatic oscillation in a quasi-neutral quantum plasma is solved exactly by elementary means. In such quantum plasmas we have treated electrons quantum mechanically and ions classically. The exact analytical solution of the nonlinear system exhibits the formation of dark and black solitons. Numerical simulation also predicts the possible periodic solution of the nonlinear system. Nonlinear analysis reveals that the system does have a bifurcation at a critical Mach number that depends on the angle of propagation of the wave. The small-amplitude limit leads to the formation of weakly nonlinear Kadomstev–Petviashvili solitons.
Nonlinear Evolution Equations for Broader Bandwidth Wave Packets in Crossing Sea States
Directory of Open Access Journals (Sweden)
S. Debsarma
2014-01-01
Full Text Available Two coupled nonlinear equations are derived describing the evolution of two broader bandwidth surface gravity wave packets propagating in two different directions in deep water. The equations, being derived for broader bandwidth wave packets, are applicable to more realistic ocean wave spectra in crossing sea states. The two coupled evolution equations derived here have been used to investigate the instability of two uniform wave trains propagating in two different directions. We have shown in figures the behaviour of the growth rate of instability of these uniform wave trains for unidirectional as well as for bidirectional perturbations. The figures drawn here confirm the fact that modulational instability in crossing sea states with broader bandwidth wave packets can lead to the formation of freak waves.
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.
Mathematical modelling of generation and forward propagation of dispersive waves
Lie She Liam, L.S.L.
2013-01-01
This dissertation concerns the mathematical theory of forward propagation and generation of dispersive waves. We derive the AB2-equation which describes forward traveling waves in two horizontal dimension. It is the generalization of the Kadomtsev-Petviashvilli (KP) equation. The derivation is based
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...
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.
Ultra-Scalable Algorithms for Large-Scale Uncertainty Quantification in Inverse Wave Propagation
2016-03-04
MCMC sampling methods for posteriors for Bayesian inverse wave propagation problems. We developed a so-called randomized maximum a posteriori (rMAP...method for generating approximate samples of posteriors in high dimensional Bayesian inverse problems governed by large-scale forward problems, with...equivalent for a linear parameter-to-observable map. Nu- merical results indicated the potential of the rMAP approach in posterior sampling of nonlinear
Pitois, S; Fatome, J; Millot, G
2008-04-28
In this work, we report the experimental observation of a polarization attraction process which can occur in optical fibers at telecommunication wavelengths. More precisely, we have numerically and experimentally shown that a polarization attractor, based on the injection of two counter-propagating waves around 1.55microm into a 2-m long high nonlinear fiber, can transform any input polarization state into a unique well-defined output polarization state.
Strongly nonlinear wave dynamics in a chain of polymer coated beads
Daraio, C.; Nesterenko, V. F.
2006-01-01
Strongly nonlinear phononic crystals were assembled from a chain of Parylene-C coated steel spheres in a polytetrafluoroethylene (PTFE) holder. This system exhibits strongly nonlinear properties and extends the range of materials supporting "sonic vacuum" type behavior. The combination of a high density core and a soft (low elastic modulus) coating ensures a relatively low velocity of wave propagation. The beads contact interaction caused by the deformation of the Parylene coating can be desc...
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
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.
Oblique propagation of whistler mode waves in the chorus source region
Santolík, O.; Gurnett, D. A.; Pickett, J. S.; Chum, J.; Cornilleau-Wehrlin, N.
2009-12-01
Whistler mode chorus has been shown to play a role in the process of local acceleration of electrons in the outer Van Allen radiation belt. Most of the quasi-linear and nonlinear theoretical studies assume that the waves propagate parallel to the terrestrial magnetic field. We show a case where this assumption is invalid. We use data from the Cluster spacecraft to characterize propagation and spectral properties of chorus. The recorded high-resolution waveforms show that chorus in the source region can be formed by a succession of discrete wave packets with decreasing frequency that sometimes change into shapeless hiss. These changes occur at the same time in the entire source region. Multicomponent measurements show that waves in both these regimes can be found at large angles to the terrestrial magnetic field. The hiss intervals contain waves propagating less than one tenth of a degree from the resonance cone. In the regime of discrete wave packets the peak of the wave energy density is found at a few degrees from the resonance cone in a broad interval of azimuth angles. The wave intensity increases with the distance from the magnetic field minimum along a given field line, indicating a gradual amplification of chorus in the source region.
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...
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
Unidirectionally propagating whistler waves in the solar wind: Particle-in-cell simulations
Seough, J.
2017-12-01
The right-handed circularly polarized whistler fluctuations have often been observed in a free solar wind region. Interestingly, the measured whistlers propagate preferentially anti-sunward and appear to be characterized by nearly unidirectional propagation quasi-parallel to the local mean magnetic field at propagation angles smaller than 20o. Even though the solar wind electrons including the core and halo components possess temperature anisotropies that could drive the whistler instability, the free energy source of locally generated whistler waves is thought to be heat flux instability due to its unidirectional property. The purpose of this study is to present the possibility that not only heat flux instability but also whistler instability could be a local source of unidirectional whistler wave generation in the solar wind. By making use of both linear Vlasov analysis and electromagnetic particle-in-cell simulation, we show that unidirectionally propagating whistler waves can be naturally generated in situ by electron core temperature anisotropy-driven whistler instability when one takes into account the core-halo relative drift velocity in the proton rest frame. We also carry out particle-in-cell simulations of heat flux instability and compare between the two possible instabilities for understanding nonlinear property such as wave-particle interaction, especially halo electrons and whistler waves.
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
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
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
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.
Detection of Electromechanical Wave Propagation Using Synchronized Phasor Measurements
Suryawanshi, Prakash; Dambhare, Sanjay; Pramanik, Ashutosh
2014-01-01
Considering electrical network as a continuum has become popular for electromechanical wave analysis. This paper reviews the concept of electromechanical wave propagation. Analysis of large number of generator ring system will be an easy way to illustrate wave propagation. The property of traveling waves is that the maximum and minimum values do not occur at the same time instants and hence the difference between these time delays can be easily calculated. The homogeneous, isotropic 10 generator ring system is modeled using electromagnetic transient simulation programs. The purpose of this study is to investigate the time delays and wave velocities using Power System Computer Aided Design (PSCAD)/Electromagnetic Transient Program (EMTP). The disturbances considered here are generator disconnections and line trips.
Propagation of shear waves in viscoelastic medium at irregular boundaries
Chattopadhyay, Amares; Gupta, Shishir; Sharma, Vikash; Kumari, Pato
2010-04-01
The aim of the paper is to study the shear wave propagation in a viscoelastic layer over a semi-infinite viscoelastic half space due to irregularity in the viscoelastic layer. It is of great interest to study the propaga-tion of shear waves in the assumed medium having a non planar boundary due to its similarity to most of the real situations. The perturbation method is applied to find the displacement field. The effect of complex wave number on dissipation factor is analysed. Finally, as an application, the result obtained has been used to get the reflected field in viscoelastic layer when the shear wave is incident on an irregular boundary in the shape of parabolic irregularity as well as triangular notch. It is observed that the amplitude of this reflected wave decreases with increasing length of the notch, and increases with increasing depth of the irregularity.
Spatial damping of propagating sausage waves in coronal cylinders
Guo, Ming-Zhe; Chen, Shao-Xia; Li, Bo; Xia, Li-Dong; Yu, Hui
2015-09-01
Context. Sausage modes are important in coronal seismology. Spatially damped propagating sausage waves were recently observed in the solar atmosphere. Aims: We examine how wave leakage influences the spatial damping of sausage waves propagating along coronal structures modeled by a cylindrical density enhancement embedded in a uniform magnetic field. Methods: Working in the framework of cold magnetohydrodynamics, we solve the dispersion relation (DR) governing sausage waves for complex-valued, longitudinal wavenumber k at given real angular frequencies ω. For validation purposes, we also provide analytical approximations to the DR in the low-frequency limit and in the vicinity of ωc, the critical angular frequency separating trapped from leaky waves. Results: In contrast to the standing case, propagating sausage waves are allowed for ω much lower than ωc. However, while able to direct their energy upward, these low-frequency waves are subject to substantial spatial attenuation. The spatial damping length shows little dependence on the density contrast between the cylinder and its surroundings, and depends only weakly on frequency. This spatial damping length is of the order of the cylinder radius for ω ≲ 1.5vAi/a, where a and vAi are the cylinder radius and the Alfvén speed in the cylinder, respectively. Conclusions: If a coronal cylinder is perturbed by symmetric boundary drivers (e.g., granular motions) with a broadband spectrum, wave leakage efficiently filters out the low-frequency components.
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
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 ...
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-propagatio......-propagation algorithms in the framework of recurrent back-propagation and present some numerical simulations of feed-forward networks on the NetTalk problem. A discussion of implementation in analog VLSI electronics concludes the paper.......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...
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.
Wave Propagation in Pipe-like Structures
DEFF Research Database (Denmark)
Morsbøl, Jonas
pipe with changing radius, which is known as the shell of revolution, it is found that classical rod and beam theory, to some extent, can be used to approximate the fundamental modes of the torsional, axial, and breathing wave. However, by means of the shell model some remarkable effects are predicted...... when even these very fundamental waves are travelling along a shell of revolution. The effects cover modal changes and excitation of localised resonances. For modes of higher order similar excitations of localised resonances are also predicted....
Unidirectional wave propagation in media with complex principal axes
Horsley, S. A. R.
2018-02-01
In an anisotropic medium, the refractive index depends on the direction of propagation. Zero index in a fixed direction implies a stretching of the wave to uniformity along that axis, reducing the effective number of dimensions by 1. Here we investigate two-dimensional gyrotropic media where the refractive index is 0 in a complex valued direction, finding that the wave becomes an analytic function of a single complex variable z . For simply connected media this analyticity implies unidirectional propagation of electromagnetic waves, similar to the edge states that occur in photonic "topological insulators." For a medium containing holes the propagation is no longer unidirectional. We illustrate the sensitivity of the field to the topology of the space using an exactly solvable example. To conclude we provide a generalization of transformation optics where a complex coordinate transformation can be used to relate ordinary anisotropic media to the recently highlighted gyrotropic ones supporting one-way edge states.
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.
Modification of sonic boom wave forms during propagation from the source to the ground.
Bass, Henry E; Raspet, Richard; Chambers, James P; Kelly, Mark
2002-01-01
A number of physical processes work to modify the shape of sonic boom wave forms as the wave form propagates from the aircraft to a receiver on the ground. These include frequency-dependent absorption, nonlinear steepening, and scattering by atmospheric turbulence. In the past two decades, each of these effects has been introduced into numerical prediction algorithms and results compared to experimental measurements. There is still some disagreement between measurements and prediction, but those differences are now in the range of tens of percent. The processes seem to be understood. The present understanding of sonic boom evolution will be presented along with experimental justification.
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.
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...
Driving Perpendicular Decay by the Parametric Instabilities of Parallel Propagating Alfven Waves
Comisel, H.; Nariyuki, Y.; Narita, Y.; Motschmann, U. M.
2017-12-01
The decay of monochromatic Alfven waves is studied by means of 2-D and 3-D hybrid simulations. The goal of the work is to follow up the long-time nonlinear development of theparametric decays after the saturation process in a multi-spatial dimension for coherent Alfven waves with three different polarizations: left-handed circularly polarized -, right-handed circularly polarized - and linearly polarized - Alfven pump waves. The analyzing is restricted for the parallel propagation with respect to the direction of the mean magnetic field in low beta plasmas. Numerical results suggest that the parametric instabilities can lead to broadband decays along the perpendicular direction, in which the magnetic field spectrum is extended towards the perpendicular direction.Perpendicular propagating daughter waves are observed atfinite perpendicular wave numbers as well as direct incompressible energy cascades driven by plasma turbulence.The density power spectrum shows inverse compressible cascades at smallerperpendicular wave numbers and direct cascades at larger wave numbers. The one-dimensional reduced spectra of the magnetic field and densities show correlations for a significant large range of perpendicular wave numbers beforedissipation. The time evolution of the anisotropy index is also determined for all the three analyzed setups.
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.
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]....
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.
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.
Ultrasonic guided wave propagation in pipes with elbows
Breon, Luke J.
Guided wave inspection of pipelines is an important and growing area of Non-Destructive Evaluation (NDE). This technique can be used for remote inspection or monitoring of buried pipelines, or pipelines with insulation. Guided waves are sensitive to flaws such as corrosion pits and cracks. They can be used to locate flaws existing on either the outer or the inner surface of a pipe. Guided wave energy focusing can be performed to concentrate guided wave energy at particular combinations of circumferential and axial locations in straight pipes. When it can be used, this practice enhances the circumferential resolution of defects. Elbows in a piping system are sufficiently disruptive to guided wave energy that the focusing methods used in practical inspections of straight pipe have not been extended to the region beyond an elbow. Counter-intuitively, elbows with a 45 degree bend are more harmful to guided waves than those with a 90 degree bend. A simple and elegant explanation for this phenomenon is provided in this dissertation. Theoretical advancements to guided wave physics propagating around an elbow have tended to be few and slow. This is at least partly due to the complexity of the mathematics involved in the conventional description of guided wave mechanics. Parametric focusing for pipes with bends has not been previously possible as it is for straight sections of pipes. While some techniques such as time-reversal mirrors and blind finite-element-method modeling have existed for focusing beyond elbows, these techniques have been limited and largely of academic value. Also, the understanding of wave behavior in a pipe elbow has in the past been generally unclear. Consequently, signal interpretation has also been very limited for guided waves initiating in, or returning from, the far side of an elbow. A new approach to understanding guided wave propagation is developed in this work. This understanding consists of the idea that the pathway a guided wave will take
Propagation of sound waves in tubes of noncircular cross section
Richards, W. B.
1986-01-01
Plane-acoustic-wave propagation in small tubes with a cross section in the shape of a flattened oval is described. Theoretical descriptions of a plane wave propagating in a tube with circular cross section and between a pair of infinite parallel plates, including viscous and thermal damping, are expressed in similar form. For a wide range of useful duct sizes, the propagation constant (whose real and imaginary parts are the amplitude attenuation rate and the wave number, respectively) is very nearly the same function of frequency for both cases if the radius of the circular tube is the same as the distance between the parallel plates. This suggests that either a circular-cross-section model or a flat-plate model can be used to calculate wave propagation in flat-oval tubing, or any other shape tubing, if its size is expressed in terms of an equivalent radius, given by g = 2 x (cross-sectional area)/(length of perimeter). Measurements of the frequency response of two sections of flat-oval tubing agree with calculations based on this idea. Flat-plate formulas are derived, the use of transmission-line matrices for calculations of plane waves in compound systems of ducts is described, and examples of computer programs written to carry out the calculations are shown.
Resonantly driven nonlinear density waves in protostellar disks
Yuan, Chi; Cassen, Pat
1994-01-01
Recent observations of binary, pre-main-sequence, solar-type stars provide evidence that such systems may coexist with circumstellar disks. The binary disk systems, besides being of general interest for the study of star formation, potentially provide useful tests of companion-disk interaction theories prominent in current hypotheses of planet formation. In this paper, we apply an asymptotic analysis of the nonlinear, resonant interaction of a stellar companion with a disk to understand the dependence of such interactions on the properties of the system: the binary mass ratio, the physical properties of the disk, and the effective dissipation (treated herein as viscosity). The method is based on a WKBJ approximation and exploits the conditions that the disk is thin and much less massive than the primary, but does not require that the companion-induced disturbance be small. Both isothermal and adiabatic responses are treated. Only circular orbit resonances are considered in this paper. It is demonstrated that the temperature of the disk as well as the relative mass of the companion affects the degree of nonlinearity, and that nonlinearity promotes high wave compression ratios, long wavelengths, and increased propagation distances. Nevertheless, the total torque exerted between the companion and the disk is well represented by linear theory. The amplitudes of density disturbances are reduced by viscosity and nonisothermality. Because resonant interactions are generally strong and capable of driving rapid evolution, one might expect observations of systems undergoing strong, resonant-driven evolution to be rare. In this connection, it is pointed out that the m = 1 resonance is distinguished by being anomalously weaker than the others and is therefore of observational interest. It is speculated that, in conditions of intrinsically small dissipation, the propagation of resonant-driven density waves is limited by the tendency of their wavelength to diminish with distance
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.
Energy Technology Data Exchange (ETDEWEB)
Mahmood, S., E-mail: shahzadm100@gmail.com; Sadiq, Safeer; Haque, Q. [Theoretical Physics Division, PINSTECH, P. O. Nilore, Islamabad 44000 (Pakistan); Ali, Munazza Z. [Department of Physics, University of the Punjab, Lahore 54590 (Pakistan)
2016-06-15
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.
Nonlinear dispersion of resonance extraordinary wave in a plasma with strong magnetic field
International Nuclear Information System (INIS)
Krasovitskiy, V. B.; Turikov, V. A.; Sotnikov, V. I.
2007-01-01
In this paper, the efficiency of electron acceleration by a short, powerful laser pulse propagating across an external magnetic field is investigated. Conditions for the decay of a laser pulse with frequency close to the upper hybrid resonance frequency are analyzed. It is also shown that a laser pulse propagating as an extraordinary wave in cold, magnetized, low-density plasma takes the form of a nonlinear wave with the modulated amplitude (envelope soliton). Finally, simulation results on the interaction of an electromagnetic pulse with a semi-infinite plasma, obtained with the help of an electromagnetic relativistic PIC code, are discussed and a comparison with the obtained theoretical results is presented
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)
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....... The analysis of time domain wave field images allows the assessment of plate dispersion, and the comparison with numerical predictions. The obtained results show the predictive ability of the considered numerical approach and illustrate how the considered plate configuration could be used as the basis...
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.
Wave propagation phenomena in metamaterials for retrieving of effective parameters
DEFF Research Database (Denmark)
Andryieuski, Andrei; Malureanu, Radu; Ha, S.
2011-01-01
reveal so-called wave effective parameters, assigned for particular ligh propagation direction in numerical or real experiments. Therefore, finding the EP is a tricky problem, which still requires a lot of contribution to get deeper insight in it. We report on our advances in restoration MMs EP taking...... into account propagation of eigen-waves in multilayered structures (thicknesses 10-100 unit cells). Thus, the question of pa-rameters convergence is naturally resolved in our approach. The method has been tested on complex three-dimensional structures like a split-cube-in-carcass and with circular polarized...... waves on chiral MMs [1, 2]. Elaborating our approach the new method has been established, where the unit-cell volume and face field averaging procedures define wave and input (Bloch) impedances correspond-ingly. The first part of the method involves the extraction of the dominating (fundamental) Bloch...
Nonlinear wave modulation of cylindrical and spherical quantum ion-acoustic solitary waves
Sabry, R.; El-Labany, S. K.; Shukla, P. K.
2008-12-01
Cylindrical and spherical amplitude modulation of quantum ion-acoustic (QIA) envelope solitary waves in a dense quantum plasma comprised of electrons and ions is investigated. For this purpose, a one-dimensional quantum hydrodynamic model and the Poisson equation are considered. By using the standard reductive perturbation technique, a modified nonlinear Schrödinger equation with the geometrical and the quantum effects is derived. The effect of quantum corrections and the effect due to the cylindrical and spherical geometries on the propagation of the QIA envelope solitary waves are examined. It is shown that there exists a modulation instability period depending on the quantum parameter, which does not exist for the one-dimensional classical case.
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.
Love wave propagation in piezoelectric layered structure with dissipation.
Du, Jianke; Xian, Kai; Wang, Ji; Yong, Yook-Kong
2009-02-01
We investigate analytically the effect of the viscous dissipation of piezoelectric material on the dispersive and attenuated characteristics of Love wave propagation in a layered structure, which involves a thin piezoelectric layer bonded perfectly to an unbounded elastic substrate. The effects of the viscous coefficient on the phase velocity of Love waves and attenuation are presented and discussed in detail. The analytical method and the results can be useful for the design of the resonators and sensors.
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.
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)
Millimetre Wave Propagation Over the Sea
1990-10-29
gases in the atmospherei (in particular oxygen and water vapour) causes part of the energy transmitted in millimetre waves to be absorbed. In order to...respectively to water vapour and oxygen reach 0.5 dB/km and 0.03 dB/km. Mlecular attenuation may vary substantially according to the meteorological conditions...significatifs de houle et d’un capteur embarcable utdl- sant cer algorithmex, Th~se de doctorat de 3tme cycle, Universiti Pierre et Marie Curie, Paris VI
Modeling ocean wave propagation under sea ice covers
Zhao, Xin; Shen, Hayley H.; Cheng, Sukun
2015-02-01
Operational ocean wave models need to work globally, yet current ocean wave models can only treat ice-covered regions crudely. The purpose of this paper is to provide a brief overview of ice effects on wave propagation and different research methodology used in studying these effects. Based on its proximity to land or sea, sea ice can be classified as: landfast ice zone, shear zone, and the marginal ice zone. All ice covers attenuate wave energy. Only long swells can penetrate deep into an ice cover. Being closest to open water, wave propagation in the marginal ice zone is the most complex to model. The physical appearance of sea ice in the marginal ice zone varies. Grease ice, pancake ice, brash ice, floe aggregates, and continuous ice sheet may be found in this zone at different times and locations. These types of ice are formed under different thermal-mechanical forcing. There are three classic models that describe wave propagation through an idealized ice cover: mass loading, thin elastic plate, and viscous layer models. From physical arguments we may conjecture that mass loading model is suitable for disjoint aggregates of ice floes much smaller than the wavelength, thin elastic plate model is suitable for a continuous ice sheet, and the viscous layer model is suitable for grease ice. For different sea ice types we may need different wave ice interaction models. A recently proposed viscoelastic model is able to synthesize all three classic models into one. Under suitable limiting conditions it converges to the three previous models. The complete theoretical framework for evaluating wave propagation through various ice covers need to be implemented in the operational ocean wave models. In this review, we introduce the sea ice types, previous wave ice interaction models, wave attenuation mechanisms, the methods to calculate wave reflection and transmission between different ice covers, and the effect of ice floe breaking on shaping the sea ice morphology
Seismic Wave Propagation in Icy Ocean Worlds
Stähler, Simon C.; Panning, Mark P.; Vance, Steven D.; Lorenz, Ralph D.; vanÂ 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.
Solitary wave solutions of two-dimensional nonlinear Kadomtsev ...
Indian Academy of Sciences (India)
2017-09-13
Sep 13, 2017 ... Home; Journals; Pramana – Journal of Physics; Volume 89; Issue 3. Solitary wave solutions of ... Nonlinear two-dimensional Kadomtsev–Petviashvili (KP) equation governs the behaviour of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions. By using the reductive ...
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 A...
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
Thermal conductivity of nonlinear waves in disordered chains
Indian Academy of Sciences (India)
Abstract. We present computational data on the thermal conductivity of nonlinear waves in disordered chains. Disorder induces Anderson localization for linear waves and results in a vanishing conductivity. Cubic nonlinearity restores normal conductivity, but with a strongly temperature-dependent conductivity (). We ﬁnd ...
Oblique Propagation and Dissipation of Alfven Waves in Coronal ...
Indian Academy of Sciences (India)
2016-01-27
Jan 27, 2016 ... We investigate the effect of viscosity and magnetic diffusivity on the oblique propagation and dissipation of Alfvén waves with respect to the normal outward direction, making use of MHD equations, density, temperature and magnetic field structure in coronal holes and underlying magnetic funnels. We find ...
Propagation of waves in a gravitating and rotating anisotropic heat ...
African Journals Online (AJOL)
Bheema
(1956) equations neglecting the heat flux vector. Gravitational instability on propagation of magnetohydrodynamic (MHD) waves in astrophysical plasma is investigated by Alemayehu and Tessema (2013a) by considering the effect of gravitational instability and viscosity with anisotropic pressure tensor and heat conducting.
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...
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] ...
Wave propagation in coated cylinders with reference to fretting fatigue
Indian Academy of Sciences (India)
The frequency of vibration or contact loading is an important parameter. The general frequency regime ... dicting initiation and propagation of micro cracks during fretting demands a proper study of stress wave .... The following expressions give the stresses and displacements in terms of potential func- tions. 2μur = ∂. ∂r. +.
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 a general anisotropic poroelastic medium ...
Indian Academy of Sciences (India)
Home; Journals; Journal of Earth System Science; Volume 116; Issue 4. Wave propagation in a general anisotropic poroelastic medium: Biot's theories and homogenisation theory. M D Sharma. Volume 116 Issue 4 August ... Keywords. Anisotropic poroelastic (APE) solid; Biot's theory; homogenisation theory; phase velocity.
Analysis of flexural wave propagation in poroelastic composite ...
African Journals Online (AJOL)
DR OKE
wave propagation in poroelastic media. A poroelastic composite hollow cylinder consists of two concentric poroelastic cylindrical layers both of which are made of different poroelastic materials with each poroelastic material as homogeneous and isotropic. The inner and outer boundaries of composite hollow poroelastic ...
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.
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)
Influence of support viscoelastic properties on the structural wave propagation
International Nuclear Information System (INIS)
Park, Jun Hong
2007-01-01
The dissipation of the structural vibration energy at viscoelastic supports is an efficient method of reducing modal resonances and consequent noise and fatigue related problems. The support stiffness has significant impact on the modal characteristics. The dissipation capabilities of the viscoelastic support depend on its stiffness. Methods to optimally tune this support stiffness are proposed in this study. The characteristic mechanical impedance for structural vibration is obtained from wave propagation analysis and non-reflecting boundary conditions. The wave propagation is analyzed near the supports installed at edges, middle of a structure, and for the tuned vibration absorber. The dependence of the optimal stiffness on the location and mass of the supports is identified. A simple analytical solution for optimal support stiffness for maximum dissipation of propagating vibration energy at supports is presented
Nonlinear heat and particle transport due to collisional drift waves
Energy Technology Data Exchange (ETDEWEB)
Nishi-kawa, K.I.; Hatori, T.; Terashima, Y.
1977-03-01
The nonlinear evolution of unstable modes which govern transport processes in magnetically confined plasmas were investigated. A nonlinear theory of unstable collisional drift wave, and the consequent nonlinear transport were extended to include electron and ion temperature gradients. Thermal transport properties are discussed and basic equations are given.
An Improved Coupling of Numerical and Physical Models for Simulating Wave Propagation
DEFF Research Database (Denmark)
Yang, Zhiwen; Liu, Shu-xue; Li, Jin-xuan
2014-01-01
An improved coupling of numerical and physical models for simulating 2D wave propagation is developed in this paper. In the proposed model, an unstructured finite element model (FEM) based Boussinesq equations is applied for the numerical wave simulation, and a 2D piston-type wavemaker is used...... for the physical wave generation. An innovative scheme combining fourth-order Lagrange interpolation and Runge-Kutta scheme is described for solving the coupling equation. A Transfer function modulation method is presented to minimize the errors induced from the hydrodynamic invalidity of the coupling model and....../or the mechanical capability of the wavemaker in area where nonlinearities or dispersion predominate. The overall performance and applicability of the coupling model has been experimentally validated by accounting for both regular and irregular waves and varying bathymetry. Experimental results show...
Femtosecond Pulse Propagation in a Highly Nonlinear Photonic Crystal Fiber
Directory of Open Access Journals (Sweden)
J. F. Gabayno
2004-12-01
Full Text Available Femtosecond pulses are launched into a highly nonlinear photonic crystal fiber (PCF. The input and output spectra were measured using a monochromator and streak camera. The spectrum of the output from a 50 cm PCF pumped at 794 nm for different pump powers features asymmetric side lobes due to intrapulse Raman scattering. Similar measurements on a 100 cm PCF pumped at 795 nm highlight the appearance of blueshifted peaks as a result of energy transfer of solitons to dispersive waves. Broadening in the spectrum is observed and attributed to Raman-scattering-induced soliton self-frequency shift. Spectrograms of both input and output pulses into a 50 cm PCF are captured using a streak camera. The spectrum reveals that individual modes observed on the spectrogram are actually a decomposition of the input pulse.
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
Spin wave propagation in a uniformly biased curved magnonic waveguide
Sadovnikov, A. V.; Davies, C. S.; Kruglyak, V. V.; Romanenko, D. V.; Grishin, S. V.; Beginin, E. N.; Sharaevskii, Y. P.; Nikitov, S. A.
2017-08-01
Using Brillouin light scattering microscopy and micromagnetic simulations, we study the propagation and transformation of magnetostatic spin waves across uniformly biased curved magnonic waveguides. Our results demonstrate that the spin wave transmission through the bend can be enhanced or weakened by modifying the distribution of the inhomogeneous internal magnetic field spanning the structure. Our results open up the possibility of optimally molding the flow of spin waves across networks of magnonic waveguides, thereby representing a step forward in the design and construction of the more complex magnonic circuitry.
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.
Tsunamis - harbor oscillations induced by nonlinear transient long waves
Lepelletier, Thierry G. (Thierry Georges)
1980-01-01
The process of excitation of harbors and bays by transient nonlinear long waves is investigated theoretically and experimentally. In addition, nonlinear shallow water waves generated in a closed rectangular basin by the motion of the basin are also examined. Two numerical methods based on finite element techniques are used to solve the weakly nonlinear-dispersive-dissipative equations of motion and are applied to the basin excitation problem and the transient harbor oscillation problem, ...
Wave propagation at the human muscle-compact bone interface
Directory of Open Access Journals (Sweden)
Hsia Shao-Yi
2006-01-01
Full Text Available Due to the improvement of the signal processing and image technology, the clinical ultrasound system becomes an important tool to assist doctors in detecting diseases. Hence, it is necessary to know the biological effects of ultrasound in human tissue. In ultrasonic waves, the discrepancy between classic elasticity and experimental elasticity becomes a particularly important problem, especially when there are higher frequencies and smaller wavelengths, i.e., in the case of wave propagation in human muscle and compact bone. Consequently, the influence of the microstructure is important and this fact leads to the generation of new types of waves unknown in classic elasticity. General continuum theories, such as couple stress theory and micropolar theory, have degrees of freedom in addition to those of classic elasticity. Such theories are thought to be applicable to composites with granular or porous structure, effective chiral composite, and human compact bone. In this work, a theoretical analysis concerning the reflected and transmitted fields of an incident plane wave P propagating at the human muscle-compact bone interface has been investigated. The results show that the wave fields are affected by microstructures of the human bone. Knowledge of this occurrence may offer some contribution to the understanding of the ultrasound propagation in the biological effects of human tissue.
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.
Spiral Calcium Wave Propagation and Annihilation in Xenopus laevis Oocytes
Lechleiter, James; Girard, Steven; Peralta, Ernest; Clapham, David
1991-04-01
Intracellular calcium (Ca2+) is a ubiquitous second messenger. Information is encoded in the magnitude, frequency, and spatial organization of changes in the concentration of cytosolic free Ca2+. Regenerative spiral waves of release of free Ca2+ were observed by confocal microscopy in Xenopus laevis oocytes expressing muscarinic acetylcholine receptor subtypes. This pattern of Ca2+ activity is characteristic of an intracellular milieu that behaves as a regenerative excitable medium. The minimal critical radius for propagation of focal Ca2+ waves (10.4 micrometers) and the effective diffusion constant for the excitation signal (2.3 x 10-6 square centimeters per second) were estimated from measurements of velocity and curvature of circular wavefronts expanding from foci. By modeling Ca2+ release with cellular automata, the absolute refractory period for Ca2+ stores (4.7 seconds) was determined. Other phenomena expected of an excitable medium, such as wave propagation of undiminished amplitude and annihilation of colliding wavefronts, were observed.
Stress Wave Propagation due to a Moving Force
DEFF Research Database (Denmark)
Rasmussen, K. M.; Nielsen, Søren R. K.; Kirkegaard, Poul Henning
1999-01-01
In this paper the performance of two numerical methods of solving the problem of a time dependent moving force on the surface of an elastic continuum will be evaluated. One method is the finite element method (FEM) formulated in convected coordinates coupled with an absorbing boundary condition...... of the impedance type. The other method to be considered is the boundary element method (BEM), where a new formulation using Green's functions transformed to a moving coordinate system is introduced. The methods are tested by the classic wave propagation problem of a Ricker Pulse propagating from the surface...... of an elastic halfspace. The time integral net impulse of the considered loading must be null for the considered FEM to work. Further, the FEM is unable to absorb Rayleigh waves, since the considered impedance condition has been tuned P- and S-waves. By contrast the BEM is able to handle also these cases...
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
Generation of dispersion in nondispersive nonlinear waves in thermal equilibrium.
Lee, Wonjung; Kovačič, Gregor; Cai, David
2013-02-26
In this work, we examine the important theoretical question of whether dispersion relations can arise from purely nonlinear interactions among waves that possess no linear dispersive characteristics. Using two prototypical examples of nondispersive waves, we demonstrate how nonlinear interactions can indeed give rise to effective dispersive-wave-like characteristics in thermal equilibrium. Physically, these example systems correspond to the strong nonlinear coupling limit in the theory of wave turbulence. We derive the form of the corresponding dispersion relation, which describes the effective dispersive structures, using the generalized Langevin equations obtained in the Zwanzig-Mori projection framework. We confirm the validity of this effective dispersion relation in our numerical study using the wavenumber-frequency spectral analysis. Our work may provide insight into an important connection between highly nonlinear turbulent wave systems, possibly with no discernible dispersive properties, and the dispersive nature of the corresponding renormalized waves.
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.
Topology Optimization for Wave Propagation Problems with Experimental Validation
DEFF Research Database (Denmark)
Christiansen, Rasmus Ellebæk
discussion of the finite element method and a hybrid ofa wave based method and the finite element method, used to discretize the modelproblems under consideration. A short discussion of the benefits and drawbacks of applying the hybrid method compared to the finite element method, used in conjunction......This Thesis treats the development and experimental validation of density-based topology optimization methods for wave propagation problems. Problems in the frequency regime where design dimensions are between approximately one fourth and ten wavelengths are considered. All examples treat problems...... from acoustics, however problems for TE or TM polarized electromagnetic waves and shear waves in solids in two dimensions may be treated using the proposed methods with minor modifications. A brief introduction to wave problems and to density-based topology optimizationis included, as is a brief...
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
Near-perfect conversion of a propagating plane wave into a surface wave using metasurfaces
Tcvetkova, S. N.; Kwon, D.-H.; Díaz-Rubio, A.; Tretyakov, S. A.
2018-03-01
In this paper theoretical and numerical studies of perfect/nearly perfect conversion of a plane wave into a surface wave are presented. The problem of determining the electromagnetic properties of an inhomogeneous lossless boundary which would fully transform an incident plane wave into a surface wave propagating along the boundary is considered. An approximate field solution which produces a slowly growing surface wave and satisfies the energy conservation law is discussed and numerically demonstrated. The results of the study are of great importance for the future development of such devices as perfect leaky-wave antennas and can potentially lead to many novel applications.
Nonlinear evolution of the modulational instability of whistler waves
DEFF Research Database (Denmark)
Karpman, V.I.; Hansen, F.R.; Huld, T.
1990-01-01
The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves is investigated in two spatial dimensions by numerical simulations. The long time evolution of the modulational instability shows a quasirecurrent behavior with a slow spreading...... of the energy, originally confined to the lowest wave numbers, to larger and larger wave numbers resulting in an apparently chaotic or random wave field. © 1990 The American Physical Society...
Role of Density Profiles for the Nonlinear Propagation of Intense Laser Beam through Plasma Channel
Directory of Open Access Journals (Sweden)
Sonu Sen
2014-01-01
Full Text Available In this work role of density profiles for the nonlinear propagation of intense laser beam through plasma channel is analyzed. By employing the expression for the dielectric function of different density profile plasma, a differential equation for beamwidth parameter is derived under WKB and paraxial approximation. The laser induces modifications of the dielectric function through nonlinearities. It is found that density profiles play vital role in laser-plasma interaction studies. To have numerical appreciation of the results the propagation equation for plasma is solved using the fourth order Runge-Kutta method for the initial plane wave front of the beam, using boundary conditions. The spot size of the laser beam decreases as the beam penetrates into the plasma and significantly adds self-focusing in plasma. This causes the laser beam to become more focused by reduction of diffraction effect, which is an important phenomenon in inertial confinement fusion and also for the understanding of self-focusing of laser pulses. Numerical computations are presented and discussed in the form of graphs for typical parameters of laser-plasma interaction.
Effect of the Blood Vessel Viscoelasticity on Periodic Blood Pressure Wave Propagation
Kitawaki, Tomoki; Shimizu, Masashi
Clinical arterial stiffness indexes such as PWV (pulse wave velocity) or PP (pulse pressure), which are obtained by analyzing blood pressure pulse waveforms in vivo, are used in the prognosis of cardiovascular diseases and thus analyses of pulse waveform are clinically important. The pulse wave in vivo, however, is complicated because of the complex viscoelastic property of the blood vessel wall. In addition, numerical flow simulations are useful for understanding pulse wave propagation in circulatory systems. Our proposed nonlinear one-dimensional numerical simulation model can accurately simulate the measurements of pressure waves in a silicone rubber tube and indicate that the viscoelasticity of the tube wall was significantly influenced by a single pulse waveform; however, the influence of viscoelasticity change on periodic pulsatile wave propagation has not yet been studied. The purpose of this study was therefore to investigate the effect of viscoelasticity change on the periodic pulsatile wave. For this purpose, we examined the effect of the viscoelasticity of a single silicone tube on periodic pulse wave propagation by comparing the calculated results using a one-dimensional model. As a result, the one-dimensional model could accurately express the experimental results with periodic pulsatile waves. In addition, both PWV and PP increase when the viscoelastic value of the dynamic modulus elasticity ratio increases, because increasing the elastic modulus is more effective than the energy dissipation effect by viscoelasticity change. Consequently, it is necessary to measure the viscoelastic property of the vessel wall accurately in order to estimate the arterial stiffness index (PWV and PP) accurately.
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.
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
Zhao, Youxuan; Li, Feilong; Cao, Peng; Liu, Yaolu; Zhang, Jianyu; Fu, Shaoyun; Zhang, Jun; Hu, Ning
2017-08-01
Since the identification of micro-cracks in engineering materials is very valuable in understanding the initial and slight changes in mechanical properties of materials under complex working environments, numerical simulations on the propagation of the low frequency S 0 Lamb wave in thin plates with randomly distributed micro-cracks were performed to study the behavior of nonlinear Lamb waves. The results showed that while the influence of the randomly distributed micro-cracks on the phase velocity of the low frequency S 0 fundamental waves could be neglected, significant ultrasonic nonlinear effects caused by the randomly distributed micro-cracks was discovered, which mainly presented as a second harmonic generation. By using a Monte Carlo simulation method, we found that the acoustic nonlinear parameter increased linearly with the micro-crack density and the size of micro-crack zone, and it was also related to the excitation frequency and friction coefficient of the micro-crack surfaces. In addition, it was found that the nonlinear effect of waves reflected by the micro-cracks was more noticeable than that of the transmitted waves. This study theoretically reveals that the low frequency S 0 mode of Lamb waves can be used as the fundamental waves to quantitatively identify micro-cracks in thin plates. Copyright © 2017 Elsevier B.V. All rights reserved.
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...
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
Bonetti, Stefano; Tiberkevich, Vasil; Consolo, Giancarlo; Finocchio, Giovanni; Muduli, Pranaba; Mancoff, Fred; Slavin, Andrei; Åkerman, Johan
2010-11-01
Through detailed experimental studies of the angular dependence of spin wave excitations in nanocontact-based spin-torque oscillators, we demonstrate that two distinct spin wave modes can be excited, with different frequency, threshold currents, and frequency tunability. Using analytical theory and micromagnetic simulations we identify one mode as an exchange-dominated propagating spin wave, and the other as a self-localized nonlinear spin wave bullet. Wavelet-based analysis of the simulations indicates that the apparent simultaneous excitation of both modes results from rapid mode hopping induced by the Oersted field.
On the Relation Between Complex Modes and Wave Propagation Phenomena
Ahmida, K. M.; Arruda, J. R. F.
2002-08-01
This paper discusses the well-known, but often misunderstood, concept of complex modes of dynamic structures. It shows how complex modes can be interpreted in terms of wave propagation phenomena caused by either localized damping or propagation to the surrounding media. Numerical simulation results are presented for different kinds of structures exhibiting modal and wave propagation characteristics: straight beams, an L-shaped beam, and a three-dimensional frame structure. The input/output transfer relations of these structures are obtained using a spectral formulation known as the spectral element method (SEM). With this method, it is straightforward to use infinite elements, usually known as throw-off elements, to represent the propagation to infinity, which is a possible cause of modal complexity. With the SEM model, the exact dynamic behavior of structures can be investigated. The mode complexity of these structures is investigated. It is shown that mode complexity characterizes a behavior that is half-way between purely modal and purely propagative. A coefficient for quantifying mode complexity is introduced. The mode complexity coefficient consists of the correlation coefficient between the real and imaginary parts of the eigenvector, or of the operational deflection shape (ODS). It is shown that, far from discontinuities, this coefficient is zero in the case of pure wave propagation in which case the plot of the ODS in the complex plane is a perfect circle. In the other extreme situation, a finite structure without damping (or with proportional damping), where the mode shape (or the ODS) is a straight line on the complex plane, has a unitary complexity coefficient. For simple beam structures, it is shown that the mode complexity factor can also be calculated by curve-fitting the mode to an ellipse and computing the ratio of its radii.
Three dimensional full-wave nonlinear acoustic simulations: Applications to ultrasound imaging
Energy Technology Data Exchange (ETDEWEB)
Pinton, Gianmarco [Joint Department of Biomedical Engineering, University of North Carolina - North Carolina State University, 348 Taylor Hall, Chapel Hill, NC 27599, USA gfp@unc.edu (United States)
2015-10-28
Characterization of acoustic waves that propagate nonlinearly in an inhomogeneous medium has significant applications to diagnostic and therapeutic ultrasound. The generation of an ultrasound image of human tissue is based on the complex physics of acoustic wave propagation: diffraction, reflection, scattering, frequency dependent attenuation, and nonlinearity. The nonlinearity of wave propagation is used to the advantage of diagnostic scanners that use the harmonic components of the ultrasonic signal to improve the resolution and penetration of clinical scanners. One approach to simulating ultrasound images is to make approximations that can reduce the physics to systems that have a low computational cost. Here a maximalist approach is taken and the full three dimensional wave physics is simulated with finite differences. This paper demonstrates how finite difference simulations for the nonlinear acoustic wave equation can be used to generate physically realistic two and three dimensional ultrasound images anywhere in the body. A specific intercostal liver imaging scenario for two cases: with the ribs in place, and with the ribs removed. This configuration provides an imaging scenario that cannot be performed in vivo but that can test the influence of the ribs on image quality. Several imaging properties are studied, in particular the beamplots, the spatial coherence at the transducer surface, the distributed phase aberration, and the lesion detectability for imaging at the fundamental and harmonic frequencies. The results indicate, counterintuitively, that at the fundamental frequency the beamplot improves due to the apodization effect of the ribs but at the same time there is more degradation from reverberation clutter. At the harmonic frequency there is significantly less improvement in the beamplot and also significantly less degradation from reverberation. It is shown that even though simulating the full propagation physics is computationally challenging it
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
SPATIAL DAMPING OF PROPAGATING KINK WAVES IN PROMINENCE THREADS
International Nuclear Information System (INIS)
Soler, R.; Oliver, R.; Ballester, J. L.
2011-01-01
Transverse oscillations and propagating waves are frequently observed in threads of solar prominences/filaments and have been interpreted as kink magnetohydrodynamic (MHD) modes. We investigate the spatial damping of propagating kink MHD waves in transversely nonuniform and partially ionized prominence threads. Resonant absorption and ion-neutral collisions (Cowling's diffusion) are the damping mechanisms taken into account. The dispersion relation of resonant kink waves in a partially ionized magnetic flux tube is numerically solved by considering prominence conditions. Analytical expressions of the wavelength and damping length as functions of the kink mode frequency are obtained in the thin tube and thin boundary approximations. For typically reported periods of thread oscillations, resonant absorption is an efficient mechanism for the kink mode spatial damping, while ion-neutral collisions have a minor role. Cowling's diffusion dominates both the propagation and damping for periods much shorter than those observed. Resonant absorption may explain the observed spatial damping of kink waves in prominence threads. The transverse inhomogeneity length scale of the threads can be estimated by comparing the observed wavelengths and damping lengths with the theoretically predicted values. However, the ignorance of the form of the density profile in the transversely nonuniform layer introduces inaccuracies in the determination of the inhomogeneity length scale.
The effect of nonlinear traveling waves on rotating machinery
Jauregui-Correa, Juan Carlos
2013-08-01
The effect of the housing stiffness on nonlinear traveling waves is presented in this work. It was found that the housing controls the synchronization of nonlinear elements and it allows nonlinear waves to travel through the structure. This phenomenon was observed in a gearbox with a soft housing, and the phenomenon was reproduced with a lump-mass dynamic model. The model included a pair of gears, the rolling bearings and the housing. The model considered all the nonlinear effects. Numerical and experimental results were analyzed with a time-frequency method using the Morlet wavelet function. A compound effect was observed when the nonlinear waves travel between the gears and the bearings: the waves increased the dynamic load amplitude and add another periodic load.
Superposed nonlinear waves in coherently coupled Bose–Einstein condensates
Energy Technology Data Exchange (ETDEWEB)
Babu Mareeswaran, R.; Kanna, T., E-mail: kanna_phy@bhc.edu.in
2016-09-23
We study the dynamics of superposed nonlinear waves in coherently coupled Gross–Pitaevskii (CCGP) equations with constant (autonomous system) and time varying (non-autonomous system) nonlinearity coefficients. By employing a linear transformation, the autonomous CCGP system is converted into two separate scalar nonlinear Schrödinger equations and we show that linear superposition of different nonlinear wave solutions of these scalar equations results into several kinds of nonlinear coherent structures namely, coexisting rogue wave-Ma breather, Akhmediev–Ma breathers, collision and bound states of Ma breathers and solitons. Next, the non-autonomous CCGP system is converted into an autonomous CCGP system with a similarity transformation. We show an interesting possibility of soliton compression and appearance of creeping solitons for kink-like and periodically modulated nonlinearity coefficient. - Highlights: • Coherently coupled Gross–Pitaevskii equations with constant and time-dependent nonlinearities are considered. • Novel superposed nonlinear structures are reported. • Breather collision and nontrivial twin-peak rogue wave are explored. • Co-existing breathers and rogue waves are observed. • Creeping solitons and compression mechanism, respectively for periodically modulated and kink-like nonlinearity are identified.
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.)
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...
Bertoldi, Katia; Boyce, M.C.
2008-01-01
Wave propagation in elastomeric materials undergoing large deformations is relevant in numerous application areas, including nondestructive testing of materials and ultrasound techniques, where finite deformations and corresponding stress states can influence wave propagation and hence
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.
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.
Local numerical modelling of ultrasonic guided waves in linear and nonlinear media
Packo, Pawel; Radecki, Rafal; Kijanka, Piotr; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.
2017-04-01
Nonlinear ultrasonic techniques provide improved damage sensitivity compared to linear approaches. The combination of attractive properties of guided waves, such as Lamb waves, with unique features of higher harmonic generation provides great potential for characterization of incipient damage, particularly in plate-like structures. Nonlinear ultrasonic structural health monitoring techniques use interrogation signals at frequencies other than the excitation frequency to detect changes in structural integrity. Signal processing techniques used in non-destructive evaluation are frequently supported by modeling and numerical simulations in order to facilitate problem solution. This paper discusses known and newly-developed local computational strategies for simulating elastic waves, and attempts characterization of their numerical properties in the context of linear and nonlinear media. A hybrid numerical approach combining advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE) is proposed for unique treatment of arbitrary strain-stress relations. The iteration equations of the method are derived directly from physical principles employing stress and displacement continuity, leading to an accurate description of the propagation in arbitrarily complex media. Numerical analysis of guided wave propagation, based on the newly developed hybrid approach, is presented and discussed in the paper for linear and nonlinear media. Comparisons to Finite Elements (FE) are also discussed.
Self-focusing of electromagnetic surface waves on a nonlinear impedance surface
Energy Technology Data Exchange (ETDEWEB)
Luo, Zhangjie, E-mail: zhangjie-luo-cn@126.com [College of Electronics and Information Engineering, Sichuan University, Chengdu 610064 (China); Applied Electromagnetics Group, Electrical and Computer Engineering Department, University of California, San Diego, California 92093 (United States); Chen, Xing [College of Electronics and Information Engineering, Sichuan University, Chengdu 610064 (China); Long, Jiang; Quarfoth, Ryan; Sievenpiper, Daniel, E-mail: dsievenpiper@eng.ucsd.edu [Applied Electromagnetics Group, Electrical and Computer Engineering Department, University of California, San Diego, California 92093 (United States)
2015-05-25
The self-focusing effect of optical beams has been a popular topic of study for quite a while, but such a nonlinear phenomenon at microwave frequencies has never been realized, partially due to the underdevelopment of nonlinear material. In this research, self-focused electromagnetic (EM) surface waves are demonstrated on a circuit-based, power-dependent impedance surface. The formation of a self-focused beam is investigated using a series of discrete-time simulations, and the result is further validated in measurement. It is experimentally observed that, in contrast to the normal scattering of low-power surface waves, high-power waves propagate through the surface while maintaining narrow beam width, and even converge extremely tightly to create a hot spot with higher power. The result is essentially a nonlinear effect of the surface that compensates for the natural tendency of surface waves to diffract. This intriguing experiment can be extended to various potential EM applications such as power-dependent beam steering antennas and nonlinear microwave propagation or dissipation.
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.
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
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.
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.
Propagation of bottom-trapped waves over variable topography
Digital Repository Service at National Institute of Oceanography (India)
Shetye, S.R.
on a topographic slope, as they propagate towards a deeper region of constant depth, is examined using a quasi-geostrophic model. It is seen that there can be no free transmitted wave to the region of constant depth. The bottom-trapped energy is thus... currents farther away. 1. INTRODUCTION Rhines (1970) showed that a stratified rotating fluid over sloping bottom topography can support free waves that are bottom-intensified. The in- crease in the kinetic energy of the currents with depth...
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...
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.
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.
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...
Ultrasonic Guided Wave Propagation through Welded Lap Joints
Directory of Open Access Journals (Sweden)
Audrius Jankauskas
2016-12-01
Full Text Available The objective of the research presented here is the investigation of ultrasonic guided wave (UGW propagation through the lap joint welded plates used in the construction of a storage tank floors. The investigations have been performed using numerical simulation by finite element method (FEM and tested by measurement of the transmission losses of the guided waves transmitted through the welded lap joints. Propagation of the symmetric S0 mode in the welded stainless steel plates in the cases of different lap joint overlap width, operation frequency, and additional plate bonding caused by corrosion were investigated. It was shown that the transmission losses of the S0 mode can vary in the range of 2 dB to 8 dB depending on the ratio between lap joint width and wavelength. It was also demonstrated that additional bonding in the overlap zone caused by corrosion can essentially reduce transmission losses.
Energy Technology Data Exchange (ETDEWEB)
El-Taibany, W. F., E-mail: eltaibany@du.edu.eg, E-mail: eltaibany@hotmail.com; Selim, M. M.; Al-Abbasy, O. M. [Department of Physics, Faculty of Science, Damietta University, New Damietta P. O. 34517 (Egypt); El-Bedwehy, N. A., E-mail: nab-elbedwehy@yahoo.com [Department of Mathematics, Faculty of Science, Damietta University, New Damietta P. O. 34517 (Egypt)
2014-07-15
The propagation of both linear and nonlinear dust acoustic waves (DAWs) in an inhomogeneous magnetized collisional and warm dusty plasma (DP) consisting of Boltzmann ions, nonextensive electrons, and inertial dust particles is investigated. The number density gradients of all DP components besides the inhomogeneities of electrostatic potential and the initial dust fluid velocity are taken into account. The linear dispersion relation and a nonlinear modified Zakharov-Kusnetsov (MZK) equation governing the propagation of the three-dimensional DAWs are derived. The analytical solution of the MZK reveals the creation of both compressive and rarefactive DAW solitons in the proposed model. It is found that the inhomogeneity dimension parameter and the electron nonextensive parameter affect significantly the nonlinear DAW's amplitude, width, and Mach number. The relations of our findings with some astrophysical situations have been given.
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.
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...... along the paper are useful for simulation and radio network planning of future wireless systems operating at 24 GHz in presence of vegetation....
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
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.
Flat lens effect on seismic waves propagation in the subsoil.
Brûlé, Stéphane; Javelaud, Emmanuel H; Enoch, Stefan; Guenneau, Sébastien
2017-12-22
We show that seismic energy simulated by an artificial source that mainly propagates Rayleigh surface waves, is focused in structured soil made of a grid of holes distributed in the ground. We carry out large-scale field tests with a structured soil made of a grid consisting of cylindrical and vertical holes in the ground and a low frequency artificial source (seismic metamaterials to counteract partially or totally the most devastating components of seismic signals.
Monograph on propagation of sound waves in curved ducts
Rostafinski, Wojciech
1991-01-01
After reviewing and evaluating the existing material on sound propagation in curved ducts without flow, it seems strange that, except for Lord Rayleigh in 1878, no book on acoustics has treated the case of wave motion in bends. This monograph reviews the available analytical and experimental material, nearly 30 papers published on this subject so far, and concisely summarizes what has been learned about the motion of sound in hard-wall and acoustically lined cylindrical bends.
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
Surface wave propagation in a fluid-saturated incompressible ...
Indian Academy of Sciences (India)
Surface wave propagation in a fluid-saturated incompressible porous medium157 where ˙xi˙xi˙xi and ¨xi¨xi¨xi(i = F,S) denote the velocities and accelerations of solid and fluid phases respectively and p is the effective pore pressure of the incompressible pore fluid. ρS and ρF are the densities of the solid and fluid phases ...
Lebiedzik, Catherine
1995-01-01
Development of design tools to furnish optimal acoustic environments for lightweight aircraft demands the ability to simulate the acoustic system on a workstation. In order to form an effective mathematical model of the phenomena at hand, we have begun by studying the propagation of acoustic waves inside closed spherical shells. Using a fully-coupled fluid-structure interaction model based upon variational principles, we have written a finite element analysis program and are in the process of examining several test cases. Future investigations are planned to increase model accuracy by incorporating non-linear and viscous effects.
Evidence and effects of a wave-driven nonlinear current in the equatorial electrojet
Directory of Open Access Journals (Sweden)
M. Oppenheim
1997-07-01
Full Text Available Ionospheric two-stream waves and gradient-drift waves nonlinearly drive a large-scale (D.C. current in the E-region ionosphere. This current flows parallel to, and with a comparable magnitude to, the fundamental Pedersen current. Evidence for the existence and magnitude of wave-driven currents derives from a theoretical understanding of E-region waves, supported by a series of nonlinear 2D simulations of two-stream waves and by data collected by rocket instruments in the equatorial electrojet. Wave-driven currents will modify the large-scale dynamics of the equatorial electrojet during highly active periods. A simple model shows how a wave-driven current appreciably reduces the horizontally flowing electron current of the electrojet. This reduction may account for the observation that type-I radar echoes almost always have a Doppler velocity close to the acoustic speed, and also for the rocket observation that electrojet regions containing gradient-drift waves do not appear also to contain horizontally propagating two-stream waves. Additionally, a simple model of a gradient-drift instability shows that wave-driven currents can cause nonsinusoidal electric fields similar to those measured in situ.
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.
Lamb waves propagation in layered piezoelectric/piezomagnetic plates.
Ezzin, Hamdi; Ben Amor, Morched; Ben Ghozlen, Mohamed Hédi
2017-04-01
A dynamic solution is presented for the propagation of harmonic waves in magneto-electro-elastic plates composed of piezoelectric BaTiO 3 (B) and magnetostrictive CoFe 2 O 4 (F) material. The state-vector approach is employed to derive the propagator matrix which connects the field variables at the upper interface to those at the lower interface of each layer. The ordinary differential approach is employed to determine the wave propagating characteristics in the plate by imposing the traction-free boundary condition on the top and bottom surfaces of the layered plate. The dispersion curves of the piezoelectric-piezomagnetic plate are shown for different thickness ratios. The numerical results show clearly the influence of different stacking sequences as well as thickness ratio on dispersion curves and on magneto-electromechanical coupling factor. These findings could be relevant to the analysis and design of high-performance surface acoustic wave (SAW) devices constructed from piezoelectric and piezomagnetic materials. Copyright Â© 2016 Elsevier B.V. All rights reserved.
Theoretical Model of Acoustic Wave Propagation in Shallow Water
Directory of Open Access Journals (Sweden)
Kozaczka Eugeniusz
2017-06-01
Full Text Available The work is devoted to the propagation of low frequency waves in a shallow sea. As a source of acoustic waves, underwater disturbances generated by ships were adopted. A specific feature of the propagation of acoustic waves in shallow water is the proximity of boundaries of the limiting media characterised by different impedance properties, which affects the acoustic field coming from a source situated in the water layer “deformed” by different phenomena. The acoustic field distribution in the real shallow sea is affected not only by multiple reflections, but also by stochastic changes in the free surface shape, and statistical changes in the seabed shape and impedance. The paper discusses fundamental problems of modal sound propagation in the water layer over different types of bottom sediments. The basic task in this case was to determine the acoustic pressure level as a function of distance and depth. The results of the conducted investigation can be useful in indirect determination of the type of bottom.
Propagation characteristics of acoustic emission wave in reinforced concrete
Directory of Open Access Journals (Sweden)
Haoxiong Feng
Full Text Available Due to the complexity of components and damage mechanism of reinforced concrete, the wave propagation characteristics in reinforced concrete are always complicated and difficult to determine. The objective of this article is to study the failure process of reinforced concrete structure under the damage caused by pencil-broken. A new method on the basis of the acoustic emission technique and the Hilbert-Huang transform theory is proposed in this work. By using acoustic emission technique, the acoustic emission wave signal is generating while the real-time damage information and the strain field of the reinforced concrete structure is receiving simultaneously. Based on the Hilbert-Huang transform (HHT theory, the peak frequency characteristics of the acoustic emission signals were extracted to identify the damage modes of the reinforced concrete structure. The results demonstrate that this method can quantitatively investigate the acoustic emission wave propagation characteristic in reinforced concrete structures and might also be promising in other civil constructions. Keywords: Acoustic emission, Reinforced concrete structure, Hilbert-Huang transform (HHT, Propagation characteristics
International Nuclear Information System (INIS)
Braginsky, V.B.; Kardashev, N.S.; Polnarev, A.G.; Novikov, I.D.
1989-12-01
Propagation of an electromagnetic wave in the field of gravitational waves is considered. Attention is given to the principal difference between the electromagnetic wave propagation in the field of random gravitational waves and the electromagnetic wave propagation in a medium with a randomly-inhomogeneous refraction index. It is shown that in the case of the gravitation wave field the phase shift of an electromagnetic wave does not increase with distance. The capability of space radio interferometry to detect relic gravitational waves as well as gravitational wave bursts of non cosmological origin are analyzed. (author). 64 refs, 2 figs
Study on the electromagnetic waves propagation characteristics in partially ionized plasma slabs
Directory of Open Access Journals (Sweden)
Zhi-Bin Wang
2016-05-01
Full Text Available Propagation characteristics of electromagnetic (EM waves in partially ionized plasma slabs are studied in this paper. Such features are significant to applications in plasma antennas, blackout of re-entry flying vehicles, wave energy injection to plasmas, and etc. We in this paper developed a theoretical model of EM wave propagation perpendicular to a plasma slab with a one-dimensional density inhomogeneity along propagation direction to investigate essential characteristics of EM wave propagation in nonuniform plasmas. Particularly, the EM wave propagation in sub-wavelength plasma slabs, where the geometric optics approximation fails, is studied and in comparison with thicker slabs where the geometric optics approximation applies. The influences of both plasma and collisional frequencies, as well as the width of the plasma slab, on the EM wave propagation characteristics are discussed. The results can help the further understanding of propagation behaviours of EM waves in nonuniform plasma, and applications of the interactions between EM waves and plasmas.
Van Allen Probe observations of EMIC wave propagation in the inner magnetosphere
Saikin, A.; Zhang, J.; Smith, C. W.; Spence, H. E.; Torbert, R. B.; Kletzing, C.; Wygant, J. R.
2017-12-01
This study examines the propagation of inner magnetosphere (L vector, , analysis on all observed EMIC wave events to determine the direction of propagation, with bi-directionally propagating EMIC waves indicating the presence of the EMIC wave source region. EMIC waves were considered bi-directional (i.e., in the source region) if at least two wave packets exhibited opposing flux components, and (W/km2), consistently for 60 seconds. Events not observed to have opposing flux components are considered unidirectional. EMIC wave events observed at relatively high magnetic latitudes, generally, are found to propagate away from the magnetic equator (i.e., unidirectional). Bi-directionally propagating EMIC waves are preferably observed at lower magnetic latitudes. The occurrence rate, spatial distribution, and the energy propagation angle of both unidirectionally and bi-directionally propagating EMIC waves are examined with respect to L, MLT, and MLAT.
Energy Technology Data Exchange (ETDEWEB)
Luquet, David; Marchiano, Régis; Coulouvrat, François, E-mail: francois.coulouvrat@upmc.fr [Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190, Institut Jean Le Rond d’Alembert, F-75005, Paris (France)
2015-10-28
Many situations involve the propagation of acoustical shock waves through flows. Natural sources such as lightning, volcano explosions, or meteoroid atmospheric entries, emit loud, low frequency, and impulsive sound that is influenced by atmospheric wind and turbulence. The sonic boom produced by a supersonic aircraft and explosion noises are examples of intense anthropogenic sources in the atmosphere. The Buzz-Saw-Noise produced by turbo-engine fan blades rotating at supersonic speed also propagates in a fast flow within the engine nacelle. Simulating these situations is challenging, given the 3D nature of the problem, the long range propagation distances relative to the central wavelength, the strongly nonlinear behavior of shocks associated to a wide-band spectrum, and finally the key role of the flow motion. With this in view, the so-called FLHOWARD (acronym for FLow and Heterogeneous One-Way Approximation for Resolution of Diffraction) method is presented with three-dimensional applications. A scalar nonlinear wave equation is established in the framework of atmospheric applications, assuming weak heterogeneities and a slow wind. It takes into account diffraction, absorption and relaxation properties of the atmosphere, quadratic nonlinearities including weak shock waves, heterogeneities of the medium in sound speed and density, and presence of a flow (assuming a mean stratified wind and 3D turbulent ? flow fluctuations of smaller amplitude). This equation is solved in the framework of the one-way method. A split-step technique allows the splitting of the non-linear wave equation into simpler equations, each corresponding to a physical effect. Each sub-equation is solved using an analytical method if possible, and finite-differences otherwise. Nonlinear effects are solved in the time domain, and others in the frequency domain. Homogeneous diffraction is handled by means of the angular spectrum method. Ground is assumed perfectly flat and rigid. Due to the 3D
Luquet, David; Marchiano, Régis; Coulouvrat, François
2015-10-01
Many situations involve the propagation of acoustical shock waves through flows. Natural sources such as lightning, volcano explosions, or meteoroid atmospheric entries, emit loud, low frequency, and impulsive sound that is influenced by atmospheric wind and turbulence. The sonic boom produced by a supersonic aircraft and explosion noises are examples of intense anthropogenic sources in the atmosphere. The Buzz-Saw-Noise produced by turbo-engine fan blades rotating at supersonic speed also propagates in a fast flow within the engine nacelle. Simulating these situations is challenging, given the 3D nature of the problem, the long range propagation distances relative to the central wavelength, the strongly nonlinear behavior of shocks associated to a wide-band spectrum, and finally the key role of the flow motion. With this in view, the so-called FLHOWARD (acronym for FLow and Heterogeneous One-Way Approximation for Resolution of Diffraction) method is presented with three-dimensional applications. A scalar nonlinear wave equation is established in the framework of atmospheric applications, assuming weak heterogeneities and a slow wind. It takes into account diffraction, absorption and relaxation properties of the atmosphere, quadratic nonlinearities including weak shock waves, heterogeneities of the medium in sound speed and density, and presence of a flow (assuming a mean stratified wind and 3D turbulent ? flow fluctuations of smaller amplitude). This equation is solved in the framework of the one-way method. A split-step technique allows the splitting of the non-linear wave equation into simpler equations, each corresponding to a physical effect. Each sub-equation is solved using an analytical method if possible, and finite-differences otherwise. Nonlinear effects are solved in the time domain, and others in the frequency domain. Homogeneous diffraction is handled by means of the angular spectrum method. Ground is assumed perfectly flat and rigid. Due to the 3D
International Nuclear Information System (INIS)
Luquet, David; Marchiano, Régis; Coulouvrat, François
2015-01-01
Many situations involve the propagation of acoustical shock waves through flows. Natural sources such as lightning, volcano explosions, or meteoroid atmospheric entries, emit loud, low frequency, and impulsive sound that is influenced by atmospheric wind and turbulence. The sonic boom produced by a supersonic aircraft and explosion noises are examples of intense anthropogenic sources in the atmosphere. The Buzz-Saw-Noise produced by turbo-engine fan blades rotating at supersonic speed also propagates in a fast flow within the engine nacelle. Simulating these situations is challenging, given the 3D nature of the problem, the long range propagation distances relative to the central wavelength, the strongly nonlinear behavior of shocks associated to a wide-band spectrum, and finally the key role of the flow motion. With this in view, the so-called FLHOWARD (acronym for FLow and Heterogeneous One-Way Approximation for Resolution of Diffraction) method is presented with three-dimensional applications. A scalar nonlinear wave equation is established in the framework of atmospheric applications, assuming weak heterogeneities and a slow wind. It takes into account diffraction, absorption and relaxation properties of the atmosphere, quadratic nonlinearities including weak shock waves, heterogeneities of the medium in sound speed and density, and presence of a flow (assuming a mean stratified wind and 3D turbulent ? flow fluctuations of smaller amplitude). This equation is solved in the framework of the one-way method. A split-step technique allows the splitting of the non-linear wave equation into simpler equations, each corresponding to a physical effect. Each sub-equation is solved using an analytical method if possible, and finite-differences otherwise. Nonlinear effects are solved in the time domain, and others in the frequency domain. Homogeneous diffraction is handled by means of the angular spectrum method. Ground is assumed perfectly flat and rigid. Due to the 3D
Numerical simulation of ultrasonic wave propagation in elastically anisotropic media
International Nuclear Information System (INIS)
Jacob, Victoria Cristina Cheade; Jospin, Reinaldo Jacques; Bittencourt, Marcelo de Siqueira Queiroz
2013-01-01
The ultrasonic non-destructive testing of components may encounter considerable difficulties to interpret some inspections results mainly in anisotropic crystalline structures. A numerical method for the simulation of elastic wave propagation in homogeneous elastically anisotropic media, based on the general finite element approach, is used to help this interpretation. The successful modeling of elastic field associated with NDE is based on the generation of a realistic pulsed ultrasonic wave, which is launched from a piezoelectric transducer into the material under inspection. The values of elastic constants are great interest information that provide the application of equations analytical models, until small and medium complexity problems through programs of numerical analysis as finite elements and/or boundary elements. The aim of this work is the comparison between the results of numerical solution of an ultrasonic wave, which is obtained from transient excitation pulse that can be specified by either force or displacement variation across the aperture of the transducer, and the results obtained from a experiment that was realized in an aluminum block in the IEN Ultrasonic Laboratory. The wave propagation can be simulated using all the characteristics of the material used in the experiment valuation associated to boundary conditions and from these results, the comparison can be made. (author)
Wave-breaking and generic singularities of nonlinear hyperbolic equations
International Nuclear Information System (INIS)
Pomeau, Yves; Le Berre, Martine; Guyenne, Philippe; Grilli, Stephan
2008-01-01
Wave-breaking is studied analytically first and the results are compared with accurate numerical simulations of 3D wave-breaking. We focus on the time dependence of various quantities becoming singular at the onset of breaking. The power laws derived from general arguments and the singular behaviour of solutions of nonlinear hyperbolic differential equations are in excellent agreement with the numerical results. This shows the power of the analysis by methods using generic concepts of nonlinear science. (open problem)
Nonlinear mechanism of tsunami wave generation by atmospheric disturbances
Pelinovsky, E.; Talipova, T.; Kurkin, A.; Kharif, C.
2001-01-01
The problem of tsunami wave generation by variable meteo-conditions is discussed. The simplified linear and nonlinear shallow water models are derived, and their analytical solutions for a basin of constant depth are discussed. The shallow-water model describes well the properties of the generated tsunami waves for all regimes, except the resonance case. The nonlinear-dispersive model based on the forced Korteweg-de Vries equation ...
Dispersion Effects in Nonlinear Light Propagation in 1-D Fiber Gratings
National Research Council Canada - National Science Library
Martel, Carlos
2003-01-01
...: The contractor will investigate the use of the so-called nonlinear coupled mode equations (NLCME) to obtain approximate solutions of Maxwells equations for light propagation in periodic optical fiber structures...
Propagation of 3D internal gravity wave beams in a slowly varying stratification
Fan, Boyu; Akylas, T. R.
2017-11-01
The time-mean flows induced by internal gravity wave beams (IGWB) with 3D variations have been shown to have dramatic implications for long-term IGWB dynamics. While uniform stratifications are convenient both theoretically and in the laboratory, stratifications in the ocean can vary by more than an order of magnitude over the ocean depth. Here, in view of this fact, we study the propagation of a 3D IGWB in a slowly varying stratification. We assume that the stratification varies slowly relative to the local variations in the wave profile. In the 2D case, the IGWB bends in response to the changing stratification, but nonlinear effects are minor even in the finite amplitude regime. For a 3D IGWB, in addition to bending, we find that nonlinearity results in the transfer of energy from waves to a large-scale time-mean flow associated with the mean potential vorticity, similar to IGWB behavior in a uniform stratification. In a weakly nonlinear setting, we derive coupled evolution equations that govern this process. We also use these equations to determine the stability properties of 2D IGWB to 3D perturbations. These findings indicate that 3D effects may be relevant and possibly fundamental to IGWB dynamics in nature. Supported by NSF Grant DMS-1512925.
Bistable states of TM polarized non-linear waves guided by symmetric layered structures
International Nuclear Information System (INIS)
Mihalache, D.
1985-04-01
Dispersion relations for TM polarized non-linear waves propagating in a symmetric single film optical waveguide are derived. The system consists of a layer of thickness d with dielectric constant epsilon 1 bounded at two sides by a non-linear medium characterized by the diagonal dielectric tensor epsilon 11 =epsilon 22 =epsilon 0 , epsilon 33 =epsilon 0 +α|E 3 | 2 , where E 3 is the normal electric field component. For sufficiently large d/lambda (lambda is the wavelength) we predict bistable states of both symmetric and antisymmetric modes provided that the power flow is the control parameter. (author)
Wave propagation, scattering and emission in complex media
Jin, Ya-Qiu
I. Polarimetric scattering and SAR imagery. EM wave propagation and scattering in polarimetric SAR interferometry / S. R. Cloude. Terrain topographic inversion from single-pass polarimetric SAR image data by using polarimetric stokes parameters and morphological algorithm / Y. Q. Jin, L. Luo. Road detection in forested area using polarimetric SAR / G. W. Dong ... [et al.]. Research on some problems about SAR radiometric resolution / G. Dong ... [et al.]. A fast image matching algorithm for remote sensing applications / Z. Q. Hou ... [et al.]. A new algorithm of noised remote sensing image fusion based on steerable filters / X. Kang ... [et al.]. Adaptive noise reduction of InSAR data based on anisotropic diffusion models and their applications to phase unwrapping / C. Wang, X. Gao, H. Zhang -- II. Scattering from randomly rough surfaces. Modeling tools for backscattering from rough surfaces / A. K. Fung, K. S. Chen. Pseudo-nondiffracting beams from rough surface scattering / E. R. Méndez, T. A. Leskova, A. A. Maradudin. Surface roughness clutter effects in GPR modeling and detection / C. Rappaport. Scattering from rough surfaces with small slopes / M. Saillard, G. Soriano. Polarization and spectral characteristics of radar signals reflected by sea-surface / V. A. Butko, V. A. Khlusov, L. I. Sharygina. Simulation of microwave scattering from wind-driven ocean surfaces / M. Y. Xia ... [et al.]. HF surface wave radar tests at the Eastern China Sea / X. B. Wu ... [et al.] -- III. Electromagnetics of complex materials. Wave propagation in plane-parallel metamaterial and constitutive relations / A. Ishimaru ... [et al.]. Two dimensional periodic approach for the study of left-handed metamaterials / T. M. Grzegorczyk ... [et al.]. Numerical analysis of the effective constitutive parameters of a random medium containing small chiral spheres / Y. Nanbu, T. Matsuoka, M. Tateiba. Wave propagation in inhomogeneous media: from the Helmholtz to the Ginzburg -Landau equation / M
Liu, Xu; Chen, Lunjin; Yang, Lixia; Xia, Zhiyang; Malaspina, David M.
2018-01-01
The effect of the plasmapause on equatorially radially propagating fast magnetosonic (MS) waves in the Earth's dipole magnetic field is studied by using finite difference time domain method. We run 1-D simulation for three different density profiles: (1) no plasmapause, (2) with a plasmapause, and (3) with a plasmapause accompanied with fine-scale density irregularity. We find that (1) without plasmapause the radially inward propagating MS wave can reach ionosphere and continuously propagate to lower altitude if no damping mechanism is considered. The wave properties follow the cold plasma dispersion relation locally along its trajectory. (2) For simulation with a plasmapause with a scale length of 0.006 RE compared to wavelength, only a small fraction of the MS wave power is reflected by the plasmapause. WKB approximation is generally valid for such plasmapause. (3) The multiple fine-scale density irregularities near the outer edge of plasmapause can effectively block the MS wave propagation, resulting in a terminating boundary for MS waves near the plasmapause.
Wave propagation and earth satellite radio emission studies
Yeh, K. C.; Liu, C. H.; Flaherty, B. J.
1974-01-01
Radio propagation studies of the ionosphere using satellite radio beacons are described. The ionosphere is known as a dispersive, inhomogeneous, irregular and sometimes even nonlinear medium. After traversing through the ionosphere the radio signal bears signatures of these characteristics. A study of these signatures will be helpful in two areas: (1) It will assist in learning the behavior of the medium, in this case the ionosphere. (2) It will provide information of the kind of signal characteristics and statistics to be expected for communication and navigational satellite systems that use the similar geometry.
Wave propagation in metamaterials and effective parameters retrieving
DEFF Research Database (Denmark)
Andryieuski, Andrei; Ha, S.; Sukhorukov, A.
2011-01-01
of the determined effective parameters and applicability to thin slabs only. The other methods based, for example, on the eigenfunctions calculations [Menzel], or analytical calculations [Simovski] require advanced skills either in numerical methods and programming or in analytical derivations and maybe considered...... as handsome for implementation. We set a goal to develop a method which is unambiguous but at the same time simple and straightforward. We assume that this can be done by observing the wave propagation inside a metamaterial slab thick enough to avoid transient effects. First, we formulated a retrieval method...... complex wave effective parameters. Extending the method further we developed the approach to determine both wave and material effective parameters through the Bloch-mode analysis [3]. The idea is to perform the Bloch mode expansion [4] of the field inside the metamaterial slab when it is illuminated...
Exact travelling wave solutions for some important nonlinear ...
Indian Academy of Sciences (India)
arising in mathematical physics. Keywords. Exact travelling wave solutions; nonlinear physical models; Kudryashov method. PACS Nos 02.30.Jr; 02.70.Wz; 04.20.Jb. 1. Introduction. The study of nonlinear partial differential equations is an active area of research in applied mathematics, theoretical physics and engineering ...
Non-linear wave packet dynamics of coherent states
Indian Academy of Sciences (India)
We have compared the non-linear wave packet dynamics of coherent states of various symmetry groups and found that certain generic features of non-linear evolution are present in each case. Thus the initial coherent structures are quickly destroyed but are followed by Schrödinger cat formation and revival. We also report ...
New travelling wave solutions for nonlinear stochastic evolution ...
Indian Academy of Sciences (India)
The nonlinear stochastic evolution equations have a wide range of applications in physics, chemistry, biology, economics and finance from various points of view. In this paper, the (′/)-expansion method is implemented for obtaining new travelling wave solutions of the nonlinear (2 + 1)-dimensional stochastic ...
Defocusing regimes of nonlinear waves in media with negative dispersion
DEFF Research Database (Denmark)
Bergé, L.; Kuznetsov, E.A.; Juul Rasmussen, J.
1996-01-01
Defocusing regimes of quasimonochromatic waves governed by a nonlinear Schrodinger equation with mixed-sign dispersion are investigated. For a power-law nonlinearity, we show that localized solutions to this equation defined at the so-called critical dimension cannot collapse in finite time...
Exact travelling wave solutions for some important nonlinear ...
Indian Academy of Sciences (India)
Abstract. The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and ...
New travelling wave solutions for nonlinear stochastic evolution
Indian Academy of Sciences (India)
The nonlinear stochastic evolution equations have a wide range of applications in physics, chemistry, biology, economics and finance from various points of view. In this paper, the (′/)-expansion method is implemented for obtaining new travelling wave solutions of the nonlinear (2 + 1)-dimensional stochastic ...
Exact travelling wave solutions for some important nonlinear ...
Indian Academy of Sciences (India)
The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical ...
Periodic and solitary wave solutions of cubic–quintic nonlinear ...
Indian Academy of Sciences (India)
odic, double-kink, bell and antikink-type solutions for cubic–quintic nonlinear reaction-diffusion equation are extracted. Such solutions can be used to explain various biological and physical phenomena. Keywords. Variable coefficient reaction-diffusion equation; solitary wave solution; cubic–quintic nonlinearity. PACS No.
Theory of electromagnetic wave propagation in ferromagnetic Rashba conductor
Shibata, Junya; Takeuchi, Akihito; Kohno, Hiroshi; Tatara, Gen
2018-02-01
We present a comprehensive study of various electromagnetic wave propagation phenomena in a ferromagnetic bulk Rashba conductor from the perspective of quantum mechanical transport. In this system, both the space inversion and time reversal symmetries are broken, as characterized by the Rashba field α and magnetization M, respectively. First, we present a general phenomenological analysis of electromagnetic wave propagation in media with broken space inversion and time reversal symmetries based on the dielectric tensor. The dependence of the dielectric tensor on the wave vector q and M is retained to first order. Then, we calculate the microscopic electromagnetic response of the current and spin of conduction electrons subjected to α and M, based on linear response theory and the Green's function method; the results are used to study the system optical properties. First, it is found that a large α enhances the anisotropic properties of the system and enlarges the frequency range in which the electromagnetic waves have hyperbolic dispersion surfaces and exhibit unusual propagations known as negative refraction and backward waves. Second, we consider the electromagnetic cross-correlation effects (direct and inverse Edelstein effects) on the wave propagation. These effects stem from the lack of space inversion symmetry and yield q-linear off-diagonal components in the dielectric tensor. This induces a Rashba-induced birefringence, in which the polarization vector rotates around the vector (α ×q ) . In the presence of M, which breaks time reversal symmetry, there arises an anomalous Hall effect and the dielectric tensor acquires off-diagonal components linear in M. For α ∥M , these components yield the Faraday effect for the Faraday configuration q ∥M and the Cotton-Mouton effect for the Voigt configuration ( q ⊥M ). When α and M are noncollinear, M- and q-induced optical phenomena are possible, which include nonreciprocal directional dichroism in the
Observations of Upward Propagating Waves in the Transition Region and Corona above Sunspots
Hou, Zhenyong; Huang, Zhenghua; Xia, Lidong; Li, Bo; Fu, Hui
2018-03-01
We present observations of persistent oscillations of some bright features in the upper-chromosphere/transition region above sunspots taken by IRIS SJ 1400 Å and upward propagating quasi-periodic disturbances along coronal loops rooted in the same region taken by the AIA 171 Å passband. The oscillations of the features are cyclic oscillatory motions without any obvious damping. The amplitudes of the spatial displacements of the oscillations are about 1″. The apparent velocities of the oscillations are comparable to the sound speed in the chromosphere, but the upward motions are slightly larger than that of the downward. The intensity variations can take 24%–53% of the background, suggesting nonlinearity of the oscillations. The FFT power spectra of the oscillations show a dominant peak at a period of about 3 minutes, which is consistent with the omnipresent 3 minute oscillations in sunspots. The amplitudes of the intensity variations of the upward propagating coronal disturbances are 10%–15% of the background. The coronal disturbances have a period of about 3 minutes, and propagate upward along the coronal loops with apparent velocities in a range of 30 ∼ 80 km s‑1. We propose a scenario in which the observed transition region oscillations are powered continuously by upward propagating shocks, and the upward propagating coronal disturbances can be the recurrent plasma flows driven by shocks or responses of degenerated shocks that become slow magnetic-acoustic waves after heating the plasma in the coronal loops at their transition-region bases.
DEFF Research Database (Denmark)
Rasmussen, Christian Jørgen
2001-01-01
Presents a simple and fast method for determination of the step size that exactly leads to a prescribed accuracy when signal propagation through nonlinear optical fibres is computed using the split-step Fourier method.......Presents a simple and fast method for determination of the step size that exactly leads to a prescribed accuracy when signal propagation through nonlinear optical fibres is computed using the split-step Fourier method....
Induced wave propagation from a vibrating containment envelope
International Nuclear Information System (INIS)
Stout, R.B.; Thigpen, L.; Rambo, J.T.
1985-09-01
Low frequency wave forms are observed in the particle velocity measurements around the cavity and containment envelope formed by an underground nuclear test. The vibration solution for a spherical shell is used to formulate a model for the low frequency wave that propagates outward from this region. In this model the containment envelope is the zone of material that is crushed by the compressive shock wave of the nuclear explosion. The containment envelope is approximated by a spherical shell of material. The material in the spherical shell is densified and is given a relatively high kinetic energy density because of the high compressive stress and particle velocity of the shock wave. After the shock wave has propagated through the spherical shell, the spherical shell vibrates in order to dissipate the kinetic energy acquired from the shock wave. Based on the model, the frequency of vibration depends on the dimensions and material properties of the spherical shell. The model can also be applied in an inverse mode to obtain global estimates of averaged materials properties. This requires using experimental data and semi-empirical relationships involving the material properties. A particular case of estimating a value for shear strength is described. Finally, the oscillation time period of the lowest frequency from five nuclear tests is correlated with the energy of the explosion. The correlation provides another diagnostic to estimate the energy of a nuclear explosion. Also, the longest oscillation time period measurement provides additional experimental data that can be used to assess and validate various computer models. 11 refs., 2 figs
ENERGY CONTENT AND PROPAGATION IN TRANSVERSE SOLAR ATMOSPHERIC WAVES
Energy Technology Data Exchange (ETDEWEB)
Goossens, M.; Van Doorsselaere, T. [Centre for mathematical Plasma Astrophysics, Mathematics Department, Celestijnenlaan 200B bus 2400, B-3001 Heverlee (Belgium); Soler, R. [Solar Physics Group, Departament de Fisica, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Verth, G., E-mail: tom.vandoorsselaere@wis.kuleuven.be [Solar Physics and Space Plasma Research Centre (SP2RC), School of Mathematics and Statistics, University of Sheffield, Hounsfield Road, Hicks Building, Sheffield S3 7RH (United Kingdom)
2013-05-10
Recently, a significant amount of transverse wave energy has been estimated propagating along solar atmospheric magnetic fields. However, these estimates have been made with the classic bulk Alfven wave model which assumes a homogeneous plasma. In this paper, the kinetic, magnetic, and total energy densities and the flux of energy are computed for transverse MHD waves in one-dimensional cylindrical flux tube models with a piecewise constant or continuous radial density profile. There are fundamental deviations from the properties for classic bulk Alfven waves. (1) There is no local equipartition between kinetic and magnetic energy. (2) The flux of energy and the velocity of energy transfer have, in addition to a component parallel to the magnetic field, components in the planes normal to the magnetic field. (3) The energy densities and the flux of energy vary spatially, contrary to the case of classic bulk Alfven waves. This last property has the important consequence that the energy flux computed with the well known expression for bulk Alfven waves could overestimate the real flux by a factor in the range 10-50, depending on the flux tube equilibrium properties.
Propagation of photosensitive chemical waves on the circular routes.
Kitahata, Hiroyuki; Yamada, Akiko; Nakata, Satoshi; Ichino, Takatoshi
2005-06-09
The propagation of chemical waves in the photosensitive Belousov-Zhabotinsky (BZ) reaction was investigated using an excitable field in the shape of a circular ring or figure "8" that was drawn by computer software and then projected on a film soaked with BZ solution using a liquid-crystal projector. For a chemical wave in a circular reaction field, the shape of the chemical wave was investigated depending on the ratio of the inner and outer radii. When two chemical waves were generated on a field shaped like a figure "8" (one chemical wave in each circle) as the initial condition, the location of the collision of the waves either was constant or alternated depending on the degree of overlap of the two circular rings. These experimental results were analyzed on the basis of a geometrical discussion and theoretically reproduced on the basis of a reaction-diffusion system using a modified Oregonator model. These results suggest that the photosensitive BZ reaction may be useful for creating spatio-temporal patterns depending on the geometric arrangement of excitable fields.
Wave energy converter effects on wave propagation: A sensitivity study in Monterey Bay, CA
Chang, G.; Jones, C. A.; Roberts, J.; Magalen, J.; Ruehl, K.; Chartrand, C.
2014-12-01
The development of renewable offshore energy in the United States is growing rapidly and wave energy is one of the largest resources currently being evaluated. The deployment of wave energy converter (WEC) arrays required to harness this resource could feasibly number in the hundreds of individual devices. The WEC arrays have the potential to alter nearshore wave propagation and circulation patterns and ecosystem processes. As the industry progresses from pilot- to commercial-scale it is important to understand and quantify the effects of WECs on the natural nearshore processes that support a local, healthy ecosystem. To help accelerate the realization of commercial-scale wave power, predictive modeling tools have been developed and utilized to evaluate the likelihood of environmental impact. At present, direct measurements of the effects of different types of WEC arrays on nearshore wave propagation are not available; therefore wave model simulations provide the groundwork for investigations of the sensitivity of model results to prescribed WEC characteristics over a range of anticipated wave conditions. The present study incorporates a modified version of an industry standard wave modeling tool, SWAN (Simulating WAves Nearshore), to simulate wave propagation through a hypothetical WEC array deployment site on the California coast. The modified SWAN, referred to as SNL-SWAN, incorporates device-specific WEC power take-off characteristics to more accurately evaluate a WEC device's effects on wave propagation. The primary objectives were to investigate the effects of a range of WEC devices and device and array characteristics (e.g., device spacing, number of WECs in an array) on nearshore wave propagation using SNL-SWAN model simulations. Results showed that significant wave height was most sensitive to variations in WEC device type and size and the number of WEC devices in an array. Locations in the lee centerline of the arrays in each modeled scenario showed the
The Development of Nonlinear Surface and Internal Wave Groups.
1982-11-01
porn (1971a3 observed groups of large amplitude waves propagating in Massachusetts Bay that seemed to rom tidal interaction with a submarine sill...provides a plan view of the tank and a platform for pictures or movies (Fig. 2.2). For these experiments the measurements from 18 wave height sensors
Wu, S. T.
1974-01-01
The responses of the solar atmosphere due to an outward propagation shock are examined by employing the Lax-Wendroff method to solve the set of nonlinear partial differential equations in the model of the solar atmosphere. It is found that this theoretical model can be used to explain the solar phenomena of surge and spray. A criterion to discriminate the surge and spray is established and detailed information concerning the density, velocity, and temperature distribution with respect to the height and time is presented. The complete computer program is also included.
Benoit, Michel; Yates, Marissa L.; Raoult, Cécile
2017-04-01
Efficient and accurate numerical models simulating wave propagation are required for a variety of engineering projects including the evaluation of coastal risks, the design of protective coastal structures, and the estimation of the potential for marine renewable energy devices. Nonlinear and dispersive effects are particularly significant in the coastal zone where waves interact with the bottom, the shoreline, and coastal structures. The main challenge in developing a numerical models is finding a compromise between computational efficiency and the required accuracy of the simulated wave field. Here, a potential approach is selected and the (fully nonlinear) water wave problem is formulated using the Euler-Zakharov equations (Zakharov, 1968) describing the temporal evolution of the free surface elevation and velocity potential. The proposed model (Yates and Benoit, 2015) uses a spectral approach in the vertical (i.e. the vertical variation of the potential is approximated by a linear combination of the first NT+1 Chebyshev polynomials, following the work of Tian and Sato (2008)). The Zakharov equations are integrated in time using a fourth-order Runge-Kutta scheme with a constant time step. At each sub-timestep, the Laplace Boundary Value Problem (BVP) is solved to estimate the free surface vertical velocity using the spectral approach, with typical values of NT between 5 to 8 for practical applications. The 1DH version of the code is validated with comparisons to the experimental data set of Becq-Girard et al. (1999), which studied the propagation of irregular waves over a beach profile with a submerged bar. The nonlinear and dispersive capacities of the model are verified with the correct representation of wave-wave interactions, in particular the transfer of energy between different harmonic components during wave propagation (analysis of the transformation of the variance spectrum along the channel). Evolution of wave skewness, asymmetry and kurtosis along the
International Nuclear Information System (INIS)
Zhang Zaiyun; Liu Zhenhai; Miao Xiujin; Chen Yuezhong
2011-01-01
In this Letter, we investigate the perturbed nonlinear Schroedinger's equation (NLSE) with Kerr law nonlinearity. All explicit expressions of the bounded traveling wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain bell-shaped solitary wave solutions, kink-shaped solitary wave solutions and Jacobi elliptic function periodic solutions. Moreover, we point out the region which these periodic wave solutions lie in. We present the relation between the bounded traveling wave solution and the energy level h. We find that these periodic wave solutions tend to the corresponding solitary wave solutions as h increases or decreases. Finally, for some special selections of the energy level h, it is shown that the exact periodic solutions evolute into solitary wave solution.
Chaos and Intermittency in the DNLS Equation Describing the Parallel Alfvén Wave Propagation
Directory of Open Access Journals (Sweden)
Gustavo Krause
2014-01-01
Full Text Available When the Hall effect is included in the magnetohydrodynamics equations (Hall-MHD model the wave propagation modes become coupled, but for propagation parallel to the ambient magnetic field the Alfvén mode decouples from the magnetosonic ones, resulting in circularly polarized waves that are described by the derivative nonlinear Schrödinger (DNLS equation. In this paper, the DNLS equation is numerically solved using spectral methods for the spatial derivatives and a fourth order Runge-Kutta scheme for time integration. Firstly, the nondiffusive DNLS equation is considered to test the validity of the method by verifying the analytical condition of modulational stability. Later, diffusive and excitatory effects are incorporated to compare the numerical results with those obtained by a three-wave truncation model. The results show that different types of attractors can exist depending on the diffusion level: for relatively large damping, there are fixed points for which the truncation model is a good approximation; for low damping, chaotic solutions appear and the three-wave truncation model fails due to the emergence of new nonnegligible modes.
Nonlinear inverse scattering methods for thermal- wave slice tomography: a wavelet domain approach
Energy Technology Data Exchange (ETDEWEB)
Miller, E.L. [Department of Electrical and Computer Engineering, Northeastern University, 235 Forsyth Building, Boston, Massachusetts02115 (United States); Nicolaides, L.; Mandelis, A. [Photothermal and Optoelectronic Diagnostics Laboratory, Department of Mechanical Engineering, University of Toronto, 5 Kings College Road, Toronto M5S3G8, Ontario (Canada)
1998-06-01
A wavelet domain, nonlinear inverse scattering approach is presented for imaging subsurface defects in a material sample, given observations of scattered thermal waves. Unlike methods using the Born linearization, our inversion scheme is based on the full wave-field model describing the propagation of thermal waves. Multiresolution techniques are employed to regularize and to lower the computational burden of this ill-posed imaging problem. We use newly developed wavelet-based regularization methods to resolve better the edge structures of defects relative to reconstructions obtained with smoothness-type regularizers. A nonlinear approximation to the exact forward-scattering model is introduced to simplify the inversion with little loss in accuracy. We demonstrate this approach on cross-section imaging problems by using synthetically generated scattering data from transmission and backprojection geometries. {copyright} 1998 Optical Society of America
Modeling the Propagation of Shock Waves in Metals
Howard, W. Michael
2005-07-01
We present modeling results for the propagation of strong shock waves in metals. In particular, we use an arbitrary Lagrange Eulerian (ALE3D) code to model the propagation of strong pressure waves (P ˜300 to 400 kbars) generated with high explosives in contact with aluminum cylinders. The aluminum cylinders are assumed to be both flat-topped and have large-amplitude curved surfaces. We use 3D Lagrange mechanics. For the aluminum we use a rate-independent Steinberg-Guinan model, where the yield strength and bulk modulus depends on pressure, density and temperature. The calculation of the melt temperature is based on the Lindermann law. At melt the yield strength and bulk modulus is set to zero. The pressure is represented as a seven-term polynomial as a function of density. For the HMX-based high explosive, we use a JWL, with a program burn model that gives the correct detonation velocity and C-J pressure (P ˜ 390 kbars). For the case of the large-amplitude curved surface, we discuss the evolving shock structure in terms of the early shock propagation experiments by Sakharov. We also discuss the dependence of our results upon our material model for aluminum.
International Nuclear Information System (INIS)
Davidson, Ronald C.; Lee, W. Wei-li; Hong Qin; Startsev, Edward
2001-01-01
This paper develops a clear procedure for solving the nonlinear Vlasov-Maxwell equations for a one-component intense charged particle beam or finite-length charge bunch propagating through a cylindrical conducting pipe (radius r = r(subscript)w = const.), and confined by an applied focusing force. In particular, the nonlinear Vlasov-Maxwell equations are Lorentz-transformed to the beam frame ('primed' variables) moving with axial velocity relative to the laboratory. In the beam frame, the particle motions are nonrelativistic for the applications of practical interest, already a major simplification. Then, in the beam frame, we make the electrostatic approximation which fully incorporates beam space-charge effects, but neglects any fast electromagnetic processes with transverse polarization (e.g., light waves). The resulting Vlasov-Maxwell equations are then Lorentz-transformed back to the laboratory frame, and properties of the self-generated fields and resulting nonlinear Vlasov-Maxwell equations in the laboratory frame are discussed
Nonlinear pulse propagation in a single-and a few-cycle regimes ...
Indian Academy of Sciences (India)
The propagation equation for a single- and a few-cycle pulses was derived in a cubic nonlinear medium including the Raman response. Using this equation, the propagation characteristics of a single- and a 4-cycle pulse, at 0.8 m wavelength, were studied numerically in one spatial dimension. It was shown that Raman ...
International Nuclear Information System (INIS)
Mizuta, Yo; Nagasawa, Minoru; Ohtani, Morimasa; Yamashita, Mikio
2005-01-01
A numerical approach called Fourier direct method (FDM) is applied to nonlinear propagation of optical pulses with the central wavelength 800 nm, the width 2.67-12.00 fs, and the peak power 25-6870 kW in a fused-silica fiber. Bidirectional propagation, delayed Raman response, nonlinear dispersion (self-steepening, core dispersion), as well as correct linear dispersion are incorporated into 'bidirectional propagation equations' which are derived directly from Maxwell's equations. These equations are solved for forward and backward waves, instead of the electric-field envelope as in the nonlinear Schroedinger equation (NLSE). They are integrated as multidimensional simultaneous evolution equations evolved in space. We investigate, both theoretically and numerically, the validity and the limitation of assumptions and approximations used for deriving the NLSE. Also, the accuracy and the efficiency of the FDM are compared quantitatively with those of the finite-difference time-domain numerical approach. The time-domain size 500 fs and the number of grid points in time 2048 are chosen to investigate numerically intensity spectra, spectral phases, and temporal electric-field profiles up to the propagation distance 1.0 mm. On the intensity spectrum of a few-optical-cycle pulses, the self-steepening, core dispersion, and the delayed Raman response appear as dominant, middle, and slight effects, respectively. The delayed Raman response and the core dispersion reduce the effective nonlinearity. Correct linear dispersion is important since it affects the intensity spectrum sensitively. For the compression of femtosecond optical pulses by the complete phase compensation, the shortness and the pulse quality of compressed pulses are remarkably improved by the intense initial peak power rather than by the short initial pulse width or by the propagation distance longer than 0.1 mm. They will be compressed as short as 0.3 fs below the damage threshold of fused-silica fiber 6 MW. It
Symbolic computation of nonlinear wave interactions on MACSYMA
International Nuclear Information System (INIS)
Bers, A.; Kulp, J.L.; Karney, C.F.F.
1976-01-01
In this paper the use of a large symbolic computation system - MACSYMA - in determining approximate analytic expressions for the nonlinear coupling of waves in an anisotropic plasma is described. MACSYMA was used to implement the solutions of a fluid plasma model nonlinear partial differential equations by perturbation expansions and subsequent iterative analytic computations. By interacting with the details of the symbolic computation, the physical processes responsible for particular nonlinear wave interactions could be uncovered and appropriate approximations introduced so as to simplify the final analytic result. Details of the MACSYMA system and its use are discussed and illustrated. (Auth.)
Aeroacoustics: Acoustic wave propagation; Aircraft noise prediction; Aeroacoustic instrumentation
Schwartz, I. R.
1976-01-01
The papers in this volume deal with recent research into acoustic-wave propagation through the atmosphere and progress in aeroacoustic instrumentation, facilities, and test techniques. Topics include the propagation of aircraft noise over long distances in the lower atmosphere, measured effects of turbulence on the rise time of a weak shock, sound scattering from atmospheric turbulence, saturation effects associated with sound propagation in a turbulent medium, and a computer model of the lightning-thunder process. Other papers discuss the development of a computer system for aircraft noise prediction; aircraft flyover noise measurements; and theories and methods for the prediction of ground effects on aircraft noise propagation, for the prediction of airframe aerodynamic noise, for turbine noise prediction, and for combustion noise prediction. Attention is also given to the use of Hartmann generators as sources of high-intensity sound in a large absorption flow-duct facility, an outdoor jet noise facility, factors in the design and performance of free-jet acoustic wind tunnels, and the use of a laser shadowgraph for jet noise diagnosis.
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...... spectrum with a spectral slope of −4.5 superimposed with a narrow band peak. The broadband fluctuations appear due to the energy cascades attributed by low-frequency magnetohydrodynamic modes, whereas, a narrow band peak is observed due to the short period lion roars bursts. The energy spectrum predicted...
Nonlinear waves in electron–positron–ion plasmas including charge ...
Indian Academy of Sciences (India)
2017-01-04
Jan 4, 2017 ... The introduction of the Poisson equation increased the Mach number required to generate the waveforms but the driving electric field E0 was reduced. The results are compared with satellite observations. Keywords. Nonlinear waves; low frequency; ion-acoustic waves. PACS Nos 52.35.Qz; 52.35.Fp; 52.35 ...
Efficient algorithms for non-linear four-wave interactions
Van Vledder, G.P.
2012-01-01
This paper addresses the on-going activities in the development of efficient methods for computing the non-linear four-wave interactions in operational discrete third-generation wind-wave models. It is generally assumed that these interactions play an important role in the evolution of wind
Effects of internal waves on sound propagation in the shallow waters of the continental shelves
Ong, Ming Yi
2016-01-01
Approved for public release; distribution is unlimited Sound waves propagating through the oceans are refracted by internal waves. In the shallow waters of the continental shelves, an additional downward refraction of sound waves due to internal waves can cause them to interact more often with the seabed, resulting in additional energy from the sound waves being dissipated into the seabed. This study investigates how internal waves affect sound propagation on the continental shelves. It fi...
Linear wave propagation in a hot axisymmetric toroidal plasma
Energy Technology Data Exchange (ETDEWEB)
Jaun, A. [Ecole Polytechnique Federale, Lausanne (Switzerland). Centre de Recherche en Physique des Plasma (CRPP)
1995-03-01
Kinetic effects on the propagation of the Alfven wave are studied for the first time in a toroidal plasma relevant for experiments. This requires the resolution of a set of coupled partial differential equations whose coefficients depend locally on the plasma parameters. For this purpose, a numerical wave propagation code called PENN has been developed using either a bilinear or a bicubic Hermite finite element discretization. It solves Maxwell`s equations in toroidal geometry, with a dielectric tensor operator that takes into account the linear response of the plasma. Two different models have been implemented and can be used comparatively to describe the same physical case: the first treats the plasma as resistive fluids and gives results which are in good agreement with toroidal fluid codes. The second is a kinetic model and takes into account the finite size of the Larmor radii; it has successfully been tested against a kinetic plasma model in cylindrical geometry. New results have been obtained when studying kinetic effects in toroidal geometry. Two different conversion mechanisms to the kinetic Alfven wave have been described: one occurs at toroidally coupled resonant surfaces and is the kinetic counterpart of the fluid models` resonance absorption. The other has no such correspondence and results directly from the toroidal coupling between the kinetic Alfven wave and the global wavefield. An analysis of a heating scenario suggests that it might be difficult to heat a plasma with Alfven waves up to temperatures that are relevant for a tokamak reactor. Kinetic effects are studied for three types of global Alfven modes (GAE, TAE, BAE) and a new class of kinetic eigenmodes is described which appear inside the fluid gap: it could be related to recent observations in the JET (Joint European Torus) tokamak. (author) 56 figs., 6 tabs., 58 refs.
Nonlinear Lamb waves for fatigue damage identification in FRP-reinforced steel plates.
Wang, Yikuan; Guan, Ruiqi; Lu, Ye
2017-09-01
A nonlinear Lamb-wave-based method for fatigue crack detection in steel plates with and without carbon fibre reinforcement polymer (CFRP) reinforcement is presented in this study. Both numerical simulation and experimental evaluation were performed for Lamb wave propagation and its interaction with a fatigue crack on these two steel plate types. With the generation of the second harmonic, the damage-induced wave nonlinearities were identified by surface-bonded piezoelectric sensors. Numerical simulation revealed that the damage-induced wave component at the second harmonic was slightly affected by the existence of CFRP laminate, although the total wave energy was decreased because of wave leakage into the CFRP laminate. Due to unavoidable nonlinearity from the experimental environments, it was impractical to directly extract the time-of-flight of the second harmonic for locating the crack. To this end, the correlation coefficient of benchmark and signal with damage at double frequency in the time domain was calculated, based on which an imaging method was introduced to locate the fatigue crack in steel plates with and without CFRP laminates. Copyright © 2017 Elsevier B.V. All rights reserved.
Transfer and scattering of wave packets by a nonlinear trap.
Li, Kai; Kevrekidis, P G; Malomed, Boris A; Frantzeskakis, D J
2011-11-01
In the framework of a one-dimensional model with a tightly localized self-attractive nonlinearity, we study the formation and transfer (dragging) of a trapped mode by "nonlinear tweezers," as well as the scattering of coherent linear wave packets on the stationary localized nonlinearity. The use of a nonlinear trap for dragging allows one to pick up and transfer the relevant structures without grabbing surrounding "radiation." A stability border for the dragged modes is identified by means of analytical estimates and systematic simulations. In the framework of the scattering problem, the shares of trapped, reflected, and transmitted wave fields are found. Quasi-Airy stationary modes with a divergent norm, which may be dragged by a nonlinear trap moving at a constant acceleration, are briefly considered too.
Wave propagation downstream of a high power helicon in a dipolelike magnetic field
International Nuclear Information System (INIS)
Prager, James; Winglee, Robert; Roberson, B. Race; Ziemba, Timothy
2010-01-01
The wave propagating downstream of a high power helicon source in a diverging magnetic field was investigated experimentally. The magnetic field of the wave has been measured both axially and radially. The three-dimensional structure of the propagating wave is observed and its wavelength and phase velocity are determined. The measurements are compared to predictions from helicon theory and that of a freely propagating whistler wave. The implications of this work on the helicon as a thruster are also discussed.
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...... does not exist - one needs to use the nonlocal description, because the nonlocal response function does not converge towards a delta-function. Also, we use the nonlocal theory to show for the first time that the coupling to second harmonic is able to generate an X-shape in the fundamental field despite...
International Nuclear Information System (INIS)
Dai Chaoqing; Wang Yueyue; Tian Qing; Zhang Jiefang
2012-01-01
We present, analytically, self-similar rogue wave solutions (rational solutions) of the inhomogeneous nonlinear Schrödinger equation (NLSE) via a similarity transformation connected with the standard NLSE. Then we discuss the propagation behaviors of controllable rogue waves under dispersion and nonlinearity management. In an exponentially dispersion-decreasing fiber, the postponement, annihilation and sustainment of self-similar rogue waves are modulated by the exponential parameter σ. Finally, we investigate the nonlinear tunneling effect for self-similar rogue waves. Results show that rogue waves can tunnel through the nonlinear barrier or well with increasing, unchanged or decreasing amplitudes via the modulation of the ratio of the amplitudes of rogue waves to the barrier or well height. - Highlights: ► Self-similar rogue wave solutions of the inhomogeneous NLSE are obtained.► Postponement, annihilation and sustainment of self-similar rogue waves are discussed. ► Nonlinear tunneling effects for self-similar rogue waves are investigated.
Exact and explicit solitary wave solutions to some nonlinear equations
International Nuclear Information System (INIS)
Jiefang Zhang
1996-01-01
Exact and explicit solitary wave solutions are obtained for some physically interesting nonlinear evolutions and wave equations in physics and other fields by using a special transformation. These equations include the KdV-Burgers equation, the MKdV-Burgers equation, the combined KdV-MKdV equation, the Newell-Whitehead equation, the dissipative Φ 4 -model equation, the generalized Fisher equation, and the elastic-medium wave equation
Nonlinear shallow water waves: A fractional order approach
Directory of Open Access Journals (Sweden)
Sarmad Arshad
2016-03-01
Full Text Available Nonlinear partial differential equations governing the obscure phenomena of shallow water waves are discussed in this article. Time fractional model is considered to understand the upcoming solutions on the basis of all historical states of the solution. A semi-analytic technique, Homotopy Perturbation Transform Method (HPTM is used in conjunction with a numerical technique to validate the approximate solutions. With the aid of graphical interpretation, the favorable wave parameters, to avoid wave breaking are estimated.
Numerical simulation of stress wave propagation from underground nuclear explosions
International Nuclear Information System (INIS)
Cherry, J.T.; Petersen, F.L.
1970-01-01
This paper presents a numerical model of stress wave propagation (SOC) which uses material properties data from a preshot testing program to predict the stress-induced effects on the rock mass involved in a Plowshare application. SOC calculates stress and particle velocity history, cavity radius, extent of brittle failure, and the rock's efficiency for transmitting stress. The calculations are based on an equation of state for the rock, which is developed from preshot field and laboratory measurements of the rock properties. The field measurements, made by hole logging, determine in situ values of the rock's density, water content, and propagation velocity for elastic waves. These logs also are useful in judging the layering of the rock and in choosing which core samples to test in the laboratory. The laboratory analysis of rock cores includes determination of hydrostatic compressibility to 40 kb, triaxial strength data, tensile strength, Hugoniot elastic limit, and, for the rock near the point of detonation, high-pressure Hugoniot data. Equation-of-state data are presented for rock from three sites subjected to high explosive or underground nuclear shots, including the Hardhat and Gasbuggy sites. SOC calculations of the effects of these two shots on the surrounding rock are compared with the observed effects. In both cases SOC predicts the size of the cavity quite closely. Results of the Gasbuggy calculations indicate that useful predictions of cavity size and chimney height can be made when an adequate preshot testing program is run to determine the rock's equation of state. Seismic coupling is very sensitive to the low-pressure part of the equation of state, and its successful prediction depends on agreement between the logging data and the static compressibility data. In general, it appears that enough progress has been made in calculating stress wave propagation to begin looking at derived numbers, such as number of cracks per zone, for some insight into the
Ying, Wenjun; Henriquez, Craig S
2015-01-01
A both space and time adaptive algorithm is presented for simulating electrical wave propagation in the Purkinje system of the heart. The equations governing the distribution of electric potential over the system are solved in time with the method of lines. At each timestep, by an operator splitting technique, the space-dependent but linear diffusion part and the nonlinear but space-independent reactions part in the partial differential equations are integrated separately with implicit schemes, which have better stability and allow larger timesteps than explicit ones. The linear diffusion equation on each edge of the system is spatially discretized with the continuous piecewise linear finite element method. The adaptive algorithm can automatically recognize when and where the electrical wave starts to leave or enter the computational domain due to external current/voltage stimulation, self-excitation, or local change of membrane properties. Numerical examples demonstrating efficiency and accuracy of the adaptive algorithm are presented.
Directory of Open Access Journals (Sweden)
Wenjun Ying
2015-01-01
Full Text Available A both space and time adaptive algorithm is presented for simulating electrical wave propagation in the Purkinje system of the heart. The equations governing the distribution of electric potential over the system are solved in time with the method of lines. At each timestep, by an operator splitting technique, the space-dependent but linear diffusion part and the nonlinear but space-independent reactions part in the partial differential equations are integrated separately with implicit schemes, which have better stability and allow larger timesteps than explicit ones. The linear diffusion equation on each edge of the system is spatially discretized with the continuous piecewise linear finite element method. The adaptive algorithm can automatically recognize when and where the electrical wave starts to leave or enter the computational domain due to external current/voltage stimulation, self-excitation, or local change of membrane properties. Numerical examples demonstrating efficiency and accuracy of the adaptive algorithm are presented.
Nonlinear evolution of oblique whistler waves in radiation belts
Sharma, R. P.; Nandal, P.; Yadav, N.; Sharma, Swati
2017-02-01
Magnetic power spectrum and formation of coherent structures have been investigated in the present work applicable to Van Allen radiation belt. The nonlinear interaction of high frequency oblique whistler wave and low frequency magnetosonic wave has been investigated. Simulation was performed of the coupled equation of these two waves. The nonlinear interaction of these waves leads to the formation of the localized structures. These resulting localized structures are of complex nature. The associated magnetic power spectrum has also been studied. Dispersive nonlinear processes account for the high frequency part of the spectrum. The resulting magnetic power spectrum shows a scaling of k^{ - 4.5}. The energy transfer process from injection scales to smaller scales is explained by the results.
Modeling nonlinear acoustic waves in media with inhomogeneities in the coefficient of nonlinearity
Demi, L.; Verweij, M.D.; Van Dongen, K.W.A.
2010-01-01
The refraction and scattering of nonlinear acoustic waves play an important role in the realistic application of medical ultrasound. One cause of these effects is the tissue dependence of the nonlinear medium behavior. A method that is able to model those effects is essential for the design of
Investigation of guided waves propagation in pipe buried in sand
International Nuclear Information System (INIS)
Leinov, Eli; Cawley, Peter; Lowe, Michael J.S.
2014-01-01
The inspection of pipelines by guided wave testing is a well-established method for the detection of corrosion defects in pipelines, and is currently used routinely in a variety of industries, e.g. petrochemical and energy. When the method is applied to pipes buried in soil, test ranges tend to be significantly compromised because of attenuation of the waves caused by energy radiating into the soil. Moreover, the variability of soil conditions dictates different attenuation characteristics, which in-turn results in different, unpredictable, test ranges. We investigate experimentally the propagation and attenuation characteristics of guided waves in pipes buried in fine sand using a well characterized full scale experimental apparatus. The apparatus consists of an 8 inch-diameter, 5.6-meters long steel pipe embedded over 3 meters of its length in a rectangular container filled with fine sand, and an air-bladder for the application of overburden pressure. Longitudinal and torsional guided waves are excited in the pipe and recorded using a transducer ring (Guided Ultrasonics Ltd). Acoustic properties of the sand are measured independently in-situ and used to make model predictions of wave behavior in the buried pipe. We present the methodology and the systematic measurements of the guided waves under a range of conditions, including loose and compacted sand. It is found that the application of overburden pressure modifies the compaction of the sand and increases the attenuation, and that the measurement of the acoustic properties of sand allows model prediction of the attenuation of guided waves in buried pipes with a high level of confidence
Development of an analysis code for pressure wave propagation, (1)
International Nuclear Information System (INIS)
Tanaka, Yoshihisa; Sakano, Kosuke; Shindo, Yoshihisa
1974-11-01
We analyzed the propagation of the pressure-wave in the piping system of SWAT-1B rig by using SWAC-5 Code. We carried out analyses on the following parts. 1) A straight pipe 2) Branches 3) A piping system The results obtained in these analyses are as follows. 1) The present our model simulates well the straight pipe and the branch with the same diameters. 2) The present our model simulates approximately the branch with the different diameters and the piping system. (auth.)
International Nuclear Information System (INIS)
Johnson, R.S.
1984-01-01
The propagation of surface waves - that is 'third' sound -on superfluid helium is considered. The fluid is treated as a continuum, using the two-fluid model of Landau, and incorporating the effects of healing, relaxation, thermal conductivity and Newtonian viscosity. A linear theory is developed which includes some discussion of the matching to the outer regions of the vapour. This results in a comprehensive propagation speed for linear waves, although a few properties of the flow are left undetermined at this order. A nonlinear theory is then outlined which leads to the Burgers equation in an appropriate far field, and enables the leading-order theory to be concluded. Some numerical results, for two temperatures, are presented by first recording the Helmholtz free energy as a polynomial in densities, but only the equilibrium state can be satisfactorily reproduced. The propagation speed, as a function of film thickness, is roughly estimated. The looked-for reduction in the predicted speeds is evident, but the magnitude of this reduction is too large for very thin films. However, these analytical results should prove more effective when a complete and accurate description of the Helmholtz free energy is available. (author)
Rafique, Danish; Mussolin, Marco; Forzati, Marco; Mårtensson, Jonas; Chugtai, Mohsan N; Ellis, Andrew D
2011-05-09
We investigate a digital back-propagation simplification method to enable computationally-efficient digital nonlinearity compensation for a coherently-detected 112 Gb/s polarization multiplexed quadrature phase shifted keying transmission over a 1,600 km link (20 x 80 km) with no inline compensation. Through numerical simulation, we report up to 80% reduction in required back-propagation steps to perform nonlinear compensation, in comparison to the standard back-propagation algorithm. This method takes into account the correlation between adjacent symbols at a given instant using a weighted-average approach, and optimization of the position of nonlinear compensator stage to enable practical digital back-propagation. © 2011 Optical Society of America
Measurements on wave propagation characteristics of spiraling electron beams
Singh, A.; Getty, W. D.
1976-01-01
Dispersion characteristics of cyclotron-harmonic waves propagating on a neutralized spiraling electron beam immersed in a uniform axial magnetic field are studied experimentally. The experimental setup consisted of a vacuum system, an electron-gun corkscrew assembly which produces a 110-eV beam with the desired delta-function velocity distribution, a measurement region where a microwave signal is injected onto the beam to measure wavelengths, and a velocity analyzer for measuring the axial electron velocity. Results of wavelength measurements made at beam currents of 0.15, 1.0, and 2.0 mA are compared with calculated values, and undesirable effects produced by increasing the beam current are discussed. It is concluded that a suitable electron beam for studies of cyclotron-harmonic waves can be generated by the corkscrew device.
Elastic Wave Propagation in Concrete and Continuous Wavelet Transform
Chiang, Chih-Hung; Gi, Yu-Fung; Pan, Chi-Ling; Cheng, Chia-Chi
2005-04-01
Elastic wave methods, such as the ultrasonic pulse velocity and the impact echo, are often subject to multiple reflections at the boundaries of various constituents of concrete. Current study aims to improve the feature identification of elastic wave propagation due to buried objects in concrete slabs and cylinders. Embedded steel reinforcement, steel and PVC tubes, wooden disks, and rubber spheres are tested. The received signals are analyzed using continuous wavelet transform. As a result, signals are decomposed into distinctive frequency bands with transient information preserved. The interpretation of multiple reflections at different boundary conditions thus becomes more straightforward. Features related to reflections from steel bar, PVC tube, and steel tube can be readily identified in the magnitude plot of wavelet coefficients. Vibration modes of the concrete slab corresponding to different buried objects can also be separated based on corresponding time duration.
Propagation of pulsed waves in a magnetized chiroplasma
International Nuclear Information System (INIS)
Torres S, H.
1998-01-01
When subject to a constant magnetic field, chiroplasmas exhibit anisotropic constitutive parameters. For electronic chiroplasmas, the focus of this paper, this anisotropy must be described by using a permittivity tensor instead of the usual scalar permittivity. Each member of this tensor is also highly frequency dependent. This paper describes a finite difference time-domain formulation which incorporates both anisotropy and frequency dispersion at the same time , enabling the wide-band transient analysis of magnetoactive chiroplasma. Results are shown for the reflection and transmission through a magnetized chiroplasma layer which show the growing modes in the RCP chiro transverse wave. This stratified model can be scaled to solar photonic frequencies and plasma density to study the wave propagation in the ionosphere contaminated by aerosols and Cfc molecules. (Author)
Nonlinear excitation of geodesic acoustic modes by drift waves
International Nuclear Information System (INIS)
Chakrabarti, N.; Singh, R.; Kaw, P. K.; Guzdar, P. N.
2007-01-01
In this paper, two mode-coupling analyses for the nonlinear excitation of the geodesic acoustic modes (GAMs) in tokamak plasmas by drift waves are presented. The first approach is a coherent parametric process, which leads to a three-wave resonant interaction. This investigation allows for the drift waves and the GAMs to have comparable scales. The second approach uses the wave-kinetic equations for the drift waves, which then couples to the GAMs. This requires that the GAM scale length be large compared to the wave packet associated with the drift waves. The resonance conditions for these two cases lead to specific predictions of the radial wave number of the excited GAMs
Nonlinear coherent four-wave-mixing in optical microscopy
Potma, Eric O.; Boeij, Wim P. de; Wiersma, Douwe A.
2000-01-01
We present a detailed theoretical analysis of the imaging properties of coherent nonlinear microscopes. We have developed a model that allows calculation of the generation and propagation of coherent signals under high numerical aperture (NA) conditions without invoking the slowly varying envelope
Nonlinear Dispersive Elastic Waves in Solids: Exact, Approximate, and Numerical Solutions
Khajehtourian, Romik
Wave motion lies at the heart of many disciplines in the physical sciences and engineering. For example, problems and applications involving light, sound, heat, or fluid flow are all likely to involve wave dynamics at some level. A particular class of problems is concerned with the propagation of elastic waves in a solid medium, such as a fiber-reinforced composite material responding to vibratory excitations, or soil and rock admitting seismic waves moments after the onset of an earthquake, or phonon transport in a semiconducting crystal like silicon. Regardless of the type of wave, the dispersion relation provides a fundamental characterization of the elastodynamic properties of the medium. The first part of the dissertation examines the propagation of a large-amplitude elastic wave in a one-dimensional homogeneous medium with a focus on the effects of inherent nonlinearities on the dispersion relation. Considering a thin rod, where the thickness is small compared to the wavelength, an exact, closed-form formulation is presented for the treatment of two types of nonlinearity in the strain-displacement gradient relation: Green-Lagrange and Hencky. The derived relation is then verified by direct time-domain simulations, examining both instantaneous dispersion (by direct observation) and short-term, pre-breaking dispersion (by Fourier transformation). A high-order perturbation analysis is also conducted yielding an explicit analytical space-time solution, which is shown to be spectrally accurate. The results establish a perfect match between theory and simulation and reveal that regardless of the strength of the nonlinearity, the dispersion relation fully embodies all information pertaining to the nonlinear harmonic generation mechanism that unfolds as an arbitrary-profiled wave evolves in the medium. In the second part of the dissertation, the analysis is extended to a continuous periodic thin rod exhibiting multiple phases or embedded local resonators. The
Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains
Przedborski, Michelle; Anco, Stephen C.
2017-09-01
A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.
Plasma and radio waves from Neptune: Source mechanisms and propagation
Wong, H. K.
1994-01-01
This report summarizes results obtained through the support of NASA Grant NAGW-2412. The objective of this project is to conduct a comprehensive investigation of the radio wave emission observed by the planetary radio astronomy (PRA) instrument on board Voyager 2 as if flew by Neptune. This study has included data analysis, theoretical and numerical calculations, ray tracing, and modeling to determine the possible source mechanism(s) and locations of the Neptune radio emissions. We have completed four papers, which are included in the appendix. The paper 'Modeling of Whistler Ray Paths in the Magnetosphere of Neptune' investigated the propagation and dispersion of lighting-generated whistler in the magnetosphere of Neptune by using three dimensional ray tracing. The two papers 'Numerical Simulations of Bursty Radio Emissions from Planetary Magnetospheres' and 'Numerical Simulations of Bursty Planetary Radio Emissions' employed numerical simulations to investigate an alternate source mechanism of bursty radio emissions in addition to the cyclotron maser instability. We have also studied the possible generation of Z and whistler mode waves by the temperature anisotropic beam instability and the result was published in 'Electron Cyclotron Wave Generation by Relativistic Electrons.' Besides the aforementioned studies, we have also collaborated with members of the PRA team to investigate various aspects of the radio wave data. Two papers have been submitted for publication and the abstracts of these papers are also listed in the appendix.
Propagation characteristics of ultrasonic guided waves in continuously welded rail
Yao, Wenqing; Sheng, Fuwei; Wei, Xiaoyuan; Zhang, Lei; Yang, Yuan
2017-07-01
Rail defects cause numerous railway accidents. Trains are derailed and serious consequences often occur. Compared to traditional bulk wave testing, ultrasonic guided waves (UGWs) can provide larger monitoring ranges and complete coverage of the waveguide cross-section. These advantages are of significant importance for the non-destructive testing (NDT) of the continuously welded rail, and the technique is therefore widely used in high-speed railways. UGWs in continuous welded rail (CWR) and their propagation characteristics have been discussed in this paper. Finite element methods (FEMs) were used to accomplish a vibration modal analysis, which is extended by a subsequent dispersion analysis. Wave structure features were illustrated by displacement profiles. It was concluded that guided waves have the ability to detect defects in the rail via choice of proper mode and frequency. Additionally, thermal conduction that is caused by temperature variation in the rail is added into modeling and simulation. The results indicated that unbalanced thermal distribution may lead to the attenuation of UGWs in the rail.
Fully resolved simulations of expansion waves propagating into particle beds
Marjanovic, Goran; Hackl, Jason; Annamalai, Subramanian; Jackson, Thomas; Balachandar, S.
2017-11-01
There is a tremendous amount of research that has been done on compression waves and shock waves moving over particles but very little concerning expansion waves. Using 3-D direct numerical simulations, this study will explore expansion waves propagating into fully resolved particle beds of varying volume fractions and geometric arrangements. The objectives of these simulations are as follows: 1) To fully resolve all (1-way coupled) forces on the particles in a time varying flow and 2) to verify state-of-the-art drag models for such complex flows. We will explore a range of volume fractions, from very low ones that are similar to single particle flows, to higher ones where nozzling effects are observed between neighboring particles. Further, we will explore two geometric arrangements: body centered cubic and face centered cubic. We will quantify the effects that volume fraction and geometric arrangement plays on the drag forces and flow fields experienced by the particles. These results will then be compared to theoretical predictions from a model based on the generalized Faxen's theorem. This work was supported in part by the U.S. Department of Energy under the Predictive Science Academic Alliance Program, under Contract No. DE-NA0002378.
Anisotropic capillary wave propagation in a ripple tank
Velazquez, Daniel; Crowder, Daniel; Linville, Jon; Wilson, Thomas
2007-10-01
A preliminary study has been undertaken to demonstrate the anisotropic wave propagation of capillary waves in a water ripple tank. We have fabricated, using a computer-controlled milling machine, a contoured surface upon a 12'' square, .5ex1-.1em/ -.15em.25ex2 '' thick Plexiglas plate with gradually deepened (˜4 mm) angular channels emanating from the center of the plate and spaced every ninety degrees, with an additional cylindrical well in the plate's center, to accept the vibrating ball of the wave generator. The plate is submerged in the ripple tank, with the cylindrical well aligned with the point source (ball), and the water level adjusted such that the minimum and maximum water depths are 2 and 6 mm respectively and resulting wavefronts have been photographed. Provided the difference between the minimum and maximum of the phase velocities (˜17, 23 cm/s) for the corresponding depths (2 and 6 mm) of the capillary waves, can be made appropriately large (˜25%) at a fixed frequency (˜5 Hz), then one would expect to observe interesting folds (`caustics') in the wavefront in the directions of largest phase velocity (along the channels), corresponding to zero-curvature inflection points in the slowness surface. (See J.P. Wolfe ``Phonon Imaging'' (Cambridge University Press, 1998)). We have observed anisotropic wavefronts but as yet, no evidence for the expected folds.
Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report
International Nuclear Information System (INIS)
Tataronis, J. A.
2004-01-01
This program treats theoretically low frequency linear and nonlinear wave processes in magnetized plasmas. A primary objective has been to evaluate the effectiveness of MHD waves to heat plasma and drive current in toroidal configurations. The research covers the following topics: (1) the existence and properties of the MHD continua in plasma equilibria without spatial symmetry; (2) low frequency nonresonant current drive and nonlinear Alfven wave effects; and (3) nonlinear electron acceleration by rf and random plasma waves. Results have contributed to the fundamental knowledge base of MHD activity in symmetric and asymmetric toroidal plasmas. Among the accomplishments of this research effort, the following are highlighted: Identification of the MHD continuum mode singularities in toroidal geometry. Derivation of a third order ordinary differential equation that governs nonlinear current drive in the singular layers of the Alfven continuum modes in axisymmetric toroidal geometry. Bounded solutions of this ODE implies a net average current parallel to the toroidal equilibrium magnetic field. Discovery of a new unstable continuum of the linearized MHD equation in axially periodic circular plasma cylinders with shear and incompressibility. This continuum, which we named ''accumulation continuum'' and which is related to ballooning modes, arises as discrete unstable eigenfrequency accumulate on the imaginary frequency axis in the limit of large mode numbers. Development of techniques to control nonlinear electron acceleration through the action of multiple coherent and random plasmas waves. Two important elements of this program aye student participation and student training in plasma theory
Nonlinear whistler wave model for lion roars in the Earth's magnetosheath
Dwivedi, N. K.; Singh, S.
2017-09-01
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 spectrum obtained by semi-analytical approach shows a spectral break point and becomes steeper at higher wave numbers. The observations of IMP 6 plasma waves and magnetometer experiment reveal the existence of short period magnetic field fluctuations in the magnetosheath. The observation shows the broadband spectrum with a spectral slope of -4.5 superimposed with a narrow band peak. The broadband fluctuations appear due to the energy cascades attributed by low-frequency magnetohydrodynamic modes, whereas, a narrow band peak is observed due to the short period lion roars bursts. The energy spectrum predicted by the present theoretical model shows a similar broadband spectrum in the wave number domain with a spectral slope of -3.2, however, it does not show any narrow band peak. Further, we present a comparison between theoretical energy spectrum and the observed spectral slope in the frequency domain. The present semi-analytical model provides exposure to the whistler wave turbulence in the Earth's magnetosheath.
An extended K-dV equation for nonlinear magnetosonic wave in a multi-ion plasma
Energy Technology Data Exchange (ETDEWEB)
Ida, A. [Nagoya Univ. (Japan). School of Engineering; Sanuki, H.; Todoroki, J.
1995-06-01
Nonlinear magnetosonic waves propagating perpendicularly to a magnetic field are studied in two-ion plasma. It is shown that high frequency magnetosonic wave under the influence of finite cut-off frequency is described by an extended K-dV equation, rather than conventional K-dV equation. Modulational stability of this mode is strongly affected by the finite cut-off frequency in two-ion plasma. (author).
Constrained non-linear waves for offshore wind turbine design
International Nuclear Information System (INIS)
Rainey, P J; Camp, T R
2007-01-01
Advancements have been made in the modelling of extreme wave loading in the offshore environment. We give an overview of wave models used at present, and their relative merits. We describe a method for embedding existing non-linear solutions for large, regular wave kinematics into linear, irregular seas. Although similar methods have been used before, the new technique is shown to offer advances in computational practicality, repeatability, and accuracy. NewWave theory has been used to constrain the linear simulation, allowing best possible fit with the large non-linear wave. GH Bladed was used to compare the effect of these models on a generic 5 MW turbine mounted on a tripod support structure
Numerical Homogenization of Jointed Rock Masses Using Wave Propagation Simulation
Gasmi, Hatem; Hamdi, Essaïeb; Bouden Romdhane, Nejla
2014-07-01
Homogenization in fractured rock analyses is essentially based on the calculation of equivalent elastic parameters. In this paper, a new numerical homogenization method that was programmed by means of a MATLAB code, called HLA-Dissim, is presented. The developed approach simulates a discontinuity network of real rock masses based on the International Society of Rock Mechanics (ISRM) scanline field mapping methodology. Then, it evaluates a series of classic joint parameters to characterize density (RQD, specific length of discontinuities). A pulse wave, characterized by its amplitude, central frequency, and duration, is propagated from a source point to a receiver point of the simulated jointed rock mass using a complex recursive method for evaluating the transmission and reflection coefficient for each simulated discontinuity. The seismic parameters, such as delay, velocity, and attenuation, are then calculated. Finally, the equivalent medium model parameters of the rock mass are computed numerically while taking into account the natural discontinuity distribution. This methodology was applied to 17 bench fronts from six aggregate quarries located in Tunisia, Spain, Austria, and Sweden. It allowed characterizing the rock mass discontinuity network, the resulting seismic performance, and the equivalent medium stiffness. The relationship between the equivalent Young's modulus and rock discontinuity parameters was also analyzed. For these different bench fronts, the proposed numerical approach was also compared to several empirical formulas, based on RQD and fracture density values, published in previous research studies, showing its usefulness and efficiency in estimating rapidly the Young's modulus of equivalent medium for wave propagation analysis.
Regional wave propagation using the discontinuous Galerkin method
Directory of Open Access Journals (Sweden)
S. Wenk
2013-01-01
Full Text Available We present an application of the discontinuous Galerkin (DG method to regional wave propagation. The method makes use of unstructured tetrahedral meshes, combined with a time integration scheme solving the arbitrary high-order derivative (ADER Riemann problem. This ADER-DG method is high-order accurate in space and time, beneficial for reliable simulations of high-frequency wavefields over long propagation distances. Due to the ease with which tetrahedral grids can be adapted to complex geometries, undulating topography of the Earth's surface and interior interfaces can be readily implemented in the computational domain. The ADER-DG method is benchmarked for the accurate radiation of elastic waves excited by an explosive and a shear dislocation source. We compare real data measurements with synthetics of the 2009 L'Aquila event (central Italy. We take advantage of the geometrical flexibility of the approach to generate a European model composed of the 3-D EPcrust model, combined with the depth-dependent ak135 velocity model in the upper mantle. The results confirm the applicability of the ADER-DG method for regional scale earthquake simulations, which provides an alternative to existing methodologies.
Surface Waves Propagating on Grounded Anisotropic Dielectric Slab
Directory of Open Access Journals (Sweden)
Zhuozhu Chen
2018-01-01
Full Text Available This paper investigates the characteristics of surface waves propagating on a grounded anisotropic dielectric slab. Distinct from the existing analyses that generally assume that the fields of surface wave uniformly distribute along the transverse direction of the infinitely large grounded slab, our method takes into account the field variations along the transverse direction of a finite-width slab. By solving Maxwell’s equations in closed-form, it is revealed that no pure transverse magnetic (TM or transverse electric (TE mode exists if the fields are non-uniformly distributed along the transverse direction of the grounded slab. Instead, two hybrid modes, namely quasi-TM and quasi-TE modes, are supported. In addition, the propagation characteristics of two hybrid modes supported by the grounded anisotropic slab are analyzed in terms of the slab thickness, slab width, as well as the relative permittivity tensor of the anisotropic slab. Furthermore, different methods are employed to compare the analyses, as well as to validate our derivations. The proposed method is very suitable for practical engineering applications.
Counter-propagating wave interaction for contrast-enhanced ultrasound imaging
G. Renaud (G.); J.G. Bosch (Hans); E.J.G. Sijbrands (Eric); V. Shamdasani (V.); R. Entrekin (R.); N. de Jong (Nico); A.F.W. van der Steen (Ton)
2012-01-01
textabstractMost 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
Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations
Zhang, Linghai
2017-10-01
The main purposes of this paper are to accomplish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear system of reaction diffusion equations ut =uxx + α [ βH (u - θ) - u ] - w, wt = ε (u - γw) and to establish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ], under different conditions on the model constants. To establish the bifurcation for the system, we will study the existence and instability of a standing pulse solution if 0 1; the existence and instability of two standing wave fronts if 2 (1 + αγ) θ = αβγ and 0 0 is a positive constant, if 0 mathematical neuroscience.
Sabry, R.; Omran, M. A.
2013-04-01
Investigation of nonlinear wave modulation of electron-acoustic solitary wave packets in planar as well as nonplanar geometry is carried out for an unmagnetized two temperature plasma composed of cold and hot (featuring q-nonextensive distribution) electrons with stationary ions. It is shown that in such plasma, propagation of EA wave packets is governed by a modified NLSE which accounts for the geometrical effect and the nonextensivity of the hot electron species. It is found that the nature of the modulational instabilities would be significantly modified due to the geometrical effects, density ratio α of the hot-to-cold electrons species as well as their temperature ratio θ. Also, there exists a modulation instability period for the cylindrical and spherical envelope excitations, which does not exist in the one-dimensional case. Furthermore, spherical EA solitary wave packets are more structurally stable to perturbations than the cylindrical ones. The relevance of the current study to EA wave modulation in auroral zone plasma is highlighted.
Nonlinear Alfvén wave dynamics in plasmas
Sarkar, Anwesa; Chakrabarti, Nikhil; Schamel, Hans
2015-07-01
Nonlinear Alfvén wave dynamics is presented using Lagrangian fluid approach in a compressible collisional magnetized plasma. In the framework of two fluid dynamics, finite electron inertia is shown to serve as a dispersive effect acting against the convective nonlinearity. In a moving frame, the Alfvén wave can, therefore, form an arbitrarily strong amplitude solitary wave structure due to the balance between nonlinearity and dispersion. Weak amplitude Alfvén waves are shown to be governed by a modified KdV equation, which extends for finite dissipation to a mKdV-Burgers equation. These equations have well known solutions. Next, we have analyzed the fourth order nonlinear Alfvén wave system of equations both numerically and by approximation method. The results indicate a collapse of the density and magnetic field irrespective of the presence of dispersion. The wave magnetic field, however, appears to be less singular showing collapse only when the dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas and are expected to be of special importance in the astrophysical context of magnetic star formation.
DEFF Research Database (Denmark)
Guo, Kai; Friis, Søren Michael Mørk; Christensen, Jesper Bjerge
2017-01-01
We derive from Maxwell's equations full-vectorial nonlinear propagation equations of four-wave mixing valid in straight semiconductor-on-insulator waveguides. Special attention is given to the resulting effective mode area, which takes a convenient form known from studies in photonic crystal fibers......, but has not been introduced in the context of integrated waveguides. We show that the difference between our full-vectorial effective mode area and the scalar equivalent often referred to in the literature may lead to mistakes when evaluating the nonlinear refractive index and optimizing designs of new...
DEFF Research Database (Denmark)
Rasmussen, Anders Rønne; Sørensen, Mads Peter; Gaididei, Yuri Borisovich
2008-01-01
, the model equation considered here is capable to describe waves propagating in opposite directions. Owing to the Hamiltonian structure of the proposed model equation, the front solution is in agreement with the classical Rankine Hugoniot relations. The exact front solution propagates at supersonic speed...
Exact traveling wave solutions for system of nonlinear evolution equations.
Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H
2016-01-01
In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.
Nonlinear approximation with general wave packets
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete...
Wave propagation simulation of radio occultations based on ECMWF refractivity profiles
DEFF Research Database (Denmark)
von Benzon, Hans-Henrik; Høeg, Per
2015-01-01
This paper describes a complete radio occultation simulation environment, including realistic refractivity profiles, wave propagation modeling, instrument modeling, and bending angle retrieval. The wave propagator is used to simulate radio occultation measurements. The radio waves are propagated...... of radio occultations. The output from the wave propagator simulator is used as input to a Full Spectrum Inversion retrieval module which calculates geophysical parameters. These parameters can be compared to the ECMWF atmospheric profiles. The comparison can be used to reveal system errors and get...... a better understanding of the physics. The wave propagation simulations will in this paper also be compared to real measurements. These radio occultations have been exposed to the same atmospheric conditions as the radio occultations simulated by the wave propagator. This comparison reveals that precise...