Sun, Wen-Rong; Liu, De-Yin; Xie, Xi-Yang
2017-04-01
We report the existence and properties of vector breather and semirational rogue-wave solutions for the coupled higher-order nonlinear Schrödinger equations, which describe the propagation of ultrashort optical pulses in birefringent optical fibers. Analytic vector breather and semirational rogue-wave solutions are obtained with Darboux dressing transformation. We observe that the superposition of the dark and bright contributions in each of the two wave components can give rise to complicated breather and semirational rogue-wave dynamics. We show that the bright-dark type vector solitons (or breather-like vector solitons) with nonconstant speed interplay with Akhmediev breathers, Kuznetsov-Ma solitons, and rogue waves. By adjusting parameters, we note that the rogue wave and bright-dark soliton merge, generating the boomeron-type bright-dark solitons. We prove that the rogue wave can be excited in the baseband modulation instability regime. These results may provide evidence of the collision between the mixed ultrashort soliton and rogue wave.
Wen, Xiao-Yong; Yan, Zhenya; Malomed, Boris A
2016-12-01
An integrable system of two-component nonlinear Ablowitz-Ladik equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system. Then, new higher-order discrete two-component RW solutions of the system are found by means of a newly derived discrete version of a generalized Darboux transformation. Finally, the perturbed evolution of these RW states is explored in terms of systematic simulations, which demonstrates that tightly and loosely bound RWs are, respectively, nearly stable and strongly unstable solutions.
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.
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.
Shatah, Jalal
2000-01-01
This volume contains notes of the lectures given at the Courant Institute and a DMV-Seminar at Oberwolfach. The focus is on the recent work of the authors on semilinear wave equations with critical Sobolev exponents and on wave maps in two space dimensions. Background material and references have been added to make the notes self-contained. The book is suitable for use in a graduate-level course on the topic.
Vector wave propagation method.
Fertig, M; Brenner, K-H
2010-04-01
In this paper, we extend the scalar wave propagation method (WPM) to vector fields. The WPM [Appl. Opt.32, 4984 (1993)] was introduced in order to overcome the major limitations of the beam propagation method (BPM). With the WPM, the range of application can be extended from the simulation of waveguides to simulation of other optical elements like lenses, prisms and gratings. In that reference it was demonstrated that the wave propagation scheme provides valid results for propagation angles up to 85 degrees and that it is not limited to small index variations in the axis of propagation. Here, we extend the WPM to three-dimensional vectorial fields (VWPMs) by considering the polarization dependent Fresnel coefficients for transmission in each propagation step. The continuity of the electric field is maintained in all three dimensions by an enhanced propagation vector and the transfer matrix. We verify the validity of the method by transmission through a prism and by comparison with the focal distribution from vectorial Debye theory. Furthermore, a two-dimensional grating is simulated and compared with the results from three-dimensional RCWA. Especially for 3D problems, the runtime of the VWPM exhibits special advantage over the RCWA.
Houlrik, Jens Madsen
2009-01-01
The Lorentz transformation applies directly to the kinematics of moving particles viewed as geometric points. Wave propagation, on the other hand, involves moving planes which are extended objects defined by simultaneity. By treating a plane wave as a geometric object moving at the phase velocity, novel results are obtained that illustrate the…
Poincar wave equations as Fourier transformations of Galilei wave equations
Gomis Torné, Joaquim; Poch Parés, Agustí; Pons Ràfols, Josep Maria
1980-01-01
The relationship between the Poincar and Galilei groups allows us to write the Poincar wave equations for arbitrary spin as a Fourier transform of the Galilean ones. The relation between the Lagrangian formulation for both cases is also studied.
Relativistic quantum mechanics wave equations
Greiner, Walter
1990-01-01
Relativistic Quantum Mechanics - Wave Equations concentrates mainly on the wave equations for spin-0 and spin-12 particles Chapter 1 deals with the Klein-Gordon equation and its properties and applications The chapters that follow introduce the Dirac equation, investigate its covariance properties and present various approaches to obtaining solutions Numerous applications are discussed in detail, including the two-center Dirac equation, hole theory, CPT symmetry, Klein's paradox, and relativistic symmetry principles Chapter 15 presents the relativistic wave equations for higher spin (Proca, Rarita-Schwinger, and Bargmann-Wigner) The extensive presentation of the mathematical tools and the 62 worked examples and problems make this a unique text for an advanced quantum mechanics course
Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems
Chen, Shihua; Baronio, Fabio; Soto-Crespo, Jose M.; Grelu, Philippe; Mihalache, Dumitru
2017-11-01
This review is dedicated to recent progress in the active field of rogue waves, with an emphasis on the analytical prediction of versatile rogue wave structures in scalar, vector, and multidimensional integrable nonlinear systems. We first give a brief outline of the historical background of the rogue wave research, including referring to relevant up-to-date experimental results. Then we present an in-depth discussion of the scalar rogue waves within two different integrable frameworks—the infinite nonlinear Schrödinger (NLS) hierarchy and the general cubic-quintic NLS equation, considering both the self-focusing and self-defocusing Kerr nonlinearities. We highlight the concept of chirped Peregrine solitons, the baseband modulation instability as an origin of rogue waves, and the relation between integrable turbulence and rogue waves, each with illuminating examples confirmed by numerical simulations. Later, we recur to the vector rogue waves in diverse coupled multicomponent systems such as the long-wave short-wave equations, the three-wave resonant interaction equations, and the vector NLS equations (alias Manakov system). In addition to their intriguing bright–dark dynamics, a series of other peculiar structures, such as coexisting rogue waves, watch-hand-like rogue waves, complementary rogue waves, and vector dark three sisters, are reviewed. Finally, for practical considerations, we also remark on higher-dimensional rogue waves occurring in three closely-related (2 + 1)D nonlinear systems, namely, the Davey–Stewartson equation, the composite (2 + 1)D NLS equation, and the Kadomtsev–Petviashvili I equation. As an interesting contrast to the peculiar X-shaped light bullets, a concept of rogue wave bullets intended for high-dimensional systems is particularly put forward by combining contexts in nonlinear optics.
Wave-equation dispersion inversion
Li, Jing
2016-12-08
We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.
Vector domain decomposition schemes for parabolic equations
Vabishchevich, P. N.
2017-09-01
A new class of domain decomposition schemes for finding approximate solutions of timedependent problems for partial differential equations is proposed and studied. A boundary value problem for a second-order parabolic equation is used as a model problem. The general approach to the construction of domain decomposition schemes is based on partition of unity. Specifically, a vector problem is set up for solving problems in individual subdomains. Stability conditions for vector regionally additive schemes of first- and second-order accuracy are obtained.
Algorithms for quadratic matrix and vector equations
Poloni, Federico
2011-01-01
This book is devoted to studying algorithms for the solution of a class of quadratic matrix and vector equations. These equations appear, in different forms, in several practical applications, especially in applied probability and control theory. The equations are first presented using a novel unifying approach; then, specific numerical methods are presented for the cases most relevant for applications, and new algorithms and theoretical results developed by the author are presented. The book focuses on “matrix multiplication-rich” iterations such as cyclic reduction and the structured doubling algorithm (SDA) and contains a variety of new research results which, as of today, are only available in articles or preprints.
Wave equations for pulse propagation
Shore, B. W.
1987-06-01
Theoretical discussions of the propagation of pulses of laser radiation through atomic or molecular vapor rely on a number of traditional approximations for idealizing the radiation and the molecules, and for quantifying their mutual interaction by various equations of propagation (for the radiation) and excitation (for the molecules). In treating short-pulse phenomena it is essential to consider coherent excitation phenomena of the sort that is manifest in Rabi oscillations of atomic or molecular populations. Such processes are not adequately treated by rate equations for excitation nor by rate equations for radiation. As part of a more comprehensive treatment of the coupled equations that describe propagation of short pulses, this memo presents background discussion of the equations that describe the field. This memo discusses the origin, in Maxwell's equations, of the wave equation used in the description of pulse propagation. It notes the separation into lamellar and solenoidal (or longitudinal and transverse) and positive and negative frequency parts. It mentions the possibility of separating the polarization field into linear and nonlinear parts, in order to define a susceptibility or index of refraction and, from these, a phase and group velocity.
Wave equations in higher dimensions
Dong, Shi-Hai
2011-01-01
Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the reader’s disposal. A comprehensive description of quantum wave equations in higher dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanics textbooks and gives scientists a fresh outlook on quantum systems in all branches of physics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higher dimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativisti...
An Object Oriented, Finite Element Framework for Linear Wave Equations
Energy Technology Data Exchange (ETDEWEB)
Koning, Joseph M. [Univ. of California, Berkeley, CA (United States)
2004-03-01
This dissertation documents an object oriented framework which can be used to solve any linear wave equation. The linear wave equations are expressed in the differential forms language. This differential forms expression allows a strict discrete interpretation of the system. The framework is implemented using the Galerkin Finite Element Method to define the discrete differential forms and operators. Finite element basis functions including standard scalar Nodal and vector Nedelec basis functions are used to implement the discrete differential forms resulting in a mixed finite element system. Discretizations of scalar and vector wave equations in the time and frequency domains will be demonstrated in both differential forms and vector calculi. This framework conserves energy, maintains physical continuity, is valid on unstructured grids, conditionally stable and second order accurate. Examples including linear electrodynamics, acoustics, elasticity and magnetohydrodynamics are demonstrated.
Fractional vector calculus and fractional Maxwell’s equations
Tarasov, Vasily E.
2008-11-01
The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper. We solve some problems of consistent formulations of FVC by using a fractional generalization of the Fundamental Theorem of Calculus. We define the differential and integral vector operations. The fractional Green's, Stokes' and Gauss's theorems are formulated. The proofs of these theorems are realized for simplest regions. A fractional generalization of exterior differential calculus of differential forms is discussed. Fractional nonlocal Maxwell's equations and the corresponding fractional wave equations are considered.
Dutta, Gaurav
2016-10-12
Strong subsurface attenuation leads to distortion of amplitudes and phases of seismic waves propagating inside the earth. The amplitude and the dispersion losses from attenuation are often compensated for during prestack depth migration. However, most attenuation compensation or Qcompensation migration algorithms require an estimate of the background Q model. We have developed a wave-equation gradient optimization method that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ∈, where ∈ is the sum of the squared differences between the observed and the predicted peak/centroid-frequency shifts of the early arrivals. The gradient is computed by migrating the observed traces weighted by the frequency shift residuals. The background Q model is perturbed until the predicted and the observed traces have the same peak frequencies or the same centroid frequencies. Numerical tests determined that an improved accuracy of the Q model by wave-equation Q tomography leads to a noticeable improvement in migration image quality. © 2016 Society of Exploration Geophysicists.
Resonance vector soliton of the Rayleigh wave.
Adamashvili, G T
2016-02-01
A theory of acoustic vector solitons of self-induced transparency of the Rayleigh wave is constructed. A thin resonance transition layer on an elastic surface is considered using a model of a two-dimensional gas of impurity paramagnetic atoms or quantum dots. Explicit analytical expressions for the profile and parameters of the Rayleigh vector soliton with two different oscillation frequencies is obtained, as well as simulations of this nonlinear surface acoustic wave with realistic parameters, which can be used in acoustic experiments. It is shown that the properties of a surface vector soliton of the Rayleigh wave depend on the parameters of the resonance layer, the elastic medium, and the transverse structure of the surface acoustic wave.
Symmetries, Conservation Laws, and Wave Equation on the Milne Metric
Directory of Open Access Journals (Sweden)
Ahmad M. Ahmad
2012-01-01
representing physical systems. For partial differential equation possessing Lagrangians these symmetries are obtained by the invariance of the corresponding action integral. In this paper we provide a systematic procedure for determining Noether symmetries and conserved vectors for a Lagrangian constructed from a Lorentzian metric of interest in mathematical physics. For completeness, we give Lie point symmetries and conservation laws admitted by the wave equation on this Lorentzian metric.
Wave Equation Inversion of Skeletonized SurfaceWaves
Zhang, Zhendong
2015-08-19
We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh dispersion curve for the fundamental-mode. We call this wave equation inversion of skeletonized surface waves because the dispersion curve for the fundamental-mode Rayleigh wave is inverted using finite-difference solutions to the wave equation. The best match between the predicted and observed dispersion curves provides the optimal S-wave velocity model. Results with synthetic and field data illustrate the benefits and limitations of this method.
Lagrangian vector field and Lagrangian formulation of partial differential equations
Directory of Open Access Journals (Sweden)
M.Chen
2005-01-01
Full Text Available In this paper we consider the Lagrangian formulation of a system of second order quasilinear partial differential equations. Specifically we construct a Lagrangian vector field such that the flows of the vector field satisfy the original system of partial differential equations.
Vector plane wave spectrum of an arbitrary polarized electromagnetic wave.
Guo, Hanming; Chen, Jiabi; Zhuang, Songlin
2006-03-20
By using the method of modal expansions of the independent transverse fields, a formula of vector plane wave spectrum (VPWS) of an arbitrary polarized electromagnetic wave in a homogenous medium is derived. In this formula VPWS is composed of TM- and TE-mode plane wave spectrum, where the amplitude and unit polarized direction of every plane wave are separable, which has more obviously physical meaning and is more convenient to apply in some cases compared to previous formula of VPWS. As an example, the formula of VPWS is applied to the well-known radially and azimuthally polarized beam. In addition, vector Fourier-Bessel transform pairs of an arbitrary polarized electromagnetic wave with circular symmetry are also derived.
Generalized Nonlinear Wave Equation in Frequency Domain
DEFF Research Database (Denmark)
Guo, Hairun; Zeng, Xianglong; Bache, Morten
2013-01-01
We interpret the forward Maxwell equation with up to third order induced polarizations and get so called nonlinear wave equation in frequency domain (NWEF), which is based on Maxwell wave equation and using slowly varying spectral amplitude approximation. The NWEF is generalized in concept...... as it directly describes the electric field dynamics rather than the envelope dynamics and because it concludes most current-interested nonlinear processes such as three-wave mixing, four-wave-mixing and material Raman effects. We give two sets of NWEF, one is a 1+1D equation describing the (approximated) planar...... wave propagation in nonlinear bulk material and the other corresponds to the propagation in a waveguide structure....
Skeletonized wave equation of surface wave dispersion inversion
Li, Jing
2016-09-06
We present the theory for wave equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. Similar to wave-equation travel-time inversion, the complicated surface-wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the (kx,ω) domain. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2D or 3D velocity models. This procedure, denoted as wave equation dispersion inversion (WD), does not require the assumption of a layered model and is less prone to the cycle skipping problems of full waveform inversion (FWI). The synthetic and field data examples demonstrate that WD can accurately reconstruct the S-wave velocity distribution in laterally heterogeneous media.
Electronic representation of wave equation
Energy Technology Data Exchange (ETDEWEB)
Veigend, Petr; Kunovský, Jiří, E-mail: kunovsky@fit.vutbr.cz; Kocina, Filip; Nečasová, Gabriela; Valenta, Václav [University of Technology, Faculty of Information Technology, Božetěchova 2, 612 66 Brno (Czech Republic); Šátek, Václav [IT4Innovations, VŠB Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava-Poruba (Czech Republic); University of Technology, Faculty of Information Technology, Božetěchova 2, 612 66 Brno (Czech Republic)
2016-06-08
The Taylor series method for solving differential equations represents a non-traditional way of a numerical solution. Even though this method is not much preferred in the literature, experimental calculations done at the Department of Intelligent Systems of the Faculty of Information Technology of TU Brno have verified that the accuracy and stability of the Taylor series method exceeds the currently used algorithms for numerically solving differential equations. This paper deals with solution of Telegraph equation using modelling of a series small pieces of the wire. Corresponding differential equations are solved by the Modern Taylor Series Method.
Electronic representation of wave equation
Veigend, Petr; Kunovský, Jiří; Kocina, Filip; Nečasová, Gabriela; Šátek, Václav; Valenta, Václav
2016-06-01
The Taylor series method for solving differential equations represents a non-traditional way of a numerical solution. Even though this method is not much preferred in the literature, experimental calculations done at the Department of Intelligent Systems of the Faculty of Information Technology of TU Brno have verified that the accuracy and stability of the Taylor series method exceeds the currently used algorithms for numerically solving differential equations. This paper deals with solution of Telegraph equation using modelling of a series small pieces of the wire. Corresponding differential equations are solved by the Modern Taylor Series Method.
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....
Octonion wave equation and tachyon electrodynamics
Indian Academy of Sciences (India)
The octonion wave equation is discussed to formulate the localization spaces for subluminal and superluminal particles. Accordingly, tachyon electrodynamics is established to obtain a consistent and manifestly covariant equation for superluminal electromagnetic fields. It is shown that the true localization space for ...
Wave Equations in Bianchi Space-Times
Directory of Open Access Journals (Sweden)
S. Jamal
2012-01-01
Full Text Available We investigate the wave equation in Bianchi type III space-time. We construct a Lagrangian of the model, calculate and classify the Noether symmetry generators, and construct corresponding conserved forms. A reduction of the underlying equations is performed to obtain invariant solutions.
Diffusion phenomenon for linear dissipative wave equations
Said-Houari, Belkacem
2012-01-01
In this paper we prove the diffusion phenomenon for the linear wave equation. To derive the diffusion phenomenon, a new method is used. In fact, for initial data in some weighted spaces, we prove that for {equation presented} decays with the rate {equation presented} [0,1] faster than that of either u or v, where u is the solution of the linear wave equation with initial data {equation presented} [0,1], and v is the solution of the related heat equation with initial data v 0 = u 0 + u 1. This result improves the result in H. Yang and A. Milani [Bull. Sci. Math. 124 (2000), 415-433] in the sense that, under the above restriction on the initial data, the decay rate given in that paper can be improved by t -γ/2. © European Mathematical Society.
Quaternion wave equations in curved space-time
Edmonds, J. D., Jr.
1974-01-01
The quaternion formulation of relativistic quantum theory is extended to include curvilinear coordinates and curved space-time in order to provide a framework for a unified quantum/gravity theory. Six basic quaternion fields are identified in curved space-time, the four-vector basis quaternions are identified, and the necessary covariant derivatives are obtained. Invariant field equations are derived, and a general invertable coordinate transformation is developed. The results yield a way of writing quaternion wave equations in curvilinear coordinates and curved space-time as well as a natural framework for solving the problem of second quantization for gravity.
Parallel Vector Fields and Einstein Equations of Gravity
African Journals Online (AJOL)
user
106. Parallel Vector Fields and. Einstein Equations of Gravity. By Isidore Mahara. National University of Rwanda. Department of Applied Mathematics. Abstract. In this paper, we prove that no nontrivial timelike or spacelike parallel vector field exists in a region where the gravitational field created by macroscopic bodies and.
Parallel Vector Fields and Einstein Equations of Gravity | Mahara ...
African Journals Online (AJOL)
In this paper, we prove that no nontrivial timelike or spacelike parallel vector field exists in a region where the gravitational field created by macroscopic bodies and governed by Einstein's equations does not vanish. In other words, we prove that the existence of such vector fields in a region implies the vanishing of the ...
A generalized Allwright formula and the vector Riccati equation
DEFF Research Database (Denmark)
Andersen, Kurt Munk; Sandqvist, Allan
2010-01-01
with a special type of a differential system called a vector Riccati equation. Moreover,the classical result that a scalar differential equation is a Riccati equation if and only if its general solution is a fractional linear function of the starting value, is also generalized to a differential system.......A classical formula of Allwright on the general solution of a scalar differential equation is generalized to a system of differential equations by means of the Kronecker product.The Allwright formula is connected with the Riccati equation, and in a similar way the generalized formula is connected...
Wave Normal and Poynting Vector Calculations using the Cassini Radio and Plasma Wave Instrument
Hospodarsky, G. B.; Averkamp, T. F.; Kurth, W. S.; Gurnett, D. A.; Dougherty, M.; Inan, Umran; Wood, Troy
2001-01-01
Wave normal and Poynting vector measurements from the Cassini radio and plasma wave instrument (RPWS) are used to examine the propagation characteristics of various plasma waves during the Earth flyby on August 18, 1999. Using the five-channel waveform receiver (WFR), the wave normal vector is determined using the Means method for a lightning-induced whistler, equatorial chorus, and a series of low-frequency emissions observed while Cassini was in the magnetosheath. The Poynting vector for these emissions is also calculated from the five components measured by the WFR. The propagation characteristics of the lightning-induced whistler were found to be consistent with the whistler wave mode of propagation, with propagation antiparallel to the magnetic field (southward) at Cassini. The sferic associated with this whistler was observed by both Cassini and the Stanford VLF group at the Palmer Station in Antarctica. Analysis of the arrival direction of the sferic at the Palmer Station suggests that the lightning stroke is in the same sector as Cassini. Chorus was observed very close (within a few degrees) to the magnetic equator during the flyby. The chorus was found to propagate primarily away from the magnetic equator and was observed to change direction as Cassini crossed the magnetic equator. This suggests that the source region of the chorus is very near the magnetic equator. The low-frequency emission in the magnetosheath has many of the characteristics of lion roars. The average value of the angle between the wave normal vector and the local magnetic field was found to be 16 degrees, and the emissions ranged in frequency from 0. 19 to 0.75 f(sub ce), where f(sub ce) is the electron cyclotron frequency. The wave normal vectors of these waves were primarily in one direction for each individual burst (either parallel or antiparallel to the local field) but varied in direction throughout the magnetosheath. This suggests that the sources of the emissions are far from
Wave-equation Qs Inversion of Skeletonized Surface Waves
Li, Jing
2017-02-08
We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data, namely the amplitude spectra of the windowed Rayleigh-wave arrivals. The optimal Qs model is the one that minimizes the difference in the peak frequencies of the predicted and observed Rayleigh wave arrivals using a gradient-based wave-equation optimization method. Solutions to the viscoelastic wave-equation are used to compute the predicted Rayleigh-wave arrivals and the misfit gradient at every iteration. This procedure, denoted as wave-equation Qs inversion (WQs), does not require the assumption of a layered model and tends to have fast and robust convergence compared to full waveform inversion (FWI). Numerical examples with synthetic and field data demonstrate that the WQs method can accurately invert for a smoothed approximation to the subsurface Qs distribution as long as the Vs model is known with sufficient accuracy.
Skeletonized wave-equation Qs tomography using surface waves
Li, Jing
2017-08-17
We present a skeletonized inversion method that inverts surface-wave data for the Qs quality factor. Similar to the inversion of dispersion curves for the S-wave velocity model, the complicated surface-wave arrivals are skeletonized as simpler data, namely the amplitude spectra of the windowed Rayleigh-wave arrivals. The optimal Qs model is then found that minimizes the difference in the peak frequencies of the predicted and observed Rayleigh wave arrivals using a gradient-based wave-equation optimization method. Solutions to the viscoelastic wave-equation are used to compute the predicted Rayleigh-wave arrivals and the misfit gradient at every iteration. This procedure, denoted as wave-equation Qs tomography (WQs), does not require the assumption of a layered model and tends to have fast and robust convergence compared to Q full waveform inversion (Q-FWI). Numerical examples with synthetic and field data demonstrate that the WQs method can accurately invert for a smoothed approximation to the subsur-face Qs distribution as long as the Vs model is known with sufficient accuracy.
A unifying fractional wave equation for compressional and shear waves.
Holm, Sverre; Sinkus, Ralph
2010-01-01
This study has been motivated by the observed difference in the range of the power-law attenuation exponent for compressional and shear waves. Usually compressional attenuation increases with frequency to a power between 1 and 2, while shear wave attenuation often is described with powers less than 1. Another motivation is the apparent lack of partial differential equations with desirable properties such as causality that describe such wave propagation. Starting with a constitutive equation which is a generalized Hooke's law with a loss term containing a fractional derivative, one can derive a causal fractional wave equation previously given by Caputo [Geophys J. R. Astron. Soc. 13, 529-539 (1967)] and Wismer [J. Acoust. Soc. Am. 120, 3493-3502 (2006)]. In the low omegatau (low-frequency) case, this equation has an attenuation with a power-law in the range from 1 to 2. This is consistent with, e.g., attenuation in tissue. In the often neglected high omegatau (high-frequency) case, it describes attenuation with a power-law between 0 and 1, consistent with what is observed in, e.g., dynamic elastography. Thus a unifying wave equation derived properly from constitutive equations can describe both cases.
Extending geometrical optics: A Lagrangian theory for vector waves
Ruiz, D. E.; Dodin, I. Y.
2017-05-01
Even when neglecting diffraction effects, the well-known equations of geometrical optics (GO) are not entirely accurate. Traditional GO treats wave rays as classical particles, which are completely described by their coordinates and momenta, but vector-wave rays have another degree of freedom, namely, their polarization. The polarization degree of freedom manifests itself as an effective (classical) "wave spin" that can be assigned to rays and can affect the wave dynamics accordingly. A well-known manifestation of polarization dynamics is mode conversion, which is the linear exchange of quanta between different wave modes and can be interpreted as a rotation of the wave spin. Another, less-known polarization effect is the polarization-driven bending of ray trajectories. This work presents an extension and reformulation of GO as a first-principle Lagrangian theory, whose effective Hamiltonian governs the aforementioned polarization phenomena simultaneously. As an example, the theory is applied to describe the polarization-driven divergence of right-hand and left-hand circularly polarized electromagnetic waves in weakly magnetized plasma.
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...
Stability of Vector Functional Differential Equations: A Survey | Gil ...
African Journals Online (AJOL)
This paper is a survey of the recent results of the author on the stability of linear and nonlinear vector differential equations with delay. Explicit conditions for the exponential and absolute stabilities are derived. Moreover, solution estimates for the considered equations are established. They provide the bounds for the regions ...
Geyer, Anna
2016-01-01
Following a general principle introduced by Ehrnstr\\"{o}m et.al. we prove that for an equation modeling the free surface evolution of moderate amplitude waves in shallow water, all symmetric waves are traveling waves.
Multicomponent integrable wave equations: II. Soliton solutions
Energy Technology Data Exchange (ETDEWEB)
Degasperis, A [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , and Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Rome (Italy); Lombardo, S [School of Mathematics, University of Manchester, Alan Turing Building, Upper Brook Street, Manchester M13 9EP (United Kingdom)], E-mail: antonio.degasperis@roma1.infn.it, E-mail: sara.lombardo@manchester.ac.uk, E-mail: sara@few.vu.nl
2009-09-25
The Darboux-dressing transformations developed in Degasperis and Lombardo (2007 J. Phys. A: Math. Theor. 40 961-77) are here applied to construct soliton solutions for a class of boomeronic-type equations. The vacuum (i.e. vanishing) solution and the generic plane wave solution are both dressed to yield one-soliton solutions. The formulae are specialized to the particularly interesting case of the resonant interaction of three waves, a well-known model which is of boomeronic type. For this equation a novel solution which describes three locked dark pulses (simulton) is introduced.
Space-time fractional Zener wave equation.
Atanackovic, T M; Janev, M; Oparnica, Lj; Pilipovic, S; Zorica, D
2015-02-08
The space-time fractional Zener wave equation, describing viscoelastic materials obeying the time-fractional Zener model and the space-fractional strain measure, is derived and analysed. This model includes waves with finite speed, as well as non-propagating disturbances. The existence and the uniqueness of the solution to the generalized Cauchy problem are proved. Special cases are investigated and numerical examples are presented.
Space–time fractional Zener wave equation
Atanackovic, T.M.; Janev, M.; Oparnica, Lj.; Pilipovic, S.; Zorica, D.
2015-01-01
The space–time fractional Zener wave equation, describing viscoelastic materials obeying the time-fractional Zener model and the space-fractional strain measure, is derived and analysed. This model includes waves with finite speed, as well as non-propagating disturbances. The existence and the uniqueness of the solution to the generalized Cauchy problem are proved. Special cases are investigated and numerical examples are presented. PMID:25663807
Gabor Wave Packet Method to Solve Plasma Wave Equations
Energy Technology Data Exchange (ETDEWEB)
A. Pletzer; C.K. Phillips; D.N. Smithe
2003-06-18
A numerical method for solving plasma wave equations arising in the context of mode conversion between the fast magnetosonic and the slow (e.g ion Bernstein) wave is presented. The numerical algorithm relies on the expansion of the solution in Gaussian wave packets known as Gabor functions, which have good resolution properties in both real and Fourier space. The wave packets are ideally suited to capture both the large and small wavelength features that characterize mode conversion problems. The accuracy of the scheme is compared with a standard finite element approach.
A Modified Wide Angle Parabolic Wave Equation
St. Mary, Donald F.; Lee, Ding; Botseas, George
1987-08-01
We demonstrate the implicit finite difference discretization of a higher order parabolic-like partial differential equation approximating the reduced wave equation in the far field and show that the discretization is unconditionally stable. We discuss a method of associating an angle of dispersion with parabolic approximations, present an example which can be used to compare methods on the basis of dispersion angle, and make comparisons among well-known methods and the new method.
Adomian decomposition method used to solve the gravity wave equations
Mungkasi, Sudi; Dheno, Maria Febronia Sedho
2017-01-01
The gravity wave equations are considered. We solve these equations using the Adomian decomposition method. We obtain that the approximate Adomian decomposition solution to the gravity wave equations is accurate (physically correct) for early stages of fluid flows.
Schmidt decompositions of parametric processes II: vector four-wave mixing.
McKinstrie, C J; Ott, J R; Karlsson, M
2013-05-06
In vector four-wave mixing, one or two strong pump waves drive two weak signal and idler waves, each of which has two polarization components. In this paper, vector four-wave mixing processes in a randomly-birefringent fiber (modulation interaction, phase conjugation and Bragg scattering) are studied in detail. For each process, the Schmidt decompositions of the coupling matrices facilitate the solution of the signal-idler equations and the Schmidt decomposition of the associated transfer matrix. The results of this paper are valid for arbitrary pump polarizations.
Partial Differential Equations and Solitary Waves Theory
Wazwaz, Abdul-Majid
2009-01-01
"Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II w...
Energy Technology Data Exchange (ETDEWEB)
Zemach, Charles [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Kurien, Susan [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-11-14
These notes present an account of the Local Wave Vector (LWV) model of a turbulent flow defined throughout physical space. The previously-developed Local Wave Number (LWN) model is taken as a point of departure. Some general properties of turbulent fields and appropriate notation are given first. The LWV model is presently restricted to incompressible flows and the incompressibility assumption is introduced at an early point in the discussion. The assumption that the turbulence is homogeneous is also introduced early on. This assumption can be relaxed by generalizing the space diffusion terms of LWN, but the present discussion is focused on a modeling of homogeneous turbulence.
Adaptive Vector Finite Element Methods for the Maxwell Equations
Harutyunyan, D.
2007-01-01
The increasing demand to understand the behaviour of electromagnetic waves in many real life problems requires solution of the Maxwell equations. In most cases the exact solution of the Maxwell equations is not available, hence numerical methods are indispensable tool to solve them numerically using
Wave-vector and polarization dependence of conical refraction
National Research Council Canada - National Science Library
Turpin, A; Loiko, Yu V; Kalkandjiev, T K; Tomizawa, H; Mompart, J
2013-01-01
We experimentally address the wave-vector and polarization dependence of the internal conical refraction phenomenon by demonstrating that an input light beam of elliptical transverse profile refracts...
Evolution of basic equations for nearshore wave field
ISOBE, Masahiko
2013-01-01
In this paper, a systematic, overall view of theories for periodic waves of permanent form, such as Stokes and cnoidal waves, is described first with their validity ranges. To deal with random waves, a method for estimating directional spectra is given. Then, various wave equations are introduced according to the assumptions included in their derivations. The mild-slope equation is derived for combined refraction and diffraction of linear periodic waves. Various parabolic approximations and time-dependent forms are proposed to include randomness and nonlinearity of waves as well as to simplify numerical calculation. Boussinesq equations are the equations developed for calculating nonlinear wave transformations in shallow water. Nonlinear mild-slope equations are derived as a set of wave equations to predict transformation of nonlinear random waves in the nearshore region. Finally, wave equations are classified systematically for a clear theoretical understanding and appropriate selection for specific applications. PMID:23318680
Wang, T.
2017-05-26
Elastic full waveform inversion (EFWI) provides high-resolution parameter estimation of the subsurface but requires good initial guess of the true model. The traveltime inversion only minimizes traveltime misfits which are more sensitive and linearly related to the low-wavenumber model perturbation. Therefore, building initial P and S wave velocity models for EFWI by using elastic wave-equation reflections traveltime inversion (WERTI) would be effective and robust, especially for the deeper part. In order to distinguish the reflection travletimes of P or S-waves in elastic media, we decompose the surface multicomponent data into vector P- and S-wave seismogram. We utilize the dynamic image warping to extract the reflected P- or S-wave traveltimes. The P-wave velocity are first inverted using P-wave traveltime followed by the S-wave velocity inversion with S-wave traveltime, during which the wave mode decomposition is applied to the gradients calculation. Synthetic example on the Sigbee2A model proves the validity of our method for recovering the long wavelength components of the model.
Skeletonized wave-equation inversion for Q
Dutta, Gaurav
2016-09-06
A wave-equation gradient optimization method is presented that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ε. Here, ε is the sum of the squared differences between the observed and the predicted peak/centroid frequency shifts of the early-arrivals. The gradient is computed by migrating the observed traces weighted by the frequency-shift residuals. The background Q model is perturbed until the predicted and the observed traces have the same peak frequencies or the same centroid frequencies. Numerical tests show that an improved accuracy of the inverted Q model by wave-equation Q tomography (WQ) leads to a noticeable improvement in the migration image quality.
Parallel Vector Fields and Einstein Equations of Gravity
African Journals Online (AJOL)
user
107. This paper uses Einstein equations of General Relativity as presented for example in Landau and Lifchitz and standard theorems of Differential. Geometry as presented, for example in Sternberg [3]. 2. Parallel vector fields on Riemannian manifolds. Let M be an n-dimensional Riemannian manifold with metric tensor g.
Skeletonized Least Squares Wave Equation Migration
Zhan, Ge
2010-10-17
The theory for skeletonized least squares wave equation migration (LSM) is presented. The key idea is, for an assumed velocity model, the source‐side Green\\'s function and the geophone‐side Green\\'s function are computed by a numerical solution of the wave equation. Only the early‐arrivals of these Green\\'s functions are saved and skeletonized to form the migration Green\\'s function (MGF) by convolution. Then the migration image is obtained by a dot product between the recorded shot gathers and the MGF for every trial image point. The key to an efficient implementation of iterative LSM is that at each conjugate gradient iteration, the MGF is reused and no new finitedifference (FD) simulations are needed to get the updated migration image. It is believed that this procedure combined with phase‐encoded multi‐source technology will allow for the efficient computation of wave equation LSM images in less time than that of conventional reverse time migration (RTM).
Wave-equation reflection traveltime inversion
Zhang, Sanzong
2011-01-01
The main difficulty with iterative waveform inversion using a gradient optimization method is that it tends to get stuck in local minima associated within the waveform misfit function. This is because the waveform misfit function is highly nonlinear with respect to changes in the velocity model. To reduce this nonlinearity, we present a reflection traveltime tomography method based on the wave equation which enjoys a more quasi-linear relationship between the model and the data. A local crosscorrelation of the windowed downgoing direct wave and the upgoing reflection wave at the image point yields the lag time that maximizes the correlation. This lag time represents the reflection traveltime residual that is back-projected into the earth model to update the velocity in the same way as wave-equation transmission traveltime inversion. No travel-time picking is needed and no high-frequency approximation is assumed. The mathematical derivation and the numerical examples are presented to partly demonstrate its efficiency and robustness. © 2011 Society of Exploration Geophysicists.
Circularly polarized inertial wave vectors in rotating fluids
Cogley, A. C.
1976-01-01
The Navier-Stokes equations for a rotating fluid are harmonically analyzed for planar motion in an infinite half-space. All solutions are shown to be a sum of two inertial wave vectors, one circularly polarized to the left (CPL) and the other circularly polarized to the right (CPR). These basic solutions are therefore presented in the same nomenclature and form as that found useful by experimentalists in analyzing flow data (called 'rotary spectra'). The CPL wave acts counter to the Coriolis force and consequently has a slower phase speed and larger damping than the CPR wave. At resonance (forcing frequency = Coriolis frequency) the CPR wave has an infinite phase speed and no damping and is the important component leading to the singular nature of the solutions for certain boundary conditions. All possible resonant singularities are explicitly shown. The unsteady development of these unbounded (limited space structure), cyclic (no time origin or structure) flows is presented to show that with time structure the resonant singularities evolve in a self-similar manner.
Invariance analysis and conservation laws of the wave equation on ...
Indian Academy of Sciences (India)
In this paper we discuss symmetries of classes of wave equations that arise as a consequence of some Vaidya metrics. We show how the wave equation is altered by the underlying geometry. In particular, a range of consequences on the form of the wave equation, the symmetries and number of conservation laws, inter alia ...
Exact traveling wave solutions of some nonlinear evolution equations
Kumar, Hitender; Chand, Fakir
2014-02-01
Using a traveling wave reduction technique, we have shown that Maccari equation, (2+1)-dimensional nonlinear Schrödinger equation, medium equal width equation, (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation, (2+1)-dimensional long wave-short wave resonance interaction equation, perturbed nonlinear Schrödinger equation can be reduced to the same family of auxiliary elliptic-like equations. Then using extended F-expansion and projective Riccati equation methods, many types of exact traveling wave solutions are obtained. With the aid of solutions of the elliptic-like equation, more explicit traveling wave solutions expressed by the hyperbolic functions, trigonometric functions and rational functions are found out. It is shown that these methods provide a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. A variety of structures of the exact solutions of the elliptic-like equation are illustrated.
Travelling Waves in Hyperbolic Chemotaxis Equations
Xue, Chuan
2010-10-16
Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s (Keller and Segel, J. Theor. Biol. 30:235-248, 1971). The system has been shown to permit travelling wave solutions which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities which are biologically unrealistic. In this paper, we formulate a model that takes into consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We prove the global existence of solutions and then show the existence of travelling wave solutions both numerically and analytically. © 2010 Society for Mathematical Biology.
Solution of partial differential equations on vector and parallel computers
Ortega, J. M.; Voigt, R. G.
1985-01-01
The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed.
From vectors to waves and streams: An alternative approach to ...
African Journals Online (AJOL)
The incorporation of qualitative evidence transforms vectored maps into waves, while the introduction of the contextual factor combines waves organised along the same grammaticalisation template into a stream. The structure of a wave delivers, in turn, the statistical prototypicality of a gram (i.e. the prototypicality that is ...
Vector wave analysis of an electromagnetic high-order Bessel vortex beam of fractional type α.
Mitri, F G
2011-03-01
The scalar wave theory of nondiffracting electromagnetic (EM) high-order Bessel vortex beams of fractional type α has been recently explored, and their novel features and promising applications have been revealed. However, complete characterization of the properties for this new type of beam requires a vector analysis to determine the fields' components in space because scalar wave theory is inadequate to describe such beams, especially when the central spot is comparable to the wavelength (k(r)/k≈1, where k(r) is the radial component of the wavenumber k). Stemming from Maxwell's vector equations and the Lorenz gauge condition, a full vector wave analysis for the electric and magnetic fields is presented. The results are of particular importance in the study of EM wave scattering of a high-order Bessel vortex beam of fractional type α by particles.
Stochastic solution to a time-fractional attenuated wave equation.
Meerschaert, Mark M; Straka, Peter; Zhou, Yuzhen; McGough, Robert J
2012-10-01
The power law wave equation uses two different fractional derivative terms to model wave propagation with power law attenuation. This equation averages complex nonlinear dynamics into a convenient, tractable form with an explicit analytical solution. This paper develops a random walk model to explain the appearance and meaning of the fractional derivative terms in that equation, and discusses an application to medical ultrasound. In the process, a new strictly causal solution to this fractional wave equation is developed.
Waves Described By The Nonlinear Fifth Order Partial Differential Equation
Kudryashov, N. A.; Soukharev, M. B.; Siroklin, S. A.
Nonlinear long waves on the water are considered taking into account the general- ization of the Korteveg - de Vries equation that is the fifth order partial differential equation. The following problems are studied. First of all it was shown the Cauchy problem can not be solved for the partial differential equation considered by the in- verse scattering transform. However a number of special solution are found in the form of solitary waves and in the form of cnoidal waves. In the general case the boundary value problem described by this fifth order nonlinear partial differential equation is solved by means of the finite difference method. With this aim the finite - difference approximations of the fifth nonlinear partial differential equations was developed. The stability condition and the convergence of the difference equation are discussed. The possible types of nonlinear waves (kinks, periodical waves and solitary waves) are considered. The stability of nonlinear waves studied is discussed taking into account the numerical approach.
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
Evaluation of a wave-vector-frequency-domain method for nonlinear wave propagation
Jing, Yun; Tao, Molei; Clement, Greg T.
2011-01-01
A wave-vector-frequency-domain method is presented to describe one-directional forward or backward acoustic wave propagation in a nonlinear homogeneous medium. Starting from a frequency-domain representation of the second-order nonlinear acoustic wave equation, an implicit solution for the nonlinear term is proposed by employing the Green’s function. Its approximation, which is more suitable for numerical implementation, is used. An error study is carried out to test the efficiency of the model by comparing the results with the Fubini solution. It is shown that the error grows as the propagation distance and step-size increase. However, for the specific case tested, even at a step size as large as one wavelength, sufficient accuracy for plane-wave propagation is observed. A two-dimensional steered transducer problem is explored to verify the nonlinear acoustic field directional independence of the model. A three-dimensional single-element transducer problem is solved to verify the forward model by comparing it with an existing nonlinear wave propagation code. Finally, backward-projection behavior is examined. The sound field over a plane in an absorptive medium is backward projected to the source and compared with the initial field, where good agreement is observed. PMID:21302985
Evaluation of a wave-vector-frequency-domain method for nonlinear wave propagation.
Jing, Yun; Tao, Molei; Clement, Greg T
2011-01-01
A wave-vector-frequency-domain method is presented to describe one-directional forward or backward acoustic wave propagation in a nonlinear homogeneous medium. Starting from a frequency-domain representation of the second-order nonlinear acoustic wave equation, an implicit solution for the nonlinear term is proposed by employing the Green's function. Its approximation, which is more suitable for numerical implementation, is used. An error study is carried out to test the efficiency of the model by comparing the results with the Fubini solution. It is shown that the error grows as the propagation distance and step-size increase. However, for the specific case tested, even at a step size as large as one wavelength, sufficient accuracy for plane-wave propagation is observed. A two-dimensional steered transducer problem is explored to verify the nonlinear acoustic field directional independence of the model. A three-dimensional single-element transducer problem is solved to verify the forward model by comparing it with an existing nonlinear wave propagation code. Finally, backward-projection behavior is examined. The sound field over a plane in an absorptive medium is backward projected to the source and compared with the initial field, where good agreement is observed.
Experimental demonstration of hyperbolic wave vector surfaces in silver nanowire arrays
Energy Technology Data Exchange (ETDEWEB)
Schilling, Joerg [ZIK, Martin-Luther-Universitaet Halle-Wittenberg, Halle (Germany); Kanungo, Jyotirmayee [Queen' s University Belfast, Belfast (United Kingdom)
2010-07-01
Arrays of metal nanowires represent uniaxial metamaterials, whose principal effective permittivities perpendicular and parallel to the wire axis have opposite sign in the infrared and visible spectral range. This property leads to a hyperbolic equi-frequency surface for the extraordinary rays in wave vector space allowing the propagation of waves with unusually large wave vectors. Here we present an experimental mapping of the hyperbolic equi-frequency surfaces of TM (p-)polarised light propagating within a silver nanowire array. To this purpose we performed angular resolved transmission measurements on a 1.7 micron high alumina film containing the silver nanowire array. From the order of the observed Fabry-Perot resonances the wave vector component k{sub z} is determined, while the lateral wave vector component k{sub x}, is obtained from the angle of incidence. The resulting markings in k{sub x}-k{sub z} wave vector diagram then result in a hyperbolic equi-frequency surface for the TM polarisation. Fitting the relationship between spectral position of the Fabry-Perot peaks and angle of incidence by a simple linear equation, we furthermore determined the values of the principal permittivities for TE and TM polarisation in a wide spectral range. All experimental results agree well with simulations based on the Maxwell-Garnett effective medium theory.
Wave-equation Based Earthquake Location
Tong, P.; Yang, D.; Yang, X.; Chen, J.; Harris, J.
2014-12-01
Precisely locating earthquakes is fundamentally important for studying earthquake physics, fault orientations and Earth's deformation. In industry, accurately determining hypocenters of microseismic events triggered in the course of a hydraulic fracturing treatment can help improve the production of oil and gas from unconventional reservoirs. We develop a novel earthquake location method based on solving full wave equations to accurately locate earthquakes (including microseismic earthquakes) in complex and heterogeneous structures. Traveltime residuals or differential traveltime measurements with the waveform cross-correlation technique are iteratively inverted to obtain the locations of earthquakes. The inversion process involves the computation of the Fréchet derivative with respect to the source (earthquake) location via the interaction between a forward wavefield emitting from the source to the receiver and an adjoint wavefield reversely propagating from the receiver to the source. When there is a source perturbation, the Fréchet derivative not only measures the influence of source location but also the effects of heterogeneity, anisotropy and attenuation of the subsurface structure on the arrival of seismic wave at the receiver. This is essential for the accuracy of earthquake location in complex media. In addition, to reduce the computational cost, we can first assume that seismic wave only propagates in a vertical plane passing through the source and the receiver. The forward wavefield, adjoint wavefield and Fréchet derivative with respect to the source location are all computed in a 2D vertical plane. By transferring the Fréchet derivative along the horizontal direction of the 2D plane into the ones along Latitude and Longitude coordinates or local 3D Cartesian coordinates, the source location can be updated in a 3D geometry. The earthquake location obtained with this combined 2D-3D approach can then be used as the initial location for a true 3D wave-equation
Separate P‐ and SV‐wave equations for VTI media
Pestana, Reynam C.
2011-01-01
In isotropic media we use the scalar acoustic wave equation to perform reverse time migration RTM of the recorded pressure wavefleld data. In anisotropic media P- and SV-waves are coupled and the elastic wave equation should be used for RTM. However, an acoustic anisotropic wave equation is often used instead. This results in significant shear wave energy in both modeling and RTM. To avoid this undesired SV-wave energy, we propose a different approach to separate P- and SV-wave components for vertical transversely isotropic VTI media. We derive independent pseudo-differential wave equations for each mode. The derived equations for P- and SV-waves are stable and reduce to the isotropic case. The equations presented here can be effectively used to model and migrate seismic data in VTI media where ε - δ is small. The SV-wave equation we develop is now well-posed and triplications in the SV wavefront are removed resulting in stable wave propagation. We show modeling and RTM results using the derived pure P-wave mode in complex VTI media and use the rapid expansion method REM to propagate the waveflelds in time. © 2011 Society of Exploration Geophysicists.
Lipschitz Metrics for a Class of Nonlinear Wave Equations
Bressan, Alberto; Chen, Geng
2017-12-01
The nonlinear wave equation {u_{tt}-c(u)(c(u)u_x)_x=0} determines a flow of conservative solutions taking values in the space {H^1(R)}. However, this flow is not continuous with respect to the natural H 1 distance. The aim of this paper is to construct a new metric which renders the flow uniformly Lipschitz continuous on bounded subsets of {H^1(R)}. For this purpose, H 1 is given the structure of a Finsler manifold, where the norm of tangent vectors is defined in terms of an optimal transportation problem. For paths of piecewise smooth solutions, one can carefully estimate how the weighted length grows in time. By the generic regularity result proved in [7], these piecewise regular paths are dense and can be used to construct a geodesic distance with the desired Lipschitz property.
Electromagnetic wave propagation and wave-vector diagram in space-time periodic media.
Elachi, C.
1972-01-01
Analysis of TE and TM wave propagation in space-time periodic media such as dielectrics, isotropic plasmas and uniaxial plasmas. A numerical solution is obtained for media with sinusoidal periodicity. Wave-vector diagrams are plotted to facilitate studies of dipole radiation, wave propagation in waveguides and wave interactions with a half-space.
Non-overlapped P- and S-wave Poynting vectors and its solution on Grid Method
Lu, Yong Ming
2017-12-12
Poynting vector represents the local directional energy flux density of seismic waves in geophysics. It is widely used in elastic reverse time migration (RTM) to analyze source illumination, suppress low-wavenumber noise, correct for image polarity and extract angle-domain common imaging gather (ADCIG). However, the P and S waves are mixed together during wavefield propagation such that the P and S energy fluxes are not clean everywhere, especially at the overlapped points. In this paper, we use a modified elastic wave equation in which the P and S vector wavefields are naturally separated. Then, we develop an efficient method to evaluate the separable P and S poynting vectors, respectively, based on the view that the group velocity and phase velocity have the same direction in isotropic elastic media. We furthermore formulate our method using an unstructured mesh based modeling method named the grid method. Finally, we verify our method using two numerical examples.
Initial-boundary value problems for the wave equation
Directory of Open Access Journals (Sweden)
Tynysbek Sh. Kalmenov
2014-02-01
Full Text Available In this work we consider an initial-boundary value problem for the one-dimensional wave equation. We prove the uniqueness of the solution and show that the solution coincides with the wave potential.
Approximate equations at breaking for nearshore wave transformation coefficients
Digital Repository Service at National Institute of Oceanography (India)
Chandramohan, P.; Nayak, B.U.; SanilKumar, V.
Based on small amplitude wave theory approximate equations are evaluated for determining the coefficients of shoaling, refraction, bottom friction, bottom percolation and viscous dissipation at breaking. The results obtainEd. by these equations...
Still one possibility to determine the wave vector onboard one spacecraft
Korepanov, Valery; Dudkin, Fedir
The wave vector calculation in general case needs measurement of three component of magnetic field B vector and three component of electric field E vector. The measurement of the electric field E with enough good precision requires long booms what is a great problem to realize, especially onboard of microsatellites. We study the possibility to avoid E measurements without of loss of wave vector k calculations generality and precision. From Maxwell equation: × B = µJ, (1) where J is vector of current density, and assumptions that 1) electromagnetic wave in plasma can be decomposed into the spectrum of plane waves: B = B0 exp (-jkr) , J˙ = J˙0 exp (-jkr) , ˙ ˙ (2) where B0 , J˙0 are in the form: ˙ i=3 ˙ A0 = exp (-jωt) ˙ xi A0i , (3) i=1 ˙ j = (-1)0.5, k is wave vector, r is radius-vector, xi are the unit vectors, A0i = A0i exp (jϕA0i ), A0i =A0xi are Cartesian component of real vector A0 (A = B, J ), ϕA0i is a phase of A0i com-ponent, ω is angular frequency, t is time; 2) the space derivatives of magnetic field and current density amplitudes are very small, i. e. ∂A0i /∂xl → 0, where i, l = 1, 2, 3, we get: k2 B03 - k3 B02 = jµ0 J˙01 , ˙ ˙ k3 B01 - k1 B03 = jµ0 J˙02 , . ˙ ˙ (4) ˙ 02 - k2 B01 = jµ0 J˙03 . k1 B ˙ The equations (??) show that wave vector components can be calculated using data from 3-component magnetometer and 3-component current density meter. Whereas B measurements are easily enough executed, J measurement was a problem up to now. For the first time reliable simultaneous measurements of B and J were realized onboard of Ukrainian satellite "Sich-1M" (2004). The obtained experimental results were in excellent agreement with calculated ones [1]. The three component J meter is rather difficult to implement due to some methodic problems not discussed here, but a creation of two-component one is not a problem. We show that the system of three equations (??) can be reduced to any two of them by use of other
Dispersion of P wave duration and P wave vector in patients with atrial septal aneurysm.
Janion, Marianna; Kurzawski, Jacek; Sielski, Janusz; Ciuraszkiewicz, Katarzyna; Sadowski, Marcin; Radomska, Edyta
2007-07-01
Atrial septal aneurysm (ASA) may be involved in the genesis of atrial arrhythmias as a consequence of disturbances in the propagation of depolarization, which may be easily assessed by P wave dispersion measurement. The aim of this study is to assess the dispersion of P wave duration and P wave vector in patients with ASA and to determine the effect of associated interatrial shunt on the magnitude of P wave dispersion. The study population consisted of 23 healthy volunteers and 88 patients with ASA base more than 15 mm and protrusion more than 7.5 mm. The size of aneurysms and atria was determined by echocardiography and P wave dispersion was measured on the surface ECG. In ASA patients, dispersion of P wave duration was significantly increased when compared with healthy controls (7.8 +/- 12.1 vs. 3.7 +/- 3.5 ms; P wave vector was also significantly increased (8.5 +/- 10.1 degrees vs. 4.6 +/- 3.6 degrees ; P wave duration and P wave vector. Variation in P wave duration was significantly correlated with the dispersion of P wave vector and age of these patients. Dispersion of P wave vector was significantly decreased in ASA patients with interatrial shunt. P wave dispersion in ASA patients may predispose to the development of atrial arrhythmias.
On the strongly damped wave equation and the heat equation with mixed boundary conditions
Directory of Open Access Journals (Sweden)
Aloisio F. Neves
2000-01-01
Full Text Available We study two one-dimensional equations: the strongly damped wave equation and the heat equation, both with mixed boundary conditions. We prove the existence of global strong solutions and the existence of compact global attractors for these equations in two different spaces.
Wave equations on anti self dual (ASD) manifolds
Bashingwa, Jean-Juste; Kara, A. H.
2017-11-01
In this paper, we study and perform analyses of the wave equation on some manifolds with non diagonal metric g_{ij} which are of neutral signatures. These include the invariance properties, variational symmetries and conservation laws. In the recent past, wave equations on the standard (space time) Lorentzian manifolds have been performed but not on the manifolds from metrics of neutral signatures.
Local energy decay for linear wave equations with variable coefficients
Ikehata, Ryo
2005-06-01
A uniform local energy decay result is derived to the linear wave equation with spatial variable coefficients. We deal with this equation in an exterior domain with a star-shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data, and its proof is quite simple. This generalizes a previous famous result due to Morawetz [The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. Pure Appl. Math. 14 (1961) 561-568]. In order to prove local energy decay, we mainly apply two types of ideas due to Ikehata-Matsuyama [L2-behaviour of solutions to the linear heat and wave equations in exterior domains, Sci. Math. Japon. 55 (2002) 33-42] and Todorova-Yordanov [Critical exponent for a nonlinear wave equation with damping, J. Differential Equations 174 (2001) 464-489].
Energy flow characteristics of vector X-Waves
Salem, Mohamed
2011-01-01
The vector form of X-Waves is obtained as a superposition of transverse electric and transverse magnetic polarized field components. It is shown that the signs of all components of the Poynting vector can be locally changed using carefully chosen complex amplitudes of the transverse electric and transverse magnetic polarization components. Negative energy flux density in the longitudinal direction can be observed in a bounded region around the centroid; in this region the local behavior of the wave field is similar to that of wave field with negative energy flow. This peculiar energy flux phenomenon is of essential importance for electromagnetic and optical traps and tweezers, where the location and momenta of microand nanoparticles are manipulated by changing the Poynting vector, and in detection of invisibility cloaks. © 2011 Optical Society of America.
Goldberger, A L
1979-08-01
Hypertrophic cardiomyopathy is a common cause of prominent non-infarctional Q waves. A retrospective analysis of previously published cases confirmed a characteristic Q wave T wave vector discordance in hypertrophic cardiomyopathy. In 41 of 44 cases with predominant Q waves (as part of QS or Qr complexes where Q wave amplitude exceeded R wave height), the T wave was positive, and in all cases with QS type complexes the T wave was positive. This characteristic electrocardiographic sign probably represents a pattern of septal hypertrophy and strain (Q waves with positive T waves and ST segment elevation) which is the inverse of the classical pattern of left ventricular hypertrophy and strain (tall R waves with inverted T waves and ST segment depression).
Orbital stability of standing waves for some nonlinear Schroedinger equations
Energy Technology Data Exchange (ETDEWEB)
Cazenave, T.; Lions, P.L.
1982-08-01
We present a general method which enables as to prove the orbital stability of some standing waves in nonlinear Schroedinger equations. For example, we treat the cases of nonlinear Schroedinger equations arising in laser beams, of time-dependent Hartree equations.
On the Exact Solution of Wave Equations on Cantor Sets
Directory of Open Access Journals (Sweden)
Dumitru Baleanu
2015-09-01
Full Text Available The transfer of heat due to the emission of electromagnetic waves is called thermal radiations. In local fractional calculus, there are numerous contributions of scientists, like Mandelbrot, who described fractal geometry and its wide range of applications in many scientific fields. Christianto and Rahul gave the derivation of Proca equations on Cantor sets. Hao et al. investigated the Helmholtz and diffusion equations in Cantorian and Cantor-Type Cylindrical Coordinates. Carpinteri and Sapora studied diffusion problems in fractal media in Cantor sets. Zhang et al. studied local fractional wave equations under fixed entropy. In this paper, we are concerned with the exact solutions of wave equations by the help of local fractional Laplace variation iteration method (LFLVIM. We develop an iterative scheme for the exact solutions of local fractional wave equations (LFWEs. The efficiency of the scheme is examined by two illustrative examples.
Single integrodifferential wave equation for a Lévy walk
Fedotov, Sergei
2016-02-01
We derive the single integrodifferential wave equation for the probability density function of the position of a classical one-dimensional Lévy walk with continuous sample paths. This equation involves a classical wave operator together with memory integrals describing the spatiotemporal coupling of the Lévy walk. It is valid at all times, not only in the long time limit, and it does not involve any large-scale approximations. It generalizes the well-known telegraph or Cattaneo equation for the persistent random walk with the exponential switching time distribution. Several non-Markovian cases are considered when the particle's velocity alternates at the gamma and power-law distributed random times. In the strong anomalous case we obtain the asymptotic solution to the integrodifferential wave equation. We implement the nonlinear reaction term of Kolmogorov-Petrovsky-Piskounov type into our equation and develop the theory of wave propagation in reaction-transport systems involving Lévy diffusion.
Parallel femtosecond laser processing with vector-wave control
Directory of Open Access Journals (Sweden)
Hayasaki Yoshio
2013-11-01
Full Text Available Parallel femtosecond laser processing with a computer-generated hologram displayed on a spatial light modulator, has the advantages of high throughput and high energy-use efficiency. for further increase of the processing efficiency, we demonstrated parallel femtosecond laser processing with vector-wave control that is based on polarization control using a pair of spatial light modulators.
Vector wave diffraction pattern of slits masked by polarizing devices
Indian Academy of Sciences (India)
Polarization property is important to the optical imaging system. It has recently been understood that the polarization properties of light can be fruitfully used for improving the characteristics of imaging system that includes polarizing devices. The vector wave imagery lends an additional degree of freedom that can be utilized ...
Vector wave diffraction pattern of slits masked by polarizing devices
Indian Academy of Sciences (India)
Amplitude and phase step filters were used on the pupil of the optical system to achieve ... of polarization Fourier optics dealing with vector wave imagery and image processing. [8–10]. Recently, Moreno et al have ..... obtained in circular aperture using. Gaussian modulation of the transmission function of a circular aperture.
Convergence of vector spherical wave expansion method applied to near-field radiative transfer.
Sasihithlu, Karthik; Narayanaswamy, Arvind
2011-07-04
Near-field radiative transfer between two objects can be computed using Rytov's theory of fluctuational electrodynamics in which the strength of electromagnetic sources is related to temperature through the fluctuation-dissipation theorem, and the resultant energy transfer is described using the dyadic Green's function of the vector Helmholtz equation. When the two objects are spheres, the dyadic Green's function can be expanded in a series of vector spherical waves. Based on comparison with the convergence criterion for the case of radiative transfer between two parallel surfaces, we derive a relation for the number of vector spherical waves required for convergence in the case of radiative transfer between two spheres. We show that when electromagnetic surface waves are active at a frequency the number of vector spherical waves required for convergence is proportional to Rmax/d when d/Rmax → 0, where Rmax is the radius of the larger sphere, and d is the smallest gap between the two spheres. This criterion for convergence applies equally well to other near-field electromagnetic scattering problems.
New exact wave solutions for Hirota equation
Indian Academy of Sciences (India)
Nonlinear partial differential equations (NPDEs) of mathematical physics are major sub- jects in physical science. With the development of soliton theory, many useful methods for obtaining exact solutions of NPDEs have been presented. Some of them are: the (G /G)- expansion method [1–4], the simplest equation method ...
Electric field vector measurements in a surface ionization wave discharge
Goldberg, Benjamin M.; Böhm, Patrick S.; Czarnetzki, Uwe; Adamovich, Igor V.; Lempert, Walter R.
2015-10-01
This work presents the results of time-resolved electric field vector measurements in a short pulse duration (60 ns full width at half maximum), surface ionization wave discharge in hydrogen using a picosecond four-wave mixing technique. Electric field vector components are measured separately, using pump and Stokes beams linearly polarized in the horizontal and vertical planes, and a polarizer placed in front of the infrared detector. The time-resolved electric field vector is measured at three different locations across the discharge gap, and for three different heights above the alumina ceramic dielectric surface, ~100, 600, and 1100 μm (total of nine different locations). The results show that after breakdown, the discharge develops as an ionization wave propagating along the dielectric surface at an average speed of 1 mm ns-1. The surface ionization wave forms near the high voltage electrode, close to the dielectric surface (~100 μm). The wave front is characterized by significant overshoot of both vertical and horizontal electric field vector components. Behind the wave front, the vertical field component is rapidly reduced. As the wave propagates along the dielectric surface, it also extends further away from the dielectric surface, up to ~1 mm near the grounded electrode. The horizontal field component behind the wave front remains quite significant, to sustain the electron current toward the high voltage electrode. After the wave reaches the grounded electrode, the horizontal field component experiences a secondary rise in the quasi-dc discharge, where it sustains the current along the near-surface plasma sheet. The measurement results indicate presence of a cathode layer formed near the grounded electrode with significant cathode voltage fall, ≈3 kV, due to high current density in the discharge. The peak reduced electric field in the surface ionization wave is 85-95 Td, consistent with dc breakdown field estimated from the Paschen curve for
Anisotropic wave-equation traveltime and waveform inversion
Feng, Shihang
2016-09-06
The wave-equation traveltime and waveform inversion (WTW) methodology is developed to invert for anisotropic parameters in a vertical transverse isotropic (VTI) meidum. The simultaneous inversion of anisotropic parameters v0, ε and δ is initially performed using the wave-equation traveltime inversion (WT) method. The WT tomograms are then used as starting background models for VTI full waveform inversion. Preliminary numerical tests on synthetic data demonstrate the feasibility of this method for multi-parameter inversion.
Implicit Vector Integral Equations Associated with Discontinuous Operators
Directory of Open Access Journals (Sweden)
Paolo Cubiotti
2014-01-01
Full Text Available Let I∶=[0,1]. We consider the vector integral equation h(u(t=ft,∫Ig(t,z,u(z,dz for a.e. t∈I, where f:I×J→R, g:I×I→ [0,+∞[, and h:X→R are given functions and X,J are suitable subsets of Rn. We prove an existence result for solutions u∈Ls(I, Rn, where the continuity of f with respect to the second variable is not assumed. More precisely, f is assumed to be a.e. equal (with respect to second variable to a function f*:I×J→R which is almost everywhere continuous, where the involved null-measure sets should have a suitable geometry. It is easily seen that such a function f can be discontinuous at each point x∈J. Our result, based on a very recent selection theorem, extends a previous result, valid for scalar case n=1.
Unified formulation of radiation conditions for the wave equation
DEFF Research Database (Denmark)
Krenk, Steen
2002-01-01
A family of radiation conditions for the wave equation is derived by truncating a rational function approxiamtion of the corresponding plane wave representation, and it is demonstrated how these boundary conditions can be formulated in terms of fictitious surface densities, governed by second...
Travelling waves in a singularly perturbed sine-Gordon equation
Derks, Gianne; Doelman, Arjen; van Gils, Stephanus A.; Visser, T.P.P.
2003-01-01
We determine the linearised stability of travelling front solutions of a perturbed sine-Gordon equation. This equation models the long Josephson junction using the RCSJ model for currents across the junction and includes surface resistance for currents along the junction. The travelling waves
Multicomponent integrable wave equations. I. Darboux-dressing transformation
Degasperis, A.; Lombardo, S.
2007-01-01
The Darboux-dressing transformations are applied to the Lax pair associated with systems of coupled nonlinear wave equations in the case of boundary values which are appropriate to both bŕight' and dárk' soliton solutions. The general formalism is set up and the relevant equations are explicitly
Invariance analysis and conservation laws of the wave equation on ...
Indian Academy of Sciences (India)
pp. 555–570. Invariance analysis and conservation laws of the wave equation on Vaidya manifolds. R NARAIN and A H KARA. ∗. School of Mathematics and Centre for Differential Equations, Continuum Mechanics and. Applications, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050,. South Africa. ∗.
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.
Shawhan, S. D.
1982-01-01
A brief summary is presented of the techniques used to receive, transmit, and display frequency-time information. The mathematical basis for extracting wave vector information from the three electric and three magnetic wave fields is stated for the simple plane wave, single-source case. For the more realistic multiple-wave, multiple source case, basic correlation schemes and model-fitting techniques are described. Examples of results are given from various satellites for which two or more wave components could be treated. Finally, expectations for the upcoming OPEN mission are presented.
New exact travelling wave solutions of bidirectional wave equations
Indian Academy of Sciences (India)
where , , and d are real constants. In general, the exact travelling wave solutions will be helpful in the theoretical and numerical study of the nonlinear evolution systems. In this paper, we obtain exact travelling wave solutions of system (1) using the modiﬁed tanh–coth function method with computerized symbolic ...
New exact travelling wave solutions of some complex nonlinear equations
Bekir, Ahmet
2009-04-01
In this paper, we establish exact solutions for complex nonlinear equations. The tanh-coth and the sine-cosine methods are used to construct exact periodic and soliton solutions of these equations. Many new families of exact travelling wave solutions of the coupled Higgs and Maccari equations are successfully obtained. These solutions may be important of significance for the explanation of some practical physical problems.
New exact travelling wave solutions of bidirectional wave equations
Indian Academy of Sciences (India)
where a, b, c and d are real constants. Here x represents the distance along the channel, t is the elapsed time, the variable v(x, t) is the dimensionless deviation of the water surface from its undisturbed position and u(x, t) is the dimensionless horizontal velocity. This set of equations is used as a model equation for the ...
Vector rogue waves and dark-bright boomeronic solitons in autonomous and nonautonomous settings
Mareeswaran, R. Babu; Charalampidis, E. G.; Kanna, T.; Kevrekidis, P. G.; Frantzeskakis, D. J.
2014-10-01
In this work we consider the dynamics of vector rogue waves and dark-bright solitons in two-component nonlinear Schrödinger equations with various physically motivated time-dependent nonlinearity coefficients, as well as spatiotemporally dependent potentials. A similarity transformation is utilized to convert the system into the integrable Manakov system and subsequently the vector rogue and dark-bright boomeronlike soliton solutions of the latter are converted back into ones of the original nonautonomous model. Using direct numerical simulations we find that, in most cases, the rogue wave formation is rapidly followed by a modulational instability that leads to the emergence of an expanding soliton train. Scenarios different than this generic phenomenology are also reported.
Diffractive S and D-wave vector mesons in deep inelastic scattering
Ivanov, I. P.; Nikolaev, N.N.
1999-01-01
We derive helicity amplitudes for diffractive leptoproduction of the S and D wave states of vector mesons. We predict a dramatically different spin dependence for production of the S and D wave vector mesons. We find very small $R=\\sigma_{L}/\\sigma_{T}$ and abnormally large higher twist effects in production of longitudinally polarized D-wave vector mesons.
Scattering of surface waves modelled by the integral equation method
Lu, Laiyu; Maupin, Valerie; Zeng, Rongsheng; Ding, Zhifeng
2008-09-01
The integral equation method is used to model the propagation of surface waves in 3-D structures. The wavefield is represented by the Fredholm integral equation, and the scattered surface waves are calculated by solving the integral equation numerically. The integration of the Green's function elements is given analytically by treating the singularity of the Hankel function at R = 0, based on the proper expression of the Green's function and the addition theorem of the Hankel function. No far-field and Born approximation is made. We investigate the scattering of surface waves propagating in layered reference models imbedding a heterogeneity with different density, as well as Lamé constant contrasts, both in frequency and time domains, for incident plane waves and point sources.
Linear fractional diffusion-wave equation for scientists and engineers
Povstenko, Yuriy
2015-01-01
This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the “long-tail” power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fourier’s, Fick’s and Darcy’s laws are considered and different kinds of boundary conditions for this equation are discussed (Dirichlet, Neumann, Robin, perfect contact). The book provides solutions to the fractional diffusion-wave equation with one, two and three space variables in Cartesian, cylindrical and spherical coordinates. The respective sections of the book can be used for university courses on fractional calculus, heat and mass transfer, transport processes in porous media and ...
New exact wave solutions for Hirota equation
Indian Academy of Sciences (India)
... integrals in polynomial form with a high accuracy for two-dimensional plane autonomous systems. Exact soliton solution is constructed through the established first integrals. This method is a powerful tool for searching exact travelling solutions of nonlinear partial differential equations (NPDEs) in mathematical physics.
Exact elegant Laguerre-Gaussian vector wave packets.
Nasalski, W
2013-03-15
An exact closed-form representation is derived of a vector elegant Laguerre-Gaussian wave packet. Its space-time representation consists of three mutually orthogonal field components--of a common azimuthal index and different radial indices--uniquely distinguished by first three powers of the paraxial parameter. The transverse components are of tm-radial and te-azimuthal polarization and appear, under their normal incidence, to be eigenmodes of any horizontally planar, homogeneous and isotropic structure, with eigenvalues given by the reflection and transmission coefficients. In this context, the interrelations between the cross-polarization symmetries of wave packets in free space and at medium planar interfaces are discussed.
On the so called rogue waves in nonlinear Schrodinger equations
Directory of Open Access Journals (Sweden)
Y. Charles Li
2016-04-01
Full Text Available The mechanism of a rogue water wave is still unknown. One popular conjecture is that the Peregrine wave solution of the nonlinear Schrodinger equation (NLS provides a mechanism. A Peregrine wave solution can be obtained by taking the infinite spatial period limit to the homoclinic solutions. In this article, from the perspective of the phase space structure of these homoclinic orbits in the infinite dimensional phase space where the NLS defines a dynamical system, we examine the observability of these homoclinic orbits (and their approximations. Our conclusion is that these approximate homoclinic orbits are the most observable solutions, and they should correspond to the most common deep ocean waves rather than the rare rogue waves. We also discuss other possibilities for the mechanism of a rogue wave: rough dependence on initial data or finite time blow up.
Finite element and discontinuous Galerkin methods for transient wave equations
Cohen, Gary
2017-01-01
This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem ...
Nonlinear electrostatic wave equations for magnetized plasmas - II
DEFF Research Database (Denmark)
Dysthe, K. B.; Mjølhus, E.; Pécseli, H. L.
1985-01-01
For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent (electrosta......For pt.I see ibid., vol.26, p.443-7 (1984). The problem of extending the high frequency part of the Zakharov equations for nonlinear electrostatic waves to magnetized plasmas, is considered. Weak electromagnetic and thermal effects are retained on an equal footing. Direction dependent...... (electrostatic) cut-off implies that various cases must be considered separately, leading to equations with rather different properties. Various equations encountered previously in the literature are recovered as limiting cases....
Ocean swell within the kinetic equation for water waves
Directory of Open Access Journals (Sweden)
S. I. Badulin
2017-06-01
Full Text Available Results of extensive simulations of swell evolution within the duration-limited setup for the kinetic Hasselmann equation for long durations of up to 2 × 106 s are presented. Basic solutions of the theory of weak turbulence, the so-called Kolmogorov–Zakharov solutions, are shown to be relevant to the results of the simulations. Features of self-similarity of wave spectra are detailed and their impact on methods of ocean swell monitoring is discussed. Essential drop in wave energy (wave height due to wave–wave interactions is found at the initial stages of swell evolution (on the order of 1000 km for typical parameters of the ocean swell. At longer times, wave–wave interactions are responsible for a universal angular distribution of wave spectra in a wide range of initial conditions. Weak power-law attenuation of swell within the Hasselmann equation is not consistent with results of ocean swell tracking from satellite altimetry and SAR (synthetic aperture radar data. At the same time, the relatively fast weakening of wave–wave interactions makes the swell evolution sensitive to other effects. In particular, as shown, coupling with locally generated wind waves can force the swell to grow in relatively light winds.
An Unconditionally Stable Method for Solving the Acoustic Wave Equation
Directory of Open Access Journals (Sweden)
Zhi-Kai Fu
2015-01-01
Full Text Available An unconditionally stable method for solving the time-domain acoustic wave equation using Associated Hermit orthogonal functions is proposed. The second-order time derivatives in acoustic wave equation are expanded by these orthogonal basis functions. By applying Galerkin temporal testing procedure, the time variable can be eliminated from the calculations. The restriction of Courant-Friedrichs-Levy (CFL condition in selecting time step for analyzing thin layer can be avoided. Numerical results show the accuracy and the efficiency of the proposed method.
Conditionally invariant solutions of the rotating shallow water wave equations
Energy Technology Data Exchange (ETDEWEB)
Huard, Benoit, E-mail: huard@dms.umontreal.c [Departement de mathematiques et de statistique, CP 6128, Succc. Centre-ville, Montreal, (QC) H3C 3J7 (Canada)
2010-06-11
This paper is devoted to the extension of the recently proposed conditional symmetry method to first-order nonhomogeneous quasilinear systems which are equivalent to homogeneous systems through a locally invertible point transformation. We perform a systematic analysis of the rank-1 and rank-2 solutions admitted by the shallow water wave equations in (2 + 1) dimensions and construct the corresponding solutions of the rotating shallow water wave equations. These solutions involve in general arbitrary functions depending on Riemann invariants, which allow us to construct new interesting classes of solutions.
Asymptotics of solutions to semilinear stochastic wave equations
Chow, Pao-Liu
2006-01-01
Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are established. Under appropriate conditions, the existence theorem for a unique global solution is given. Next the questions of bounded solutions and the exponential stability of an equilibrium solution, in mean-square and the almost sure sense, are studied. Then...
Resolution limits for wave equation imaging
Huang, Yunsong
2014-08-01
Formulas are derived for the resolution limits of migration-data kernels associated with diving waves, primary reflections, diffractions, and multiple reflections. They are applicable to images formed by reverse time migration (RTM), least squares migration (LSM), and full waveform inversion (FWI), and suggest a multiscale approach to iterative FWI based on multiscale physics. That is, at the early stages of the inversion, events that only generate low-wavenumber resolution should be emphasized relative to the high-wavenumber resolution events. As the iterations proceed, the higher-resolution events should be emphasized. The formulas also suggest that inverting multiples can provide some low- and intermediate-wavenumber components of the velocity model not available in the primaries. Finally, diffractions can provide twice or better the resolution than specular reflections for comparable depths of the reflector and diffractor. The width of the diffraction-transmission wavepath is approximately λ at the diffractor location for the diffraction-transmission wavepath. © 2014 Elsevier B.V.
An acoustic wave equation for pure P wave in 2D TTI media
Zhan, Ge
2011-01-01
In this paper, a pure P wave equation for an acoustic 2D TTI media is derived. Compared with conventional TTI coupled equations, the resulting equation is unconditionally stable due to the complete isolation of the SV wave mode. To avoid numerical dispersion and produce high quality images, the rapid expansion method REM is employed for numerical implementation. Synthetic results validate the proposed equation and show that it is a stable algorithm for modeling and reverse time migration RTM in a TTI media for any anisotropic parameter values. © 2011 Society of Exploration Geophysicists.
Study of nonlinear waves described by the cubic Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Walstead, A.E.
1980-03-12
The cubic Schroedinger equation (CSE) is ubiquitous as a model equation for the long-time evolution of finite-amplitude near-monochromatic dispersive waves. It incorporates the effects of the radiation field pressure on the constitutive properties of the supporting medium in a self-consistent manner. The properties of the uniformly transiating periodic wave solutions of the one-dimensional CSE are studied here. These (so-called cnoidal) waves are characterized by the values of four parameters. Whitham's averaged variational principle is used to derive a system of quasilinear evolution equations (the modulational equations) for the values of these parameters when they are slowly varying in space and time. Explicit expressions for the characteristic velocities of the modulational equations are obtained for the full set of cnoidal waves. Riemann invariants are obtained for several limits for the stable case, and growth rates are obtained for several limits, including the solitary wave chain, for the unstable case. The results for several nontrivial limiting cases agree with those obtained by independent methods by others. The dynamics of the CSE generalized to two spatial dimensions are studied for the unstable case. A large class of similarity solutions with cylindrical symmetry are obtained systematically using infinitesimal transformation group techniques. The methods are adapted to obtain the symmetries of the action functional of the CSE and to deduce nine integral invariants. A numerical study of the self-similar solutions reveals that they are modulationally unstable and that singularities dominate the dynamics of the CSE in two dimensions. The CSE is derived using perturbation theory for a specific problem in plasma physics: the evolution of the envelope of a near-monochromatic electromagnetic wave in a cold magnetized plasma. 13 figures, 2 tables.
Plane waves and spherical means applied to partial differential equations
John, Fritz
2004-01-01
Elementary and self-contained, this heterogeneous collection of results on partial differential equations employs certain elementary identities for plane and spherical integrals of an arbitrary function, showing how a variety of results on fairly general differential equations follow from those identities. The first chapter deals with the decomposition of arbitrary functions into functions of the type of plane waves. Succeeding chapters introduce the first application of the Radon transformation and examine the solution of the initial value problem for homogeneous hyperbolic equations with con
The wave equation: From eikonal to anti-eikonal approximation
Directory of Open Access Journals (Sweden)
Luis Vázquez
2016-06-01
Full Text Available When the refractive index changes very slowly compared to the wave-length we may use the eikonal approximation to the wave equation. In the opposite case, when the refractive index highly variates over the distance of one wave-length, we have what can be termed as the anti-eikonal limit. This situation is addressed in this work. The anti-eikonal limit seems to be a relevant tool in the modelling and design of new optical media. Besides, it describes a basic universal behaviour, independent of the actual values of the refractive index and, thus, of the media, for the components of a wave with wave-length much greater than the characteristic scale of the refractive index.
On Approximate Solutions of Functional Equations in Vector Lattices
Directory of Open Access Journals (Sweden)
Bogdan Batko
2014-01-01
Full Text Available We provide a method of approximation of approximate solutions of functional equations in the class of functions acting into a Riesz space (algebra. The main aim of the paper is to provide a general theorem that can act as a tool applicable to a possibly wide class of functional equations. The idea is based on the use of the Spectral Representation Theory for Riesz spaces. The main result will be applied to prove the stability of an alternative Cauchy functional equation F(x+y+F(x+F(y≠0⇒F(x+y=F(x+F(y in Riesz spaces, the Cauchy equation with squares F(x+y2=(F(x+F(y2 in f-algebras, and the quadratic functional equation F(x+y+F(x-y=2F(x+2F(y in Riesz spaces.
The general time fractional wave equation for a vibrating string
Energy Technology Data Exchange (ETDEWEB)
Sandev, Trifce [Radiation Safety Directorate, Blv. Partizanski odredi 143, PO Box 22, 1020 Skopje (Macedonia, The Former Yugoslav Republic of); Tomovski, Zivorad, E-mail: trifce.sandev@avis.gov.m, E-mail: tomovski@iunona.pmf.ukim.edu.m [Faculty of Natural Sciences and Mathematics, Institute of Mathematics, 1000 Skopje (Macedonia, The Former Yugoslav Republic of)
2010-02-05
The solution of a general time fractional wave equation for a vibrating string is obtained in terms of the Mittag-Leffler-type functions and complete set of eigenfunctions of the Sturm-Liouville problem. The time fractional derivative used is taken in the Caputo sense, and the method of separation of variables and the Laplace transform method are used to solve the equation. Some results for special cases of the initial and boundary conditions are obtained and it is shown that the corresponding solutions of the integer order equations are special cases of those of time fractional equations. The proposed general equation may be used for modeling different processes in complex or viscoelastic media, disordered materials, etc.
Wave-vector and polarization dependence of conical refraction.
Turpin, A; Loiko, Yu V; Kalkandjiev, T K; Tomizawa, H; Mompart, J
2013-02-25
We experimentally address the wave-vector and polarization dependence of the internal conical refraction phenomenon by demonstrating that an input light beam of elliptical transverse profile refracts into two beams after passing along one of the optic axes of a biaxial crystal, i.e. it exhibits double refraction instead of refracting conically. Such double refraction is investigated by the independent rotation of a linear polarizer and a cylindrical lens. Expressions to describe the position and the intensity pattern of the refracted beams are presented and applied to predict the intensity pattern for an axicon beam propagating along the optic axis of a biaxial crystal.
Comparison of fractional wave equations for power law attenuation in ultrasound and elastography.
Holm, Sverre; Näsholm, Sven Peter
2014-04-01
A set of wave equations with fractional loss operators in time and space are analyzed. The fractional Szabo equation, the power law wave equation and the causal fractional Laplacian wave equation are all found to be low-frequency approximations of the fractional Kelvin-Voigt wave equation and the more general fractional Zener wave equation. The latter two equations are based on fractional constitutive equations, whereas the former wave equations have been derived from the desire to model power law attenuation in applications like medical ultrasound. This has consequences for use in modeling and simulation, especially for applications that do not satisfy the low-frequency approximation, such as shear wave elastography. In such applications, the wave equations based on constitutive equations are the viable ones. Copyright © 2014 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.
Derivation of relativistic wave equation from the Poisson process
Indian Academy of Sciences (India)
A generalized linear photon wave equation in dispersive and homogeneous medium with dissipation is derived using the formulation of the Poisson process. This formulation provides a possible interpretation of the passage time of a photon moving in the medium, which never exceeds the speed of light in vacuum.
Blowing-up semilinear wave equation with exponential nonlinearity ...
Indian Academy of Sciences (India)
Indian Acad. Sci. (Math. Sci.) Vol. 123, No. 3, August 2013, pp. 365–372. c Indian Academy of Sciences. Blowing-up semilinear wave equation with exponential nonlinearity in two space dimensions. T SAANOUNI. Department of Mathematics, Faculty of Sciences of Tunis,. University of Tunis El Manar, El Manar 2092, Tunisia.
Invariant Solutions for a Class of Perturbed Nonlinear Wave Equations
Directory of Open Access Journals (Sweden)
Waheed A. Ahmed
2017-11-01
Full Text Available Approximate symmetries of a class of perturbed nonlinear wave equations are computed using two newly-developed methods. Invariant solutions associated with the approximate symmetries are constructed for both methods. Symmetries and solutions are compared through discussing the advantages and disadvantages of each method.
Exponential decay for solutions to semilinear damped wave equation
Gerbi, Stéphane
2011-10-01
This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Intro- ducing an appropriate Lyapunov function, we prove that when the damping is linear, we can find initial data, for which the solution decays exponentially. This result improves an early one in [4].
Finite element solution of the Boussinesq wave equation | Akpobi ...
African Journals Online (AJOL)
In this work, we investigate a Boussinesq-type flow model for nonlinear dispersive waves by developing a computational model based on the finite element discretisation technique. Hermite interpolation functions were used to interpolate approximation elements. The system is modeled using a time dependent equation.
Solitary wave solutions to nonlinear evolution equations in ...
Indian Academy of Sciences (India)
Solitary wave solutions to nonlinear evolution equations in mathematical physics. ANWAR JA'AFAR MOHAMAD JAWAD1, M MIRZAZADEH2,∗ and. ANJAN BISWAS3,4. 1Computer Engineering Technique Department, Al-Rafidain University College, Baghdad, Iraq. 2Department of Engineering Sciences, Faculty of ...
Blowing-up semilinear wave equation with exponential nonlinearity ...
Indian Academy of Sciences (India)
We investigate the initial value problem for some semi-linear wave equation in two space dimensions with exponential nonlinearity growth. Author Affiliations. T Saanouni1. Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El Manar, El Manar 2092, Tunisia. Dates. Manuscript received: 26 April ...
Traveling wave solutions of the BBM-like equations
Energy Technology Data Exchange (ETDEWEB)
Kuru, S [Department of Physics, Faculty of Science, Ankara University 06100 Ankara (Turkey)], E-mail: kuru@science.ankara.edu.tr
2009-09-18
In this work, we apply the factorization technique to the Benjamin-Bona-Mahony-like equations, B(m, n), in order to get traveling wave solutions. We will focus on some special cases for which m {ne} n, and we will obtain these solutions in terms of the special forms of Weierstrass functions.
Derivation of relativistic wave equation from the Poisson process
Indian Academy of Sciences (India)
Abstract. A Poisson process is one of the fundamental descriptions for relativistic particles: both fermions and bosons. A generalized linear photon wave equation in dispersive and homogeneous medium with dissipation is derived using the formulation of the Poisson process. This formulation provides a possible ...
Spin waves in terbium. III. Magnetic anisotropy at zero wave vector
DEFF Research Database (Denmark)
Houmann, Jens Christian Gylden; Jensen, J.; Touborg, P.
1975-01-01
The energy gap at zero wave vector in the spin-wave dispersion relation of ferromagnetic. Tb has been studied by inelastic neutron scattering. The energy was measured as a function of temperature and applied magnetic field, and the dynamic anisotropy parameters were deduced from the results....... The axial anisotropy is found to depend sensitively on the orientation of the magnetic moments in the basal plane. This behavior is shown to be a convincing indication of considerable two-ion contributions to the magnetic anisotropy at zero wave vector. With the exception of the sixfold basal...... the effects of zero-point deviations from the fully aligned ground state, and we tentatively propose polarization-dependent two-ion couplings as their origin....
Localised Nonlinear Waves in the Three-Component Coupled Hirota Equations
Xu, Tao; Chen, Yong
2017-10-01
We construct the Lax pair and Darboux transformation for the three-component coupled Hirota equations including higher-order effects such as third-order dispersion, self-steepening, and stimulated Raman scattering. A special vector solution of the Lax pair with 4×4 matrices for the three-component Hirota system is elaborately generated, based on this vector solution, various types of mixed higher-order localised waves are derived through the generalised Darboux transformation. Instead of considering various arrangements of the three potential functions q1, q2, and q3, here, the same combination is considered as the same type solution. The first- and second-order localised waves are mainly discussed in six mixed types: (1) the hybrid solutions degenerate to the rational ones and three components are all rogue waves; (2) two components are hybrid solutions between rogue wave (RW) and breather (RW+breather), and one component is interactional solution between RW and dark soliton (RW+dark soliton); (3) two components are RW+dark soliton, and one component is RW+bright soliton; (4) two components are RW+breather, and one component is RW+bright soliton; (5) two components are RW+dark soliton, and one component is RW+bright soliton; (6) three components are all RW+breather. Moreover, these nonlinear localised waves merge with each other by increasing the absolute values of two free parameters α, β. These results further uncover some striking dynamic structures in the multicomponent coupled system.
Comparison of artificial absorbing boundaries for acoustic wave equation modelling
Gao, Yingjie; Song, Hanjie; Zhang, Jinhai; Yao, Zhenxing
2017-12-01
Absorbing boundary conditions are necessary in numerical simulation for reducing the artificial reflections from model boundaries. In this paper, we overview the most important and typical absorbing boundary conditions developed throughout history. We first derive the wave equations of similar methods in unified forms; then, we compare their absorbing performance via theoretical analyses and numerical experiments. The Higdon boundary condition is shown to be the best one among the three main absorbing boundary conditions that are based on a one-way wave equation. The Clayton and Engquist boundary is a special case of the Higdon boundary but has difficulty in dealing with the corner points in implementaion. The Reynolds boundary does not have this problem but its absorbing performance is the poorest among these three methods. The sponge boundary has difficulties in determining the optimal parameters in advance and too many layers are required to achieve a good enough absorbing performance. The hybrid absorbing boundary condition (hybrid ABC) has a better absorbing performance than the Higdon boundary does; however, it is still less efficient for absorbing nearly grazing waves since it is based on the one-way wave equation. In contrast, the perfectly matched layer (PML) can perform much better using a few layers. For example, the 10-layer PML would perform well for absorbing most reflected waves except the nearly grazing incident waves. The 20-layer PML is suggested for most practical applications. For nearly grazing incident waves, convolutional PML shows superiority over the PML when the source is close to the boundary for large-scale models. The Higdon boundary and hybrid ABC are preferred when the computational cost is high and high-level absorbing performance is not required, such as migration and migration velocity analyses, since they are not as sensitive to the amplitude errors as the full waveform inversion.
Reinterpretation of Matter-Wave Interference Experiments Based on the Local-Ether Wave Equation
Su, Ching-Chuan
2002-01-01
Based on the local-ether wave equation for free particle, the dispersion of matter wave is examined. From the dispersion relation, the angular frequency and wavelength of matter wave are derived. These formulas look like the postulates of de Broglie in conjunction with the Lorentz mass-variation law. However, the fundamental difference is that for terrestrial particles their speeds are referred specifically to a geocentric inertial frame and hence incorporate the speed due to earth's rotation...
Hypergeometric series, modular linear differential equations, and vector-valued modular forms
Franc, Cameron; Mason, Geoffrey
2015-01-01
We survey the theory of vector-valued modular forms and their connections with modular differential equations and Fuchsian equations over the three-punctured sphere. We present a number of numerical examples showing how the theory in dimensions 2 and 3 leads naturally to close connections between modular forms and hypergeometric series.
Form Factors and Wave Functions of Vector Mesons in Holographic QCD
Energy Technology Data Exchange (ETDEWEB)
Hovhannes R. Grigoryan; Anatoly V. Radyushkin
2007-07-01
Within the framework of a holographic dual model of QCD, we develop a formalism for calculating form factors of vector mesons. We show that the holographic bound states can be described not only in terms of eigenfunctions of the equation of motion, but also in terms of conjugate wave functions that are close analogues of quantum-mechanical bound state wave functions. We derive a generalized VMD representation for form factors, and find a very specific VMD pattern, in which form factors are essentially given by contributions due to the first two bound states in the Q^2-channel. We calculate electric radius of the \\rho-meson, finding the value < r_\\rho^2>_C = 0.53 fm^2.
The wave equation for stiff strings and piano tuning
Gràcia, Xavier
2016-01-01
We study the wave equation for a string with stiffness. We solve the equation and provide a uniqueness theorem with suitable boundary conditions. For a pinned string we compute the spectrum, which is slightly inharmonic. Therefore, the widespread scale of 12 equal divisions of the just octave is not the best choice to tune instruments like the piano. Basing in the theory of dissonance, we provide a way to tune the piano in order to improve its consonance. A good solution is obtained by tuning a note and its fifth by minimizing their beats.
Stochastic regulator theory for a class of abstract wave equations
Balakrishnan, A. V.
1991-01-01
A class of steady-state stochastic regulator problems for abstract wave equations in a Hilbert space - of relevance to the problem of feedback control of large space structures using co-located controls/sensors - is studied. Both the control operator, as well as the observation operator, are finite-dimensional. As a result, the usual condition of exponential stabilizability invoked for existence of solutions to the steady-state Riccati equations is not valid. Fortunately, for the problems considered it turns out that strong stabilizability suffices. In particular, a closed form expression is obtained for the minimal (asymptotic) performance criterion as the control effort is allowed to grow without bound.
Energy Technology Data Exchange (ETDEWEB)
Barnes, S.E.; Mehran, F.
1986-10-01
The elementary theory of in situ measurements of the wave-vector-dependent dynamic susceptibility chi(q,..omega..) in superconductor-insulator-superconductor (SIS) and superconductor--normal-metal--superconductor (SNS) Josephson junctions is presented in some detail. The theory for more complicated SISN and SINS junctions is also described. In addition, the theory of point-contact and superconducting quantum interference device geometries, relevant to the recent experiments of Baberschke, Bures, and Barnes is developed. Involved is a detailed application of the Maxwell and London equations along with the distributed Josephson effect. In a measurement of chi(q,..omega..), the frequency ..omega.. is determined by the relation 2eV/sub 0/ = h-dash-bar..omega.. where V/sub 0/ is the voltage applied across the junction, and the wave vector q is determined by the relation 2edB/sub 0/ = h-dash-barq where d is the effective width of the junction and B/sub 0/ is the magnetic field applied perpendicular to the direction of the current. The relative merits of the different types of junctions are discussed and the expected signal strengths are estimated. The limitations for the maximum measurable frequency and wave vector are also given. It seems probable that the proposed technique can be used to measure spin-wave branches from zero wave vector up to about 10% of the way to the Brillouin zone edge.
Multiobjective optimal control of the linear wave equation
Directory of Open Access Journals (Sweden)
Hassan Zarei
2014-12-01
Full Text Available In this paper, we propose a method for the solution of a multiobjective optimal control problem (MOOCP in a linear distributed-parameter system governed by a wave equation. An explicit solution for the wave equation is derived and the control problem of this distributed-parameter system is reduced to an approximate multiobjective programming problem. The fuzzy goals are incorporated for objectives and the equilibrium problem in terms of maximization of the degree of attainment for the aggregated fuzzy goals is considered. The solution of the equilibrium optimization problem is a Pareto optimal solution with the best satisfaction performance which is achieved by using a metaheuristic algorithm such as the simulated annealing (SA together with the simplex method of linear programming (LP problems. An illustrative numerical example is presented to indicate the efficiency of the proposed method and the capability of the SA in finding optimal solution compared with two popular metaheurestics.
Control Operator for the Two-Dimensional Energized Wave Equation
Directory of Open Access Journals (Sweden)
Sunday Augustus REJU
2006-07-01
Full Text Available This paper studies the analytical model for the construction of the two-dimensional Energized wave equation. The control operator is given in term of space and time t independent variables. The integral quadratic objective cost functional is subject to the constraint of two-dimensional Energized diffusion, Heat and a source. The operator that shall be obtained extends the Conjugate Gradient method (ECGM as developed by Hestenes et al (1952, [1]. The new operator enables the computation of the penalty cost, optimal controls and state trajectories of the two-dimensional energized wave equation when apply to the Conjugate Gradient methods in (Waziri & Reju, LEJPT & LJS, Issues 9, 2006, [2-4] to appear in this series.
What determines the Fermi wave vector of composite fermions?
Kamburov, D; Liu, Yang; Mueed, M A; Shayegan, M; Pfeiffer, L N; West, K W; Baldwin, K W
2014-11-07
Composite fermions (CFs), exotic particles formed by pairing an even number of flux quanta to each electron, provide a fascinating description of phenomena exhibited by interacting two-dimensional electrons at high magnetic fields. At and near Landau level filling ν=1/2, CFs occupy a Fermi sea and exhibit commensurability effects when subjected to a periodic potential modulation. We observe a pronounced asymmetry in the magnetic field positions of the commensurability resistance minima of CFs with respect to the field at ν=1/2. This unexpected asymmetry is consistent with the CFs' Fermi wave vector being determined by the minority carriers in the lowest Landau level, and suggests a breaking of the particle-hole symmetry for CFs near ν=1/2.
A boundary value problem for the wave equation
Directory of Open Access Journals (Sweden)
Nezam Iraniparast
1999-01-01
Full Text Available Traditionally, boundary value problems have been studied for elliptic differential equations. The mathematical systems described in these cases turn out to be “well posed”. However, it is also important, both mathematically and physically, to investigate the question of boundary value problems for hyperbolic partial differential equations. In this regard, prescribing data along characteristics as formulated by Kalmenov [5] is of special interest. The most recent works in this area have resulted in a number of interesting discoveries [3, 4, 5, 7, 8]. Our aim here is to extend some of these results to a more general domain which includes the characteristics of the underlying wave equation as a part of its boundary.
Solving Potential Scattering Equations without Partial Wave Decomposition
Energy Technology Data Exchange (ETDEWEB)
Caia, George; Pascalutsa, Vladimir; Wright, Louis E
2004-03-01
Considering two-body integral equations we show how they can be dimensionally reduced by integrating exactly over the azimuthal angle of the intermediate momentum. Numerical solution of the resulting equation is feasible without employing a partial-wave expansion. We illustrate this procedure for the Bethe-Salpeter equation for pion-nucleon scattering and give explicit details for the one-nucleon-exchange term in the potential. Finally, we show how this method can be applied to pion photoproduction from the nucleon with {pi}N rescattering being treated so as to maintain unitarity to first order in the electromagnetic coupling. The procedure for removing the azimuthal angle dependence becomes increasingly complex as the spin of the particles involved increases.
Wave-equation Migration Velocity Analysis Using Plane-wave Common Image Gathers
Guo, Bowen
2017-06-01
Wave-equation migration velocity analysis (WEMVA) based on subsurface-offset, angle domain or time-lag common image gathers (CIGs) requires significant computational and memory resources because it computes higher dimensional migration images in the extended image domain. To mitigate this problem, a WEMVA method using plane-wave CIGs is presented. Plane-wave CIGs reduce the computational cost and memory storage because they are directly calculated from prestack plane-wave migration, and the number of plane waves is often much smaller than the number of shots. In the case of an inaccurate migration velocity, the moveout of plane-wave CIGs is automatically picked by a semblance analysis method, which is then linked to the migration velocity update by a connective function. Numerical tests on two synthetic datasets and a field dataset validate the efficiency and effectiveness of this method.
An improved wave-vector frequency-domain method for nonlinear wave modeling.
Jing, Yun; Tao, Molei; Cannata, Jonathan
2014-03-01
In this paper, a recently developed wave-vector frequency-domain method for nonlinear wave modeling is improved and verified by numerical simulations and underwater experiments. Higher order numeric schemes are proposed that significantly increase the modeling accuracy, thereby allowing for a larger step size and shorter computation time. The improved algorithms replace the left-point Riemann sum in the original algorithm by the trapezoidal or Simpson's integration. Plane waves and a phased array were first studied to numerically validate the model. It is shown that the left-point Riemann sum, trapezoidal, and Simpson's integration have first-, second-, and third-order global accuracy, respectively. A highly focused therapeutic transducer was then used for experimental verifications. Short high-intensity pulses were generated. 2-D scans were conducted at a prefocal plane, which were later used as the input to the numerical model to predict the acoustic field at other planes. Good agreement is observed between simulations and experiments.
Parsimonious wave-equation travel-time inversion for refraction waves
Fu, Lei
2017-02-14
We present a parsimonious wave-equation travel-time inversion technique for refraction waves. A dense virtual refraction dataset can be generated from just two reciprocal shot gathers for the sources at the endpoints of the survey line, with N geophones evenly deployed along the line. These two reciprocal shots contain approximately 2N refraction travel times, which can be spawned into O(N2) refraction travel times by an interferometric transformation. Then, these virtual refraction travel times are used with a source wavelet to create N virtual refraction shot gathers, which are the input data for wave-equation travel-time inversion. Numerical results show that the parsimonious wave-equation travel-time tomogram has about the same accuracy as the tomogram computed by standard wave-equation travel-time inversion. The most significant benefit is that a reciprocal survey is far less time consuming than the standard refraction survey where a source is excited at each geophone location.
Wave Vector Dependent Susceptibility at T>Tc in a Dipolar Ising Ferromagnet
DEFF Research Database (Denmark)
Als-Nielsen, Jens Aage; Holmes, L. M:; Guggenheim, H. J.
1974-01-01
The wave-vector-dependent susceptibility of LiTbF4 has been investigated by means of neutron scattering. The observations show a singularity of the susceptibility near wave vector Q=0 which is characteristic of the dipolar Coulomb interaction and good agreement with theory is obtained...
A Compact Numerical Implementation for Solving Stokes Equations Using Matrix-vector Operations
Zhang, Tao
2015-06-01
In this work, a numerical scheme is implemented to solve Stokes equations based on cell-centered finite difference over staggered grid. In this scheme, all the difference operations have been vectorized thereby eliminating loops. This is particularly important when using programming languages that require interpretations, e.g., MATLAB and Python. Using this scheme, the execution time becomes significantly smaller compared with non-vectorized operations and also become comparable with those languages that require no repeated interpretations like FORTRAN, C, etc. This technique has also been applied to Navier-Stokes equations under laminar flow conditions.
Wave vector dependent damping of THz collective modes in a liquid metal
Demmel, F.
2017-11-01
Well-defined damped collective modes have been observed in liquid metals over a wide range of wave vectors. Hydrodynamics predicts that viscosity and thermal conductivity are the cause for the damping of the collective modes. Here we present experimental data from neutron spectroscopy on the damping of collective modes of liquid rubidium over a wide range of wave vectors. We propose a phenomenological model derived from generalized hydrodynamics to describe the damping of the modes and the evolution with increasing wave vector based on the viscoelastic picture of liquid response. As necessary ingredients a wave vector dependent high frequency shear modulus and shear relaxation time appear. We obtain a remarkable good agreement on a quantitative basis between experiment and calculation over a wide range of wave vectors. The emergent picture is that the lifetime of the collective modes in the THz regime is mainly limited through the diffusion of momentum. The proposed methodology might be applicable to a wide range of liquids.
A new iterative solver for the time-harmonic wave equation
Riyanti, C.D.; Erlangga, Y.A.; Plessix, R.E.; Mulder, W.A.; Vuik, C.; Oosterlee, C.
2006-01-01
The time-harmonic wave equation, also known as the Helmholtz equation, is obtained if the constant-density acoustic wave equation is transformed from the time domain to the frequency domain. Its discretization results in a large, sparse, linear system of equations. In two dimensions, this system can
TRAVELING WAVE SOLUTIONS OF SOME FRACTIONAL DIFFERENTIAL EQUATIONS
Directory of Open Access Journals (Sweden)
SERIFE MUGE EGE
2016-07-01
Full Text Available The modified Kudryashov method is powerful, efficient and can be used as an alternative to establish new solutions of different type of fractional differential equations applied in mathematical physics. In this article, we’ve constructed new traveling wave solutions including symmetrical Fibonacci function solutions, hyperbolic function solutions and rational solutions of the space-time fractional Cahn Hillihard equation D_t^α u − γD_x^α u − 6u(D_x^α u^2 − (3u^2 − 1D_x^α (D_x^α u + D_x^α(D_x^α(D_x^α(D_x^α u = 0 and the space-time fractional symmetric regularized long wave (SRLW equation D_t^α(D_t^α u + D_x^α(D_x^α u + uD_t^α(D_x^α u + D_x^α u D_t^α u + D_t^α(D_t^α(D_x^α(D_x^α u = 0 via modified Kudryashov method. In addition, some of the solutions are described in the figures with the help of Mathematica.
The double-gradient model of flapping instability with oblique wave vector
Korovinskiy, Daniil; Kiehas, Stefan
2017-04-01
The double-gradient model of magnetotail flapping oscillations/instability is generalized for the case of oblique propagation in the equatorial plane. The transversal direction Y (in GSM reference system) of the wave vector is found to be preferable, showing the highest growth rates of kink and sausage double-gradient unstable modes. Growth rates decrease with the wave vector rotating toward the X direction. It is found that neither waves nor instability with a wave vector pointing toward the Earth/magnetotail can develop.
Diffusive Wave Approximation to the Shallow Water Equations: Computational Approach
Collier, Nathan
2011-05-14
We discuss the use of time adaptivity applied to the one dimensional diffusive wave approximation to the shallow water equations. A simple and computationally economical error estimator is discussed which enables time-step size adaptivity. This robust adaptive time discretization corrects the initial time step size to achieve a user specified bound on the discretization error and allows time step size variations of several orders of magnitude. In particular, in the one dimensional results presented in this work feature a change of four orders of magnitudes for the time step over the entire simulation.
Second-Order Time-Dependent Mild-Slope Equation for Wave Transformation
Directory of Open Access Journals (Sweden)
Ching-Piao Tsai
2014-01-01
Full Text Available This study is to propose a wave model with both wave dispersivity and nonlinearity for the wave field without water depth restriction. A narrow-banded sea state centred around a certain dominant wave frequency is considered for applications in coastal engineering. A system of fully nonlinear governing equations is first derived by depth integration of the incompressible Navier-Stokes equation in conservative form. A set of second-order nonlinear time-dependent mild-slope equations is then developed by a perturbation scheme. The present nonlinear equations can be simplified to the linear time-dependent mild-slope equation, nonlinear long wave equation, and traditional Boussinesq wave equation, respectively. A finite volume method with the fourth-order Adams-Moulton predictor-corrector numerical scheme is adopted to directly compute the wave transformation. The validity of the present model is demonstrated by the simulation of the Stokes wave, cnoidal wave, and solitary wave on uniform depth, nonlinear wave shoaling on a sloping beach, and wave propagation over an elliptic shoal. The nearshore wave transformation across the surf zone is simulated for 1D wave on a uniform slope and on a composite bar profile and 2D wave field around a jetty. These computed wave height distributions show very good agreement with the experimental results available.
Application of the full reduction technique for solution of equations with vector form non-linearity
Saliuk, D. A.
2013-12-01
We consider making use of the full reduction algorithm for solving the equations with a vector non-linearity. The solutions of such the equations describe the planetary scale non-linear vortex structures of the Earth atmosphere, ionosphere and magnetosphere. We present the modification of full reduction technique for Charney-Obukhov equation with periodic boundary conditions. This technique allows to reduce significantly calculation time and to apply much more detailed spatial grid for studying non-linear processes in the near-Earth space.
Exact solitary wave and quasi-periodic wave solutions of the KdV-Sawada-Kotera-Ramani equation
National Research Council Canada - National Science Library
Zhang, Lijun; Khalique, Chaudry Masood
2015-01-01
In this paper we derive new exact solitary wave solutions and quasi-periodic traveling wave solutions of the KdV-Sawada-Kotera-Ramani equation by using a method which we introduce here for the first time...
Generalized vector wave theory for ultrahigh resolution confocal optical microscopy.
Yang, Ken; Xie, Xiangsheng; Zhou, Jianying
2017-01-01
Polarization modulation of a tightly focused beam in a confocal imaging scheme is considered for incident and collected light fields. Rigorous vector wave theory of a confocal optical microscopy is developed, which provides clear physical pictures without the requirement for fragmentary calculations. Multiple spatial modulations on polarization, phase, or amplitude of the illuminating and the detected beams can be mathematically described by a uniform expression. Linear and nonlinear excitation schemes are derived with tailored excitation and detection fields within this generalized theory, whose results show that the ultimate resolution achieved with the linear excitation can reach one-fifth of the excitation wavelength (or λ/5), while the nonlinear excitation scheme gives rise to a resolution better than λ/12 for two-photon fluorescence excitation and λ/20 for three-photon fluorescence excitation. Hence the resolution of optical microscopy with a near-infrared excitation can routinely reach sub-60 nm. In addition, simulations for confocal laser scanning microscopy are carried out with the linear excitation scheme and the fluorescent one, respectively.
Wave equation based microseismic source location and velocity inversion
Zheng, Yikang; Wang, Yibo; Chang, Xu
2016-12-01
The microseismic event locations and velocity information can be used to infer the stress field and guide hydraulic fracturing process, as well as to image the subsurface structures. How to get accurate microseismic event locations and velocity model is the principal problem in reservoir monitoring. For most location methods, the velocity model has significant relation with the accuracy of the location results. The velocity obtained from log data is usually too rough to be used for location directly. It is necessary to discuss how to combine the location and velocity inversion. Among the main techniques for locating microseismic events, time reversal imaging (TRI) based on wave equation avoids traveltime picking and offers high-resolution locations. Frequency dependent wave equation traveltime inversion (FWT) is an inversion method that can invert velocity model with source uncertainty at certain frequency band. Thus we combine TRI with FWT to produce improved event locations and velocity model. In the proposed approach, the location and model information are interactively used and updated. Through the proposed workflow, the inverted model is better resolved and the event locations are more accurate. We test this method on synthetic borehole data and filed data of a hydraulic fracturing experiment. The results verify the effectiveness of the method and prove it has potential for real-time microseismic monitoring.
Zecca, Antonio
2017-03-01
The arbitrary spin field equations that are not separable, contrarily to what happens in the Robertson-Walker and Schwarzschild metrics, are studied in a general comoving spherically symmetric metric. They result to be separable by variable separation in a class of metrics governing the Lemâitre Tolman Bondi cosmological models whose physical radius has a special factorized parametric representation. The result is proved by induction by explicitly considering the spin 1, 3/2, 2 case and then the higher spin values. The procedure is based on the Newman-Penrose formalism, which takes into account the strong analogy with the Robertson-Walker metric case. The existence of a nontrivial Weyl spinor requires a symmetrization of one of the spinor wave equations for spin values greater than 1.
Wang, Xueen; Fan, Zhaozhong; Tang, Tiantong
2006-04-01
A method is proposed, on the basis of the vector electromagnetic theory, for the numerical calculation of the diffraction of a converging electromagnetic wave by a circular aperture by using Borgnis potentials as auxiliary functions. The diffraction problem of vector electromagnetic fields is simplified greatly by solving the scalar Borgnis potentials. The diffractive field is calculated on the basis of the boundary integral equation, taking into consideration the contribution of the field variables on the diffraction screen surface, which is ignored in the Kirchhoff assumption. An example is given to show the effectiveness and suitability of this method and the distinctiveness of the diffractive fields caused by the vector characteristics of the electromagnetic fields.
Symmetry reductions and exact solutions of Shallow water wave equations
Clarkson, P A
1994-01-01
In this paper we study symmetry reductions and exact solutions of the shallow water wave (SWW) equation u_{xxxt} + \\alpha u_x u_{xt} + \\beta u_t u_{xx} - u_{xt} - u_{xx} = 0,\\eqno(1) where \\alpha and \\beta are arbitrary, nonzero, constants, which is derivable using the so-called Boussinesq approximation. Two special cases of this equation, or the equivalent nonlocal equation obtained by setting u_x=U, have been discussed in the literature. The case \\alpha=2\\beta was discussed by Ablowitz, Kaup, Newell and Segur [{\\it Stud.\\ Appl.\\ Math.}, {\\bf53} (1974) 249], who showed that this case was solvable by inverse scattering through a second order linear problem. This case and the case \\alpha=\\beta were studied by Hirota and Satsuma [{\\it J.\\ Phys.\\ Soc.\\ Japan}, {\\bf40} (1976) 611] using Hirota's bi-linear technique. Further the case \\alpha=\\beta is solvable by inverse scattering through a third order linear problem. In this paper a catalogue of symmetry reductions is obtained using the classical Lie method and th...
Well-posedness of semilinear stochastic wave equations with Hölder continuous coefficients
Masiero, Federica; Priola, Enrico
2017-08-01
We prove that semilinear stochastic abstract wave equations, including wave and plate equations, are well-posed in the strong sense with an α-Hölder continuous drift coefficient, if α ∈ (2 / 3 , 1). The uniqueness may fail for the corresponding deterministic PDE and well-posedness is restored by adding an external random forcing of white noise type. This shows a kind of regularization by noise for the semilinear wave equation. To prove the result we introduce an approach based on backward stochastic differential equations. We also establish regularizing properties of the transition semigroup associated to the stochastic wave equation by using control theoretic results.
Wave-equation dispersion inversion of surface waves recorded on irregular topography
Li, Jing
2017-08-17
Significant topographic variations will strongly influence the amplitudes and phases of propagating surface waves. Such effects should be taken into account, otherwise the S-velocity model inverted from the Rayleigh dispersion curves will contain significant inaccuracies. We now show that the recently developed wave-equation dispersion inversion (WD) method naturally takes into account the effects of topography to give accurate S-velocity tomograms. Application of topographic WD to demonstrates that WD can accurately invert dispersion curves from seismic data recorded over variable topography. We also apply this method to field data recorded on the crest of mountainous terrain and find with higher resolution than the standard WD tomogram.
Reflection and transmission of full-vector X-waves normally incident on dielectric half spaces
Salem, Mohamed
2011-08-01
The reflection and transmission of full-vector X-Waves incident normally on a planar interface between two lossless dielectric half-spaces are investigated. Full-vector X-Waves are obtained by superimposing transverse electric and magnetic polarization components, which are derived from the scalar X-Wave solution. The analysis of transmission and reflection is carried out via a straightforward but yet effective method: First, the X-Wave is decomposed into vector Bessel beams via the Bessel-Fourier transform. Then, the reflection and transmission coefficients of the beams are obtained in the spectral domain. Finally, the transmitted and reflected X-Waves are obtained via the inverse Bessel-Fourier transform carried out on the X-wave spectrum weighted with the corresponding coefficient. © 2011 IEEE.
On an Acoustic Wave Equation Arising in Non-Equilibrium Gasdynamics. Classroom Notes
Chandran, Pallath
2004-01-01
The sixth-order wave equation governing the propagation of one-dimensional acoustic waves in a viscous, heat conducting gaseous medium subject to relaxation effects has been considered. It has been reduced to a system of lower order equations corresponding to the finite speeds occurring in the equation, following a method due to Whitham. The lower…
Wave-equation migration in generalized coordinate systems
Shragge, Jeffrey
Wave-equation migration using one-way wavefield extrapolation operators is commonly used in industry to generate images of complex geologic structure from 3D seismic data. By design, most conventional wave-equation approaches restrict propagation to downward continuation, where wavefields are recursively extrapolated to depth on Cartesian meshes. In practice, this approach is limited in high-angle accuracy and is restricted to down-going waves, which precludes the use of some steep dip and all turning wave components important for imaging targets in such areas as steep salt body flanks. This thesis discusses a strategy for improving wavefield extrapolation based on extending wavefield propagation to generalized coordinate system geometries that are more conformal to the wavefield propagation direction and permit imaging with turning waves. Wavefield propagation in non-Cartesian coordinates requires properly specifying the Laplacian operator in the governing Helmholtz equation. By employing differential geometry theory, I demonstrate how generalized a Riemannian wavefield extrapolation (RWE) procedure can be developed for any 3D non-orthogonal coordinate system, including those constructed by smoothing ray-based coordinate meshes formed from a suite of traced rays. I present 2D and 3D generalized RWE propagation examples illustrating the improved steep-dip propagation afforded by the coordinate transformation. One consequence of using non-Cartesian coordinates, though, is that the corresponding 3D extrapolation operators have up to 10 non-stationary coefficients, which can lead to imposing (and limiting) computer memory constraints for realistic 3D applications. To circumvent this difficulty, I apply the generalized RWE theory to analytic coordinate systems, rather than numerically generated meshes. Analytic coordinates offer the advantage of having straightforward analytic dispersion relationships and easy-to-implement extrapolation operators that add little
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Mostafa M.A. Khater
Full Text Available In this article and for the first time, we introduce and describe Khater method which is a new technique for solving nonlinear partial differential equations (PDEs.. We apply this method for each of the following models Bogoyavlenskii equation, couple Boiti-Leon-Pempinelli system and Time-fractional Cahn-Allen equation. Khater method is very powerful, Effective, felicitous and fabulous method to get exact and solitary wave solution of (PDEs.. Not only just like that but it considers too one of the general methods for solving that kind of equations since it involves some methods as we will see in our discuss of the results. We make a comparison between the results of this new method and another method. Keywords: Bogoyavlenskii equations system, Couple Boiti-Leon-Pempinelli equations system, Time-fractional Cahn-Allen equation, Khater method, Traveling wave solutions, Solitary wave solutions
Parker, A.
1995-07-01
In this second of two articles (designated I and II), the bilinear transformation method is used to obtain stationary periodic solutions of the partially integrable regularized long-wave (RLW) equation. These solutions are expressed in terms of Riemann theta functions, and this approach leads to a new and compact expression for the important dispersion relation. The periodic solution (or cnoidal wave) can be represented as an infinite sum of sech2 ``solitary waves'': this remarkable property may be interpreted in the context of a nonlinear superposition principle. The RLW cnoidal wave approximates to a sinusoidal wave and a solitary wave in the limits of small and large amplitudes, respectively. Analytic approximations and error estimates are given which shed light on the character of the cnoidal wave in the different parameter regimes. Similar results are presented in brief for the related RLW Boussinesq (RLWB) equation.
Analysis and classification of ECG-waves and rhythms using circular statistics and vector strength
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Janßen Jan-Dirk
2017-09-01
Full Text Available The most common way to analyse heart rhythm is to calculate the RR-interval and the heart rate variability. For further evaluation, descriptive statistics are often used. Here we introduce a new and more natural heart rhythm analysis tool that is based on circular statistics and vector strength. Vector strength is a tool to measure the periodicity or lack of periodicity of a signal. We divide the signal into non-overlapping window segments and project the detected R-waves around the unit circle using the complex exponential function and the median RR-interval. In addition, we calculate the vector strength and apply circular statistics as wells as an angular histogram on the R-wave vectors. This approach enables an intuitive visualization and analysis of rhythmicity. Our results show that ECG-waves and rhythms can be easily visualized, analysed and classified by circular statistics and vector strength.
Thermal diffuse scattering as a probe of large-wave-vector phonons in silicon nanostructures.
Gopalakrishnan, Gokul; Holt, Martin V; McElhinny, Kyle M; Spalenka, Josef W; Czaplewski, David A; Schülli, Tobias U; Evans, Paul G
2013-05-17
Large-wave-vector phonons have an important role in determining the thermal and electronic properties of nanoscale materials. The small volumes of such structures, however, have posed significant challenges to experimental studies of the phonon dispersion. We show that synchrotron x-ray thermal diffuse scattering can be adapted to probe phonons with wave vectors spanning the entire Brillouin zone of nanoscale silicon membranes. The thermal diffuse scattering signal from flat Si nanomembranes with thicknesses from 315 to 6 nm, and a sample volume as small as 5 μm(3), has the expected linear dependence on the membrane thickness and also exhibits excess intensity at large wave vectors, consistent with the scattering signature expected from low-lying large-wave-vector modes of the membranes.
Numerical treatment of interfaces for second-order wave equations
Cécere, Mariana; Reula, Oscar
2011-01-01
In this article we develop a numerical scheme to deal with interfaces between touching numerical grids when solving the second-order wave equation. In the spirit of the Simultaneous Approximation Term (SAT) schemes introduced in \\cite{Carpenter1999341}, information is passed among grids using the values of the fields only at the contact points between them (actually, in our case, just the values of the field corresponding to the time derivative of the field). The scheme seems to be as accurate as the space and time discretizations used for the corresponding derivatives. The semi-discrete approximation preserves the norm and uses standard finite-difference operators satisfying summation by parts. For the time integrator we use a semi-implicit IMEX Runge-Kutta method. This is crucial for, otherwise, the methods will be impractical given the severe restrictions its stiff parts would put on totally explicit integrators.
Time evolution of the wave equation using rapid expansion method
Pestana, Reynam C.
2010-07-01
Forward modeling of seismic data and reverse time migration are based on the time evolution of wavefields. For the case of spatially varying velocity, we have worked on two approaches to evaluate the time evolution of seismic wavefields. An exact solution for the constant-velocity acoustic wave equation can be used to simulate the pressure response at any time. For a spatially varying velocity, a one-step method can be developed where no intermediate time responses are required. Using this approach, we have solved for the pressure response at intermediate times and have developed a recursive solution. The solution has a very high degree of accuracy and can be reduced to various finite-difference time-derivative methods, depending on the approximations used. Although the two approaches are closely related, each has advantages, depending on the problem being solved. © 2010 Society of Exploration Geophysicists.
Characteristics of phase-averaged equations for modulated wave groups
Klopman, G.; Petit, H.A.H.; Battjes, J.A.
2000-01-01
The project concerns the influence of long waves on coastal morphology. The modelling of the combined motion of the long waves and short waves in the horizontal plane is done by phase-averaging over the short wave motion and using intra-wave modelling for the long waves, see e.g. Roelvink (1993).
2013 CIME Course Vector-valued Partial Differential Equations and Applications
Marcellini, Paolo
2017-01-01
Collating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini. It contains the following contributions: The pullback equation (Bernard Dacorogna), The stability of the isoperimetric inequality (Nicola Fusco), Mathematical problems in thin elastic sheets: scaling limits, packing, crumpling and singularities (Stefan Müller), and Aspects of PDEs related to fluid flows (Vladimir Sverák). These lectures are addressed to graduate students and researchers in the field.
Directory of Open Access Journals (Sweden)
Domoshnitsky Alexander
2010-01-01
Full Text Available The method to compare only one component of the solution vector of linear functional differential systems, which does not require heavy sign restrictions on their coefficients, is proposed in this paper. Necessary and sufficient conditions of the positivity of elements in a corresponding row of Green's matrix are obtained in the form of theorems about differential inequalities. The main idea of our approach is to construct a first order functional differential equation for the th component of the solution vector and then to use assertions about positivity of its Green's functions. This demonstrates the importance to study scalar equations written in a general operator form, where only properties of the operators and not their forms are assumed. It should be also noted that the sufficient conditions, obtained in this paper, cannot be improved in a corresponding sense and does not require any smallness of the interval , where the system is considered.
Limiting Behavior of Travelling Waves for the Modified Degasperis-Procesi Equation
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Jiuli Yin
2014-01-01
Full Text Available Using an improved qualitative method which combines characteristics of several methods, we classify all travelling wave solutions of the modified Degasperis-Procesi equation in specified regions of the parametric space. Besides some popular exotic solutions including peaked waves, and looped and cusped waves, this equation also admits some very particular waves, such as fractal-like waves, double stumpons, double kinked waves, and butterfly-like waves. The last three types of solutions have not been reported in the literature. Furthermore, we give the limiting behavior of all periodic solutions as the parameters trend to some special values.
Wave-vector dependence of magnetic-turbulence spectra in the solar wind.
Narita, Y; Glassmeier, K-H; Sahraoui, F; Goldstein, M L
2010-04-30
Using four-point measurements of the Cluster spacecraft, the energy distribution was determined for magnetic field fluctuations in the solar wind directly in the three-dimensional wave-vector domain in the range |k|wave vector anisotropy is estimated with respect to directions parallel and perpendicular to the mean magnetic field, and the result suggests the dominance of quasi-two-dimensional turbulence toward smaller spatial scales.
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H. Ullah
2015-01-01
Full Text Available The two-dimensional nonlinear wave equations are considered. Solution to the problem is approximated by using optimal homotopy asymptotic method (OHAM. The residual and convergence of the proposed method to nonlinear wave equation are presented through graphs. The resultant analytic series solution of the two-dimensional nonlinear wave equation shows the effectiveness of the proposed method. The comparison of results has been made with the existing results available in the literature.
Vector soliton of self-induced transparency of a generalized love wave
Adamashvili, G. T.
2017-09-01
A theory of acoustic self-induced transparency of a two-component vector soliton for a generalized Love wave is constructed. The three-layer system contains a resonance transition layer with paramagnetic impurity atoms or quantum dots. It is shown that, under these conditions, a vector soliton of the generalized Love wave can be formed. It oscillates at the sum and difference frequencies in the vicinity of the carrier wave frequency. Explicit analytical expressions for the parameters of a nonlinear surface acoustic wave are presented. The parameters depend on the elastic properties of the contacting media, the resonance transition layer, and the transverse structure of the wave. Numerical calculations are carried out for the three-layer Al2O3/ZnO/SiO2 system. The significant difference between the two-component vector soliton and singlecomponent soliton is shown.
Energy Technology Data Exchange (ETDEWEB)
Uesaka, S. [Kyoto University, Kyoto (Japan). Faculty of Engineering; Watanabe, T.; Sassa, K. [Kyoto University, Kyoto (Japan)
1997-05-27
Algorithm is constructed and a program developed for a full-wave inversion (FWI) method utilizing the elastic wave equation in seismic exploration. The FWI method is a method for obtaining a physical property distribution using the whole observed waveforms as the data. It is capable of high resolution which is several times smaller than the wavelength since it can handle such phenomena as wave reflection and dispersion. The method for determining the P-wave velocity structure by use of the acoustic wave equation does not provide information about the S-wave velocity since it does not consider S-waves or converted waves. In an analysis using the elastic wave equation, on the other hand, not only P-wave data but also S-wave data can be utilized. In this report, under such circumstances, an inverse analysis algorithm is constructed on the basis of the elastic wave equation, and a basic program is developed. On the basis of the methods of Mora and of Luo and Schuster, the correction factors for P-wave and S-wave velocities are formulated directly from the elastic wave equation. Computations are performed and the effects of the hypocenter frequency and vibration transmission direction are examined. 6 refs., 8 figs.
Wave-equation Q tomography and least-squares migration
Dutta, Gaurav
2016-03-01
This thesis designs new methods for Q tomography and Q-compensated prestack depth migration when the recorded seismic data suffer from strong attenuation. A motivation of this work is that the presence of gas clouds or mud channels in overburden structures leads to the distortion of amplitudes and phases in seismic waves propagating inside the earth. If the attenuation parameter Q is very strong, i.e., Q<30, ignoring the anelastic effects in imaging can lead to dimming of migration amplitudes and loss of resolution. This, in turn, adversely affects the ability to accurately predict reservoir properties below such layers. To mitigate this problem, I first develop an anelastic least-squares reverse time migration (Q-LSRTM) technique. I reformulate the conventional acoustic least-squares migration problem as a viscoacoustic linearized inversion problem. Using linearized viscoacoustic modeling and adjoint operators during the least-squares iterations, I show with numerical tests that Q-LSRTM can compensate for the amplitude loss and produce images with better balanced amplitudes than conventional migration. To estimate the background Q model that can be used for any Q-compensating migration algorithm, I then develop a wave-equation based optimization method that inverts for the subsurface Q distribution by minimizing a skeletonized misfit function ε. Here, ε is the sum of the squared differences between the observed and the predicted peak/centroid-frequency shifts of the early-arrivals. Through numerical tests on synthetic and field data, I show that noticeable improvements in the migration image quality can be obtained from Q models inverted using wave-equation Q tomography. A key feature of skeletonized inversion is that it is much less likely to get stuck in a local minimum than a standard waveform inversion method. Finally, I develop a preconditioning technique for least-squares migration using a directional Gabor-based preconditioning approach for isotropic
Nurijanyan, S.; van der Vegt, Jacobus J.W.; Bokhove, Onno
2013-01-01
A discontinuous Galerkin finite element method (DGFEM) has been developed and tested for the linear, three-dimensional, rotating incompressible Euler equations. These equations admit complicated wave solutions, which poses numerical challenges. These challenges concern: (i) discretisation of a
Expansion of arbitrary electromagnetic fields in terms of vector spherical wave functions.
Moreira, Wendel Lopes; Neves, Antonio Alvaro Ranha; Garbos, Martin K; Euser, Tijmen G; Cesar, Carlos Lenz
2016-02-08
Since 1908, when Mie reported analytical expressions for the fields scattered by a spherical particle upon incidence of plane-waves, generalizing his analysis for the case of an arbitrary incident wave has been an open question because of the cancellation of the prefactor radial spherical Bessel function. This cancellation was obtained before by our own group for a highly focused beam centered in the objective. In this work, however, we show for the first time how these terms can be canceled out for any arbitrary incident field that satisfies Maxwells equations, and obtain analytical expressions for the beam shape coefficients. We show several examples on how to use our method to obtain analytical beam shape coefficients for: Bessel beams, general hollow waveguide modes and specific geometries such as cylindrical and rectangular. Our method uses the vector potential, which shows the interesting characteristic of being gauge invariant. These results are highly relevant for speeding up numerical calculation of light scattering applications such as the radiation forces acting on spherical particles placed in an arbitrary electromagnetic field, as in an optical tweezers system.
Aly R. Seadawy; Dianchen Lu; Mostafa M.A. Khater
2017-01-01
In this paper, we utilize the exp(−φ(ξ))-expansion method to find exact and solitary wave solutions of the generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony nonlinear evolution equation. The generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony nonlinear evolution equation describes the model for the propagation of long waves that mingle with nonlinear and dissipative impact. This model is used in the analysis of the surface waves of long wavelength in hydro magnetic waves in cold plasma, liq...
Reflection and transmission of normally incident full-vector X waves on planar interfaces
Salem, Mohamed
2011-12-23
The reflection and transmission of full-vector X waves normally incident on planar half-spaces and slabs are studied. For this purpose, X waves are expanded in terms of weighted vector Bessel beams; this new decomposition and reconstruction method offers a more lucid and intuitive interpretation of the physical phenomena observed upon the reflection or transmission of X waves when compared to the conventional plane-wave decomposition technique. Using the Bessel beam expansion approach, we have characterized changes in the field shape and the intensity distribution of the transmitted and reflected full-vector X waves. We have also identified a novel longitudinal shift, which is observed when a full-vector X wave is transmitted through a dielectric slab under frustrated total reflection condition. The results of our studies presented here are valuable in understanding the behavior of full-vector X waves when they are utilized in practical applications in electromagnetics, optics, and photonics, such as trap and tweezer setups, optical lithography, and immaterial probing. © 2011 Optical Society of America.
Destrade, M.
2010-12-08
We study the propagation of two-dimensional finite-amplitude shear waves in a nonlinear pre-strained incompressible solid, and derive several asymptotic amplitude equations in a simple, consistent and rigorous manner. The scalar Zabolotskaya (Z) equation is shown to be the asymptotic limit of the equations of motion for all elastic generalized neo-Hookean solids (with strain energy depending only on the first principal invariant of Cauchy-Green strain). However, we show that the Z equation cannot be a scalar equation for the propagation of two-dimensional shear waves in general elastic materials (with strain energy depending on the first and second principal invariants of strain). Then, we introduce dispersive and dissipative terms to deduce the scalar Kadomtsev-Petviashvili (KP), Zabolotskaya-Khokhlov (ZK) and Khokhlov- Zabolotskaya-Kuznetsov (KZK) equations of incompressible solid mechanics. © 2010 The Royal Society.
Sub- and superluminal kink-like waves in the kinetic limit of Maxwell-Bloch equations
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Janowicz, Maciej [Instytut Fizyki Polskiej Akademii Nauk, Aleja Lotnikow 32/46, 02-668 Warszawa (Poland); Holthaus, Martin, E-mail: mjanow@ifpan.edu.pl [Institut fuer Physik, Carl von Ossietzky Universitaet, D-26111 Oldenburg (Germany)
2011-01-14
Running-wave solutions to three systems of partial differential equations describing wave propagation in atomic media in the kinetic limit have been obtained. Those systems include approximations to (i) standard two-level Maxwell-Bloch equations; (ii) equations describing processes with saturated absorption in three-level systems and (iii) equations describing processes with reversed saturation in four-level systems. It has been shown that in all three cases kink-like solitary waves can emerge if the dynamical equation for the intensity includes a linear contribution to the Lambert-Beer law. Those solitary waves can propagate with either sub- or superluminal velocity of the edge of the kink, and in a direction which can be either the same as or opposite to that of the carrier wave. In addition, simple qualitative information about the behaviour of waves near the wavefronts has been obtained.
A tensor approach to double wave vector diffusion-weighting experiments on restricted diffusion.
Finsterbusch, Jürgen; Koch, Martin A
2008-11-01
Previously, it has been shown theoretically that in case of restricted diffusion, e.g. within isolated pores or cells, a measure of the pore size, the mean radius of gyration, can be estimated from double wave vector diffusion-weighting experiments. However, these results are based on the assumption of an isotropic orientation distribution of the pores or cells which hampers the applicability to samples with anisotropic or unknown orientation distributions, such as biological tissue. Here, the theoretical considerations are re-investigated and generalized in order to describe the signal dependency for arbitrary orientation distributions. The second-order Taylor expansion of the signal delivers a symmetric rank-2 tensor with six independent elements if the two wave vectors are concatenated to a single six-element vector. With this tensor approach the signal behavior for arbitrary wave vectors and orientation distributions can be described as is demonstrated by numerical simulations. The rotationally invariant trace of the tensor represents a pore size measure and can be determined from three orthogonal directions with parallel and antiparallel orientation of the two wave vectors. Thus, the presented tensor approach may help to improve the applicability of double wave vector diffusion-weighting experiments to determine pore or cell sizes, in particular in biological tissue.
Third order wave equation in Duffin-Kemmer-Petiau theory: Massive case
Markov, Yu. A.; Markova, M. A.; Bondarenko, A. I.
2015-11-01
Within the framework of the Duffin-Kemmer-Petiau (DKP) formalism a more consistent approach to the derivation of the third order wave equation obtained earlier by M. Nowakowski [1] on the basis of heuristic considerations is suggested. For this purpose an additional algebraic object, the so-called q -commutator (q is a primitive cubic root of unity) and a new set of matrices ημ instead of the original matrices βμ of the DKP algebra are introduced. It is shown that in terms of these ημ matrices we have succeeded in reducing a procedure of the construction of cubic root of the third order wave operator to a few simple algebraic transformations and to a certain operation of the passage to the limit z →q , where z is some complex deformation parameter entering into the definition of the η -matrices. A corresponding generalization of the result obtained to the case of the interaction with an external electromagnetic field introduced through the minimal coupling scheme is carried out and a comparison with M. Nowakowski's result is performed. A detailed analysis of the general structure for a solution of the first order differential equation for the wave function ψ (x ;z ) is performed and it is shown that the solution is singular in the z →q limit. The application to the problem of construction within the DKP approach of the path integral representation in parasuperspace for the propagator of a massive vector particle in a background gauge field is discussed.
Some Further Results on Traveling Wave Solutions for the ZK-BBM( Equations
Directory of Open Access Journals (Sweden)
Shaoyong Li
2013-01-01
Full Text Available We investigate the traveling wave solutions for the ZK-BBM( equations by using bifurcation method of dynamical systems. Firstly, for ZK-BBM(2, 2 equation, we obtain peakon wave, periodic peakon wave, and smooth periodic wave solutions and point out that the peakon wave is the limit form of the periodic peakon wave. Secondly, for ZK-BBM(3, 2 equation, we obtain some elliptic function solutions which include periodic blow-up and periodic wave. Furthermore, from the limit forms of the elliptic function solutions, we obtain some trigonometric and hyperbolic function solutions which include periodic blow-up, blow-up, and smooth solitary wave. We also show that our work extends some previous results.
Li, Jing
2017-12-22
A robust imaging technology is reviewed that provide subsurface information in challenging environments: wave-equation dispersion inversion (WD) of surface waves for the shear velocity model. We demonstrate the benefits and liabilities of the method with synthetic seismograms and field data. The benefits of WD are that 1) there is no layered medium assumption, as there is in conventional inversion of dispersion curves, so that the 2D or 3D S-velocity model can be reliably obtained with seismic surveys over rugged topography, and 2) WD mostly avoids getting stuck in local minima. The synthetic and field data examples demonstrate that WD can accurately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic media and the inversion of dispersion curves associated with Love wave. The liability is that is almost as expensive as FWI and only recovers the Vs distribution to a depth no deeper than about 1/2~1/3 wavelength.
On the wave equations with memory in noncylindrical domains
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Mauro de Lima Santos
2007-10-01
Full Text Available In this paper we prove the exponential and polynomial decays rates in the case $n > 2$, as time approaches infinity of regular solutions of the wave equations with memory $$ u_{tt}-Delta u+int^{t}_{0}g(t-sDelta u(sds=0 quad mbox{in } widehat{Q} $$ where $widehat{Q}$ is a non cylindrical domains of $mathbb{R}^{n+1}$, $(nge1$. We show that the dissipation produced by memory effect is strong enough to produce exponential decay of solution provided the relaxation function $g$ also decays exponentially. When the relaxation function decay polynomially, we show that the solution decays polynomially with the same rate. For this we introduced a new multiplier that makes an important role in the obtaining of the exponential and polynomial decays of the energy of the system. Existence, uniqueness and regularity of solutions for any $n ge 1$ are investigated. The obtained result extends known results from cylindrical to non-cylindrical domains.
On the wave equation with semilinear porous acoustic boundary conditions
Graber, Philip Jameson
2012-05-01
The goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary/interior sources and a nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. The main difficulty in proving the local existence result is that the Neumann boundary conditions experience loss of regularity due to boundary sources. Using an approximation method involving truncated sources and adapting the ideas in Lasiecka and Tataru (1993) [28], we show that the existence of solutions can still be obtained. Second, we prove that under some restrictions on the source terms, then the local solution can be extended to be global in time. In addition, it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ODE and depends on the behavior of the damping terms. In several situations, the obtained ODE can be easily solved and the decay rates can be given explicitly. Third, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution ceases to exists and blows up in finite time. Moreover, in either the absence of the interior source or the boundary source, then we prove that the solution is unbounded and grows as an exponential function. © 2012 Elsevier Inc.
Diffusion phenomenon for linear dissipative wave equations in an exterior domain
Ikehata, Ryo
Under the general condition of the initial data, we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain. In order to derive the diffusion phenomenon for dissipative wave equations, the time integral method which was developed by Ikehata and Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.
Travelling wave solutions of the generalized Benjamin-Bona-Mahony equation
Energy Technology Data Exchange (ETDEWEB)
Estevez, P.G. [Departamento de Fisica Fundamental, Area de Fisica Teorica, Universidad de Salamanca, 37008 Salamanca (Spain); Kuru, S. [Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47071 Valladolid (Spain); Department of Physics, Faculty of Science, Ankara University, 06100 Ankara (Turkey); Negro, J. [Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47071 Valladolid (Spain)], E-mail: jnegro@fta.uva.es; Nieto, L.M. [Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47071 Valladolid (Spain)
2009-05-30
A class of particular travelling wave solutions of the generalized Benjamin-Bona-Mahony equation is studied systematically using the factorization technique. Then, the general travelling wave solutions of Benjamin-Bona-Mahony equation, and of its modified version, are also recovered.
Rogue wave solutions of the nonlinear Schrödinger equation with ...
Indian Academy of Sciences (India)
solutions of the variable coefficient Schrödinger equation are also obtained. Two free functions of time t and several arbitrary parameters are involved to generate a large number of wave structures. Keywords. Nonlinear Schrödinger equation; exp-function method; breather soliton; rogue wave. PACS Nos 02.30.Jr; 05.45.
Radiation Boundary Conditions for the Two-Dimensional Wave Equation from a Variational Principle
Broeze, J.; Broeze, Jan; van Daalen, Edwin F.G.; van Daalen, E.F.G.
1992-01-01
A variational principle is used to derive a new radiation boundary condition for the two-dimensional wave equation. This boundary condition is obtained from an expression for the local energy flux velocity on the boundary in normal direction. The wellposedness of the wave equation with this boundary
New soliton solutions of the system of equations for the ion sound and Langmuir waves
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Seyma Tuluce Demiray
2016-11-01
Full Text Available This study is based on new soliton solutions of the system of equations for the ion sound wave under the action of the ponderomotive force due to high-frequency field and for the Langmuir wave. The generalized Kudryashov method (GKM, which is one of the analytical methods, has been tackled for finding exact solutions of the system of equations for the ion sound wave and the Langmuir wave. By using this method, dark soliton solutions of this system of equations have been obtained. Also, by using Mathematica Release 9, some graphical simulations were designed to see the behavior of these solutions.
Babaniyi, Olalekan A; Barbone, Paul E
2015-01-01
We consider the problem of estimating the $2D$ vector displacement field in a heterogeneous elastic solid deforming under plane stress conditions. The problem is motivated by applications in quasistatic elastography. From precise and accurate measurements of one component of the $2D$ vector displacement field and very limited information of the second component, the method reconstructs the second component quite accurately. No a priori knowledge of the heterogeneous distribution of material properties is required. This method relies on using a special form of the momentum equations to filter ultrasound displacement measurements to produce more precise estimates. We verify the method with applications to simulated displacement data. We validate the method with applications to displacement data measured from a tissue mimicking phantom, and in-vivo data; significant improvements are noticed in the filtered displacements recovered from all the tests. In verification studies, error in lateral displacement estimate...
Approximate analytical time-domain Green's functions for the Caputo fractional wave equation.
Kelly, James F; McGough, Robert J
2016-08-01
The Caputo fractional wave equation [Geophys. J. R. Astron. Soc. 13, 529-539 (1967)] models power-law attenuation and dispersion for both viscoelastic and ultrasound wave propagation. The Caputo model can be derived from an underlying fractional constitutive equation and is causal. In this study, an approximate analytical time-domain Green's function is derived for the Caputo equation in three dimensions (3D) for power law exponents greater than one. The Green's function consists of a shifted and scaled maximally skewed stable distribution multiplied by a spherical spreading factor 1/(4πR). The approximate one dimensional (1D) and two dimensional (2D) Green's functions are also computed in terms of stable distributions. Finally, this Green's function is decomposed into a loss component and a diffraction component, revealing that the Caputo wave equation may be approximated by a coupled lossless wave equation and a fractional diffusion equation.
Polarization speckles and generalized Stokes vector wave: a review [invited
DEFF Research Database (Denmark)
Takeda, Mitsuo; Wang, Wei; Hanson, Steen Grüner
2010-01-01
We review some of the statistical properties of polarization-related speckle phenomena, with an introduction of a less known concept of polarization speckles and their spatial degree of polarization. As a useful means to characterize twopoint vector field correlations, we review the generalized...
Transition, coexistence, and interaction of vector localized waves arising from higher-order effects
Energy Technology Data Exchange (ETDEWEB)
Liu, Chong [School of Physics, Northwest University, Xi’an 710069 (China); Yang, Zhan-Ying, E-mail: zyyang@nwu.edu.cn [School of Physics, Northwest University, Xi’an 710069 (China); Zhao, Li-Chen, E-mail: zhaolichen3@163.com [School of Physics, Northwest University, Xi’an 710069 (China); Yang, Wen-Li [Institute of Modern Physics, Northwest University, Xi’an 710069 (China)
2015-11-15
We study vector localized waves on continuous wave background with higher-order effects in a two-mode optical fiber. The striking properties of transition, coexistence, and interaction of these localized waves arising from higher-order effects are revealed in combination with corresponding modulation instability (MI) characteristics. It shows that these vector localized wave properties have no analogues in the case without higher-order effects. Specifically, compared to the scalar case, an intriguing transition between bright–dark rogue waves and w-shaped–anti-w-shaped solitons, which occurs as a result of the attenuation of MI growth rate to vanishing in the zero-frequency perturbation region, is exhibited with the relative background frequency. In particular, our results show that the w-shaped–anti-w-shaped solitons can coexist with breathers, coinciding with the MI analysis where the coexistence condition is a mixture of a modulation stability and MI region. It is interesting that their interaction is inelastic and describes a fusion process. In addition, we demonstrate an annihilation phenomenon for the interaction of two w-shaped solitons which is identified essentially as an inelastic collision in this system. -- Highlights: •Vector rogue wave properties induced by higher-order effects are studied. •A transition between vector rogue waves and solitons is obtained. •The link between the transition and modulation instability (MI) is demonstrated. •The coexistence of vector solitons and breathers coincides with the MI features. •An annihilation phenomenon for the vector two w-shaped solitons is presented.
Higher-Order Wave Equation Within the Duffin-Kemmer-Petiau Formalism
Markov, Yu. A.; Markova, M. A.; Bondarenko, A. I.
2017-03-01
Within the framework of the Duffin-Kemmer-Petiau (DKP) formalism a consistent approach to derivation of the third-order wave equation is suggested. For this purpose, an additional algebraic object, the so-called q-commutator ( q is a primitive cubic root of unity) and a new set of matrices ημ instead of the original matrices βμ of the DKP algebra are introduced. It is shown that in terms of these η-matrices, we have succeeded to reduce the procedure of the construction of cubic root of the third-order wave operator to a few simple algebraic transformations and to a certain operation of passage to the limit z → q, where z is some complex deformation parameter entering into the definition of the ημ-matrices. A corresponding generalization of the result obtained to the case of interaction with an external electromagnetic field introduced through the minimal coupling scheme is performed. The application to the problem of construction within the DKP approach of the path integral representation in parasuperspace for the propagator of a massive vector particle in a background gauge field is discussed.
The (′/-Expansion Method for Abundant Traveling Wave Solutions of Caudrey-Dodd-Gibbon Equation
Directory of Open Access Journals (Sweden)
Hasibun Naher
2011-01-01
Full Text Available We construct the traveling wave solutions of the fifth-order Caudrey-Dodd-Gibbon (CDG equation by the (/-expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, the trigonometric, and the rational functions. It is shown that the (/-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations.
Energy decay of a variable-coefficient wave equation with nonlinear time-dependent localized damping
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Jieqiong Wu
2015-09-01
Full Text Available We study the energy decay for the Cauchy problem of the wave equation with nonlinear time-dependent and space-dependent damping. The damping is localized in a bounded domain and near infinity, and the principal part of the wave equation has a variable-coefficient. We apply the multiplier method for variable-coefficient equations, and obtain an energy decay that depends on the property of the coefficient of the damping term.
Directory of Open Access Journals (Sweden)
Aly R. Seadawy
2017-06-01
Full Text Available In this paper, we utilize the exp(−φ(ξ-expansion method to find exact and solitary wave solutions of the generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony nonlinear evolution equation. The generalized Zakharov–Kuznetsov–Benjamin–Bona–Mahony nonlinear evolution equation describes the model for the propagation of long waves that mingle with nonlinear and dissipative impact. This model is used in the analysis of the surface waves of long wavelength in hydro magnetic waves in cold plasma, liquids, acoustic waves in harmonic crystals and acoustic–gravity waves in compressible fluids. By using this method, seven different kinds of traveling wave solutions are successfully obtained for this model. The considered method and transformation techniques are efficient and consistent for solving nonlinear evolution equations and obtain exact solutions that are applied to the science and engineering fields.
Phase conjugation of vector fields by degenerate four-wave mixing in a Fe-doped LiNbO₃.
Qian, Sheng-Xia; Li, Yongnan; Kong, Ling-Jun; Tu, Chenghou; Wang, Hui-Tian
2014-08-15
We propose a method to generate the phase-conjugate wave of the vector field by degenerate four-wave mixing in a c-cut Fe-doped LiNbO3 crystal. We demonstrate experimentally that the phase-conjugate wave of the vector field can be generated. In particular, the phase-conjugate vector field has also the peculiar function of compensating the polarization distortion, as the traditional phase-conjugate scaler field can compensate the phase distortion.
Wave-Breaking Phenomena and Existence of Peakons for a Generalized Compressible Elastic-Rod Equation
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Xiaolian Ai
2014-01-01
Full Text Available Consideration in this paper is the Cauchy problem of a generalized hyperelastic-rod wave equation. We first derive a wave-breaking mechanism for strong solutions, which occurs in finite time for certain initial profiles. In addition, we determine the existence of some new peaked solitary wave solutions.
Local discontinuous Galerkin methods for two classes of two-dimensional nonlinear wave equations
Xu, Y.; Shu, Chi-Wang
2005-01-01
In this paper, we develop, analyze and test local discontinuous Galerkin (DG) methods to solve two classes of two-dimensional nonlinear wave equations formulated by the Kadomtsev–Petviashvili (KP) equation and the Zakharov–Kuznetsov (ZK) equation. Our proposed scheme for the Kadomtsev–Petviashvili
Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves
DEFF Research Database (Denmark)
Eldeberky, Y.; Madsen, Per A.
1999-01-01
This paper presents a new and more accurate set of deterministic evolution equations for the propagation of fully dispersive, weakly nonlinear, irregular, multidirectional waves. The equations are derived directly from the Laplace equation with leading order nonlinearity in the surface boundary c...
Vector single- and double-hump solitons for the coupled Sasa-Satsuma equations in optical media
Jiang, Yan; Tian, Bo
2017-11-01
In this paper, the coupled Sasa-Satsuma equations are investigated for the propagation of the ultrashort pulse in such optical media as multi-mode and birefringent fibers. With the Hirota method and introduction of three auxiliary functions, a different bilinear form is obtained. Vector one- and two-soliton solutions in the bright-bright form are constructed. Based on the vector one-soliton solutions, parametric conditions for the existence of the vector single- and double-hump solitons are presented. From the vector two-soliton solutions, elastic and inelastic interactions can both be observed between the (i) two vector single-hump solitons, (ii) two vector double-hump solitons, and (iii) vector single- and double-hump solitons.
Pandey, Vikash; Holm, Sverre
2016-12-01
The characteristic time-dependent viscosity of the intergranular pore-fluid in Buckingham's grain-shearing (GS) model [Buckingham, J. Acoust. Soc. Am. 108, 2796-2815 (2000)] is identified as the property of rheopecty. The property corresponds to a rare type of a non-Newtonian fluid in rheology which has largely remained unexplored. The material impulse response function from the GS model is found to be similar to the power-law memory kernel which is inherent in the framework of fractional calculus. The compressional wave equation and the shear wave equation derived from the GS model are shown to take the form of the Kelvin-Voigt fractional-derivative wave equation and the fractional diffusion-wave equation, respectively. Therefore, an analogy is drawn between the dispersion relations obtained from the fractional framework and those from the GS model to establish the equivalence of the respective wave equations. Further, a physical interpretation of the characteristic fractional order present in the wave equations is inferred from the GS model. The overall goal is to show that fractional calculus is not just a mathematical framework which can be used to curve-fit the complex behavior of materials. Rather, it can also be derived from real physical processes as illustrated in this work by the example of GS.
Shock wave equation of state of powder material
Dijken, D.K.; Hosson, J.Th.M. De
1994-01-01
A model is proposed to predict the following quantities for powder materials compacted by shock waves: the pressure, the specific volume, the internal energy behind the shock wave, and the shock-wave velocity U-s. They are calculated as a function of flyerplate velocity u(p) and initial powder
Sokolov, Sergey V.; Shcherban', I. V.; Shcherban', O. G.
2007-01-01
Identification algorithm of the right part of a dynamic system described with non-linear vector stochastic equation is considered. The main benefit of the suggested approach is the possibility of forming in real time and in explicit form the searched function’s right part approximate estimation of the object’s differential equations system.
Zhang, Zhendong
2016-07-26
We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh wave dispersion curve using a difference approximation to the gradient of the misfit function. We call this wave equation inversion of skeletonized surface waves because the skeletonized dispersion curve for the fundamental-mode Rayleigh wave is inverted using finite-difference solutions to the multi-dimensional elastic wave equation. The best match between the predicted and observed dispersion curves provides the optimal S-wave velocity model. Our method can invert for lateral velocity variations and also can mitigate the local minimum problem in full waveform inversion with a reasonable computation cost for simple models. Results with synthetic and field data illustrate the benefits and limitations of this method. © 2016 Elsevier B.V.
Linking multiple relaxation, power-law attenuation, and fractional wave equations.
Näsholm, Sven Peter; Holm, Sverre
2011-11-01
The acoustic wave attenuation is described by an experimentally established frequency power law in a variety of complex media, e.g., biological tissue, polymers, rocks, and rubber. Recent papers present a variety of acoustical fractional derivative wave equations that have the ability to model power-law attenuation. On the other hand, a multiple relaxation model is widely recognized as a physically based description of the acoustic loss mechanisms as developed by Nachman et al. [J. Acoust. Soc. Am. 88, 1584-1595 (1990)]. Through assumption of a continuum of relaxation mechanisms, each with an effective compressibility described by a distribution related to the Mittag-Leffler function, this paper shows that the wave equation corresponding to the multiple relaxation approach is identical to a given fractional derivative wave equation. This work therefore provides a physically based motivation for use of fractional wave equations in acoustic modeling.
Radiative transfer of acoustic waves in continuous complex media: Beyond the Helmholtz equation
Baydoun, Ibrahim; Pierrat, Romain; Derode, Arnaud
2016-01-01
Heterogeneity can be accounted for by a random potential in the wave equation. For acoustic waves in a fluid with fluctuations of both density and compressibility (as well as for electromagnetic waves in a medium with fluctuation of both permittivity and permeability) the random potential entails a scalar and an operator contribution. For simplicity, the latter is usually overlooked in multiple scattering theory: whatever the type of waves, this simplification amounts to considering the Helmholtz equation with a sound speed $c$ depending on position $\\mathbf{r}$. In this work, a radiative transfer equation is derived from the wave equation, in order to study energy transport through a multiple scattering medium. In particular, the influence of the operator term on various transport parameters is studied, based on the diagrammatic approach of multiple scattering. Analytical results are obtained for fundamental quantities of transport theory such as the transport mean-free path $\\ell^*$, scattering phase functi...
Observation of multi-component spatial vector solitons of four-wave mixing.
Wang, Ruimin; Wu, Zhenkun; Zhang, Yiqi; Zhang, Zhaoyang; Yuan, Chenzhi; Zheng, Huaibin; Li, Yuanyuan; Zhang, Jinhai; Zhang, Yanpeng
2012-06-18
We report the observation of multi-component dipole and vortex vector solitons composed of eight coexisting four-wave mixing (FWM) signals in two-level atomic system. The formation and stability of the multi-component dipole and vortex vector solitons are observed via changing the experiment parameters, including the frequency detuning, powers, and spatial configuration of the involved beams and the temperature of the medium. The transformation between modulated vortex solitons and rotating dipole solitons is observed at different frequency detunings. The interaction forces between different components of vector solitons are also investigated.
Poynting vector measurements of electromagnetic ion cyclotron waves in the plasmasphere
Labelle, J.; Treumann, R. A.
1992-01-01
Results are presented from an analysis of the June 6, 1985 Pc 2 measurements for which E, B, and delta-N were all analyzed. The event occurred in the duskside overlap region between the plasmaspheric bulge and the ion ring current. Results of the Poynting vector analysis of the R and L mode components show both of them to be characterized by northward Poynting vector, indicating energy flux away from the equator. The value of the Poynting vector was found to be about 3 microW/sq m.
Energy Technology Data Exchange (ETDEWEB)
Kamon, M.; Phillips, J.R. [Massachusetts Institute of Technology, Cambridge, MA (United States)
1994-12-31
In this paper techniques are presented for preconditioning equations generated by discretizing constrained vector integral equations associated with magnetoquasistatic analysis. Standard preconditioning approaches often fail on these problems. The authors present a specialized preconditioning technique and prove convergence bounds independent of the constraint equations and electromagnetic excitation frequency. Computational results from analyzing several electronic packaging examples are given to demonstrate that the new preconditioning approach can sometimes reduce the number of GMRES iterations by more than an order of magnitude.
Gusev, Vitalyi; Aleshin, Vladislav
2002-12-01
Nonlinear wave propagation in materials, where distribution function of mesoscopic mechanical elements has very different scales of variation along and normally to diagonal of Preisach-Mayergoyz space, is analyzed. An evolution equation for strain wave, which takes into account localization of element distribution near the diagonal and its slow variation along the diagonal, is proposed. The evolution equation provides opportunity to model propagation of elastic waves with strain amplitudes comparable to and even higher than characteristic scale of element localization near Preisach-Mayergoyz space diagonal. Analytical solutions of evolution equation predict nonmonotonous dependence of wave absorption on its amplitude in a particular regime. The regime of self-induced absorption for small-amplitude nonlinear waves is followed by the regime of self-induced transparency for high-amplitude waves. The developed theory might be useful in seismology, in high-pressure nonlinear acoustics, and in nonlinear acoustic diagnostics of damaged and fatigued materials.
Witten, Matthew
1983-01-01
Hyperbolic Partial Differential Equations, Volume 1: Population, Reactors, Tides and Waves: Theory and Applications covers three general areas of hyperbolic partial differential equation applications. These areas include problems related to the McKendrick/Von Foerster population equations, other hyperbolic form equations, and the numerical solution.This text is composed of 15 chapters and begins with surveys of age specific population interactions, populations models of diffusion, nonlinear age dependent population growth with harvesting, local and global stability for the nonlinear renewal eq
On the Generalized Maxwell Equations and Their Prediction of Electroscalar Wave
Directory of Open Access Journals (Sweden)
Arbab A. I.
2009-04-01
Full Text Available We have formulated the basic laws of electromagnetic theory in quaternion form. The formalism shows that Maxwell equations and Lorentz force are derivable from just one quaternion equation that only requires the Lorentz gauge. We proposed a quaternion form of the continuity equation from which we have derived the ordinary continuity equation. We introduce new transformations that produces a scalar wave and generalize the continuity equation to a set of three equations. These equations imply that both current and density are waves. Moreover, we have shown that the current can not cir- culate around a point emanating from it. Maxwell equations are invariant under these transformations. An electroscalar wave propagating with speed of light is derived upon requiring the invariance of the energy conservation equation under the new transforma- tions. The electroscalar wave function is found to be proportional to the electric field component along the charged particle motion. This scalar wave exists with or without considering the Lorentz gauge. We have shown that the electromagnetic fields travel with speed of light in the presence or absence of free charges.
Traveling Wave Solutions of Space-Time Fractional Generalized Fifth-Order KdV Equation
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Dianchen Lu
2017-01-01
Full Text Available The Korteweg-de Vries (KdV equation, especially the fractional higher order one, provides a relatively accurate description of motions of long waves in shallow water under gravity and wave propagation in one-dimensional nonlinear lattice. In this article, the generalized exp(-Φ(ξ-expansion method is proposed to construct exact solutions of space-time fractional generalized fifth-order KdV equation with Jumarie’s modified Riemann-Liouville derivatives. At the end, three types of exact traveling wave solutions are obtained which indicate that the method is very practical and suitable for solving nonlinear fractional partial differential equations.
Stability estimates for the anisotropic wave equation from the Dirichlet-to-Neumann map
Bellassoued, Mourad; Ferreira, David Dos Santos
2010-01-01
In this article we seek stability estimates in the inverse problem of determining the potential or the velocity in a wave equation in an anisotropic medium from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the wave equation. We prove in dimension $n\\geq 2$ that the knowledge of the Dirichlet-to-Neumann map for the wave equation uniquely determines the electric potential and we prove H\\"older-type stability in dete...
Shock wave equation of state of powder material
Dijken, D. K.; De Hosson, J. Th. M.
1994-01-01
A model is proposed to predict the following quantities for powder materials compacted by shock waves: the pressure, the specific volume, the internal energy behind the shock wave, and the shock-wave velocity Us. They are calculated as a function of flyerplate velocity up and initial powder specific volume V00. The model is tested on Cu, Al2024, and Fe. Calculated Us vs up curves agree well with experiments provided V00 is smaller than about two times the solid specific volume. The model can be used to predict shock-wave state points of powder or solid material with a lower or higher initial temperature than room temperature.
Runge-Kutta Integration of the Equal Width Wave Equation Using the Method of Lines
Directory of Open Access Journals (Sweden)
M. A. Banaja
2015-01-01
Full Text Available The equal width (EW equation governs nonlinear wave phenomena like waves in shallow water. Numerical solution of the (EW equation is obtained by using the method of lines (MOL based on Runge-Kutta integration. Using von Neumann stability analysis, the scheme is found to be unconditionally stable. Solitary wave motion and interaction of two solitary waves are studied using the proposed method. The three invariants of the motion are evaluated to determine the conservation properties of the generated scheme. Accuracy of the proposed method is discussed by computing the L2 and L∞ error norms. The results are found in good agreement with exact solution.
DEFF Research Database (Denmark)
Guo, Hairun; Zeng, Xianglong; Zhou, Binbin
2013-01-01
We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...... nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due...
Speed ot travelling waves in reaction-diffusion equations
Energy Technology Data Exchange (ETDEWEB)
Benguria, R.D.; Depassier, M.C. [Facultad de Fisica, Pontificia Universidad Catolica de Chile, Avda. Vicuna Mackenna 4860, Santiago (Chile); Mendez, V. [Facultat de Ciencies de la Salut, Universidad Internacional de Catalunya, Gomera s/n 08190 Sant Cugat del Valles, Barcelona (Spain)
2002-07-01
Reaction diffusion equations arise in several problems of population dynamics, flame propagation and others. In one dimensional cases the systems may evolve into travelling fronts. Here we concentrate on a reaction diffusion equation which arises as a simple model for chemotaxis and present results for the speed of the travelling fronts. (Author)
From Galilean-invariant to relativistic wave equations
Elizalde, E. (Emili), 1950-; Lobo Gutiérrez, José Alberto
1980-01-01
Through an imaginary change of coordinates in the Galilei algebra in 4 space dimensions and making use of an original idea of Dirac and Lvy-Leblond, we are able to obtain the relativistic equations of Dirac and of Bargmann and Wigner starting with the (Galilean-invariant) Schrdinger equation.
Comments on ``The Depth-Dependent Current and Wave Interaction Equations: A Revision''
Bennis, Anne-Claire; Ardhuin, Fabrice
2011-10-01
Equations for the wave-averaged three-dimensional momentum equations have been published in this journal. It appears that these equations are not consistent with the known depth-integrated momentum balance, especially over a sloping bottom. These equations should thus be considered with caution as they can produce erroneous flows, in particular outside of the surf zone. It is suggested that the inconsistency in the equations may arise from the different averaging operators applied to the different terms of the momentum equation. It is concluded that other forms of the momentum equations, expressed in terms of the quasi-Eulerian velocity, are better suited for three dimensional modelling of wave-current interactions.
Perturbation series for the double cnoidal wave of the Korteweg-de Vries equation
Boyd, John P.
1984-12-01
By means of the theorems proved earlier by the author, the problem of the double cnoidal wave of the Korteweg-de Vries equation is reduced to four algebraic equations in four unknowns. Two of the unknowns are the nonlinear phase speeds c1 and c2. Another is a physically irrelevant integration constant. The fourth unknown is the off-diagonal element of the symmetric, 2×2 theta matrix, which in turn gives the explicit coefficients of the Riemann theta function. The double cnoidal wave u(x,t) is then obtained by taking the second x-derivative of the logarithm of the theta function. Two separate forms of these four nonlinear ``residual'' equations are given. One is obtained from the Fourier series of the theta function and is useful for small wave amplitude. The other is based on the Gaussian series of the theta function and is highly efficient in the large amplitude regime where the double cnoidal wave is the sum of two solitary waves. Both sets of residual equations can be solved via perturbation theory and results are given to fourth order in the Fourier case and second order in the Gaussian case. The Gaussian-based perturbation series has the remarkable property that it converges more and more rapidly as the wave amplitude increases; the zeroth-order solution is the familiar double solitary wave. Numerical comparisons show that the two complementary perturbation series give accurate results in all the important regions of parameter space. (The ``unimportant'' regions are those in which the double cnoidal wave is an ordinary cnoidal wave subject to a very weak perturbation.) This is turn implies that even for moderate wave amplitude where the nonlinear interactions are not weak, and yet the solitary wave peaks are not well separated, at least to the eye, it is still qualitatively legitimate to describe the double cnoidal wave as either the sum of two sine waves or of two solitary waves of different heights.
Extension of the double-wave-vector diffusion-weighting experiment to multiple concatenations.
Finsterbusch, Jürgen
2009-06-01
Experiments involving two diffusion-weightings in a single acquisition, so-called double- or two-wave-vector experiments, have recently been applied to measure the microscopic anisotropy in macroscopically isotropic samples or to estimate pore or compartment sizes. These informations are derived from the signal modulation observed when varying the wave vectors' orientations. However, the modulation amplitude can be small and, for short mixing times between the two diffusion-weightings, decays with increased gradient pulse lengths which hampers its detectability on whole-body MR systems. Here, an approach is investigated that involves multiple concatenations of the two diffusion-weightings in a single experiment. The theoretical framework for double-wave-vector experiments of fully restricted diffusion is adapted and the corresponding tensor approach recently presented for short mixing times extended and compared to numerical simulations. It is shown that for short mixing times (i) the extended tensor approach well describes the signal behavior observed for multiple concatenations and (ii) the relative amplitude of the signal modulation increases with the number of concatenations. Thus, the presented extension of the double-wave-vector experiment may help to improve the detectability of the signal modulations observed for short mixing times, in particular on whole-body MR systems with their limited gradient amplitudes.
BALZUWEIT, K; HOVESTAD, A; MEEKES, H; DEBOER, JL
Single crystals of incommensurately modulated calaverite, with and without silver were grown and analysed using different techniques. The modulation wave vectors of some well characterised samples were measured as a function of both composition and temperature. The thus obtained results were
Vector-based plane-wave spectrum method for the propagation of cylindrical electromagnetic fields.
Shi, S; Prather, D W
1999-11-01
We present a vector-based plane-wave spectrum (VPWS) method for efficient propagation of cylindrical electromagnetic fields. In comparison with electromagnetic propagation integrals, the VPWS method significantly reduces time of propagation. Numerical results that illustrate the utility of this method are presented.
DEFF Research Database (Denmark)
Nour, Baqer; Breinbjerg, Olav
2010-01-01
This article addresses the problem of communication in near field region. The proposed example is the communication between two small antennas, which are modelled as an electric dipole antenna (transmitter) and a small box (receiver), near a sphere that models a head. Spherical vector wave...
Accuracy and Precision of Plane Wave Vector Flow Imaging for Laminar and Complex Flow In Vivo
DEFF Research Database (Denmark)
Jensen, Jonas; Traberg, Marie Sand; Villagómez Hoyos, Carlos Armando
2017-01-01
In this study, a comparison between velocity fields for a plane wave 2-D vector flow imaging (VFI) method and a computational fluid dynamics (CFD) simulation is made. VFI estimates are obtained from the scan of a flow phantom, which mimics the complex flow conditions in the carotid artery. Furthe...
Wave-Vector Dependence of the Jahn-Teller Interactions in TmVO4
DEFF Research Database (Denmark)
Kjems, Jørgen; Hayes, W.; Smith, S. H.
1975-01-01
The resonant Jahn-Teller coupling of the B2g acoustic phonon and the Zeeman-split ground doublet in TmVO4 has been studied by inelastic neutron scattering. Tuning of the magnetic field provides a means for investigating the wave-vector dependence of the interactions. We find that the coupling...
Fermi wave vector for the partially spin-polarized composite-fermion Fermi sea
DEFF Research Database (Denmark)
Coimbatore Balram, Ajit; Jain, Jainendra
2017-01-01
The fully spin polarized composite fermion (CF) Fermi sea at half filled lowest Landau level has a Fermi wave vector $k^*_{\\rm F}=\\sqrt{4\\pi\\rho_e}$, where $\\rho_e$ is the density of electrons or composite fermions, supporting the notion that the interaction between composite fermions can...... CFFSs at $\
DEFF Research Database (Denmark)
Webb, Garry; Sørensen, Mads Peter; Brio, Moysey
2004-01-01
the electromagnetic momentum and energy conservation laws, corresponding to the space and time translation invariance symmetries. The symmetries are used to obtain classical similarity solutions of the equations. The traveling wave similarity solutions for the case of a cubic Kerr nonlinearity, are shown to reduce...... to a single ordinary differential equation for the variable $y=E^2$, where $E$ is the electric field intensity. The differential equation has solutions $y=y(\\xi)$, where $\\xi=z-st$ is the traveling wave variable and $s$ is the velocity of the wave. These solutions exhibit new phenomena not obtainable...... by the NLS approximation. The characteristics of the solutions depends on the values of the wave velocity $s$ and the energy integration constant $\\epsilon$. Both smooth periodic traveling waves and non-smooth solutions in which the electric field gradient diverges (i.e. solutions in which $|E...
Spinor-electron wave guided modes in coupled quantum wells structures by solving the Dirac equation
Energy Technology Data Exchange (ETDEWEB)
Linares, Jesus [Area de Optica, Departamento de Fisica Aplicada, Facultade de Fisica, Escola Universitaria de Optica e Optometria, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Galicia (Spain)], E-mail: suso.linares.beiras@usc.es; Nistal, Maria C. [Area de Optica, Departamento de Fisica Aplicada, Facultade de Fisica, Escola Universitaria de Optica e Optometria, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Galicia (Spain)
2009-05-04
A quantum analysis based on the Dirac equation of the propagation of spinor-electron waves in coupled quantum wells, or equivalently coupled electron waveguides, is presented. The complete optical wave equations for Spin-Up (SU) and Spin-Down (SD) spinor-electron waves in these electron guides couplers are derived from the Dirac equation. The relativistic amplitudes and dispersion equations of the spinor-electron wave-guided modes in a planar quantum coupler formed by two coupled quantum wells, or equivalently by two coupled slab electron waveguides, are exactly derived. The main outcomes related to the spinor modal structure, such as the breaking of the non-relativistic degenerate spin states, the appearance of phase shifts associated with the spin polarization and so on, are shown.
Critical string wave equations and the QCD (U(N{sub c})) string. (Some comments)
Energy Technology Data Exchange (ETDEWEB)
Botelho, Luiz C.L. [Universidade Federal Fluminense (UFF), Niteroi, RJ (Brazil). Inst. de Matematica. Dept. de Matematica Aplicada], e-mail: botelho.luiz@superig.com.br
2009-07-01
We present a simple proof that self-avoiding fermionic strings solutions solve formally (in a Quantum Mechanical Framework) the QCD(U(N{sub c})) loop wave equation written in terms of random loops. (author)
Traveling Wave Solutions of ZK-BBM Equation Sine-Cosine Method
Directory of Open Access Journals (Sweden)
Sadaf Bibi
2014-03-01
Full Text Available Travelling wave solutions are obtained by using a relatively new technique which is called sine-cosine method for ZK-BBM equations. Solution procedure and obtained results re-confirm the efficiency of the proposed scheme.
Small amplitude periodic solutions in time for one-dimensional nonlinear wave equations
Liu, Zhenjie
2017-09-01
This paper is devoted to the construction of solutions for one-dimensional wave equations with Dirichlet or Neumann boundary conditions by means of a Nash-Moser iteration scheme, for a large set of frequencies.
Jiang, Lijian
2010-08-01
In this paper, we discuss a numerical multiscale approach for solving wave equations with heterogeneous coefficients. Our interest comes from geophysics applications and we assume that there is no scale separation with respect to spatial variables. To obtain the solution of these multiscale problems on a coarse grid, we compute global fields such that the solution smoothly depends on these fields. We present a Galerkin multiscale finite element method using the global information and provide a convergence analysis when applied to solve the wave equations. We investigate the relation between the smoothness of the global fields and convergence rates of the global Galerkin multiscale finite element method for the wave equations. Numerical examples demonstrate that the use of global information renders better accuracy for wave equations with heterogeneous coefficients than the local multiscale finite element method. © 2010 IMACS.
Four ways to justify temporal memory operators in the lossy wave equation
Holm, Sverre
2015-01-01
Attenuation of ultrasound often follows near power laws which cannot be modeled with conventional viscous or relaxation wave equations. The same is often the case for shear wave propagation in tissue also. More general temporal memory operators in the wave equation can describe such behavior. They can be justified in four ways: 1) Power laws for attenuation with exponents other than two correspond to the use of convolution operators with a temporal memory kernel which is a power law in time. 2) The corresponding constitutive equation is also a convolution, often with a temporal power law function. 3) It is also equivalent to an infinite set of relaxation processes which can be formulated via the complex compressibility. 4) The constitutive equation can also be expressed as an infinite sum of higher order derivatives. An extension to longitudinal waves in a nonlinear medium is also provided.
Energy Technology Data Exchange (ETDEWEB)
Barut, A.O. (Colorado Univ., Boulder (USA). Dept. of Physics); Oezaltin, O.; Uenal, N. (Dicle Univ., Diyarbakir (Turkey). Dept. of Physics)
1985-01-01
The Heisenberg equations for the Dirac electron in an external electromagnetic plane wave have been solved exactly in terms of incomplete ..gamma..-functions. As a special case the solution for a crossed constant electric and magnetic field is given.
Yang, Zhijian; Liu, Zhiming
2017-03-01
The paper investigates the well-posedness and the longtime dynamics of the quasilinear wave equations with structural damping and supercritical nonlinearities: {{u}tt}- Δ u+{{≤ft(- Δ \\right)}α}{{u}t}-\
Pointwise estimates for solutions to a system of nonlinear damped wave equations
Directory of Open Access Journals (Sweden)
Wenjun Wang
2013-11-01
Full Text Available In this article, we consider the existence of global solutions and pointwise estimates for the Cauchy problem of a nonlinear damped wave equation. We obtain the existence by using the approach introduced by Li and Chen in [7] and some estimates of the solution. The proofs of the estimates are based on a detailed analysis of the Green function of the linear damped wave equations. Also, we show the L^p convergence rate of the solution.
On exact traveling-wave solutions for local fractional Korteweg-de Vries equation
Yang, Xiao-Jun; Tenreiro Machado, J. A.; Baleanu, Dumitru; Cattani, Carlo
2016-08-01
This paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces.
A nine-point finite difference scheme for one-dimensional wave equation
Szyszka, Barbara
2017-07-01
The paper is devoted to an implicit finite difference method (FDM) for solving initial-boundary value problems (IBVP) for one-dimensional wave equation. The second-order derivatives in the wave equation have been approximated at the four intermediate points, as a consequence, an implicit nine-point difference scheme has been obtained. Von Neumann stability analysis has been conducted and we have demonstrated, that the presented difference scheme is unconditionally stable.
On exact traveling-wave solutions for local fractional Korteweg-de Vries equation.
Yang, Xiao-Jun; Tenreiro Machado, J A; Baleanu, Dumitru; Cattani, Carlo
2016-08-01
This paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces.
The influence of damping and source terms on solutions of nonlinear wave equations
Directory of Open Access Journals (Sweden)
Mohammad A. Rammaha
2007-11-01
Full Text Available We discuss in this paper some recent development in the study of nonlinear wave equations. In particular, we focus on those results that deal with wave equations that feature two competing forces.One force is a damping term and the other is a strong source. Our central interest here is to analyze the influence of these forces on the long-time behavior of solutions.
Hamilton, Brian; Bilbao, Stefan
2013-01-01
Finite difference schemes for the 2-D wave equation operating on hexagonal grids and the accompanyingnumerical dispersion properties have received little attention in comparison to schemes operating on rectilinear grids. This paper considers the hexagonal tiling of the wavenumber plane in order to show that thehexagonal grid is a more natural choice to emulate the isotropy of the Laplacian operator and the wave equation. Performance of the 7-point scheme on a hexagonal grid is better than pre...
Alvarez, Roberto; van Hecke, Martin; van Saarloos, Wim
1996-01-01
In many pattern forming systems that exhibit traveling waves, sources and sinks occur which separate patches of oppositely traveling waves. We show that simple qualitative features of their dynamics can be compared to predictions from coupled amplitude equations. In heated wire convection experiments, we find a discrepancy between the observed multiplicity of sources and theoretical predictions. The expression for the observed motion of sinks is incompatible with any amplitude equation descri...
Existence and Stability of Steady Waves for the Hasegawa-Mima Equation
Directory of Open Access Journals (Sweden)
Guo Boling
2009-01-01
Full Text Available Abstract By introducing a compactness lemma and considering a constrained variational problem, we obtain a set of steady waves for Hasegawa-Mima equation, which describes the motion of drift waves in plasma. Moreover, we prove that is a stable set for the initial value problem of the equation, in the sense that a solution which starts near will remain near it for all time.
Said-Houari, Belkacem
2012-03-01
In this paper, we consider a viscoelastic wave equation with an absorbing term and space-time dependent damping term. Based on the weighted energy method, and by assuming that the kernel decaying exponentially, we obtain the L2 decay rates of the solutions. More precisely, we show that the decay rates are the same as those obtained in Lin et al. (2010) [15] for the semilinear wave equation with absorption term. © 2011 Elsevier Inc.
Wapenaar, Kees
2017-06-01
A unified scalar wave equation is formulated, which covers three-dimensional (3D) acoustic waves, 2D horizontally-polarised shear waves, 2D transverse-electric EM waves, 2D transverse-magnetic EM waves, 3D quantum-mechanical waves and 2D flexural waves. The homogeneous Green's function of this wave equation is a combination of the causal Green's function and its time-reversal, such that their singularities at the source position cancel each other. A classical representation expresses this homogeneous Green's function as a closed boundary integral. This representation finds applications in holographic imaging, time-reversed wave propagation and Green's function retrieval by cross correlation. The main drawback of the classical representation in those applications is that it requires access to a closed boundary around the medium of interest, whereas in many practical situations the medium can be accessed from one side only. Therefore, a single-sided representation is derived for the homogeneous Green's function of the unified scalar wave equation. Like the classical representation, this single-sided representation fully accounts for multiple scattering. The single-sided representation has the same applications as the classical representation, but unlike the classical representation it is applicable in situations where the medium of interest is accessible from one side only.
Directory of Open Access Journals (Sweden)
T. D. Carozzi
2004-07-01
Full Text Available We introduce a technique to determine instantaneous local properties of waves based on discrete-time sampled, real-valued measurements from 4 or more spatial points. The technique is a generalisation to the spatial domain of the notion of instantaneous frequency used in signal processing. The quantities derived by our technique are closely related to those used in geometrical optics, namely the local wave vector and instantaneous phase velocity. Thus, this experimental technique complements ray-tracing. We provide example applications of the technique to electric field and potential data from the EFW instrument on Cluster. Cluster is the first space mission for which direct determination of the full 3-dimensional local wave vector is possible, as described here.
Wave Breaking Phenomenon for DGH Equation with Strong Dissipation
Directory of Open Access Journals (Sweden)
Zhengguang Guo
2014-01-01
Full Text Available The present work is mainly concerned with the Dullin-Gottwald-Holm (DGH equation with strong dissipative term. We establish some sufficient conditions to guarantee finite time blow-up of strong solutions.
Wide-azimuth angle gathers for anisotropic wave-equation migration
Sava, Paul C.
2012-10-15
Extended common-image-point gathers (CIP) constructed by wide-azimuth TI wave-equation migration contain all the necessary information for angle decomposition as a function of the reflection and azimuth angles at selected locations in the subsurface. The aperture and azimuth angles are derived from the extended images using analytic relations between the space- and time-lag extensions using information which is already available at the time of migration, i.e. the anisotropic model parameters. CIPs are cheap to compute because they can be distributed in the image at the most relevant positions, as indicated by the geologic structure. If the reflector dip is known at the CIP locations, then the computational cost can be reduced by evaluating only two components of the space-lag vector. The transformation from extended images to angle gathers is a planar Radon transform which depends on the local medium parameters. This transformation allows us to separate all illumination directions for a given experiment, or between different experiments. We do not need to decompose the reconstructed wavefields or to choose the most energetic directions for decomposition. Applications of the method include illumination studies in complex areas where ray-based methods fail, and assuming that the subsurface illumination is sufficiently dense, the study of amplitude variation with aperture and azimuth angles. © 2012 European Association of Geoscientists & Engineers.
Directory of Open Access Journals (Sweden)
M.G. Hafez
2015-06-01
Full Text Available The modeling of wave propagation in microstructured materials should be able to account for various scales of microstructure. Based on the proposed new exponential expansion method, we obtained the multiple explicit and exact traveling wave solutions of the strain wave equation for describing different types of wave propagation in microstructured solids. The solutions obtained in this paper include the solitary wave solutions of topological kink, singular kink, non-topological bell type solutions, solitons, compacton, cuspon, periodic solutions, and solitary wave solutions of rational functions. It is shown that the new exponential method, with the help of symbolic computation, provides an effective and straightforward mathematical tool for solving nonlinear evolution equations arising in mathematical physics and engineering.
Rogue wave solutions of the nonlinear Schrödinger equation with ...
Indian Academy of Sciences (India)
In this paper, a unified formula of a series of rogue wave solutions for the standard (1+1)-dimensional nonlinear Schrödinger equation is obtained through exp-function method. Further, by means of an appropriate transformation and previously obtained solutions, rogue wave solutions of the variable coefficient Schrödinger ...
Fundamental solutions of the wave equation in Robertson-Walker spaces
Yagdjian, Karen; Galstian, Anahit
2008-10-01
In this article we construct the fundamental solutions for the wave equation in the Robertson-Walker spaces arising in the de Sitter model of the universe. We then use these fundamental solutions to represent solutions of the Cauchy problem for the equation with and without a source term.
A similarity relation of the coupled equations for RF waves in a tokamak
Lee, Jungpyo; Smithe, David; Jaeger, Erwin; Berry, Lee; Harvey, R. W.; Bonoli, Paul
2017-10-01
The propagation and damping of RF waves in plasmas are modeled kinetically by solving the coupled equations between Maxwell's equation and Fokker-Planck equation. When the plasmas are magnetized, the wave dielectric tensor strongly depends on the background magnetic field, which can be calculated using Grad-Shafranov equation in a toroidally symmetric geometry. We found a similarity in the solutions of the coupled equations above, which keep the several dimensionless parameters constant. By changing plasma density and pressure, machine geometry (major radius), and RF wave frequency and power according to the similarity rule, there exists a set of solutions that show the consistent change in the background magnetic fields in the Grad-Shafranov equation, the electric and magnetic fields in the Maxwell's equation, and the distribution function of the Fokker-Planck equation. By investigating the numerical errors of the solutions from the expected results by the similarity rule, we verify the coupled numerical code for the RF waves in a tokamak (e.g. TORIC or AORSA/CQL3D/ECOM). This work was supported by US DoE Contract No. DE-FC02-01ER54648 under a Scientific Discovery through Advanced Computing Initiative.
Global Existence of Solutions to the Fowler Equation in a Neighbourhood of Travelling-Waves
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Afaf Bouharguane
2011-01-01
Full Text Available We investigate a fractional diffusion/anti-diffusion equation proposed by Andrew C. Fowler to describe the dynamics of sand dunes sheared by a fluid flow. In this paper, we prove the global-in-time well-posedness in the neighbourhood of travelling-waves solutions of the Fowler equation.
Nurijanyan, S.; van der Vegt, Jacobus J.W.; Bokhove, Onno
2011-01-01
A discontinuous Galerkin nite element method (DGFEM) has been developed and tested for linear, three-dimensional, rotating incompressible Euler equations. These equations admit complicated wave solutions. The numerical challenges concern: (i) discretisation of a divergence-free velocity eld; (ii)
Energy Technology Data Exchange (ETDEWEB)
Fierros Palacios, Angel [Instituto de Investigaciones Electricas, Temixco, Morelos (Mexico)
2001-02-01
In this work the complete set of differential field equations which describes the dynamic state of a continuos conducting media which flow in presence of a perturbed magnetic field is obtained. Then, the thermic equation of state, the wave equation and the conservation law of energy for the Alfven MHD waves are obtained. [Spanish] Es este trabajo se obtiene el conjunto completo de ecuaciones diferenciales de campo que describen el estado dinamico de un medio continuo conductor que se mueve en presencia de un campo magnetico externo perturbado. Asi, se obtiene la ecuacion termica de estado, la ecuacion de onda y la ley de la conservacion de la energia para las ondas de Alfven de la MHD.
Exact Traveling Wave Solutions for Wick-Type Stochastic Schamel KdV Equation
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Hossam A. Ghany
2014-01-01
Full Text Available F-expansion method is proposed to seek exact solutions of nonlinear partial differential equations. By means of Hermite transform, inverse Hermite transform, and white noise analysis, the variable coefficients and Wick-type stochastic Schamel KdV equations are completely described. Abundant exact traveling wave solutions for variable coefficients Schamel KdV equations are given. These solutions include exact stochastic Jacobi elliptic functions, trigonometric functions, and hyperbolic functions solutions.
Global existence and decay of solutions of a nonlinear system of wave equations
Said-Houari, Belkacem
2012-03-01
This work is concerned with a system of two wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we show that our problem has a unique local solution. Also, we prove that, for some restrictions on the initial data, the rate of decay of the total energy is exponential or polynomial depending on the exponents of the damping terms in both equations.
A Possible Generalization of Acoustic Wave Equation Using the Concept of Perturbed Derivative Order
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Abdon Atangana
2013-01-01
Full Text Available The standard version of acoustic wave equation is modified using the concept of the generalized Riemann-Liouville fractional order derivative. Some properties of the generalized Riemann-Liouville fractional derivative approximation are presented. Some theorems are generalized. The modified equation is approximately solved by using the variational iteration method and the Green function technique. The numerical simulation of solution of the modified equation gives a better prediction than the standard one.
Conservation Laws and Traveling Wave Solutions of a Generalized Nonlinear ZK-BBM Equation
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Khadijo Rashid Adem
2014-01-01
Full Text Available We study a generalized two-dimensional nonlinear Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM equation, which is in fact Benjamin-Bona-Mahony equation formulated in the ZK sense. Conservation laws for this equation are constructed by using the new conservation theorem due to Ibragimov and the multiplier method. Furthermore, traveling wave solutions are obtained by employing the (G'/G-expansion method.
Traveling Wave Solutions of Reaction-Diffusion Equations Arising in Atherosclerosis Models
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Narcisa Apreutesei
2014-05-01
Full Text Available In this short review article, two atherosclerosis models are presented, one as a scalar equation and the other one as a system of two equations. They are given in terms of reaction-diffusion equations in an infinite strip with nonlinear boundary conditions. The existence of traveling wave solutions is studied for these models. The monostable and bistable cases are introduced and analyzed.
Dutta, Gaurav
2013-08-20
Attenuation leads to distortion of amplitude and phase of seismic waves propagating inside the earth. Conventional acoustic and least-squares reverse time migration do not account for this distortion which leads to defocusing of migration images in highly attenuative geological environments. To account for this distortion, we propose to use the visco-acoustic wave equation for least-squares reverse time migration. Numerical tests on synthetic data show that least-squares reverse time migration with the visco-acoustic wave equation corrects for this distortion and produces images with better balanced amplitudes compared to the conventional approach. © 2013 SEG.
DEFF Research Database (Denmark)
Boeriis, Morten; van Leeuwen, Theo
2017-01-01
This article revisits the concept of vectors, which, in Kress and van Leeuwen’s Reading Images (2006), plays a crucial role in distinguishing between ‘narrative’, action-oriented processes and ‘conceptual’, state-oriented processes. The use of this concept in image analysis has usually focused...... on the most salient vectors, and this works well, but many images contain a plethora of vectors, which makes their structure quite different from the linguistic transitivity structures with which Kress and van Leeuwen have compared ‘narrative’ images. It can also be asked whether facial expression vectors...... should be taken into account in discussing ‘reactions’, which Kress and van Leeuwen link only to eyeline vectors. Finally, the question can be raised as to whether actions are always realized by vectors. Drawing on a re-reading of Rudolf Arnheim’s account of vectors, these issues are outlined...
Some Exact Results for the Schroedinger Wave Equation with a Time Dependent Potential
Campbell, Joel
2009-01-01
The time dependent Schroedinger equation with a time dependent delta function potential is solved exactly for many special cases. In all other cases the problem can be reduced to an integral equation of the Volterra type. It is shown that by knowing the wave function at the origin, one may derive the wave function everywhere. Thus, the problem is reduced from a PDE in two variables to an integral equation in one. These results are used to compare adiabatic versus sudden changes in the potential. It is shown that adiabatic changes in the p otential lead to conservation of the normalization of the probability density.
Stochastic wave-function unravelling of the generalized Lindblad equation
Semin, V.; Semina, I.; Petruccione, F.
2017-12-01
We investigate generalized non-Markovian stochastic Schrödinger equations (SSEs), driven by a multidimensional counting process and multidimensional Brownian motion introduced by A. Barchielli and C. Pellegrini [J. Math. Phys. 51, 112104 (2010), 10.1063/1.3514539]. We show that these SSEs can be translated in a nonlinear form, which can be efficiently simulated. The simulation is illustrated by the model of a two-level system in a structured bath, and the results of the simulations are compared with the exact solution of the generalized master equation.
Lawrenz, Marco; Koch, Martin A; Finsterbusch, Jürgen
2010-01-01
Experiments with two diffusion-weighting periods applied successively in a single experiment, so-called double-wave-vector (DWV) diffusion-weighting experiments, are a promising tool for the investigation of material or tissue structure on a microscopic level, e.g. to determine cell or compartment sizes or to detect pore or cell anisotropy. However, the theoretical descriptions presented so far for experiments that aim to investigate the microscopic anisotropy with a long mixing time between the two diffusion weightings, are limited to certain wave vector orientations, specific pore shapes, and macroscopically isotropic samples. Here, the signal equations for fully restricted diffusion are re-investigated in more detail. A general description of the signal behavior for arbitrary wave vector directions, pore or cell shapes, and orientation distributions of the pores or cells is obtained that involves a fourth-order tensor approach. From these equations, a rotationally invariant measure of the microscopic anisotropy, termed MA, is derived that yields information complementary to that of the (macroscopic) anisotropy measures of standard diffusion-tensor acquisitions. Furthermore, the detailed angular modulation for arbitrary cell shapes with an isotropic orientation distribution is derived. Numerical simulations of the MR signal with a Monte-Carlo algorithms confirm the theoretical considerations. The extended theoretical description and the introduction of a reliable measure of the microscopic anisotropy may help to improve the applicability and reliability of corresponding experiments. Copyright 2009 Elsevier Inc. All rights reserved.
Roberts, O. W.; Narita, Y.; Escoubet, C. P.
2017-12-01
This analysis represents the first time that a simultaneous measurement of parallel and perpendicular spectral indices at both inertial and kinetic scales has been made directly in wave vector space, using a single interval of solar wind plasma. An interferometric wave vector analysis method is applied to four-point magnetometer data from the Cluster spacecraft to study for the first time the anisotropic and axially asymmetric energy spectrum directly in the three-dimensional wave vector space in the solar wind on spatial scales for the fluid picture (at about 6000 km) down to the ion kinetic regime (at about 400 km) without invoking Taylor’s frozen-in flow hypothesis. At fluid scales, the spectral index is found to transition from -2 along the large-scale magnetic field direction to a spectral index approaching -5/3 in the perpendicular direction. The wave number for the spectral break between ion inertial and kinetic scales occurs at larger scales in the parallel projection, compared to the perpendicular. At ion kinetic scales, the spectrum in the parallel direction is difficult to measure, while the two perpendicular directions are also anisotropic and vary between -8/3 and -11/3. This suggests that a single anisotropic process where symmetry is broken in a single direction cannot account for the results.
Least-Squares Multi-Angle Doppler Estimators for Plane-Wave Vector Flow Imaging.
Yiu, Billy Y S; Yu, Alfred C H
2016-11-01
Designing robust Doppler vector estimation strategies for use in plane-wave imaging schemes based on unfocused transmissions is a topic that has yet to be studied in depth. One potential solution is to use a multi-angle Doppler estimation approach that computes flow vectors via least-squares fitting, but its performance has not been established. Here, we investigated the efficacy of multi-angle Doppler vector estimators by: 1) comparing its performance with respect to the classical dual-angle (cross-beam) Doppler vector estimator and 2) examining the working effects of multi-angle Doppler vector estimators on flow visualization quality in the context of dynamic flow path rendering. Implementing Doppler vector estimators that use different combinations of transmit (Tx) and receive (Rx) steering angles, our analysis has compared the classical dual-angle Doppler method, a 5-Tx version of dual-angle Doppler, and various multi-angle Doppler configurations based on 3 Tx and 5 Tx. Two angle spans (10°, 20°) were examined in forming the steering angles. In imaging scenarios with known flow profiles (rotating disk and straight-tube parabolic flow), the 3-Tx, 3-Rx and 5-Tx, 5-Rx multi-angle configurations produced vector estimates with smaller variability compared with the dual-angle method, and the estimation results were more consistent with the use of a 20° angle span. Flow vectors derived from multi-angle Doppler estimators were also found to be effective in rendering the expected flow paths in both rotating disk and straight-tube imaging scenarios, while the ones derived from the dual-angle estimator yielded flow paths that deviated from the expected course. These results serve to attest that using multi-angle least-squares Doppler vector estimators, flow visualization can be consistently achieved.
Least-Squares Multi-Angle Doppler Estimators for Plane Wave Vector Flow Imaging.
Yiu, Billy Y S; Yu, Alfred C H
2016-06-20
Designing robust Doppler vector estimation strategies for use in plane wave imaging schemes based on unfocused transmissions is a topic that has yet to be studied in depth. One potential solution is to use a multi-angle Doppler estimation approach that computes flow vectors via least-squares fitting, but its performance has not been established. Here, we investigated the efficacy of multi-angle Doppler vector estimators by: (i) comparing its performance with respect to the classical dual-angle (cross-beam) Doppler vector estimator; (ii) examining the working effects of multi-angle Doppler vector estimators on flow visualization quality in the context of dynamic flow path rendering. Implementing Doppler vector estimators that use different combinations of transmit (Tx) and receive (Rx) steering angles, our analysis has compared the classical dual-angle Doppler method, a 5-Tx version of dual-angle Doppler, and various multi-angle Doppler configurations based on 3 Tx and 5 Tx. Two angle spans (10°, 20°) were examined in forming the steering angles. In imaging scenarios with known flow profiles (rotating disc and straight-tube parabolic flow), the 3-Tx, 3-Rx and 5-Tx, 5-Rx multi-angle configurations produced vector estimates with smaller variability comparing to the dual-angle method, and the estimation results were more consistent with the use of a 20° angle span. Flow vectors derived from multi-angle Doppler estimators were also found to be effective in rendering the expected flow paths in both rotating disc and straight-tube imaging scenarios, while the ones derived from the dual-angle estimator yielded flow paths that deviated from the expected course. These results serve to attest that, using multi-angle least-squares Doppler vector estimators, flow visualization can be consistently achieved.
Gravitational waves induced by massless vector fields with non-minimal coupling to gravity
Feng, Kaixi
2016-01-01
In this paper, we calculate the contribution of the late time mode of a massless vector field to the power spectrum of the primordial gravitational wave using retarded Green's propagator. We consider a non-trivial coupling between gravity and the vector field. We find that the correction is scale-invariant and of order $\\frac{H^4}{M_P^4}$. The non-minimal coupling leads to a dependence of $\\frac{H^2}{M^2}$, which can amplify the correlation function up to the level of $\\frac{H^2}{M^2_P}$.
Polynomial expansions for solution of wave equation in quantum calculus
Directory of Open Access Journals (Sweden)
Akram Nemri
2010-12-01
Full Text Available In this paper, using the q^2 -Laplace transform early introduced by Abdi [1], we study q-Wave polynomials related with the q-difference operator ∆q,x . We show in particular that they are linked to the q-little Jacobi polynomials p_n (x; α, β | q^2 .
A causal and fractional all-frequency wave equation for lossy media.
Holm, Sverre; Näsholm, Sven Peter
2011-10-01
This work presents a lossy partial differential acoustic wave equation including fractional derivative terms. It is derived from first principles of physics (mass and momentum conservation) and an equation of state given by the fractional Zener stress-strain constitutive relation. For a derivative order α in the fractional Zener relation, the resulting absorption α(k) obeys frequency power-laws as α(k) ∝ ω(1+α) in a low-frequency regime, α(k) ∝ ω(1-α/2) in an intermediate-frequency regime, and α(k) ∝ ω(1-α) in a high-frequency regime. The value α=1 corresponds to the case of a single relaxation process. The wave equation is causal for all frequencies. In addition the sound speed does not diverge as the frequency approaches infinity. This is an improvement over a previously published wave equation building on the fractional Kelvin-Voigt constitutive relation. © 2011 Acoustical Society of America
Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue
2018-01-01
This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0 . Furthermore, we prove the global existence and uniqueness of C^{α ,β } -solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1 -space. The exponential convergence rate is also derived.
Solitary wave solutions to nonlinear evolution equations in ...
Indian Academy of Sciences (India)
This paper obtains solitons as well as other solutions to a few nonlinear evolution equations that appear in various areas of mathematical physics. The two analytical integrators that are applied to extract solutions are tan–cot method and functional variable approaches. The soliton solutions can be used in the further study of ...
Measurement of the wave-normal vector of proton whistlers on Ogo 6.
Chan, K. W.; Burton, R. K.; Holzer, R. E.; Smith, E. J.
1972-01-01
Description of the first experimental determination of the wave-normal vector of proton whistlers in the ionosphere. Between the crossover frequency and the proton gyrofrequency, both right-hand and left-hand modes of propagation can occur for upgoing waves. Theoretically, the amount of energy in the respective modes depends on theta, the angle between the wave normal and the magnetic field. For proton whistlers with only left-hand mode energy between the crossover and proton gyrofrequency, theta ranged from 36 to 51 deg. For proton whistlers with strong right-hand and left-hand mode signals, theta ranged from 24 to 29 deg. The result is in good agreement with Wang's (1971) collisionless mode-coupling model. The angle between the wave normal and the vertical is found to increase with increasing altitude.
Measurements of the Poynting vector of standing hydromagnetic waves at geosynchronous orbit
Cummings, W. D.; Deforest, S. E.; Mcpherron, R. L.
1978-01-01
The observation is discussed of a train of hydromagnetic waves with a period of about 150 sec seen at synchronous orbit by the ATS 6 spacecraft on June 27, 1974. The critical observation is a phase shift of 90 deg between east-west oscillations of the particle flow and the east-west component of magnetic field oscillations. This phase shift alone suggests a standing rather than a propagating hydromagnetic wave. Careful processing of the particle data makes it possible to determine the drift velocity and hence the electric field of the wave. The wave electric field together with the time-varying magnetic field reveals an oscillating Poynting vector with zero mean component aligned with the ambient magnetic field and nonzero azimuthal (westward) component.
Solitary Wave Solutions of the Boussinesq Equation and Its Improved Form
Directory of Open Access Journals (Sweden)
Reza Abazari
2013-01-01
Full Text Available This paper presents the general case study of previous works on generalized Boussinesq equations, (Abazari, 2011 and (Kılıcman and Abazari, 2012, that focuses on the application of G′/G-expansion method with the aid of Maple to construct more general exact solutions for the coupled Boussinesq equations. In this work, the mentioned method is applied to construct more general exact solutions of Boussinesq equation and improved Boussinesq equation, which the French scientist Joseph Valentin Boussinesq (1842–1929 described in the 1870s model equations for the propagation of long waves on the surface of water with small amplitude. Our work is motivated by the fact that the G′/G-expansion method provides not only more general forms of solutions but also periodic, solitary waves and rational solutions. The method appears to be easier and faster by means of a symbolic computation.
Galilean exotic planar supersymmetries and nonrelativistic supersymmetric wave equations
Energy Technology Data Exchange (ETDEWEB)
Lukierski, J. [Institute for Theoretical Physics, University of Wroclaw, pl. Maxa Borna 9, 50-205 Wroclaw (Poland)]. E-mail: lukier@ift.uni.wroc.pl; Prochnicka, I. [Institute for Theoretical Physics, University of Wroclaw, pl. Maxa Borna 9, 50-205 Wroclaw (Poland)]. E-mail: ipro@ift.uni.wroc.pl; Stichel, P.C. [An der Krebskuhle 21, D-33619 Bielefeld (Germany)]. E-mail: peter@physik.uni-bielefeld.de; Zakrzewski, W.J. [Department of Mathematical Sciences, University of Durham, Durham DH1 3LE (United Kingdom)]. E-mail: w.j.zakrzewski@durham.ac.uk
2006-08-10
We describe the general class of N-extended D=(2+1) Galilean supersymmetries obtained, respectively, from the N-extended D=3 Poincare superalgebras with maximal sets of central charges. We confirm the consistency of supersymmetry with the presenc the 'exotic' second central charge {theta}. We show further how to introduce a N=2 Galilean superfield equation describing nonrelativistic spin 0 and spin 12 free particles.
In Vivo High Frame Rate Vector Flow Imaging Using Plane Waves and Directional Beamforming
DEFF Research Database (Denmark)
Jensen, Jonas; Villagómez Hoyos, Carlos Armando; Stuart, Matthias Bo
2016-01-01
oscillation (TO) estimators and only 3 directional beamformed lines. The suggested DB vector flow estimator is employed with steered plane wave transmissions for high frame rate imaging.Two distinct plane wave sequences are used: a short sequence(3 angles) for fast flow and an interleaved long sequence (21....... The long sequence has a higher sensitivity, and when used forestimation of slow flow with a peak velocity of 0.04 m/s, the SDis 2.5 % and bias is 0.1 %. This is a factor of 4 better than ifthe short sequence is used. The carotid bifurcation was scanned on a healthy volunteer, and the short sequence...
High Frame Rate Vector Velocity Estimation using Plane Waves and Transverse Oscillation
DEFF Research Database (Denmark)
Jensen, Jonas; Stuart, Matthias Bo; Jensen, Jørgen Arendt
2015-01-01
is obtained by filtering the beamformed RF images in the Fourier domain using a Gaussian filter centered at a desired oscillation frequency. Performance of the method is quantified through measurements with the experimental scanner SARUS and the BK 2L8 linear array transducer. Constant parabolic flow......This paper presents a method for estimating 2-D vector velocities using plane waves and transverse oscillation. The approach uses emission of a low number of steered plane waves, which result in a high frame rate and continuous acquisition of data for the whole image. A transverse oscillating field...
Hu, Wenjing
2017-08-01
This paper uses Fourier’s triple integral transform method to simplify the calculation of the non-homogeneous wave equations of the time-varying electromagnetic field. By adding several special definite conditions to the wave equation, it becomes a mathematical problem of definite condition. Then by using Fourier’s triple integral transform method, this three-dimension non-homogeneous partial differential wave equation is changed into an ordinary differential equation. Through the solution to this ordinary differential equation, the expression of the relationship between the time-varying scalar potential and electromagnetic wave excitation source is developed precisely. This method simplifies the solving process effectively.
Coupled equations of electromagnetic waves in nonlinear metamaterial waveguides.
Azari, Mina; Hatami, Mohsen; Meygoli, Vahid; Yousefi, Elham
2016-11-01
Over the past decades, scientists have presented ways to manipulate the macroscopic properties of a material at levels unachieved before, and called them metamaterials. This research can be considered an important step forward in electromagnetics and optics. In this study, higher-order nonlinear coupled equations in a special kind of metamaterial waveguides (a planar waveguide with metamaterial core) will be derived from both electric and magnetic components of the transverse electric mode of electromagnetic pulse propagation. On the other hand, achieving the refractive index in this research is worthwhile. It is also shown that the coupled equations are not symmetric with respect to the electric and magnetic fields, unlike these kinds of equations in fiber optics and dielectric waveguides. Simulations on the propagation of a fundamental soliton pulse in a nonlinear metamaterial waveguide near the resonance frequency (a little lower than the magnetic resonant frequency) are performed to study its behavior. These pulses are recommended to practice in optical communications in controlled switching by external voltage, even in low power.
Orbital stability of periodic traveling-wave solutions for the log-KdV equation
Natali, Fábio; Pastor, Ademir; Cristófani, Fabrício
2017-09-01
In this paper we establish the orbital stability of periodic waves related to the logarithmic Korteweg-de Vries equation. Our motivation is inspired in the recent work [3], in which the authors established the well-posedness and the linear stability of Gaussian solitary waves. By using the approach put forward recently in [20] to construct a smooth branch of periodic waves as well as to get the spectral properties of the associated linearized operator, we apply the abstract theories in [13] and [25] to deduce the orbital stability of the periodic traveling waves in the energy space.
Wave-vector dependence of spin and density multipole excitations in quantum dots
Barranco, Manuel; Colletti, Leonardo; Lipparini, Enrico; Emperador, Agustí; Pi, Martí; Serra, Llorenç
2000-03-01
We have employed time-dependent local-spin density-functional theory to analyze the multipole spin and charge density excitations in GaAs-AlxGa1-xAs quantum dots. The on-plane transferred momentum degree of freedom has been taken into account, and the wave-vector dependence of the excitations is discussed. In agreement with previous experiments, we have found that the energies of these modes do not depend on the transferred wave vector, although their intensities do. Comparison with a recent resonant Raman scattering experiment [C. Schüller et al., Phys. Rev. Lett. 80, 2673 (1998)] is made. This allows us to identify the angular momentum of several of the observed modes as well as to reproduce their energies.
Development of a standing wave apparatus for calibrating acoustic vector sensors and hydrophones.
Lenhart, Richard D; Sagers, Jason D; Wilson, Preston S
2016-01-01
An apparatus was developed to calibrate acoustic hydrophones and vector sensors between 25 and 2000 Hz. A standing wave field is established inside a vertically oriented, water-filled, elastic-walled waveguide by a piston velocity source at the bottom and a pressure-release boundary condition at the air/water interface. A computer-controlled linear positioning system allows a device under test to be precisely located in the water column while the acoustic response is measured. Some of the challenges of calibrating hydrophones and vector sensors in such an apparatus are discussed, including designing the waveguide to mitigate dispersion, understanding the impact of waveguide structural resonances on the acoustic field, and developing algorithms to post-process calibration measurement data performed in a standing wave field. Data from waveguide characterization experiments and calibration measurements are presented and calibration uncertainty is reported.
Exact Travelling Wave Solutions of two Important Nonlinear Partial Differential Equations
Kim, Hyunsoo; Bae, Jae-Hyeong; Sakthivel, Rathinasamy
2014-04-01
Coupled nonlinear partial differential equations describing the spatio-temporal dynamics of predator-prey systems and nonlinear telegraph equations have been widely applied in many real world problems. So, finding exact solutions of such equations is very helpful in the theories and numerical studies. In this paper, the Kudryashov method is implemented to obtain exact travelling wave solutions of such physical models. Further, graphic illustrations in two and three dimensional plots of some of the obtained solutions are also given to predict their behaviour. The results reveal that the Kudryashov method is very simple, reliable, and effective, and can be used for finding exact solution of many other nonlinear evolution equations.
Energy Technology Data Exchange (ETDEWEB)
Watanabe, T.; Sassa, K. [Kyoto University, Kyoto (Japan); Uesaka, S. [Kyoto University, Kyoto (Japan). Faculty of Engineering
1996-10-01
The effect of initial models on full-wave inversion (FWI) analysis based on acoustic wave-equation was studied for elastic wave tomography of underground structures. At present, travel time inversion using initial motion travel time is generally used, and inverse analysis is conducted using the concept `ray,` assuming very high wave frequency. Although this method can derive stable solutions relatively unaffected by initial model, it uses only the data of initial motion travel time. FWI calculates theoretical waveform at each receiver using all of observed waveforms as data by wave equation modeling where 2-D underground structure is calculated by difference calculus under the assumption that wave propagation is described by wave equation of P wave. Although it is a weak point that FWI is easily affected by noises in an initial model and data, it is featured by high resolution of solutions. This method offers very excellent convergence as a proper initial model is used, resulting in sufficient performance, however, it is strongly affected by initial model. 2 refs., 7 figs., 1 tab.
Contributions in anomalous fermion momenta of neutral vector boson in plane-wave field
Klimenko, E Y
2002-01-01
The contributions of the neutral vector boson to the anomalous magnetic and electric momenta of the polarized fermion moving in the plane-wave electromagnetic field are considered in this paper. The contributions are divided by the fermion spin polarization states, which makes it possible to investigate the important problem on the contributions to the fermion anomalous momenta, coming from the the fermion transition to the intermediate state spin-nonflip or spin flip of fermion
Scattering from cylinders using the two-dimensional vector plane wave spectrum: addendum.
Pawliuk, Peter; Yedlin, Matthew
2012-03-01
The solution for the vector plane wave spectrum scattering from multiple cylinders by Pawliuk and Yedlin [J. Opt. Soc. A28, 1177 (2011)] only provided the single scattering coefficients for the TM polarization case. The TE solution is similar except for the form of the single scattering coefficients. Here we describe the single scattering coefficients for both polarizations and three types of cylinders: dielectrics, perfect electric conductors, and perfect magnetic conductors.
Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity
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Claudio Cremaschini
2017-07-01
Full Text Available Key aspects of the manifestly-covariant theory of quantum gravity (Cremaschini and Tessarotto 2015–2017 are investigated. These refer, first, to the establishment of the four-scalar, manifestly-covariant evolution quantum wave equation, denoted as covariant quantum gravity (CQG wave equation, which advances the quantum state ψ associated with a prescribed background space-time. In this paper, the CQG-wave equation is proved to follow at once by means of a Hamilton–Jacobi quantization of the classical variational tensor field g ≡ g μ ν and its conjugate momentum, referred to as (canonical g-quantization. The same equation is also shown to be variational and to follow from a synchronous variational principle identified here with the quantum Hamilton variational principle. The corresponding quantum hydrodynamic equations are then obtained upon introducing the Madelung representation for ψ , which provides an equivalent statistical interpretation of the CQG-wave equation. Finally, the quantum state ψ is proven to fulfill generalized Heisenberg inequalities, relating the statistical measurement errors of quantum observables. These are shown to be represented in terms of the standard deviations of the metric tensor g ≡ g μ ν and its quantum conjugate momentum operator.
Spectral power density of the random excitation for the photoacoustic wave equation
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Hakan Erkol
2014-09-01
Full Text Available The superposition of the Green's function and its time reversal can be extracted from the photoacoustic point sources applying the representation theorems of the convolution and correlation type. It is shown that photoacoustic pressure waves at locations of random point sources can be calculated with the solution of the photoacoustic wave equation and utilization of the continuity and the discontinuity conditions of the pressure waves in the frequency domain although the pressure waves cannot be measured at these locations directly. Therefore, with the calculated pressure waves at the positions of the sources, the spectral power density can be obtained for any system consisting of two random point sources. The methodology presented here can also be generalized to any finite number of point like sources. The physical application of this study includes the utilization of the cross-correlation of photoacoustic waves to extract functional information associated with the flow dynamics inside the tissue.
Visco-acoustic wave-equation traveltime inversion and its sensitivity to attenuation errors
Yu, Han
2018-02-23
A visco-acoustic wave-equation traveltime inversion method is presented that inverts for the shallow subsurface velocity distribution. Similar to the classical wave equation traveltime inversion, this method finds the velocity model that minimizes the squared sum of the traveltime residuals. Even though, wave-equation traveltime inversion can partly avoid the cycle skipping problem, a good initial velocity model is required for the inversion to converge to a reasonable tomogram with different attenuation profiles. When Q model is far away from the real model, the final tomogram is very sensitive to the starting velocity model. Nevertheless, a minor or moderate perturbation of the Q model from the true one does not strongly affect the inversion if the low wavenumber information of the initial velocity model is mostly correct. These claims are validated with numerical tests on both the synthetic and field data sets.
On radiating solitary waves in bi-layers with delamination and coupled Ostrovsky equations.
Khusnutdinova, K R; Tranter, M R
2017-01-01
We study the scattering of a long longitudinal radiating bulk strain solitary wave in the delaminated area of a two-layered elastic structure with soft ("imperfect") bonding between the layers within the scope of the coupled Boussinesq equations. The direct numerical modelling of this and similar problems is challenging and has natural limitations. We develop a semi-analytical approach, based on the use of several matched asymptotic multiple-scale expansions and averaging with respect to the fast space variable, leading to the coupled Ostrovsky equations in bonded regions and uncoupled Korteweg-de Vries equations in the delaminated region. We show that the semi-analytical approach agrees well with direct numerical simulations and use it to study the nonlinear dynamics and scattering of the radiating solitary wave in a wide range of bi-layers with delamination. The results indicate that radiating solitary waves could help us to control the integrity of layered structures with imperfect interfaces.
Theory of a ring laser. [electromagnetic field and wave equations
Menegozzi, L. N.; Lamb, W. E., Jr.
1973-01-01
Development of a systematic formulation of the theory of a ring laser which is based on first principles and uses a well-known model for laser operation. A simple physical derivation of the electromagnetic field equations for a noninertial reference frame in uniform rotation is presented, and an attempt is made to clarify the nature of the Fox-Li modes for an open polygonal resonator. The polarization of the active medium is obtained by using a Fourier-series method which permits the formulation of a strong-signal theory, and solutions are given in terms of continued fractions. It is shown that when such a continued fraction is expanded to third order in the fields, the familiar small-signal ring-laser theory is obtained.
Traveling Waves for Nonlinear Schrödinger Equations with Nonzero Conditions at Infinity
Chiron, David; Mariş, Mihai
2017-10-01
We prove the existence of nontrivial finite energy traveling waves for a large class of nonlinear Schrödinger equations with nonzero conditions at infinity (includindg the Gross-Pitaevskii and the so-called "cubic-quintic" equations) in space dimension { N ≥ 2}. We show that minimization of the energy at fixed momentum can be used whenever the associated nonlinear potential is nonnegative and it gives a set of orbitally stable traveling waves, while minimization of the action at constant kinetic energy can be used in all cases. We also explore the relationship between the families of traveling waves obtained by different methods and we prove a sharp nonexistence result for traveling waves with small energy.
Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.
2018-01-01
High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw [1] how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemann problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. The upwind scheme is shown to be robust and provide high-order accuracy.
On the new soliton and optical wave structures to some nonlinear evolution equations
Bulut, Hasan; Sulaiman, Tukur Abdulkadir; Baskonus, Haci Mehmet
2017-11-01
In this study, with the aid of the Wolfram Mathematica software, the powerful sine-Gordon expansion method is utilized to search for the solutions to some important nonlinear mathematical models arising in nonlinear sciences, namely, the (2 + 1) -dimensional Zakharov-Kuznetsov modified equal width equation, the cubic Boussinesq equation and the modified regularized long wave equation. We successfully obtain some new soliton, singular soliton, singular periodic waves and kink-type solutions with complex hyperbolic structures to these equations. We also present the two- and three-dimensional shapes of all the solutions obtained in this study. We further give the physical meaning of all the obtained solutions. We compare our results with the existing results in the literature.
Shock formation in small-data solutions to 3D quasilinear wave equations
Speck, Jared
2016-01-01
In 1848 James Challis showed that smooth solutions to the compressible Euler equations can become multivalued, thus signifying the onset of a shock singularity. Today it is known that, for many hyperbolic systems, such singularities often develop. However, most shock-formation results have been proved only in one spatial dimension. Serge Alinhac's groundbreaking work on wave equations in the late 1990s was the first to treat more than one spatial dimension. In 2007, for the compressible Euler equations in vorticity-free regions, Demetrios Christodoulou remarkably sharpened Alinhac's results and gave a complete description of shock formation. In this monograph, Christodoulou's framework is extended to two classes of wave equations in three spatial dimensions. It is shown that if the nonlinear terms fail to satisfy the null condition, then for small data, shocks are the only possible singularities that can develop. Moreover, the author exhibits an open set of small data whose solutions form a shock, and he prov...
Hydromagnetic waves in a compressed-dipole field via field-aligned Klein–Gordon equations
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J. Zheng
2016-05-01
Full Text Available Hydromagnetic waves, especially those of frequencies in the range of a few millihertz to a few hertz observed in the Earth's magnetosphere, are categorized as ultra low-frequency (ULF waves or pulsations. They have been extensively studied due to their importance in the interaction with radiation belt particles and in probing the structures of the magnetosphere. We developed an approach to examining the toroidal standing Aflvén waves in a background magnetic field by recasting the wave equation into a Klein–Gordon (KG form along individual field lines. The eigenvalue solutions to the system are characteristic of a propagation type when the corresponding eigenfrequency is greater than a critical frequency and a decaying type otherwise. We apply the approach to a compressed-dipole magnetic field model of the inner magnetosphere and obtain the spatial profiles of relevant parameters and the spatial wave forms of harmonic oscillations. We further extend the approach to poloidal-mode standing Alfvén waves along field lines. In particular, we present a quantitative comparison with a recent spacecraft observation of a poloidal standing Alfvén wave in the Earth's magnetosphere. Our analysis based on the KG equation yields consistent results which agree with the spacecraft measurements of the wave period and the amplitude ratio between the magnetic field and electric field perturbations.
Application of neural networks and support vector machine for significant wave height prediction
Directory of Open Access Journals (Sweden)
Jadran Berbić
2017-07-01
Full Text Available For the purposes of planning and operation of maritime activities, information about wave height dynamics is of great importance. In the paper, real-time prediction of significant wave heights for the following 0.5–5.5 h is provided, using information from 3 or more time points. In the first stage, predictions are made by varying the quantity of significant wave heights from previous time points and various ways of using data are discussed. Afterwards, in the best model, according to the criteria of practicality and accuracy, the influence of wind is taken into account. Predictions are made using two machine learning methods – artificial neural networks (ANN and support vector machine (SVM. The models were built using the built-in functions of software Weka, developed by Waikato University, New Zealand.
Directory of Open Access Journals (Sweden)
Victor Onomza WAZIRI
2006-07-01
Full Text Available The paper computes the optimal control and state of the two-dimensional Energized wave equation using the Extended Conjugate gradient Method (ECGM. This piece of work has to do with all the vital computational elements as derived in the implementation of the ECGM algorithm on the two-dimensional Energized Wave equation in (Waziri, 1 and (Waziri & Reju, LEJPT & LJS, Issues 9, 2006, [7-9]. With these recalls, program codes were derived which gave various numerical optimal controls and states. These optimal controls and states were considered at various points in a plane surface.
Exact solutions of time fractional heat-like and wave-like equations with variable coefficients
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Zhang Sheng
2016-01-01
Full Text Available In this paper, a variable-coefficient time fractional heat-like and wave-like equation with initial and boundary conditions is solved by the use of variable separation method and the properties of Mittag-Leffler function. As a result, exact solutions are obtained, from which some known special solutions are recovered. It is shown that the variable separation method can also be used to solve some others time fractional heat-like and wave-like equation in science and engineering.
Baumeiste, K. J.
1983-01-01
A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.
Baumeister, K. J.
1983-01-01
A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.
NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.
Liu, F; Meerschaert, M M; McGough, R J; Zhuang, P; Liu, Q
2013-03-01
In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.
Grosse, Ralf
1990-01-01
Propagation of sound through the turbulent atmosphere is a statistical problem. The randomness of the refractive index field causes sound pressure fluctuations. Although no general theory to predict sound pressure statistics from given refractive index statistics exists, there are several approximate solutions to the problem. The most common approximation is the parabolic equation method. Results obtained by this method are restricted to small refractive index fluctuations and to small wave lengths. While the first condition is generally met in the atmosphere, it is desirable to overcome the second. A generalization of the parabolic equation method with respect to the small wave length restriction is presented.
Three-dimensional wave-induced current model equations and radiation stresses
Xia, Hua-yong
2017-08-01
After the approach by Mellor (2003, 2008), the present paper reports on a repeated effort to derive the equations for three-dimensional wave-induced current. Via the vertical momentum equation and a proper coordinate transformation, the phase-averaged wave dynamic pressure is well treated, and a continuous and depth-dependent radiation stress tensor, rather than the controversial delta Dirac function at the surface shown in Mellor (2008), is provided. Besides, a phase-averaged vertical momentum flux over a sloping bottom is introduced. All the inconsistencies in Mellor (2003, 2008), pointed out by Ardhuin et al. (2008) and Bennis and Ardhuin (2011), are overcome in the presently revised equations. In a test case with a sloping sea bed, as shown in Ardhuin et al. (2008), the wave-driving forces derived in the present equations are in good balance, and no spurious vertical circulation occurs outside the surf zone, indicating that Airy's wave theory and the approach of Mellor (2003, 2008) are applicable for the derivation of the wave-induced current model.
Tchinang Tchameu, J. D.; Togueu Motcheyo, A. B.; Tchawoua, C.
2016-09-01
The discrete multi-rogue waves (DMRW) as solution of the discrete nonlinear Schrödinger (DNLS) equation with saturable nonlinearities is studied numerically. These biological rogue waves represent the complex probability amplitude of finding an amide-I vibrational quantum at a site. We observe that the growth in the higher order saturable nonlinearity implies the formation of DMRW including an increase in the short-living DMRW and a decrease in amplitude of the long-living DMRW.
Water Wave Solutions of the Coupled System Zakharov-Kuznetsov and Generalized Coupled KdV Equations
Seadawy, A. R.; El-Rashidy, K.
2014-01-01
An analytic study was conducted on coupled partial differential equations. We formally derived new solitary wave solutions of generalized coupled system of Zakharov-Kuznetsov (ZK) and KdV equations by using modified extended tanh method. The traveling wave solutions for each generalized coupled system of ZK and KdV equations are shown in form of periodic, dark, and bright solitary wave solutions. The structures of the obtained solutions are distinct and stable. PMID:25374940
Some Wave Simulation Properties of the (2+1 Dimensional Breaking Soliton Equation
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Aksan Emine Nesligül
2017-01-01
Full Text Available In this paper, we apply an efficient method which is improved Bernoulli sub-equation function method (IBSEFM to (2+1 dimensional Breaking Soliton equation. It gives some new wave simulations like complex and exponential structures. We test whether all structures verify the (2+1 dimensional Breaking Soliton model. Then, we draw three and two dimensional plane by using Wolfram Mathematica 9.
A memory type boundary stabilization of a mildly damped wave equation
Directory of Open Access Journals (Sweden)
Mokhtar Kirane
1999-01-01
Full Text Available We consider the wave equation with a mild internal dissipation. It is proved that any small dissipation inside the domain is sufficient to uniformly stabilize the solution of this equation by means of a nonlinear feedback of memory type acting on a part of the boundary. This is established without any restriction on the space dimension and without geometrical conditions on the domain or its boundary.
Mixing and large deviations for nonlinear wave equation with white noise
Martirosyan, Davit
2015-01-01
This thesis is devoted to the study of ergodicity and large deviations for the stochastic nonlinear wave (NLW) equation with smooth white noise in 3D. Under some standard growth and dissipativity assumptions on the nonlinearity, we show that the Markov process associated with the flow of NLW equation has a unique stationary measure that attracts the law of any solution with exponential rate. This result implies, in particular, the strong law of large numbers as well as the central limit theor...
Al Ali, Usamah S.; Bokhari, Ashfaque H.; Kara, A. H.; Zaman, F. D.
Nonlinear evolution equations represent some of the most fundamental processes in both physics as well engineering. Considering this, we analyze and classify the three dimensional wave equation with a power law nonlinearity in presence of damping and external force terms. In view of the significance of conservation laws in physics, a study of the invariance properties is presented and conservation laws are constructed and classified. An illustrative case of a symmetry reduction in one special case is presented.
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Nilesh P. BARDE
2015-05-01
Full Text Available The concept of time dependent Schrödinger equation (TDSE illustrated in literature and even during class room teaching is mostly either complex or meant for advanced learners. This article is intended to enlighten the concept to the beginners in the field and further to improve knowledge about detailed steps for abstract mathematical formulation used which helps in understanding to derive TDSE using various tools and in more comprehensible manner. It is shown that TDSE may be derived using wave mechanics, time independent equation, classical & Hamilton-Jacobi’s equations. Similar attempts have been done earlier by some researchers. However, this article provides a comprehensive, lucid and well derived derivation, derived using various approaches, which would make this article unique.
Multi-wave solutions of the space–time fractional Burgers and Sharma–Tasso–Olver equations
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Emad A.-B. Abdel-Salam
2016-03-01
Full Text Available Based on the improved generalized exp-function method, the space–time fractional Burgers and Sharma–Tasso–Olver equations were studied. The single-wave, double-wave, three-wave and four-wave solution discussed. With the best of our knowledge, some of the results are obtained for the first time. The improved generalized exp-function method can be applied to other fractional differential equations.
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.
Ayub, Kamran; Khan, M. Yaqub; Mahmood-Ul-Hassan, Qazi; Ahmad, Jamshad
2017-09-01
Nonlinear mathematical problems and their solutions attain much attention in solitary waves. In soliton theory, an efficient tool to attain various types of soliton solutions is the \\exp (-φ (ζ ))-expansion technique. This article is devoted to find exact travelling wave solutions of Drinfeld-Sokolov equation via a reliable mathematical technique. By using the proposed technique, we attain soliton wave solution of various types. It is observed that the technique under discussion is user friendly with minimum computational work, and can be extended for physical problems of different nature in mathematical physics.
Unified Theory of Wave-Particle Duality and the Schr\\"odinger Equations
Gilson, Greyson
2011-01-01
Individual quantum objects display coexisting wave properties and particle properties. A wave is ordinarily associated with spatial extension while a particle is ordinarily associated with a point-like locality. Coexistence of spatial extension and a point-like locality as properties of a single entity seems paradoxical. The apparent paradox is resolved by the unified theory of wave-particle duality developed in this paper. Using this theory, a straightforward derivation of the Schr\\"odinger equations (time-independent and time-dependent) is presented where previously no such derivation was considered to be possible.
DEFF Research Database (Denmark)
Beels, Charlotte; Troch, Peter; Visch, Kenneth De
2010-01-01
Time-dependent mild-slope equations have been extensively used to compute wave transformations near coastal and offshore structures for more than 20 years. Recently the wave absorption characteristics of a Wave Energy Converter (abbreviated as WEC) of the overtopping type have been implemented...... in a time-dependent mild-slope equation model by using numerical sponge layers. In this paper the developed WEC implementation is applied to a single Wave Dragon WEC and multiple Wave Dragon WECs. The Wave Dragon WEC is a floating offshore converter of the overtopping type. Two wave reflectors focus...... the incident wave power towards a ramp. The focussed waves run up the ramp and overtop in a water reservoir above mean sea level. The obtained potential energy is converted into electricity when the stored water drains back to the sea through hydro turbines. The wave reflectors and the main body (ramp...
Wang, Yang; Brennan, Kevin F.
1994-01-01
We present calculations of the interband impact ionization rate calculated using a wave vector dependent (k-dependent) semiclassical formulation of the transition rate. The transition rate is determined using Fermi's golden rule from a two-body screened Coulomb interaction assuming energy and momentum conservation. The transition rate is calculated for the first two conduction bands of silicon by numerically integrating over the full Brillouin zone. The overlap integrals in the expression for the transition rate are determined numerically using a 15 band k-p calculation. It is found that the transition rate depends strongly on the initiating electron wave vector (k vector) and that the transition rate is greatest for electrons originating within the second conduction band than the first conduction band. An ensemble Monte Carlo simulation, which includes the numerically determined ionization transition rate as well as the full details of the first two conduction bands, is used to calculate the total impact ionization rate in bulk silicon. Good agreement with the experimentally determined electron ionization rate data is obtained.
Measuring curvature and velocity vector fields for waves of cardiac excitation in 2-D media.
Kay, Matthew W; Gray, Richard A
2005-01-01
Excitable media theory predicts the effect of electrical wavefront morphology on the dynamics of propagation in cardiac tissue. It specifies that a convex wavefront propagates slower and a concave wavefront propagates faster than a planar wavefront. Because of this, wavefront curvature is thought to be an important functional mechanism of cardiac arrhythmias. However, the curvature of wavefronts during an arrhythmia are generally unknown. We introduce a robust, automated method to measure the curvature vector field of discretely characterized, arbitrarily shaped, two-dimensional (2-D) wavefronts. The method relies on generating a smooth, continuous parameterization of the shape of a wave using cubic smoothing splines fitted to an isopotential at a specified level, which we choose to be -30 mV. Twice differentiating the parametric form provides local curvature vectors along the wavefront and waveback. Local conduction velocities are computed as the wave speed along lines normal to the parametric form. In this way, the curvature and velocity vector field for wavefronts and wavebacks can be measured. We applied the method to data sampled from a 2-D numerical model and several examples are provided to illustrate its usefulness for studying the dynamics of cardiac propagation in 2-D media.
Ermstål, Johan
2012-01-01
Two nonlinear dispersive wave equations arising in elasto-plastic flow have been investigated for self-adjointness. For these equations their symmetries are calculated and conservation laws are constructed using two different methods: an old method based on Noether´s Theorem and a new one developed by Prof. Nail Ibragimov. The new method works for a larger number of equations than the old one. It is complementing the old one in the way that it gives some conservation laws that otherwise would...
Modified wave operators for nonlinear Schrodinger equations in one and two dimensions
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Nakao Hayashi
2004-04-01
Full Text Available We study the asymptotic behavior of solutions, in particular the scattering theory, for the nonlinear Schr"{o}dinger equations with cubic and quadratic nonlinearities in one or two space dimensions. The nonlinearities are summation of gauge invariant term and non-gauge invariant terms. The scattering problem of these equations belongs to the long range case. We prove the existence of the modified wave operators to those equations for small final data. Our result is an improvement of the previous work [13
High-order rogue wave solutions of the classical massive Thirring model equations
Guo, Lijuan; Wang, Lihong; Cheng, Yi; He, Jingsong
2017-11-01
The nth-order solutions of the classical massive Thirring model (MTM) equations are derived by using the n-fold Darboux transformation. These solutions are expressed by the ratios of the two determinants consisted of 2n eigenfunctions under the reduction conditions. Using this method, rogue waves are constructed explicitly up to the third-order. Three patterns, i.e., fundamental, triangular and circular patterns, of the rogue waves are discussed. The parameter μ in the MTM model plays the role of the mass in the relativistic field theory while in optics it is related to the medium periodic constant, which also results in a significant rotation and a remarkable lengthening of the first-order rogue wave. These results provide new opportunities to observe rouge waves by using a combination of electromagnetically induced transparency and the Bragg scattering four-wave mixing because of large amplitudes.
Ding, Yi S; He, Yang
2017-08-21
An isotropic impedance sheet model is proposed for a loop-type hexagonal periodic metasurface. Both frequency and wave-vector dispersion are considered near the resonance frequency. Therefore both the angle and polarization dependences of the metasurface impedance can be properly and simultaneously described in our model. The constitutive relation of this model is transformed into auxiliary differential equations which are integrated into the finite-difference time-domain algorithm. Finally, a finite large metasurface sample under oblique illumination is used to test the model and the algorithm. Our model and algorithm can significantly increase the accuracy of the homogenization methods for modeling periodic metasurfaces.
Alfonso, S; Alberdi, C; Diñeiro, J M; Berrogui, M; Hernández, B; Sáenz, C
2004-09-01
We introduce a formalism based on complex unitary vectors for the direction of propagation and for the polarization in order to describe in detail the propagation of inhomogeneous plane waves in absorbing isotropic media. We obtain analytic expressions for the displacement vector, the electric field, the magnetic field, and the Poynting vector, and we study their geometry in terms of the geometrical interpretation of the complex directions of propagation inside the material. We introduce a complex coordinate system based on complex unitary vectors, where the description of the polarization states of the field vectors and the Poynting vector becomes simpler. The physical meaning and the interpretation of the mathematical operations involving these complex unitary vectors is provided.
Chin-Joe-Kong, M.J.S.; Mulder, W.A.; van Veldhuizen, M.
1999-01-01
The higher-order finite-element scheme with mass lumping for triangles and tetrahedra is an efficient method for solving the wave equation. A number of lower-order elements have already been found. Here the search for elements of higher order is continued. Elements are constructed in a systematic
Global existence of solutions for semilinear damped wave equation in 2-D exterior domain
Ikehata, Ryo
We consider a mixed problem of a damped wave equation utt-Δ u+ ut=| u| p in the two dimensional exterior domain case. Small global in time solutions can be constructed in the case when the power p on the nonlinear term | u| p satisfies p ∗=2Japon. 55 (2002) 33) plays an effective role.
Non-monotonic Travelling Wave Fronts in a System of Fractional Flow Equations from Porous Media
Zegeling, P.A.; Hönig, O.; Doster, F.; Hilfer, R.
2016-01-01
Motivated by observations of saturation overshoot, this article investigates generic classes of smooth travelling wave solutions of a system of two coupled nonlinear parabolic partial differential equations resulting from a flux function of high symmetry. All boundary resp. limit value problems of
On spurious reflections, nonuniform grids and finite difference discretizations of wave equations
J.E. Frank (Jason); S. Reich
2004-01-01
textabstractThis paper addresses nonphysical reflections encountered in the discretization of wave equations on nonuniform grids. Such nonphysical solutions are commonly attributed to spurious modes in the numerical dispersion relation. We provide an example of a discretization in which a
Decay estimates for fractional wave equations on H-type groups
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Manli Song
2016-10-01
Full Text Available Abstract The aim of this paper is to establish the decay estimate for the fractional wave equation semigroup on H-type groups given by e i t Δ α $e^{it\\Delta^{\\alpha}}$ , 0 < α < 1 $0<\\alpha<1$ . Combining the dispersive estimate and a standard duality argument, we also derive the corresponding Strichartz inequalities.
Magnetic virial identities and applications to blow-up for Schroedinger and wave equations
Energy Technology Data Exchange (ETDEWEB)
Garcia, Andoni, E-mail: andoni.garcia@ehu.es [Departamento de Matematicas, Universidad del Pais Vasco, Apartado 644, 48080 Bilbao (Spain)
2012-01-13
We prove blow-up results for the solution of the initial-value problem with negative energy of the focusing mass-critical and supercritical nonlinear Schroedinger and the focusing energy-subcritical nonlinear wave equations with electromagnetic potential. (paper)
Blow-Up of Solutions for a Class of Sixth Order Nonlinear Strongly Damped Wave Equation
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Huafei Di
2014-01-01
Full Text Available We consider the blow-up phenomenon of sixth order nonlinear strongly damped wave equation. By using the concavity method, we prove a finite time blow-up result under assumptions on the nonlinear term and the initial data.
van Oers, A.M.; Maas, L.R.M.; Bokhove, O.
2017-01-01
The linear equations governing internal gravity waves in a stratified ideal fluid possess a Hamiltonian structure. A discontinuous Galerkin finite element method has been developed in which this Hamiltonian structure is discretized, resulting in conservation of discrete analogs of phase space and
Newton's method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion.
Leszczynski, Henryk; Wrzosek, Monika
2017-02-01
We consider nonlinear stochastic wave equations driven by one-dimensional white noise with respect to time. The existence of solutions is proved by means of Picard iterations. Next we apply Newton's method. Moreover, a second-order convergence in a probabilistic sense is demonstrated.
Coarse-Graining Can Beat the Rotating Wave Approximation in Quantum Markovian Master Equations
DEFF Research Database (Denmark)
Majenz, Christian; Albash, Tameem; Breuer, Heinz-Peter
2013-01-01
We present a first-principles derivation of the Markovian semi-group master equation without invoking the rotating wave approximation (RWA). Instead we use a time coarse-graining approach which leaves us with a free timescale parameter, which we can optimize. Comparing this approach to the standard...
Traveling wave solutions of the nonlinear Schrödinger equation
Akbari-Moghanjoughi, M.
2017-10-01
In this paper, we investigate the traveling soliton and the periodic wave solutions of the nonlinear Schrödinger equation (NLSE) with generalized nonlinear functionality. We also explore the underlying close connection between the well-known KdV equation and the NLSE. It is remarked that both one-dimensional KdV and NLSE models share the same pseudoenergy spectrum. We also derive the traveling wave solutions for two cases of weakly nonlinear mathematical models, namely, the Helmholtz and the Duffing oscillators' potentials. It is found that these models only allow gray-type NLSE solitary propagations. It is also found that the pseudofrequency ratio for the Helmholtz potential between the nonlinear periodic carrier and the modulated sinusoidal waves is always in the range 0.5 ≤ Ω/ω ≤ 0.537285 regardless of the potential parameter values. The values of Ω/ω = {0.5, 0.537285} correspond to the cnoidal waves modulus of m = {0, 1} for soliton and sinusoidal limits and m = 0.5, respectively. Moreover, the current NLSE model is extended to fully NLSE (FNLSE) situation for Sagdeev oscillator pseudopotential which can be derived using a closed set of hydrodynamic fluid equations with a fully integrable Hamiltonian system. The generalized quasi-three-dimensional traveling wave solution is also derived. The current simple hydrodynamic plasma model may also be generalized to two dimensions and other complex situations including different charged species and cases with magnetic or gravitational field effects.
Anomalous wave structure in magnetized materials described by non-convex equations of state
Energy Technology Data Exchange (ETDEWEB)
Serna, Susana, E-mail: serna@mat.uab.es [Departament de Matematiques, Universitat Autonoma de Barcelona, 08193 Bellaterra, Barcelona (Spain); Marquina, Antonio, E-mail: marquina@uv.es [Departamento de Matematicas, Universidad de Valencia, 46100 Burjassot, Valencia (Spain)
2014-01-15
We analyze the anomalous wave structure appearing in flow dynamics under the influence of magnetic field in materials described by non-ideal equations of state. We consider the system of magnetohydrodynamics equations closed by a general equation of state (EOS) and propose a complete spectral decomposition of the fluxes that allows us to derive an expression of the nonlinearity factor as the mathematical tool to determine the nature of the wave phenomena. We prove that the possible formation of non-classical wave structure is determined by both the thermodynamic properties of the material and the magnetic field as well as its possible rotation. We demonstrate that phase transitions induced by material properties do not necessarily imply the loss of genuine nonlinearity of the wavefields as is the case in classical hydrodynamics. The analytical expression of the nonlinearity factor allows us to determine the specific amount of magnetic field necessary to prevent formation of complex structure induced by phase transition in the material. We illustrate our analytical approach by considering two non-convex EOS that exhibit phase transitions and anomalous behavior in the evolution. We present numerical experiments validating the analysis performed through a set of one-dimensional Riemann problems. In the examples we show how to determine the appropriate amount of magnetic field in the initial conditions of the Riemann problem to transform a thermodynamic composite wave into a simple nonlinear wave.
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.
An energy absorbing far-field boundary condition for the elastic wave equation
Energy Technology Data Exchange (ETDEWEB)
Petersson, N A; Sjogreen, B
2008-07-15
The authors present an energy absorbing non-reflecting boundary condition of Clayton-Engquist type for the elastic wave equation together with a discretization which is stable for any ratio of compressional to shear wave speed. They prove stability for a second order accurate finite-difference discretization of the elastic wave equation in three space dimensions together with a discretization of the proposed non-reflecting boundary condition. The stability proof is based on a discrete energy estimate and is valid for heterogeneous materials. The proof includes all six boundaries of the computational domain where special discretizations are needed at the edges and corners. The stability proof holds also when a free surface boundary condition is imposed on some sides of the computational domain.
DEFF Research Database (Denmark)
Mariegaard, Jesper Sandvig
We consider a control problem for the wave equation: Given the initial state, find a specific boundary condition, called a control, that steers the system to a desired final state. The Hilbert uniqueness method (HUM) is a mathematical method for the solution of such control problems. It builds....... As an example, we employ a HUM solution to an inverse source problem for the wave equation: Given boundary measurements for a wave problem with a separable source, find the spatial part of the source term. The reconstruction formula depends on a set of HUM eigenfunction controls; we suggest a discretization...... and show its convergence. We compare results obtained by L-FEM controls and DG-FEM controls. The reconstruction formula is seen to be quite sensitive to control inaccuracies which indeed favors DG-FEM over L-FEM....
A goal-oriented reduced basis method for the wave equation in inverse analysis
Hoang, Khac Chi; Bordas, Stephane P A
2013-01-01
In this paper, we extend the reduced-basis methods developed earlier for wave equations to goal-oriented wave equations with affine parameter dependence. The essential new ingredient is the dual (or adjoint) problem and the use of its solution in a sampling procedure to pick up "goal-orientedly" parameter samples. First, we introduce the reduced-basis recipe --- Galerkin projection onto a space $Y_N$ spanned by the reduced basis functions which are constructed from the solutions of the governing partial differential equation at several selected points in parameter space. Second, we propose a new "goal-oriented" Proper Orthogonal Decomposition (POD)--Greedy sampling procedure to construct these associated basis functions. Third, based on the assumption of affine parameter dependence, we use the offline-online computational procedures developed earlier to split the computational procedure into offline and online stages. We verify the proposed computational procedure by applying it to a three-dimensional simulat...
A space-time spectral collocation algorithm for the variable order fractional wave equation.
Bhrawy, A H; Doha, E H; Alzaidy, J F; Abdelkawy, M A
2016-01-01
The variable order wave equation plays a major role in acoustics, electromagnetics, and fluid dynamics. In this paper, we consider the space-time variable order fractional wave equation with variable coefficients. We propose an effective numerical method for solving the aforementioned problem in a bounded domain. The shifted Jacobi polynomials are used as basis functions, and the variable-order fractional derivative is described in the Caputo sense. The proposed method is a combination of shifted Jacobi-Gauss-Lobatto collocation scheme for the spatial discretization and the shifted Jacobi-Gauss-Radau collocation scheme for temporal discretization. The aforementioned problem is then reduced to a problem consists of a system of easily solvable algebraic equations. Finally, numerical examples are presented to show the effectiveness of the proposed numerical method.
Application of perturbation theory to a P-wave eikonal equation in orthorhombic media
Stovas, Alexey
2016-10-12
The P-wave eikonal equation for orthorhombic (ORT) anisotropic media is a highly nonlinear partial differential equation requiring the solution of a sixth-order polynomial to obtain traveltimes, resulting in complex and time-consuming numerical solutions. To alleviate this complexity, we approximate the solution of this equation by applying a multiparametric perturbation approach. We also investigated the sensitivity of traveltime surfaces inORT mediawith respect to three anelliptic parameters. As a result, a simple and accurate P-wave traveltime approximation valid for ORT media was derived. Two different possible anelliptic parameterizations were compared. One of the parameterizations includes anelliptic parameters defined at zero offset: η1, η2, and ηxy. Another parameterization includes anelliptic parameters defined for all symmetry planes: η1, η2, and η3. The azimuthal behavior of sensitivity coefficients with different parameterizations was used to analyze the crosstalk between anelliptic parameters. © 2016 Society of Exploration Geophysicists.
An Inverse Source Problem for a One-dimensional Wave Equation: An Observer-Based Approach
Asiri, Sharefa M.
2013-05-25
Observers are well known in the theory of dynamical systems. They are used to estimate the states of a system from some measurements. However, recently observers have also been developed to estimate some unknowns for systems governed by Partial differential equations. Our aim is to design an observer to solve inverse source problem for a one dimensional wave equation. Firstly, the problem is discretized in both space and time and then an adaptive observer based on partial field measurements (i.e measurements taken form the solution of the wave equation) is applied to estimate both the states and the source. We see the effectiveness of this observer in both noise-free and noisy cases. In each case, numerical simulations are provided to illustrate the effectiveness of this approach. Finally, we compare the performance of the observer approach with Tikhonov regularization approach.
Dissipation-preserving spectral element method for damped seismic wave equations
Cai, Wenjun; Zhang, Huai; Wang, Yushun
2017-12-01
This article describes the extension of the conformal symplectic method to solve the damped acoustic wave equation and the elastic wave equations in the framework of the spectral element method. The conformal symplectic method is a variation of conventional symplectic methods to treat non-conservative time evolution problems, which has superior behaviors in long-time stability and dissipation preservation. To reveal the intrinsic dissipative properties of the model equations, we first reformulate the original systems in their equivalent conformal multi-symplectic structures and derive the corresponding conformal symplectic conservation laws. We thereafter separate each system into a conservative Hamiltonian system and a purely dissipative ordinary differential equation system. Based on the splitting methodology, we solve the two subsystems respectively. The dissipative one is cheaply solved by its analytic solution. While for the conservative system, we combine a fourth-order symplectic Nyström method in time and the spectral element method in space to cover the circumstances in realistic geological structures involving complex free-surface topography. The Strang composition method is adopted thereby to concatenate the corresponding two parts of solutions and generate the completed conformal symplectic method. A relative larger Courant number than that of the traditional Newmark scheme is found in the numerical experiments in conjunction with a spatial sampling of approximately 5 points per wavelength. A benchmark test for the damped acoustic wave equation validates the effectiveness of our proposed method in precisely capturing dissipation rate. The classical Lamb problem is used to demonstrate the ability of modeling Rayleigh wave in elastic wave propagation. More comprehensive numerical experiments are presented to investigate the long-time simulation, low dispersion and energy conservation properties of the conformal symplectic methods in both the attenuating
Three-dimensional vector modeling and restoration of flat finite wave tank radiometric measurements
Truman, W. M.; Balanis, C. A.
1977-01-01
The three-dimensional vector interaction between a microwave radiometer and a wave tank was modeled. Computer programs for predicting the response of the radiometer to the brightness temperature characteristics of the surroundings were developed along with a computer program that can invert (restore) the radiometer measurements. It is shown that the computer programs can be used to simulate the viewing of large bodies of water, and is applicable to radiometer measurements received from satellites monitoring the ocean. The water temperature, salinity, and wind speed can be determined.
Acoustic wave and eikonal equations in a transformed metric space for various types of anisotropy.
Noack, Marcus M; Clark, Stuart
2017-03-01
Acoustic waves propagating in anisotropic media are important for various applications. Even though these wave phenomena do not generally occur in nature, they can be used to approximate wave motion in various physical settings. We propose a method to derive wave equations for anisotropic wave propagation by adjusting the dispersion relation according to a selected type of anisotropy and transforming it into another metric space. The proposed method allows for the derivation of acoustic wave and eikonal equations for various types of anisotropy, and generalizes anisotropy by interpreting it as a change of the metric instead of a change of velocity with direction. The presented method reduces the scope of acoustic anisotropy to a selection of a velocity or slowness surface and a tensor that describes the transformation into a new metric space. Experiments are shown for spatially dependent ellipsoidal anisotropy in homogeneous and inhomogeneous media and sandstone, which shows vertical transverse isotropy. The results demonstrate the stability and simplicity of the solution process for certain types of anisotropy and the equivalency of the solutions.
On the tunneling of full-vector X-Waves through a slab under frustrated total reflection condition
Salem, Mohamed
2012-07-01
Tunneling of full-vector X-Waves through a dielectric slab under frustrated total reflection condition is investigated. Full-vector X-Waves are obtained by superimposing transverse electric and magnetic polarization components, which are derived from the scalar X-Wave solution. The analysis of reflection and transmission at the dielectric interfaces is carried out analytically in a straightforward fashion using vector Bessel beam expansion. Investigation of the fields propagating away from the farther end of the slab (transmitted fields) shows an advanced (superluminal) transmission of the X-Wave peak. Additionally, a similar advanced reflection is also observed. The apparent tunneling of the peak is shown to be due to the phase shift in the fields\\' spectra and not to be causally related to the incident peak. © 2012 IEEE.
Optical image encoding based on digital holographic recording on polarization state of vector wave.
Lin, Chao; Shen, Xueju; Xu, Qinzu
2013-10-01
We propose and analyze a compact optical image encoder based on the principle of digital holographic recording on the polarization state of a vector wave. The optical architecture is a Mach-Zehnder interferometer with in-line digital holographic recording mechanism. The original image is represented by distinct polarization states of elliptically polarized light. This state of polarization distribution is scrambled and then recorded by a two-step digital polarization holography method with random phase distributed reference wave. Introduction of a rotation key in the object arm and phase keys in the reference arm can achieve the randomization of plaintext. Statistical property of cyphertext is analyzed from confusion and diffusion point of view. Fault tolerance and key sensitivity of the proposed approach are also investigated. A chosen plaintext attack on the proposed algorithm exhibits its high security level. Simulation results that support the theoretical analysis are presented.
Directory of Open Access Journals (Sweden)
Md. Nur Alam
2014-03-01
Full Text Available The new approach of generalized (G′/G-expansion method is significant, powerful and straightforward mathematical tool for finding exact traveling wave solutions of nonlinear evolution equations (NLEEs arise in the field of engineering, applied mathematics and physics. Dispersive effects due to microstructure of materials combined with nonlinearities give rise to solitary waves. In this article, the new approach of generalized (G′/G-expansion method has been applied to construct general traveling wave solutions of the strain wave equation in microstructured solids. Abundant exact traveling wave solutions including solitons, kink, periodic and rational solutions have been found. These solutions might play important role in engineering fields.
Galka, Andreas; Ozaki, Tohru; Muhle, Hiltrud; Stephani, Ulrich; Siniatchkin, Michael
2008-06-01
We discuss a model for the dynamics of the primary current density vector field within the grey matter of human brain. The model is based on a linear damped wave equation, driven by a stochastic term. By employing a realistically shaped average brain model and an estimate of the matrix which maps the primary currents distributed over grey matter to the electric potentials at the surface of the head, the model can be put into relation with recordings of the electroencephalogram (EEG). Through this step it becomes possible to employ EEG recordings for the purpose of estimating the primary current density vector field, i.e. finding a solution of the inverse problem of EEG generation. As a technique for inferring the unobserved high-dimensional primary current density field from EEG data of much lower dimension, a linear state space modelling approach is suggested, based on a generalisation of Kalman filtering, in combination with maximum-likelihood parameter estimation. The resulting algorithm for estimating dynamical solutions of the EEG inverse problem is applied to the task of localising the source of an epileptic spike from a clinical EEG data set; for comparison, we apply to the same task also a non-dynamical standard algorithm.
Directory of Open Access Journals (Sweden)
L. B. Castro
2014-01-01
Full Text Available We point out a misleading treatment in the recent literature regarding analytical solutions for nonminimal vector interaction for spin-one particles in the context of the Duffin-Kemmer-Petiau (DKP formalism. In those papers, the authors use improperly the nonminimal vector interaction endangering in their main conclusions. We present a few properties of the nonminimal vector interactions and also present the correct equations to this problem. We show that the solution can be easily found by solving Schrödinger-like equations. As an application of this procedure, we consider spin-one particles in presence of a nonminimal vector linear potential.
A family of nonlinear Schrödinger equations admitting q-plane wave solutions
Nobre, F. D.; Plastino, A. R.
2017-08-01
Nonlinear Schrödinger equations with power-law nonlinearities have attracted considerable attention recently. Two previous proposals for these types of equations, corresponding respectively to the Gross-Pitaievsky equation and to the one associated with nonextensive statistical mechanics, are here unified into a single, parameterized family of nonlinear Schrödinger equations. Power-law nonlinear terms characterized by exponents depending on a real index q, typical of nonextensive statistical mechanics, are considered in such a way that the Gross-Pitaievsky equation is recovered in the limit q → 1. A classical field theory shows that, due to these nonlinearities, an extra field Φ (x → , t) (besides the usual one Ψ (x → , t)) must be introduced for consistency. The new field can be identified with Ψ* (x → , t) only when q → 1. For q ≠ 1 one has a pair of coupled nonlinear wave equations governing the joint evolution of the complex valued fields Ψ (x → , t) and Φ (x → , t). These equations reduce to the usual pair of complex-conjugate ones only in the q → 1 limit. Interestingly, the nonlinear equations obeyed by Ψ (x → , t) and Φ (x → , t) exhibit a common, soliton-like, traveling solution, which is expressible in terms of the q-exponential function that naturally emerges within nonextensive statistical mechanics.
Gluon fragmentation into a vector charmonium J/psi considering the effect of meson wave function
Directory of Open Access Journals (Sweden)
Seyed Mohammad Moosavi nejad
2017-05-01
Full Text Available Studying the production or decay processes of heavy quarkonia (the bound state of heavy quark-antiquark is a powerful tool to test our understanding of strong interaction dynamics and QCD theory. Fragmentation is the dominant production mechanism for heavy quarkonia with large transverse momentum. The fragmentation refers to the production process of a parton with high transverse momentum which subsequently decays into a heavy quarkonia. In all previous manuscript where the fragmentation functions of heavy mesons or baryons are calculated, authors have used the approximation of a Dirac delta function for the meson wave function. In the present paper by working in a perturbative QCD framework and by considering the effect of meson wave functions we calculate the fragmentation function of a gluon into a spin-triplet S-wave charmonium J/psi. To consider the real aspect of meson bound state we apply a mesonic wave function which is different of Dirac delta function and is a nonrelativistic limit of the Bethe-Salpeter equation. Finally, we present our numerical results and show that how the proposed wave function improves the previous results.
The Cauchy Problem and Stability of Solitary-Wave Solutions for RLW-KP-Type Equations
Bona, Jerry L.; Liu, Yue; Tom, Michael M.
The Kadomtsev-Petviashvilli (KP) equation,( ut+ ux+ uux+ uxxx) x+ ɛuyy=0, (*) arises in various contexts where nonlinear dispersive waves propagate principally along the x-axis, but with weak dispersive effects being felt in the direction parallel to the y-axis perpendicular to the main direction of propagation. We propose and analyze here a class of evolution equations of the form ( ut+ ux+ upux+ Lut) x+ ɛuyy=0, (**) which provides an alternative to Eq.(*) in the same way the regularized long-wave equation is related to the classical Korteweg-de Vries (KdV) equation. The operator L is a pseudo-differential operator in the x-variable, p⩾1 is an integer and ɛ=±1. After discussing the underlying motivation for the class (**), a local well-posedness theory for the initial-value problem is developed. With assumptions on L and p that include conditions appertaining to models of interesting physical phenomenon, the solutions defined locally in time t are shown to be smoothly extendable to the entire time-axis. In the particularly interesting case where L=-∂ x2 and ɛ=-1, (*) possesses travelling-wave solutions u( x, y, t)=π c( x- ct, y) provided c>1 and 01 and for {4}/{3}(4 p)/(4+ p). The paper concludes with commentary on extensions of the present theory to more than two space dimensions.
Going Wave as a Model of Particle
Goryunov, A V
2010-01-01
The concept of going wave is introduced from classical positions (including the special relativity theory). One- and three-dimensional going waves considered with their wave equations and dispersion equations. It is shown that wave characteristics (de Broglie's and Compton's wavelengths) and corpuscular characteristics (energy-momentum vector and the rest mass) of particle may be expressed through parameters of going wave. By that the new view on a number concepts of physic related with particle-wave dualism is suggested.
Transverse acoustic phonon anomalies at intermediate wave vectors in MgV2O4
Weber, T.; Roessli, B.; Stock, C.; Keller, T.; Schmalzl, K.; Bourdarot, F.; Georgii, R.; Ewings, R. A.; Perry, R. S.; Böni, P.
2017-11-01
Magnetic spinels (with chemical formula A X2O4 , with X a 3 d transition metal ion) that also have an orbital degeneracy are Jahn-Teller active and hence possess a coupling between spin and lattice degrees of freedom. At high temperatures, MgV2O4 is a cubic spinel based on V3 + ions with a spin S =1 and a triply degenerate orbital ground state. A structural transition occurs at TOO=63 K to an orbitally ordered phase with a tetragonal unit cell followed by an antiferromagnetic transition of TN=42 K on cooling. We apply neutron spectroscopy in single crystals of MgV2O4 to show an anomaly for intermediate wave vectors at TOO associated with the acoustic phonon sensitive to the shear elastic modulus (C11-C12)/2 . On warming, the shear mode softens for momentum transfers near close to half the Brillouin zone boundary, but recovers near the zone center. High resolution spin-echo measurements further illustrate a temporal broadening with increased temperature over this intermediate range of wave vectors, indicative of a reduction in phonon lifetime. A subtle shift in phonon frequencies over the same range of momentum transfers is observed with magnetic fields. We discuss this acoustic anomaly in context of coupling to orbital and charge fluctuations.
Directory of Open Access Journals (Sweden)
Weiguo Rui
2014-01-01
Full Text Available By using the integral bifurcation method together with factoring technique, we study a water wave model, a high-order nonlinear wave equation of KdV type under some newly solvable conditions. Based on our previous research works, some exact traveling wave solutions such as broken-soliton solutions, periodic wave solutions of blow-up type, smooth solitary wave solutions, and nonsmooth peakon solutions within more extensive parameter ranges are obtained. In particular, a series of smooth solitary wave solutions and nonsmooth peakon solutions are obtained. In order to show the properties of these exact solutions visually, we plot the graphs of some representative traveling wave solutions.
On Dirac equations for linear magnetoacoustic waves propagating in an isothermal atmosphere
Alicki, R.; Musielak, E. Z.; Sikorski, J.; Makowiec, D.
1994-01-01
A new analytical approach to study linear magnetoacoustic waves propagating in an isothermal, stratified, and uniformly magnetized atmosphere is presented. The approach is based on Dirac equations, and the theory of Sturm-Liouville operators is used to investigate spectral properties of the obtained Dirac Hamiltonians. Two cases are considered: (1) the background magnetic field is vertical, and the waves are separated into purely magnetic (transverse) and purely acoustic (longitudinal) modes; and (2) the field is tilted with respect to the vertical direction and the magnetic and acoustic modes become coupled giving magnetoacoustic waves. For the first case, the Dirac Hamiltonian possesses either a discrete spectrum, which corresponds to standing magnetic waves, or a continuous spectrum, which can be clearly identified with freely propagating acoustic waves. For the second case, the quantum mechanical perturbation calculus is used to study coupling and energy exchange between the magnetic and acoustic components of magnetoacoustic waves. It is shown that this coupling may efficiently prevent trapping of magnetoacoustic waves instellar atmospheres.
Initial-value problem for the Gardner equation applied to nonlinear internal waves
Rouvinskaya, Ekaterina; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim
2017-04-01
The Gardner equation is a fundamental mathematical model for the description of weakly nonlinear weakly dispersive internal waves, when cubic nonlinearity cannot be neglected. Within this model coefficients of quadratic and cubic nonlinearity can both be positive as well as negative, depending on background conditions of the medium, where waves propagate (sea water density stratification, shear flow profile) [Rouvinskaya et al., 2014, Kurkina et al., 2011, 2015]. For the investigation of weakly dispersive behavior in the framework of nondimensional Gardner equation with fixed (positive) sign of quadratic nonlinearity and positive or negative cubic nonlinearity {eq1} partial η/partial t+6η( {1± η} )partial η/partial x+partial ^3η/partial x^3=0, } the series of numerical experiments of initial-value problem was carried out for evolution of a bell-shaped impulse of negative polarity (opposite to the sign of quadratic nonlinear coefficient): {eq2} η(x,t=0)=-asech2 ( {x/x0 } ), for which amplitude a and width x0 was varied. Similar initial-value problem was considered in the paper [Trillo et al., 2016] for the Korteweg - de Vries equation. For the Gardner equation with different signs of cubic nonlinearity the initial-value problem for piece-wise constant initial condition was considered in detail in [Grimshaw et al., 2002, 2010]. It is widely known, for example, [Pelinovsky et al., 2007], that the Gardner equation (1) with negative cubic nonlinearity has a family of classic solitary wave solutions with only positive polarity,and with limiting amplitude equal to 1. Therefore evolution of impulses (2) of negative polarity (whose amplitudes a were varied from 0.1 to 3, and widths at the level of a/2 were equal to triple width of solitons with the same amplitude for a 1) was going on a universal scenario with the generation of nonlinear Airy wave. For the Gardner equation (1) with the positive cubic nonlinearity coefficient there exist two one-parametric families of
Mostafa M.A. Khater; Dipankar Kumar
2017-01-01
The aim of the article is to construct exact solutions for the time fractional coupled Boussinesq–Burger and approximate long water wave equations by using the generalized Kudryashov method. The fractional differential equation is converted into ordinary differential equations with the help of fractional complex transform and the modified Riemann–Liouville derivative sense. Applying the generalized Kudryashov method through with symbolic computer maple package, numerous new exact solutions ar...
Exact Traveling-Wave Solution for Local Fractional Boussinesq Equation in Fractal Domain
Yang, Xiao-Jun; Machado, J. A. Tenreiro; Baleanu, Dumitru
The new Boussinesq-type model in a fractal domain is derived based on the formulation of the local fractional derivative. The novel traveling wave transform of the non-differentiable type is adopted to convert the local fractional Boussinesq equation into a nonlinear local fractional ODE. The exact traveling wave solution is also obtained with aid of the non-differentiable graph. The proposed method, involving the fractal special functions, is efficient for finding the exact solutions of the nonlinear PDEs in fractal domains.
Laser driven shock wave experiments for equation of state studies at megabar pressures
Pant, H C; Senecha, V K; Bandyopadhyay, S; Rai, V N; Khare, P; Bhat, R K; Gupta, N K; Godwal, B K
2002-01-01
We present the results from laser driven shock wave experiments for equation of state (EOS) studies of gold metal. An Nd:YAG laser chain (2 J, 1.06 mu m wavelength, 200 ps pulse FWHM) is used to generate shocks in planar Al foils and Al + Au layered targets. The EOS of gold in the pressure range of 9-13 Mbar is obtained using the impedance matching technique. The numerical simulations performed using the one-dimensional radiation hydrodynamic code support the experimental results. The present experimental data show remarkable agreement with the existing standard EOS models and with other experimental data obtained independently using laser driven shock wave experiments.
Gilbert, Kenneth E
2015-01-01
The original formulation of the Green's function parabolic equation (GFPE) can have numerical accuracy problems for large normalized surface impedances. To solve the accuracy problem, an improved form of the GFPE has been developed. The improved GFPE formulation is similar to the original formulation, but it has the surface-wave pole "subtracted." The improved GFPE is shown to be accurate for surface impedances varying over 2 orders of magnitude, with the largest having a magnitude exceeding 1000. Also, the improved formulation is slightly faster than the original formulation because the surface-wave component does not have to be computed separately.
ON FINITE DIFFERENCE SCHEMES FOR THE 3-D WAVE EQUATION USING NON-CARTESIAN GRIDS
B. Hamilton; S. Bilbao
2013-01-01
In this paper, we investigate ﬁnite difference schemes forthe 3-D wave equation using 27-point stencils on the cubiclattice, a 13-point stencil on the face-centered cubic (FCC)lattice, and a 9-point stencil on the body-centered cubic(BCC) lattice. The tiling of the wavenumber space for nonCartesian grids is considered in order to analyse numericaldispersion. Schemes are compared for computational efﬁ-ciency in terms of minimising numerical wave speed error.It is shown that the 13-point scheme...
van Oers, Alexander M.; Maas, Leo R. M.; Bokhove, Onno
2017-02-01
The linear equations governing internal gravity waves in a stratified ideal fluid possess a Hamiltonian structure. A discontinuous Galerkin finite element method has been developed in which this Hamiltonian structure is discretized, resulting in conservation of discrete analogs of phase space and energy. This required (i) the discretization of the Hamiltonian structure using alternating flux functions and symplectic time integration, (ii) the discretization of a divergence-free velocity field using Dirac's theory of constraints and (iii) the handling of large-scale computational demands due to the 3-dimensional nature of internal gravity waves and, in confined, symmetry-breaking fluid domains, possibly its narrow zones of attraction.
Self-similar shock wave solutions of the non-linear Maxwell equations
Barna, I F
2013-01-01
In our study we consider nonlinear, power-law field-dependent electrical permitivity and magnetic permeability and investigate the time-dependent Maxwell equations with the self-similar Ansatz. This is a first-order hyperbolic PDE system which can conserve non-continuous initial conditions describing electromagnetic shock-waves. Besides shock-waves other interesting solutions (e.g. with localized compact support) can be found with delicate physical properties. Such phenomena may happen in complex materials induced by the planned powerful Extreme Light Infrastructure(ELI) laser pulses.
An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation
Asiri, Sharefa M.
2015-08-31
Observers are well known in control theory. Originally designed to estimate the hidden states of dynamical systems given some measurements, the observers scope has been recently extended to the estimation of some unknowns, for systems governed by partial differential equations. In this paper, observers are used to solve inverse source problem for a one-dimensional wave equation. An adaptive observer is designed to estimate the state and source components for a fully discretized system. The effectiveness of the algorithm is emphasized in noise-free and noisy cases and an insight on the impact of measurements’ size and location is provided.
Exact controllability for a wave equation with mixed boundary conditions in a non-cylindrical domain
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Lizhi Cui
2014-04-01
Full Text Available In this article we study the exact controllability of a one-dimensional wave equation with mixed boundary conditions in a non-cylindrical domain. The fixed endpoint has a Dirichlet-type boundary condition, while the moving end has a Neumann-type condition. When the speed of the moving endpoint is less than the characteristic speed, the exact controllability of this equation is established by Hilbert Uniqueness Method. Moreover, we shall give the explicit dependence of the controllability time on the speed of the moving endpoint.
A study of wave forces on an offshore platform by direct CFD and Morison equation
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Zhang D.
2015-01-01
The next step is the presentation of 3D multiphase RANS simulation of the wind-turbine platform in single-harmonic regular waves. Simulation results from full 3D simulation will be compared to the results from Morison’s equation. We are motivated by the challenges of a floating platform which has complex underwater geometry (e.g. tethered semi-submersible. In cases like this, our hypothesis is that Morison’s equation will result in inaccurate prediction of forces, due to the limitations of 2D coefficients of simple geometries, and that 3D multiphase RANS CFD will be required to generate reliable predictions of platform loads and motions.
Viscoacoustic wave-equation traveltime inversion with correct and incorrect attenuation profiles
Yu, Han
2017-08-17
A visco-acoustic wave-equation traveltime inversion method is presented that inverts for a shallow subsurface velocity distribution with correct and incorrect attenuation profiles. Similar to the classical wave equation traveltime inversion, this method applies the misfit functional that minimizes the first break differences between the observed and predicted data. Although, WT can partly avoid the cycle skipping problem, an initial velocity model approaches to the right or wrong velocity models under different setups of the attenuation profiles. However, with a Q model far away from the real model, the inverted tomogram is obviously different from the true velocity model while a small change of the Q model does not improve the inversion quality in a strong manner if low frequency information is not lost.
Directory of Open Access Journals (Sweden)
Ibrahim K. Abu Seif
2015-01-01
Full Text Available In this paper a fast numerical algorithm to solve an integral equation model for wave propagation along a perfectly conducting two-dimensional terrain is suggested. It is applied to different actual terrain profiles and the results indicate very good agreement with published work. In addition, the proposed algorithm has achieved considerable saving in processing time. The formulation is extended to solve the propagation over lossy dielectric surfaces. A combined field integral equation (CFIE for wave propagation over dielectric terrain is solved efficiently by utilizing the method of moments with complex basis functions. The numerical results for different cases of dielectric surfaces are compared with the results of perfectly conducting surface evaluated by the IE conventional algorithm.
Liquid-gas asymmetry and the wave-vector-dependent surface tension.
Parry, A O; Rascón, C; Evans, R
2015-03-01
Attempts to extend the capillary-wave theory of fluid interfacial fluctuations to microscopic wavelengths, by introducing an effective wave-vector (q)-dependent surface tension σeff(q), have encountered difficulties. There is no consensus as to even the shape of σeff(q). By analyzing a simple density functional model of the liquid-gas interface, we identify different schemes for separating microscopic observables into background and interfacial contributions. In order for the backgrounds of the density-density correlation function and local structure factor to have a consistent and physically meaningful interpretation in terms of weighted bulk gas and liquid contributions, the background of the total structure factor must be characterized by a microscopic q-dependent length ζ(q) not identified previously. The necessity of including the q dependence of ζ(q) is illustrated explicitly in our model and has wider implications; i.e., in typical experimental and simulation studies, an indeterminacy in ζ(q) will always be present, reminiscent of the cutoff used in capillary-wave theory. This leads inevitably to a large uncertainty in the q dependence of σeff(q).
Numerical Simulations for the Space-Time Variable Order Nonlinear Fractional Wave Equation
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Nasser Hassan Sweilam
2013-01-01
Full Text Available The explicit finite-difference method for solving variable order fractional space-time wave equation with a nonlinear source term is considered. The concept of variable order fractional derivative is considered in the sense of Caputo. The stability analysis and the truncation error of the method are discussed. To demonstrate the effectiveness of the method, some numerical test examples are presented.
The use of adomian decomposition method for solving the regularized long-wave equation
Energy Technology Data Exchange (ETDEWEB)
El-Danaf, Talaat S. [Department of Mathematics, Faculty of Science, Menoufia University, Shiben El-Kom (Egypt); Ramadan, Mohamed A. [Department of Mathematics, Faculty of Science, Menoufia University, Shiben El-Kom (Egypt)] e-mail: mramadan@mailer.eun.eg; Abd Alaal, Faysal E.I. [Department of Mathematics, Faculty of Science, Menoufia University, Shiben El-Kom (Egypt)
2005-11-01
In this paper, an accurate method to obtain an approximate numerical solution for the nonlinear regularized long-wave (in short RLW) equation is considered. The theoretical analysis of the method is investigated. The performance and the accuracy of the algorithm are illustrated by solving two test examples of the problem. The obtained results are presented and compared with the analytical solutions. It is observed that only few terms of the series expansion are required to obtain approximate solutions with good accuracy.
Povstenko, Y.
2013-09-01
The axisymmetric time-fractional diffusion-wave equation with the Caputo derivative of the order 0 function and the values of its normal derivative at the boundary. The fundamental solutions to the Cauchy, source, and boundary problems are investigated. The Laplace transform with respect to time and finite Hankel transform with respect to the radial coordinate are used. The solutions are obtained in terms of Mittag-Leffler functions. The numerical results are illustrated graphically.
Solutions to Time-Fractional Diffusion-Wave Equation in Cylindrical Coordinates
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Povstenko YZ
2011-01-01
Full Text Available Nonaxisymmetric solutions to time-fractional diffusion-wave equation with a source term in cylindrical coordinates are obtained for an infinite medium. The solutions are found using the Laplace transform with respect to time , the Hankel transform with respect to the radial coordinate , the finite Fourier transform with respect to the angular coordinate , and the exponential Fourier transform with respect to the spatial coordinate . Numerical results are illustrated graphically.
Gerbi, Stéphane
2011-12-01
In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the KelvinVoigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained. © 2011 Elsevier Ltd. All rights reserved.
Variational Approach to the Orbital Stability of Standing Waves of the Gross-Pitaevskii Equation
Hadj Selem, Fouad
2014-08-26
This paper is concerned with the mathematical analysis of a masssubcritical nonlinear Schrödinger equation arising from fiber optic applications. We show the existence and symmetry of minimizers of the associated constrained variational problem. We also prove the orbital stability of such solutions referred to as standing waves and characterize the associated orbit. In the last section, we illustrate our results with few numerical simulations. © 2014 Springer Basel.
A functional integral approach to shock wave solutions of Euler equations with spherical symmetry
Yang, Tong
1995-08-01
For n×n systems of conservation laws in one dimension without source terms, the existence of global weak solutions was proved by Glimm [1]. Glimm constructed approximate solutions using a difference scheme by solving a class of Riemann problems. In this paper, we consider the Cauchy problem for the Euler equations in the spherically symmetric case when the initial data are small perturbations of the trivial solution, i.e., u≡0 and ρ≡ constant, where u is velocity and ρ is density. We show that this Cauchy problem can be reduced to an ideal nonlinear problem approximately. If we assume all the waves move at constant speeds in the ideal problem, by using Glimm's scheme and an integral approach to sum the contributions of the reflected waves that correspond to each path through the solution, we get uniform bounds on the L ∞ norm and total variational norm of the solutions for all time. The geometric effects of spherical symmetry leads to a non-integrable source term in the Euler equations. Correspondingly, we consider an infinite reflection problem and solve it by considering the cancellations between reflections of different orders in our ideal problem. Thus we view this as an analysis of the interaction effects at the quadratic level in a nonlinear model problem for the Euler equations. Although it is far more difficult to obtain estimates in the exact solutions of the Euler equations due to the problem of controlling the time at which the cancellations occur, we believe that this analysis of the wave behaviour will be the first step in solving the problem of existence of global weak solutions for the spherically symmetric Euler equations outside of fixed ball.
Hydromagnetic Waves in a Compressed Dipole Field via Field-Aligned Klein-Gordon Equations
Zheng, Jinlei; McKenzie, J F; Webb, G M
2014-01-01
Hydromagnetic waves, especially those of frequencies in the range of a few milli-Hz to a few Hz observed in the Earth's magnetosphere, are categorized as Ultra Low Frequency (ULF) waves or pulsations. They have been extensively studied due to their importance in the interaction with radiation belt particles and in probing the structures of the magnetosphere. We developed an approach in examining the toroidal standing Aflv\\'{e}n waves in a background magnetic field by recasting the wave equation into a Klein-Gordon (KG) form along individual field lines. The eigenvalue solutions to the system are characteristic of a propagation type when the corresponding eigen-frequency is greater than a cut-off frequency and an evanescent type otherwise. We apply the approach to a compressed dipole magnetic field model of the inner magnetosphere, and obtain the spatial profiles of relevant parameters and the spatial wave forms of harmonic oscillations. We further extend the approach to poloidal mode standing Alfv\\'{e}n waves...
Derivation of asymptotic two-dimensional time-dependent equations for ocean wave propagation
Lannes, David
2007-01-01
A general method for the derivation of asymptotic nonlinear shallow water and deep water models is presented. Starting from a general dimensionless version of the water-wave equations, we reduce the problem to a system of two equations on the surface elevation and the velocity potential at the free surface. These equations involve a Dirichlet-Neumann operator and we show that all the asymptotic models can be recovered by a simple asymptotic expansion of this operator, in function of the shallowness parameter (shallow water limit) or the steepness parameter (deep water limit). Based on this method, a new two-dimensional fully dispersive model for small wave steepness is also derived, which extends to uneven bottom the approach developed by Matsuno \\cite{matsuno3} and Choi \\cite{choi}. This model is still valid in shallow water but with less precision than what can be achieved with Green-Naghdi model, when fully nonlinear waves are considered. The combination, or the coupling, of the new fully dispersive equati...
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N. N. Romanova
1998-01-01
Full Text Available The dynamics of weakly nonlinear wave trains in unstable media is studied. This dynamics is investigated in the framework of a broad class of dynamical systems having a Hamiltonian structure. Two different types of instability are considered. The first one is the instability in a weakly supercritical media. The simplest example of instability of this type is the Kelvin-Helmholtz instability. The second one is the instability due to a weak linear coupling of modes of different nature. The simplest example of a geophysical system where the instability of this and only of this type takes place is the three-layer model of a stratified shear flow with a continuous velocity profile. For both types of instability we obtain nonlinear evolution equations describing the dynamics of wave trains having an unstable spectral interval of wavenumbers. The transformation to appropriate canonical variables turns out to be different for each case, and equations we obtained are different for the two types of instability we considered. Also obtained are evolution equations governing the dynamics of wave trains in weakly subcritical media and in media where modes are coupled in a stable way. Presented results do not depend on a specific physical nature of a medium and refer to a broad class of dynamical systems having the Hamiltonian structure of a special form.
Seadawy, Aly R.
2017-09-01
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 perturbation method, the two-dimensional dust-acoustic solitary waves (DASWs) in unmagnetized cold plasma consisting of dust fluid, ions and electrons lead to a KP equation. We derived the solitary travelling wave solutions of the two-dimensional nonlinear KP equation by implementing sech-tanh, sinh-cosh, extended direct algebraic and fraction direct algebraic methods. We found the electrostatic field potential and electric field in the form travelling wave solutions for two-dimensional nonlinear KP equation. The solutions for the KP equation obtained by using these methods can be demonstrated precisely and efficiency. As an illustration, we used the readymade package of Mathematica program 10.1 to solve the original problem. These solutions are in good agreement with the analytical one.
National Research Council Canada - National Science Library
Li, Xinying; Xu, Yuming; Xiao, Jiangnan; Yu, Jianjun
2016-01-01
We propose W-band photonic millimeter-wave (mm-wave) vector signal generation employing a precoding-assisted random frequency tripling scheme enabled by a single phase modulator cascaded with a wavelength selective switch (WSS...
Energy Technology Data Exchange (ETDEWEB)
Tchinang Tchameu, J.D., E-mail: jtchinang@gmail.com; Togueu Motcheyo, A.B., E-mail: abtogueu@yahoo.fr; Tchawoua, C., E-mail: ctchawa@yahoo.fr
2016-09-07
The discrete multi-rogue waves (DMRW) as solution of the discrete nonlinear Schrödinger (DNLS) equation with saturable nonlinearities is studied numerically. These biological rogue waves represent the complex probability amplitude of finding an amide-I vibrational quantum at a site. We observe that the growth in the higher order saturable nonlinearity implies the formation of DMRW including an increase in the short-living DMRW and a decrease in amplitude of the long-living DMRW. - Highlights: • Discrete Multi-Rogue Waves (DMRW), representing the localization of vibrational energy in protein chain, are found numerically. • The higher order saturable nonlinearity of DNLS promotes the increase in the short-living RW. • The higher order saturable nonlinearity of DNLS promotes the decrease in amplitude of the long-living RW.
Nonlinear interaction of impulsive gravitational waves for the vacuum Einstein equations
Luk, Jonathan
2013-01-01
In this paper, we study the problem of the nonlinear interaction of impulsive gravitational waves for the Einstein vacuum equations. The problem is studied in the context of a characteristic initial value problem with data given on two null hypersurfaces and containing curvature delta singularities. We establish an existence and uniqueness result for the spacetime arising from such data and show that the resulting spacetime represents the interaction of two impulsive gravitational waves germinating from the initial singularities. In the spacetime, the curvature delta singularities propagate along 3-dimensional null hypersurfaces intersecting to the future of the data. To the past of the intersection, the spacetime can be thought of as containing two independent, non-interacting impulsive gravitational waves and the intersection represents the first instance of their nonlinear interaction. Our analysis extends to the region past their first interaction and shows that the spacetime still remains smooth away fro...
Solution of the nonrelativistic wave equation using the tridiagonal representation approach
Alhaidari, A. D.
2017-07-01
We choose a complete set of square integrable functions as a basis for the expansion of the wavefunction in configuration space such that the matrix representation of the nonrelativistic time-independent linear wave operator is tridiagonal and symmetric. Consequently, the matrix wave equation becomes a symmetric three-term recursion relation for the expansion coefficients of the wavefunction. The recursion relation is then solved exactly in terms of orthogonal polynomials in the energy. Some of these polynomials are not found in the mathematics literature. The asymptotics of these polynomials give the phase shift for the continuous energy scattering states and the spectrum for the discrete energy bound states. Depending on the space and boundary conditions, the basis functions are written in terms of either the Laguerre or Jacobi polynomials. The tridiagonal requirement limits the number of potential functions that yield exact solutions of the wave equation. Nonetheless, the class of exactly solvable problems in this approach is larger than the conventional class (see, for example, Table XII in the text). We also give very accurate results for cases where the wave operator matrix is not tridiagonal but its elements could be evaluated either exactly or numerically with high precision.
Angle-domain Migration Velocity Analysis using Wave-equation Reflection Traveltime Inversion
Zhang, Sanzong
2012-11-04
The main difficulty with an iterative waveform inversion is that it tends to get stuck in a local minima associated with the waveform misfit function. This is because the waveform misfit function is highly non-linear with respect to changes in the velocity model. To reduce this nonlinearity, we present a reflection traveltime tomography method based on the wave equation which enjoys a more quasi-linear relationship between the model and the data. A local crosscorrelation of the windowed downgoing direct wave and the upgoing reflection wave at the image point yields the lag time that maximizes the correlation. This lag time represents the reflection traveltime residual that is back-projected into the earth model to update the velocity in the same way as wave-equation transmission traveltime inversion. The residual movemout analysis in the angle-domain common image gathers provides a robust estimate of the depth residual which is converted to the reflection traveltime residual for the velocity inversion. We present numerical examples to demonstrate its efficiency in inverting seismic data for complex velocity model.
Shot- and angle-domain wave-equation traveltime inversion of reflection data: Theory
Zhang, Sanzong
2015-05-26
The main difficulty with iterative waveform inversion is that it tends to get stuck in local minima associated with the waveform misfit function. To mitigate this problem and avoid the need to fit amplitudes in the data, we have developed a wave-equation method that inverts the traveltimes of reflection events, and so it is less prone to the local minima problem. Instead of a waveform misfit function, the penalty function was a crosscorrelation of the downgoing direct wave and the upgoing reflection wave at the trial image point. The time lag, which maximized the crosscorrelation amplitude, represented the reflection-traveltime residual (RTR) that was back projected along the reflection wavepath to update the velocity. Shot- and angle-domain crosscorrelation functions were introduced to estimate the RTR by semblance analysis and scanning. In theory, only the traveltime information was inverted and there was no need to precisely fit the amplitudes or assume a high-frequency approximation. Results with synthetic data and field records revealed the benefits and limitations of wave-equation reflection traveltime inversion.
On analytic solutions of wave equations in regular coordinate systems on Schwarzschild background
Philipp, Dennis
2015-01-01
The propagation of (massless) scalar, electromagnetic and gravitational waves on fixed Schwarzschild background spacetime is described by the general time-dependent Regge-Wheeler equation. We transform this wave equation to usual Schwarzschild, Eddington-Finkelstein, Painleve-Gullstrand and Kruskal-Szekeres coordinates. In the first three cases, but not in the last one, it is possible to separate a harmonic time-dependence. Then the resulting radial equations belong to the class of confluent Heun equations, i.e., we can identify one irregular and two regular singularities. Using the generalized Riemann scheme we collect properties of all the singular points and construct analytic (local) solutions in terms of the standard confluent Heun function HeunC, Frobenius and asymptotic Thome series. We study the Eddington-Finkelstein case in detail and obtain a solution that is regular at the black hole horizon. This solution satisfies causal boundary conditions, i.e., it describes purely ingoing radiation at $r=2M$. ...
Boundary-value problems for wave equations with data on the whole boundary
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Makhmud A. Sadybekov
2016-10-01
Full Text Available In this article we propose a new formulation of boundary-value problem for a one-dimensional wave equation in a rectangular domain in which boundary conditions are given on the whole boundary. We prove the well-posedness of boundary-value problem in the classical and generalized senses. To substantiate the well-posedness of this problem it is necessary to have an effective representation of the general solution of the problem. In this direction we obtain a convenient representation of the general solution for the wave equation in a rectangular domain based on d'Alembert classical formula. The constructed general solution automatically satisfies the boundary conditions by a spatial variable. Further, by setting different boundary conditions according to temporary variable, we get some functional or functional-differential equations. Thus, the proof of the well-posedness of the formulated problem is reduced to question of the existence and uniqueness of solutions of the corresponding functional equations.
Wave equations and computational models for sonic boom propagation through a turbulent atmosphere
Pierce, Allan D.
1992-01-01
The improved simulation of sonic boom propagation through the real atmosphere requires greater understanding of how the transient acoustic pulses popularly termed sonic booms are affected by atmospheric turbulence. A nonlinear partial differential equation that can be used to simulate the effects of smaller-scale atmospheric turbulence on sonic boom waveforms is described. The equation is first order in the time derivative and involves an extension of geometrical acoustics to include diffraction phenomena. Various terms in the equation are explained in physical terms. Such terms include those representing convection at the wave speed, diffraction, molecular relaxation, classical dissipation, and nonlinear steepening. The atmospheric turbulence enters through an effective sound speed, which varies with all three spatial coordinates, and which is the sum of the local sound speed and the component of the turbulent flow velocity projected along a central ray that connects the aircraft trajectory with the listener.
Comparison of ν-support vector regression and logistic equation for ...
African Journals Online (AJOL)
Jane
2011-07-04
Jul 4, 2011 ... Prediction of key state variables using support vector machines in bioprocess. Chem. Eng. Technol. 29: 313-319. Lin, W.Z., Xiao, X., and Chou, K.C., 2009. GPCR-GIA: a web-server for identifying G-protein coupled receptors and their families with grey incidence analysis. Protein Eng Des Sel 22, 699-705.
Comparison of ν-support vector regression and logistic equation for ...
African Journals Online (AJOL)
Due to the complexity and high non-linearity of bioprocess, most simple mathematical models fail to describe the exact behavior of biochemistry systems. As a novel type of learning method, support vector regression (SVR) owns the powerful capability to characterize problems via small sample, nonlinearity, high dimension ...
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Wei Li
2014-01-01
Full Text Available Based on Jumarie’s modified Riemann-Liouville derivative, the fractional complex transformation is used to transform fractional differential equations to ordinary differential equations. Exact solutions including the hyperbolic functions, the trigonometric functions, and the rational functions for the space-time fractional bidirectional wave equations are obtained using the (G′/G-expansion method. The method provides a promising tool for solving nonlinear fractional differential equations.
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Hongwei Yang
2014-01-01
Full Text Available In the paper, by using multiple-scale method, the Benjamin-Ono-Burgers-MKdV (BO-B-MKdV equation is obtained which governs algebraic Rossby solitary waves in stratified fluids. This equation is first derived for Rossby waves. By analysis and calculation, some conservation laws are derived from the BO-B-MKdV equation without dissipation. The results show that the mass, momentum, energy, and velocity of the center of gravity of algebraic Rossby waves are conserved and the presence of a small dissipation destroys these conservations.
Wazwaz, Abdul-Majid
2012-06-01
In this work, we explore a variety of solitary wave ansatze and periodic wave ansatze to some nonlinear equations. Three complex systems of nonlinear equations that appear in mathematical physics are investigated. We derive abundant soliton and periodic wave solutions for the coupled Higgs field equation, the Maccari system and the Hirota-Maccari system. The results obtained show that these three coupled equations exhibit the richness of explicit solutions: solitons, periodic and rational wave solutions.
Luo, Si; Yang, Hangbo; Yang, Yuanqing; Zhao, Ding; Chen, Xingxing; Qiu, Min; Li, Qiang
2015-08-25
Surface plasmon polaritons (SPPs) propagating at metal nanostructures play an important role in breaking the diffraction limit. Chemically synthesized single-crystalline metal nanoplates with atomically flat surfaces provide favorable features compared with traditional polycrystalline metal films. The excitation and propagation of leaky SPPs on micrometer sized (10-20 μm) and thin (30 nm) gold nanoplates are investigated utilizing leakage radiation microscopy. By varying polarization and excitation positions of incident light on apexes of nanoplates, wave-vector (including propagation constant and propagation direction) distributions of leaky SPPs in Fourier planes can be controlled, indicating tunable SPP propagation. These results hold promise for potential development of chemically synthesized single-crystalline metal nanoplates as plasmonic platforms in future applications.
Scattering from cylinders using the two-dimensional vector plane wave spectrum.
Pawliuk, Peter; Yedlin, Matthew
2011-06-01
The two-dimensional vector plane wave spectrum (VPWS) is scattered from parallel circular cylinders using a boundary value solution with the T-matrix formalism. The VPWS allows us to define the incident, two-dimensional electromagnetic field with an arbitrary distribution and polarization, including both radiative and evanescent components. Using the fast Fourier transform, we can quickly compute the multiple scattering of fields that have any particular functional or numerical form. We perform numerical simulations to investigate a grating of cylinders that is capable of converting an evanescent field into a set of propagating beams. The direction of propagation of each beam is directly related to a spatial frequency component of the incident evanescent field.
Fast Plane Wave 2-D Vector Flow Imaging Using Transverse Oscillation and Directional Beamforming
DEFF Research Database (Denmark)
Jensen, Jonas; Villagómez Hoyos, Carlos Armando; Stuart, Matthias Bo
2017-01-01
Several techniques can estimate the 2-D velocity vector in ultrasound. Directional beamforming (DB) estimates blood flow velocities with a higher precision and accuracy than transverse oscillation (TO), but at the cost of a high beamforming load when estimating the flow angle. In this paper......, it is proposed to use TO to estimate an initial flow angle, which is then refined in a DB step. Velocity magnitude is estimated along the flow direction using cross-correlation. It is shown that the suggested TO-DB method can improve the performance of velocity estimates compared to TO, and with a beamforming...... load, which is 4.6 times larger than for TO and seven times smaller than for conventional DB. Steered plane wave transmissions are employed for high frame rate imaging, and parabolic flow with a peak velocity of 0.5 m/s is simulated in straight vessels at beamto- flow angles from 45 to 90. The TO...
Manipulable wave-vector filtering in a hybrid magnetic-electric-barrier nanostructure
Liu, Gui-Xiang; Zhang, Lan-Lan; Zhang, Gui-Lian; Shen, Li-Hua
2017-04-01
We theoretically explore the control of the wave-vector filtering (WVF) effect in a hybrid magnetic-electric-barrier nanostructure, which can be experimentally realized by depositing a ferromagnetic (FM) stripe and a Schottky-metal (SM) stripe on top and bottom of a GaAs/Al_{ {x}}Ga_{1-x}As heterostructure, respectively. It is shown that an obvious WVF effect appears in such a device. It is also shown that the degree of the WVF effect is related to the width and position of the SM stripe. In particular, the WVF effect can be tuned by the applied voltage to the SM stripe, and thus a manipulable momentum filter can be obtained for nanoelectronics applications.
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Y. Narita
2009-08-01
Full Text Available Aliasing is a general problem in the analysis of any measurements that make sampling at discrete points. Sampling in the spatial domain results in a periodic pattern of spectra in the wave vector domain. This effect is called spatial aliasing, and it is of particular importance for multi-spacecraft measurements in space. We first present the theoretical background of aliasing problems in the frequency domain and generalize it to the wave vector domain, and then present model calculations of spatial aliasing. The model calculations are performed for various configurations of the reciprocal vectors and energy spectra or distribution that are placed at different positions in the wave vector domain, and exhibit two effects on aliasing. One is weak aliasing, in which the true spectrum is distorted because of non-uniform aliasing contributions in the Brillouin zone. It is demonstrated that the energy distribution becomes elongated in the shortest reciprocal lattice vector direction in the wave vector domain. The other effect is strong aliasing, in which aliases have a significant contribution in the Brillouin zone and the energy distribution shows a false peak. These results give a caveat in multi-spacecraft data analysis in that spectral anisotropy obtained by a measurement has in general two origins: (1 natural and physical origins like anisotropy imposed by a mean magnetic field or a flow direction; and (2 aliasing effects that are imposed by the configuration of the measurement array (or the set of reciprocal vectors. This manuscript also discusses a possible method to estimate aliasing contributions in the Brillouin zone based on the measured spectrum and to correct the spectra for aliasing.
Plane-wave transverse oscillation for high-frame-rate 2-D vector flow imaging.
Lenge, Matteo; Ramalli, Alessandro; Tortoli, Piero; Cachard, Christian; Liebgott, Hervé
2015-12-01
Transverse oscillation (TO) methods introduce oscillations in the pulse-echo field (PEF) along the direction transverse to the ultrasound propagation direction. This may be exploited to extend flow investigations toward multidimensional estimates. In this paper, the TOs are coupled with the transmission of plane waves (PWs) to reconstruct high-framerate RF images with bidirectional oscillations in the pulse-echo field. Such RF images are then processed by a 2-D phase-based displacement estimator to produce 2-D vector flow maps at thousands of frames per second. First, the capability of generating TOs after PW transmissions was thoroughly investigated by varying the lateral wavelength, the burst length, and the transmission frequency. Over the entire region of interest, the generated lateral wavelengths, compared with the designed ones, presented bias and standard deviation of -3.3 ± 5.7% and 10.6 ± 7.4% in simulations and experiments, respectively. The performance of the ultrafast vector flow mapping method was also assessed by evaluating the differences between the estimated velocities and the expected ones. Both simulations and experiments show overall biases lower than 20% when varying the beam-to-flow angle, the peak velocity, and the depth of interest. In vivo applications of the method on the common carotid and the brachial arteries are also presented.
Analysis and Computation of Acoustic and Elastic Wave Equations in Random Media
Motamed, Mohammad
2014-01-06
We propose stochastic collocation methods for solving the second order acoustic and elastic wave equations in heterogeneous random media and subject to deterministic boundary and initial conditions [1, 4]. We assume that the medium consists of non-overlapping sub-domains with smooth interfaces. In each sub-domain, the materials coefficients are smooth and given or approximated by a finite number of random variable. One important example is wave propagation in multi-layered media with smooth interfaces. The numerical scheme consists of a finite difference or finite element method in the physical space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space. We provide a rigorous convergence analysis and demonstrate different types of convergence of the probability error with respect to the number of collocation points under some regularity assumptions on the data. In particular, we show that, unlike in elliptic and parabolic problems [2, 3], the solution to hyperbolic problems is not in general analytic with respect to the random variables. Therefore, the rate of convergence is only algebraic. A fast spectral rate of convergence is still possible for some quantities of interest and for the wave solutions with particular types of data. We also show that the semi-discrete solution is analytic with respect to the random variables with the radius of analyticity proportional to the grid/mesh size h. We therefore obtain an exponential rate of convergence which deteriorates as the quantity h p gets smaller, with p representing the polynomial degree in the stochastic space. We have shown that analytical results and numerical examples are consistent and that the stochastic collocation method may be a valid alternative to the more traditional Monte Carlo method. Here we focus on the stochastic acoustic wave equation. Similar results are obtained for stochastic elastic equations.
Energy Technology Data Exchange (ETDEWEB)
Erlangga, Mokhammad Puput [Geophysical Engineering, Institut Teknologi Bandung, Ganesha Street no.10 Basic Science B Buliding fl.2-3 Bandung, 40132, West Java Indonesia puput.erlangga@gmail.com (Indonesia)
2015-04-16
Separation between signal and noise, incoherent or coherent, is important in seismic data processing. Although we have processed the seismic data, the coherent noise is still mixing with the primary signal. Multiple reflections are a kind of coherent noise. In this research, we processed seismic data to attenuate multiple reflections in the both synthetic and real seismic data of Mentawai. There are several methods to attenuate multiple reflection, one of them is Radon filter method that discriminates between primary reflection and multiple reflection in the τ-p domain based on move out difference between primary reflection and multiple reflection. However, in case where the move out difference is too small, the Radon filter method is not enough to attenuate the multiple reflections. The Radon filter also produces the artifacts on the gathers data. Except the Radon filter method, we also use the Wave Equation Multiple Elimination (WEMR) method to attenuate the long period multiple reflection. The WEMR method can attenuate the long period multiple reflection based on wave equation inversion. Refer to the inversion of wave equation and the magnitude of the seismic wave amplitude that observed on the free surface, we get the water bottom reflectivity which is used to eliminate the multiple reflections. The WEMR method does not depend on the move out difference to attenuate the long period multiple reflection. Therefore, the WEMR method can be applied to the seismic data which has small move out difference as the Mentawai seismic data. The small move out difference on the Mentawai seismic data is caused by the restrictiveness of far offset, which is only 705 meter. We compared the real free multiple stacking data after processing with Radon filter and WEMR process. The conclusion is the WEMR method can more attenuate the long period multiple reflection than the Radon filter method on the real (Mentawai) seismic data.
Traveltime sensitivity kernels for wave equation tomography using the unwrapped phase
Djebbi, Ramzi
2014-02-18
Wave equation tomography attempts to improve on traveltime tomography, by better adhering to the requirements of our finite-frequency data. Conventional wave equation tomography, based on the first-order Born approximation followed by cross-correlation traveltime lag measurement, or on the Rytov approximation for the phase, yields the popular hollow banana sensitivity kernel indicating that the measured traveltime at a point is insensitive to perturbations along the ray theoretical path at certain finite frequencies. Using the instantaneous traveltime, which is able to unwrap the phase of the signal, instead of the cross-correlation lag, we derive new finite-frequency traveltime sensitivity kernels. The kernel reflects more the model-data dependency, we typically encounter in full waveform inversion. This result confirms that the hollow banana shape is borne of the cross-correlation lag measurement, which exposes the Born approximations weakness in representing transmitted waves. The instantaneous traveltime can thus mitigate the additional component of nonlinearity introduced by the hollow banana sensitivity kernels in finite-frequency traveltime tomography. The instantaneous traveltime simply represents the unwrapped phase of Rytov approximation, and thus is a good alternative to Born and Rytov to compute the misfit function for wave equation tomography. We show the limitations of the cross-correlation associated with Born approximation for traveltime lag measurement when the source signatures of the measured and modelled data are different. The instantaneous traveltime is proven to be less sensitive to the distortions in the data signature. The unwrapped phase full banana shape of the sensitivity kernels shows smoother update compared to the banana–doughnut kernels. The measurement of the traveltime delay caused by a small spherical anomaly, embedded into a 3-D homogeneous model, supports the full banana sensitivity assertion for the unwrapped phase.
Energy Technology Data Exchange (ETDEWEB)
Huang, Lianjie [Los Alamos National Laboratory; Simonetti, Francesco [IMPERIAL COLLEGE LONDON; Huthwaite, Peter [IMPERIAL COLLEGE LONDON; Rosenberg, Robert [UNM; Williamson, Michael [UNM
2010-01-01
Ultrasound image resolution and quality need to be significantly improved for breast microcalcification detection. Super-resolution imaging with the factorization method has recently been developed as a promising tool to break through the resolution limit of conventional imaging. In addition, wave-equation reflection imaging has become an effective method to reduce image speckles by properly handling ultrasound scattering/diffraction from breast heterogeneities during image reconstruction. We explore the capabilities of a novel super-resolution ultrasound imaging method and a wave-equation reflection imaging scheme for detecting breast microcalcifications. Super-resolution imaging uses the singular value decomposition and a factorization scheme to achieve an image resolution that is not possible for conventional ultrasound imaging. Wave-equation reflection imaging employs a solution to the acoustic-wave equation in heterogeneous media to backpropagate ultrasound scattering/diffraction waves to scatters and form images of heterogeneities. We construct numerical breast phantoms using in vivo breast images, and use a finite-difference wave-equation scheme to generate ultrasound data scattered from inclusions that mimic microcalcifications. We demonstrate that microcalcifications can be detected at full spatial resolution using the super-resolution ultrasound imaging and wave-equation reflection imaging methods.
Cui, Lei; Tong, Fei-Fei; Shi, Feng
2011-09-01
Researches on breaking-induced currents by waves are summarized firstly in this paper. Then, a combined numerical model in orthogonal curvilinear coordinates is presented to simulate wave-induced current in areas with curved boundary or irregular coastline. The proposed wave-induced current model includes a nearshore current module established through orthogonal curvilinear transformation form of shallow water equations and a wave module based on the curvilinear parabolic approximation wave equation. The wave module actually serves as the driving force to provide the current module with required radiation stresses. The Crank-Nicolson finite difference scheme and the alternating directions implicit method are used to solve the wave and current module, respectively. The established surf zone currents model is validated by two numerical experiments about longshore currents and rip currents in basins with rip channel and breakwater. The numerical results are compared with the measured data and published numerical results.
Born reflection kernel analysis and wave-equation reflection traveltime inversion in elastic media
Wang, Tengfei
2017-08-17
Elastic reflection waveform inversion (ERWI) utilize the reflections to update the low and intermediate wavenumbers in the deeper part of model. However, ERWI suffers from the cycle-skipping problem due to the objective function of waveform residual. Since traveltime information relates to the background model more linearly, we use the traveltime residuals as objective function to update background velocity model using wave equation reflected traveltime inversion (WERTI). The reflection kernel analysis shows that mode decomposition can suppress the artifacts in gradient calculation. We design a two-step inversion strategy, in which PP reflections are firstly used to invert P wave velocity (Vp), followed by S wave velocity (Vs) inversion with PS reflections. P/S separation of multi-component seismograms and spatial wave mode decomposition can reduce the nonlinearity of inversion effectively by selecting suitable P or S wave subsets for hierarchical inversion. Numerical example of Sigsbee2A model validates the effectiveness of the algorithms and strategies for elastic WERTI (E-WERTI).
A comparative study of diffraction of shallow-water waves by high-level IGN and GN equations
Energy Technology Data Exchange (ETDEWEB)
Zhao, B.B. [College of Shipbuilding Engineering, Harbin Engineering University, 150001 Harbin (China); Ertekin, R.C. [Department of Ocean and Resources Engineering, University of Hawai' i, Honolulu, HI 96822 (United States); College of Shipbuilding Engineering, Harbin Engineering University, 150001 Harbin (China); Duan, W.Y., E-mail: duanwenyangheu@hotmail.com [College of Shipbuilding Engineering, Harbin Engineering University, 150001 Harbin (China)
2015-02-15
This work is on the nonlinear diffraction analysis of shallow-water waves, impinging on submerged obstacles, by two related theories, namely the classical Green–Naghdi (GN) equations and the Irrotational Green–Naghdi (IGN) equations, both sets of equations being at high levels and derived for incompressible and inviscid flows. Recently, the high-level Green–Naghdi equations have been applied to some wave transformation problems. The high-level IGN equations have also been used in the last decade to study certain wave propagation problems. However, past works on these theories used different numerical methods to solve these nonlinear and unsteady sets of differential equations and at different levels. Moreover, different physical problems have been solved in the past. Therefore, it has not been possible to understand the differences produced by these two sets of theories and their range of applicability so far. We are thus motivated to make a direct comparison of the results produced by these theories by use of the same numerical method to solve physically the same wave diffraction problems. We focus on comparing these two theories by using similar codes; only the equations used are different but other parts of the codes, such as the wave-maker, damping zone, discretion method, matrix solver, etc., are exactly the same. This way, we eliminate many potential sources of differences that could be produced by the solution of different equations. The physical problems include the presence of various submerged obstacles that can be used for example as breakwaters or to represent the continental shelf. A numerical wave tank is created by placing a wavemaker on one end and a wave absorbing beach on the other. The nonlinear and unsteady sets of differential equations are solved by the finite-difference method. The results are compared with different equations as well as with the available experimental data.
Local energy decay for wave equation in the absence of resonance at zero energy in 3D
Georgiev, Vladimir; Tarulli, Mirko
2011-01-01
In this paper we study spectral properties associated to Schrodinger operator with potential that is an exponential decaying function. As applications we prove local energy decay for solutions to the perturbed wave equation and lack of resonances for the NLS.
Dispersion equations for field-aligned cyclotron waves in axisymmetric magnetospheric plasmas
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N. I. Grishanov
2006-03-01
Full Text Available In this paper, we derive the dispersion equations for field-aligned cyclotron waves in two-dimensional (2-D magnetospheric plasmas with anisotropic temperature. Two magnetic field configurations are considered with dipole and circular magnetic field lines. The main contribution of the trapped particles to the transverse dielectric permittivity is estimated by solving the linearized Vlasov equation for their perturbed distribution functions, accounting for the cyclotron and bounce resonances, neglecting the drift effects, and assuming the weak connection of the left-hand and right-hand polarized waves. Both the bi-Maxwellian and bi-Lorentzian distribution functions are considered to model the ring current ions and electrons in the dipole magnetosphere. A numerical code has been developed to analyze the dispersion characteristics of electromagnetic ion-cyclotron waves in an electron-proton magnetospheric plasma with circular magnetic field lines, assuming that the steady-state distribution function of the energetic protons is bi-Maxwellian. As in the uniform magnetic field case, the growth rate of the proton-cyclotron instability (PCI in the 2-D magnetospheric plasmas is defined by the contribution of the energetic ions/protons to the imaginary part of the transverse permittivity elements. We demonstrate that the PCI growth rate in the 2-D axisymmetric plasmasphere can be significantly smaller than that for the straight magnetic field case with the same macroscopic bulk parameters.
Wave front-ray synthesis for solving the multidimensional quantum Hamilton-Jacobi equation
Energy Technology Data Exchange (ETDEWEB)
Wyatt, Robert E.; Chou, Chia-Chun [Institute for Theoretical Chemistry and Department of Chemistry and Biochemistry, University of Texas at Austin, Austin, Texas 78712 (United States)
2011-08-21
A Cauchy initial-value approach to the complex-valued quantum Hamilton-Jacobi equation (QHJE) is investigated for multidimensional systems. In this approach, ray segments foliate configuration space which is laminated by surfaces of constant action. The QHJE incorporates all quantum effects through a term involving the divergence of the quantum momentum function (QMF). The divergence term may be expressed as a sum of two terms, one involving displacement along the ray and the other incorporating the local curvature of the action surface. It is shown that curvature of the wave front may be computed from coefficients of the first and second fundamental forms from differential geometry that are associated with the surface. Using the expression for the divergence, the QHJE becomes a Riccati-type ordinary differential equation (ODE) for the complex-valued QMF, which is parametrized by the arc length along the ray. In order to integrate over possible singularities in the QMF, a stable and accurate Moebius propagator is introduced. This method is then used to evolve rays and wave fronts for four systems in two and three dimensions. From the QMF along each ray, the wave function can be easily computed. Computational difficulties that may arise are described and some ways to circumvent them are presented.
Fast solution of elliptic partial differential equations using linear combinations of plane waves.
Pérez-Jordá, José M
2016-02-01
Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations Ax=b, where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O(NlogN) memory and executing an iteration in O(Nlog(2)N) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.
A correction function method for the wave equation with interface jump conditions
Abraham, David S.; Marques, Alexandre Noll; Nave, Jean-Christophe
2018-01-01
In this paper a novel method to solve the constant coefficient wave equation, subject to interface jump conditions, is presented. In general, such problems pose issues for standard finite difference solvers, as the inherent discontinuity in the solution results in erroneous derivative information wherever the stencils straddle the given interface. Here, however, the recently proposed Correction Function Method (CFM) is used, in which correction terms are computed from the interface conditions, and added to affected nodes to compensate for the discontinuity. In contrast to existing methods, these corrections are not simply defined at affected nodes, but rather generalized to a continuous function within a small region surrounding the interface. As a result, the correction function may be defined in terms of its own governing partial differential equation (PDE) which may be solved, in principle, to arbitrary order of accuracy. The resulting scheme is not only arbitrarily high order, but also robust, having already seen application to Poisson problems and the heat equation. By extending the CFM to this new class of PDEs, the treatment of wave interface discontinuities in homogeneous media becomes possible. This allows, for example, for the straightforward treatment of infinitesimal source terms and sharp boundaries, free of staircasing errors. Additionally, new modifications to the CFM are derived, allowing compatibility with explicit multi-step methods, such as Runge-Kutta (RK4), without a reduction in accuracy. These results are then verified through numerous numerical experiments in one and two spatial dimensions.
Johnson, Kennita A.; Vormohr, Hannah R.; Doinikov, Alexander A.; Bouakaz, Ayache; Shields, C. Wyatt; López, Gabriel P.; Dayton, Paul A.
2016-05-01
Acoustophoresis uses acoustic radiation force to remotely manipulate particles suspended in a host fluid for many scientific, technological, and medical applications, such as acoustic levitation, acoustic coagulation, contrast ultrasound imaging, ultrasound-assisted drug delivery, etc. To estimate the magnitude of acoustic radiation forces, equations derived for an inviscid host fluid are commonly used. However, there are theoretical predictions that, in the case of a traveling wave, viscous effects can dramatically change the magnitude of acoustic radiation forces, which make the equations obtained for an inviscid host fluid invalid for proper estimation of acoustic radiation forces. To date, experimental verification of these predictions has not been published. Experimental measurements of viscous effects on acoustic radiation forces in a traveling wave were conducted using a confocal optical and acoustic system and values were compared with available theories. Our results show that, even in a low-viscosity fluid such as water, the magnitude of acoustic radiation forces is increased manyfold by viscous effects in comparison with what follows from the equations derived for an inviscid fluid.
Lawrenz, Marco; Finsterbusch, Jürgen
2011-11-01
Double-wave-vector diffusion-weighting experiments can detect diffusion anisotropy on a microscopic level which, e.g., could distinguish lower fiber densities from reduced fiber coherence. The underlying signal difference between parallel and orthogonal wave vector orientations has been observed on vertical-bore MR systems (≥500 mT m(-1) ); however, numerical simulations reveal that it is expected to be considerably reduced for typical whole-body MR gradient pulse durations. Here, pig spinal cord tissue and a reference fluid phantom were investigated on a 3 T clinical MR system (40 mT m(-1) ). By averaging over different absolute wave vector orientations, signal variations caused by experimental imperfections like background gradient fields and eddy currents were minimized and a rotationally invariant anisotropy measure could be assessed. A significant microscopic anisotropy was observed in gray and white matter tissue even in the plane perpendicular to the cord which is consistent with previous vertical-bore experiments. Thus, it is demonstrated that double-wave-vector experiments can investigate the microscopic anisotropy on whole-body MR systems. Copyright © 2011 Wiley Periodicals, Inc.
Li, Xinying; Xu, Yuming; Yu, Jianjun
2016-09-15
We propose a new scheme to generate single-sideband (SSB) photonic vector millimeter-wave (mm-wave) signal adopting asymmetrical SSB modulation enabled by a single in-phase/quadrature (I/Q) modulator. The driving signal for the I/Q modulator is generated by software-based digital signal processing (DSP) instead of a complicated transmitter electrical circuit, which significantly simplifies the system architecture and increases system stability. One vector-modulated optical sideband and one unmodulated optical sideband, with different sideband frequencies, located at two sides of a significantly suppressed central optical carrier, are generated by the I/Q modulator and used for heterodyne beating to generate the electrical vector mm-wave signal. The two optical sidebands are robust to fiber dispersion and can be transmitted over relatively long-haul fiber. We experimentally demonstrate the generation and transmission of 4-Gbaud 80-GHz quadrature-phase-shift-keying-modulated (QPSK-modulated) SSB vector mm-wave signal over 240-km single-mode fiber-28 without optical dispersion compensation.
Lawrenz, Marco; Finsterbusch, Jürgen
2013-04-01
Diffusion-tensor imaging is widely used to characterize diffusion in biological tissue, however, the derived anisotropy information, e.g., the fractional anisotropy, is ambiguous. For instance, low values of the diffusion anisotropy in brain white matter voxels may reflect a reduced axon density, i.e., a loss of fibers, or a lower fiber coherence within the voxel, e.g., more crossing fibers. This ambiguity can be avoided with experiments involving two diffusion-weighting periods applied successively in a single acquisition, so-called double-wave-vector or double-pulsed-field-gradient experiments. For a long mixing time between the two periods such experiments are sensitive to the cells' eccentricity, i.e., the diffusion anisotropy present on a microscopic scale. In this study, it is shown that this microscopic diffusion anisotropy can be detected in white matter in the living human brain, even in a macroscopically isotropic region-of-interest (fractional anisotropy = 0). The underlying signal difference between parallel and orthogonal wave vector orientations does not show up in standard diffusion-weighting experiments but is specific to the double-wave-vector experiment. Furthermore, the modulation amplitude observed is very similar for regions-of-interest with different fractional anisotrpy values. Thus, double-wave-vector experiments may provide a direct and reliable access to white matter integrity independent of the actual fiber orientation distribution within the voxel. Copyright © 2012 Wiley Periodicals, Inc.
Barada, Daisuke; Ochiai, Takanori; Fukuda, Takashi; Kawata, Shigeo; Kuroda, Kazuo; Yatagai, Toyohiko
2012-11-01
In this Letter, the principle of polarization holography for recording an arbitrary vector wave on a thin polarization-sensitive recording medium is proposed. It is analytically shown that the complex amplitudes of p- and s-polarization components are simultaneously recorded and independently reconstructed by using an s-polarized reference beam. The characteristics are experimentally verified.
Hoenders, B.J.
1996-01-01
The geometrical optical concept of rays is generalized for fields generated by any system of coupled non-linear partial differential equations of arbitrary order like the vector wave equations for (non)linear media, the Maxwell equations, the equations of magneto-hydrodynamics, the system of
Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru; Sushila
2018-02-01
In this work, we aim to present a new fractional extension of regularized long-wave equation. The regularized long-wave equation is a very important mathematical model in physical sciences, which unfolds the nature of shallow water waves and ion acoustic plasma waves. The existence and uniqueness of the solution of the regularized long-wave equation associated with Atangana-Baleanu fractional derivative having Mittag-Leffler type kernel is verified by implementing the fixed-point theorem. The numerical results are derived with the help of an iterative algorithm. In order to show the effects of various parameters and variables on the displacement, the numerical results are presented in graphical and tabular form.
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).
Manning, Robert M.
2004-01-01
The extended wide-angle parabolic wave equation applied to electromagnetic wave propagation in random media is considered. A general operator equation is derived which gives the statistical moments of an electric field of a propagating wave. This expression is used to obtain the first and second order moments of the wave field and solutions are found that transcend those which incorporate the full paraxial approximation at the outset. Although these equations can be applied to any propagation scenario that satisfies the conditions of application of the extended parabolic wave equation, the example of propagation through atmospheric turbulence is used. It is shown that in the case of atmospheric wave propagation and under the Markov approximation (i.e., the delta-correlation of the fluctuations in the direction of propagation), the usual parabolic equation in the paraxial approximation is accurate even at millimeter wavelengths. The comprehensive operator solution also allows one to obtain expressions for the longitudinal (generalized) second order moment. This is also considered and the solution for the atmospheric case is obtained and discussed. The methodology developed here can be applied to any qualifying situation involving random propagation through turbid or plasma environments that can be represented by a spectral density of permittivity fluctuations.
Singular solutions to Protter's problem for the 3-D wave equation involving lower order terms
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Myron K. Grammatikopoulos
2003-01-01
Full Text Available In 1952, at a conference in New York, Protter formulated some boundary value problems for the wave equation, which are three-dimensional analogues of the Darboux problems (or Cauchy-Goursat problems on the plane. Protter studied these problems in a 3-D domain $Omega_0$, bounded by two characteristic cones $Sigma_1$ and $Sigma_{2,0}$, and by a plane region $Sigma_0$. It is well known that, for an infinite number of smooth functions in the right-hand side, these problems do not have classical solutions. Popivanov and Schneider (1995 discovered the reason of this fact for the case of Dirichlet's and Neumann's conditions on $Sigma_0$: the strong power-type singularity appears in the generalized solution on the characteristic cone $Sigma_{2,0}$. In the present paper we consider the case of third boundary-value problem on $Sigma_0$ and obtain the existence of many singular solutions for the wave equation involving lower order terms. Especifica ally, for Protter's problems in $mathbb{R}^{3}$ it is shown here that for any $nin N$ there exists a $C^{n}({Omega}_0$-function, for which the corresponding unique generalized solution belongs to $C^{n}({Omega}_0slash O$ and has a strong power type singularity at the point $O$. This singularity is isolated at the vertex $O$ of the characteristic cone $Sigma_{2,0}$ and does not propagate along the cone. For the wave equation without lower order terms, we presented the exact behavior of the singular solutions at the point $O$.
A scattering theory for the wave equation on Kerr black hole exteriors
Dafermos, Mihalis; Shlapentokh-Rothman, Yakov
2014-01-01
We develop a definitive physical-space scattering theory for the scalar wave equation on Kerr exterior backgrounds in the general subextremal case |a|
An arbitrary-order staggered time integrator for the linear acoustic wave equation
Lee, Jaejoon; Park, Hyunseo; Park, Yoonseo; Shin, Changsoo
2018-02-01
We suggest a staggered time integrator whose order of accuracy can arbitrarily be extended to solve the linear acoustic wave equation. A strategy to select the appropriate order of accuracy is also proposed based on the error analysis that quantitatively predicts the truncation error of the numerical solution. This strategy not only reduces the computational cost several times, but also allows us to flexibly set the modelling parameters such as the time step length, grid interval and P-wave speed. It is demonstrated that the proposed method can almost eliminate temporal dispersive errors during long term simulations regardless of the heterogeneity of the media and time step lengths. The method can also be successfully applied to the source problem with an absorbing boundary condition, which is frequently encountered in the practical usage for the imaging algorithms or the inverse problems.
Mixed Initial-Boundary Value Problem for the Capillary Wave Equation
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B. Juarez Campos
2016-01-01
Full Text Available We study the mixed initial-boundary value problem for the capillary wave equation: iut+u2u=∂x3/2u, t>0, x>0; u(x,0=u0(x, x>0; u(0,t+βux(0,t=h(t, t>0, where ∂x3/2u=(1/2π∫0∞signx-y/x-yuyy(y dy. We prove the global in-time existence of solutions of IBV problem for nonlinear capillary equation with inhomogeneous Robin boundary conditions. Also we are interested in the study of the asymptotic behavior of solutions.
General decay of solutions of a nonlinear system of viscoelastic wave equations
Said-Houari, Belkacem
2011-04-16
This work is concerned with a system of two viscoelastic wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we prove that, for certain class of relaxation functions and for some restrictions on the initial data, the rate of decay of the total energy depends on those of the relaxation functions. This result improves many results in the literature, such as the ones in Messaoudi and Tatar (Appl. Anal. 87(3):247-263, 2008) and Liu (Nonlinear Anal. 71:2257-2267, 2009) in which only the exponential and polynomial decay rates are considered. © 2011 Springer Basel AG.
On global attraction to solitary waves for the Klein–Gordon equation with concentrated nonlinearity
Kopylova, Elena
2017-11-01
The global attraction is proved for the nonlinear three-dimensional Klein–Gordon equation with a nonlinearity concentrated at one point. Our main result is the convergence of each ‘finite energy solution’ to the manifold of all solitary waves as t\\to+/-∞ . This global attraction is caused by the nonlinear energy transfer from lower harmonics to the continuous spectrum and subsequent dispersion radiation. We justify this mechanism by the following strategy based on inflation of spectrum by the nonlinearity. We show that any omega-limit trajectory has the time-spectrum in the spectral gap [-m, m] and satisfies the original equation. Then the application of the Titchmarsh convolution theorem reduces the spectrum of each omega-limit trajectory to a single frequency \
Equation of state with scale-invariant hidden local symmetry and gravitational waves
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Lee Hyun Kyu
2018-01-01
Full Text Available The equation of state (EoS for the effective theory proposed recently in the frame work of the scale-invariant hidden local symmetry is discussed briefly. The EoS is found to be relatively stiffer at lower density and but relatively softer at higher density. The particular features of EoS on the gravitational waves are discussed. A relatively stiffer EoS for the neutron stars with the lower density induces a larger deviation of the gravitational wave form from the point-particle-approximation. On the other hand, a relatively softer EoS for the merger remnant of the higher density inside might invoke a possibility of the immediate formation of a black hole for short gamma ray bursts or the appearance of the higher peak frequency for gravitational waves from remnant oscillations. It is anticipated that this particular features could be probed in detail by the detections of gravitational waves from the binary neutron star mergers.
Fundamental solutions to the p-Laplace equation in a class of Grushin vector fields
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Thomas Bieske
2011-06-01
Full Text Available We find the fundamental solution to the p-Laplace equation in a class of Grushin-type spaces. The singularity occurs at the sub-Riemannian points, which naturally corresponds to finding the fundamental solution of a generalized Grushin operator in Euclidean space. We then use this solution to find an infinite harmonic function with specific boundary data and to compute the capacity of annuli centered at the singularity.
Global Nonexistence of Solutions for Viscoelastic Wave Equations of Kirchhoff Type with High Energy
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Gang Li
2012-01-01
Full Text Available We consider viscoelastic wave equations of the Kirchhoff type utt-M(∥∇u∥22Δu+∫0tg(t-sΔu(sds+ut=|u|p-1u with Dirichlet boundary conditions, where ∥⋅∥p denotes the norm in the Lebesgue space Lp. Under some suitable assumptions on g and the initial data, we establish a global nonexistence result for certain solutions with arbitrarily high energy, in the sense that limt→T*-(∥u(t∥22+∫0t∥u(s∥22ds=∞ for some 0
Skeletonized Wave Equation Inversion in VTI Media without too much Math
Feng, Shihang
2017-05-17
We present a tutorial for skeletonized inversion of pseudo-acoustic anisotropic VTI data. We first invert for the anisotropic models using wave equation traveltime inversion. Here, the skeletonized data are the traveltimes of transmitted and/or reflected arrivals that lead to simpler misfit functions and more robust convergence compared to full waveform inversion. This provides a good starting model for waveform inversion. The effectiveness of this procedure is illustrated with synthetic data examples and a marine data set recorded in the Gulf of Mexico.
Gerbi, Stéphane
2013-01-15
The goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin method combined with the fixed point theorem, we show the existence and uniqueness of a local in time solution. Second, we show that under some restrictions on the initial data, the solution continues to exist globally in time. On the other hand, if the interior source dominates the boundary damping, then the solution is unbounded and grows as an exponential function. In addition, in the absence of the strong damping, then the solution ceases to exist and blows up in finite time.
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Hassan Kamil Jassim
2016-01-01
Full Text Available We used the local fractional variational iteration transform method (LFVITM coupled by the local fractional Laplace transform and variational iteration method to solve three-dimensional diffusion and wave equations with local fractional derivative operator. This method has Lagrange multiplier equal to minus one, which makes the calculations more easily. The obtained results show that the presented method is efficient and yields a solution in a closed form. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new method.
Solitary and Jacobi elliptic wave solutions of the generalized Benjamin-Bona-Mahony equation
Belobo, Didier Belobo; Das, Tapas
2017-07-01
Exact bright, dark, antikink solitary waves and Jacobi elliptic function solutions of the generalized Benjamin-Bona-Mahony equation with arbitrary power-law nonlinearity will be constructed in this work. The method used to carry out the integration is the F-expansion method. Solutions obtained have fractional and integer negative or positive power-law nonlinearities. These solutions have many free parameters such that they may be used to simulate many experimental situations, and to precisely control the dynamics of the system.
On asymptotic stability of standing waves of discrete Schr\\"odinger equation in $\\Bbb Z$
Cuccagna, Scipio; Tarulli, Mirko
2008-01-01
We prove an analogue of a classical asymptotic stability result of standing waves of the Schr\\"odinger equation originating in work by Soffer and Weinstein. Specifically, our result is a transposition on the lattice Z of a result by Mizumachi and it involves a discrete Schr\\"odinger operator H. The decay rates on the potential are less stringent than in Mizumachi, since we require for the potential $q\\in \\ell ^{1,1}$. We also prove $|e^{itH}(n,m)|\\le C ^{-1/3}$ for a fixed $C$ requiring...
High frequency computation in wave equations and optimal design for a cavity
Lai, Jun
Two types of problems are studied in this thesis. One part of the thesis is devoted to high frequency computation. Motivated by fast multiscale Gaussian wavepacket transforms and multiscale Gaussian beam methods which were originally designed for initial value problems of wave equations in the high frequency regime, we develop fast multiscale Gaussian beam methods for wave equations in bounded convex domains in the high frequency regime. To compute the wave propagation in bounded convex domains, we have to take into account reflecting multiscale Gaussian beams, which are accomplished by enforcing reflecting boundary conditions during beam propagation and carrying out suitable reflecting beam summation. To propagate multiscale beams efficiently, we prove that the ratio of the squared magnitude of beam amplitude and the beam width is roughly conserved, and accordingly we propose an effective indicator to identify significant beams. We also prove that the resulting multiscale Gaussian beam methods converge asymptotically. Numerical examples demonstrate the accuracy and efficiency of the method. The second part of the thesis studies the reduction of backscatter radar cross section (RCS) for a cavity embedded in the ground plane. One approach for RCS reduction is through the coating material. Assume the bottom of the cavity is coated by a thin, multilayered radar absorbing material (RAM) with possibly different permittivities. The objective is to minimize the backscatter RCS by the incidence of a plane wave over a single or a set of incident angles and frequencies. By formulating the scattering problem as a Helmholtz equation with artificial boundary condition, the gradient with respect to the material permittivities is determined efficiently by the adjoint state method, which is integrated into a nonlinear optimization scheme. Numerical example shows the RCS may be significantly reduced. Another approach is through shape optimization. By introducing a transparent
Time adaptivity in the diffusive wave approximation to the shallow water equations
Collier, Nathan
2013-05-01
We discuss the use of time adaptivity applied to the one dimensional diffusive wave approximation to the shallow water equations. A simple and computationally economical error estimator is discussed which enables time-step size adaptivity. This robust adaptive time discretization corrects the initial time step size to achieve a user specified bound on the discretization error and allows time step size variations of several orders of magnitude. In particular, the one dimensional results presented in this work feature a change of four orders of magnitudes for the time step over the entire simulation. © 2011 Elsevier B.V.
Super-Grid Modeling of the Elastic Wave Equation in Semi-Bounded Domains
Energy Technology Data Exchange (ETDEWEB)
Petersson, N. Anders; Sjögreen, Björn
2014-10-01
We develop a super-grid modeling technique for solving the elastic wave equation in semi-bounded two- and three-dimensional spatial domains. In this method, waves are slowed down and dissipated in sponge layers near the far-field boundaries. Mathematically, this is equivalent to a coordinate mapping that transforms a very large physical domain to a significantly smaller computational domain, where the elastic wave equation is solved numerically on a regular grid. To damp out waves that become poorly resolved because of the coordinate mapping, a high order artificial dissipation operator is added in layers near the boundaries of the computational domain. We prove by energy estimates that the super-grid modeling leads to a stable numerical method with decreasing energy, which is valid for heterogeneous material properties and a free surface boundary condition on one side of the domain. Our spatial discretization is based on a fourth order accurate finite difference method, which satisfies the principle of summation by parts. We show that the discrete energy estimate holds also when a centered finite difference stencil is combined with homogeneous Dirichlet conditions at several ghost points outside of the far-field boundaries. Therefore, the coefficients in the finite difference stencils need only be boundary modified near the free surface. This allows for improved computational efficiency and significant simplifications of the implementation of the proposed method in multi-dimensional domains. Numerical experiments in three space dimensions show that the modeling error from truncating the domain can be made very small by choosing a sufficiently wide super-grid damping layer. The numerical accuracy is first evaluated against analytical solutions of Lamb’s problem, where fourth order accuracy is observed with a sixth order artificial dissipation. We then use successive grid refinements to study the numerical accuracy in the more
Uysal, Ismail Enes
2016-08-09
Transient electromagnetic interactions on plasmonic nanostructures are analyzed by solving the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) surface integral equation (SIE). Equivalent (unknown) electric and magnetic current densities, which are introduced on the surfaces of the nanostructures, are expanded using Rao-Wilton-Glisson and polynomial basis functions in space and time, respectively. Inserting this expansion into the PMCHWT-SIE and Galerkin testing the resulting equation at discrete times yield a system of equations that is solved for the current expansion coefficients by a marching on-in-time (MOT) scheme. The resulting MOT-PMCHWT-SIE solver calls for computation of additional convolutions between the temporal basis function and the plasmonic medium\\'s permittivity and Green function. This computation is carried out with almost no additional cost and without changing the computational complexity of the solver. Time-domain samples of the permittivity and the Green function required by these convolutions are obtained from their frequency-domain samples using a fast relaxed vector fitting algorithm. Numerical results demonstrate the accuracy and applicability of the proposed MOT-PMCHWT solver. © 2016 Optical Society of America.
Poznanski, R R
2010-09-01
A reaction-diffusion model is presented to encapsulate calcium-induced calcium release (CICR) as a potential mechanism for somatofugal bias of dendritic calcium movement in starburst amacrine cells. Calcium dynamics involves a simple calcium extrusion (pump) and a buffering mechanism of calcium binding proteins homogeneously distributed over the plasma membrane of the endoplasmic reticulum within starburst amacrine cells. The system of reaction-diffusion equations in the excess buffer (or low calcium concentration) approximation are reformulated as a nonlinear Volterra integral equation which is solved analytically via a regular perturbation series expansion in response to calcium feedback from a continuously and uniformly distributed calcium sources. Calculation of luminal calcium diffusion in the absence of buffering enables a wave to travel at distances of 120 μm from the soma to distal tips of a starburst amacrine cell dendrite in 100 msec, yet in the presence of discretely distributed calcium-binding proteins it is unknown whether the propagating calcium wave-front in the somatofugal direction is further impeded by endogenous buffers. If so, this would indicate CICR to be an unlikely mechanism of retinal direction selectivity in starburst amacrine cells.
Chen, Wen; Fang, Jun; Pang, Guofei; Holm, Sverre
2017-01-01
This paper proposes a fractional biharmonic operator equation model in the time-space domain to describe scattering attenuation of acoustic waves in heterogeneous media. Compared with the existing models, the proposed fractional model is able to describe arbitrary frequency-dependent scattering attenuation, which typically obeys an empirical power law with an exponent ranging from 0 to 4. In stark contrast to an extensive and rapidly increasing application of the fractional derivative models for wave absorption attenuation in the literature, little has been reported on frequency-dependent scattering attenuation. This is largely because the order of the fractional Laplacian is from 0 to 2 and is infeasible for scattering attenuation. In this study, the definition of the fractional biharmonic operator in space with an order varying from 0 to 4 is proposed, as well as a fractional biharmonic operator equation model of scattering attenuation which is consistent with arbitrary frequency power-law dependency and obeys the causal relation under the smallness approximation. Finally, the correlation between the fractional order and the ratio of wavelength to the diameter of the scattering heterogeneity is investigated and an expression on exponential form is also provided.
Extended common-image-point gathers for anisotropic wave-equation migration
Sava, Paul C.
2010-01-01
In regions characterized by complex subsurface structure, wave-equation depth migration is a powerful tool for accurately imaging the earth’s interior. The quality of the final image greatly depends on the quality of the model which includes anisotropy parameters (Gray et al., 2001). In particular, it is important to construct subsurface velocity models using techniques that are consistent with the methods used for imaging. Generally speaking, there are two possible strategies for velocity estimation from surface seismic data in the context of wavefield-based imaging (Sava et al., 2010). One possibility is to formulate an objective function in the data space, prior to migration, by matching the recorded data with simulated data. Techniques in this category are known by the name of waveform inversion. Another possibility is to formulate an objective function in the image space, after migration, by measuring and correcting image features that indicate model inaccuracies. Techniques in this category are known as wave-equation migration velocity analysis (MVA).
Eigenvalue solution for the convected wave equation in a circular soft wall duct
Alonso, Jose S.; Burdisso, Ricardo A.
2008-09-01
A numerical approach to find the eigenvalues of the wave equation applied in a circular duct with convective flow and soft wall boundary conditions is proposed. The characteristic equation is solved in the frequency domain as a function of a locally reacting acoustic impedance and the flow Mach number. In addition, the presence of the convective flow couples the solution of the eigenvalues with the axial propagation constants. The unknown eigenvalues are also related to these propagation constants by a quadratic expression that leads to two solutions. These two solutions replaced into the characteristic equation generate two separate eigenvalue problems depending on the direction of propagation. Given that the resulting nonlinear complex-valued equations do not provide the solution explicitly, a numerical technique must be used. The proposed approach is based on the minimization of the absolute value of the characteristic equation by the Nelder-Mead simplex method. The main advantage of this method is that it only uses function evaluations, rather than derivatives, and geometric reasoning. The minimization is performed starting from very low frequencies and increasing by small steps to the particular frequency of interest. The initial guess for the first frequency of calculation is provided as the hard wall eigenvalue solution. Then, the solution from the previous step is used as the initial value for the next calculation. This approach was specifically developed for applications with resonator-type liners commonly used in the commercial aviation industry, where the low-frequency behavior resembles that of a hard wall and agrees with the first initial guess for the first frequency of calculation. The numerical technique was found to be very robust in terms of convergence and stability. Also, the method provides a physical meaning for each eigenvalue since the variation as a function of frequency can be clearly followed with respect to the values that are originally
On exact solutions of a heat-wave type with logarithmic front for the porous medium equation
Kazakov, A. L.; Lempert, A. A.; Orlov, S. S.; Orlov, S. S.
2017-10-01
The paper deals with a nonlinear second-order parabolic equation with partial derivatives, which is usually called “the porous medium equation”. It describes the processes of heat and mass transfer as well as filtration of liquids and gases in porous media. In addition, it is used for mathematical modeling of growth and migration of population. Usually this equation is studied numerically like most other nonlinear equations of mathematical physics. So, the construction of exact solution in an explicit form is important to verify the numerical algorithms. The authors deal with a special solutions which are usually called “heat waves”. A new class of heat-wave type solutions of one-dimensional (plane-symmetric) porous medium equation is proposed and analyzed. A logarithmic heat wave front is studied in details. Considered equation has a singularity at the heat wave front, because the factor of the highest (second) derivative vanishes. The construction of these exact solutions reduces to the integration of a nonlinear second-order ordinary differential equation (ODE). Moreover, the Cauchy conditions lead us to the fact that this equation has a singularity at the initial point. In other words, the ODE inherits the singularity of the original problem. The qualitative analysis of the solutions of the ODE is carried out. The obtained results are interpreted from the point of view of the corresponding heat waves’ behavior. The most interesting is a damped solitary wave, the length of which is constant, and the amplitude decreases.
Pagán, Vincent R; Murphy, Thomas E
2015-06-01
We describe and demonstrate an electro-optic technique to simultaneously downconvert and demodulate vector-modulated millimeter-wave signals. The system uses electro-optic phase modulation and optical filtering to perform harmonic downconversion of the RF signal to an intermediate frequency (IF) or to baseband. We demonstrate downconversion of RF signals between 7 and 70-GHz to IFs below 20-GHz. Furthermore, we show harmonic downconversion and vector demodulation of 2.5-Gb/s QPSK and 5-Gb/s 16-QAM signals at carrier frequencies of 40-GHz to baseband.
Sun, Wen-Rong; Wang, Lei
2018-01-01
To show the existence and properties of matter rogue waves in an F =1 spinor Bose-Einstein condensate (BEC), we work on the three-component Gross-Pitaevskii (GP) equations. Via the Darboux-dressing transformation, we obtain a family of rational solutions describing the extreme events, i.e. rogue waves. This family of solutions includes bright-dark-bright and bright-bright-bright rogue waves. The algebraic construction depends on Lax matrices and their Jordan form. The conditions for the existence of rogue wave solutions in an F =1 spinor BEC are discussed. For the three-component GP equations, if there is modulation instability, it is of baseband type only, confirming our analytic conditions. The energy transfers between the waves are discussed.
Sun, Wen-Rong; Wang, Lei
2018-01-01
To show the existence and properties of matter rogue waves in an F=1 spinor Bose-Einstein condensate (BEC), we work on the three-component Gross-Pitaevskii (GP) equations. Via the Darboux-dressing transformation, we obtain a family of rational solutions describing the extreme events, i.e. rogue waves. This family of solutions includes bright-dark-bright and bright-bright-bright rogue waves. The algebraic construction depends on Lax matrices and their Jordan form. The conditions for the existence of rogue wave solutions in an F=1 spinor BEC are discussed. For the three-component GP equations, if there is modulation instability, it is of baseband type only, confirming our analytic conditions. The energy transfers between the waves are discussed.
WAVE EQUATION DATUMING TO CORRECT TOPOGRAPHY EFFECT ON FOOTHILL SEISMIC DATA
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Montes Vides Luis Alfredo
2005-08-01
Full Text Available The current seismic processing applies Static Corrections to overcome the effects associated to rough topography, based in the assumption that velocity in near surface is lower than in the substratum, which force going up rays travel near to vertical. However, when the velocity contrast between these layers is not large enough, the trajectory of the up going rays deviate from vertical raveling the reflectors erroneously. A better alternative to correct this is to continue the wave field to a datum, because it does not assume vertical ray trajectory and solves the acoustic wave equation to extrapolate sources and receivers. The Kirchhoff approach was tested in synthetic shots continuing their wave field to a datum and finally it was applied instead of Static Corrections in real data acquired in foothill zones. First shot and receiver gathers were downward continued to the base of weathering layer and later upward continued to a final flat datum. Comparing the obtained results we observed that continuation approach provides a noticeable enhancement of reflectors in seismic records, displaying a better continuity of the reflectors and an increment in frequency content.
A stochastic collocation method for the second order wave equation with a discontinuous random speed
Motamed, Mohammad
2012-08-31
In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical space and depends on a finite number of random variables. The numerical scheme consists of a finite difference or finite element method in the physical space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space. This approach leads to the solution of uncoupled deterministic problems as in the Monte Carlo method. We consider both full and sparse tensor product spaces of orthogonal polynomials. We provide a rigorous convergence analysis and demonstrate different types of convergence of the probability error with respect to the number of collocation points for full and sparse tensor product spaces and under some regularity assumptions on the data. In particular, we show that, unlike in elliptic and parabolic problems, the solution to hyperbolic problems is not in general analytic with respect to the random variables. Therefore, the rate of convergence may only be algebraic. An exponential/fast rate of convergence is still possible for some quantities of interest and for the wave solution with particular types of data. We present numerical examples, which confirm the analysis and show that the collocation method is a valid alternative to the more traditional Monte Carlo method for this class of problems. © 2012 Springer-Verlag.
DG-FEM solution for nonlinear wave-structure interaction using Boussinesq-type equations
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Hesthaven, Jan; Bingham, Harry B.
2008-01-01
We present a high-order nodal Discontinuous Galerkin Finite Element Method (DG-FEM) solution based on a set of highly accurate Boussinesq-type equations for solving general water-wave problems in complex geometries. A nodal DG-FEM is used for the spatial discretization to solve the Boussinesq equ...... and absorbed in the interior of the computational domain using a flexible relaxation technique applied on the free surface variables....... waters within the breaking limit. To demonstrate the current applicability of the model both linear and mildly nonlinear test cases are considered in two horizontal dimensions where the water waves interact with bottom-mounted fully reflecting structures. It is established that, by simple symmetry...... considerations combined with a mirror principle, it is possible to impose weak slip boundary conditions for both structured and general curvilinear wall boundaries while maintaining the accuracy of the scheme. As is standard for current high-order Boussinesq-type models, arbitrary waves can be generated...
Deng, Gao-Fu; Gao, Yi-Tian
2017-06-01
Under investigation in this paper is a generalized (3+1)-dimensional varible-coefficient nonlinear-wave equation, which has been presented for nonlinear waves in liquid with gas bubbles. The bilinear form, Bäcklund transformation, Lax pair and infinitely-many conservation laws are obtained via the binary Bell polynomials. One-, two- and three-soliton solutions are generated by virtue of the Hirota method. Travelling-wave solutions are derived with the aid of the polynomial expansion method. The one-periodic wave solutions are constructed by the Hirota-Riemann method. Discussions among the soliton, periodic- and travelling-wave solutions are presented: I) the soliton velocities are related to the variable coefficients, while the soliton amplitudes are unaffected; II) the interaction between the solitons is elastic; III) there are three cases of the travelling-wave solutions, i.e., the triangle-type periodical, bell-type and soliton-type travelling-wave solutions, while we notice that bell-type travelling-wave solutions can be converted into one-soliton solutions via taking suitable parameters; IV) the one-periodic waves approach to the solitary waves under some conditions and can be viewed as a superposition of overlapping solitary waves, placed one period apart.
Sabry, A H; W Hasan, W Z; Ab Kadir, M Z A; Radzi, M A M; Shafie, S
2018-01-01
The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system's modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model.
W. Hasan, W. Z.
2018-01-01
The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system’s modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model. PMID:29351554
Directory of Open Access Journals (Sweden)
A H Sabry
Full Text Available The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system's modeling equations based on the Bode plot equations and the vector fitting (VF algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model.
A Linear System of Differential Equations Related to Vector-Valued Jack Polynomials on the Torus
Dunkl, Charles F.
2017-06-01
For each irreducible module of the symmetric group S_{N} there is a set of parametrized nonsymmetric Jack polynomials in N variables taking values in the module. These polynomials are simultaneous eigenfunctions of a commutative set of operators, self-adjoint with respect to two Hermitian forms, one called the contravariant form and the other is with respect to a matrix-valued measure on the N-torus. The latter is valid for the parameter lying in an interval about zero which depends on the module. The author in a previous paper [SIGMA 12 (2016), 033, 27 pages] proved the existence of the measure and that its absolutely continuous part satisfies a system of linear differential equations. In this paper the system is analyzed in detail. The N-torus is divided into (N-1)! connected components by the hyperplanes x_{i}=x_{j}, i
An efficient hybrid pseudospectral/finite-difference scheme for solving the TTI pure P-wave equation
Zhan, Ge
2013-02-19
The pure P-wave equation for modelling and migration in tilted transversely isotropic (TTI) media has attracted more and more attention in imaging seismic data with anisotropy. The desirable feature is that it is absolutely free of shear-wave artefacts and the consequent alleviation of numerical instabilities generally suffered by some systems of coupled equations. However, due to several forward-backward Fourier transforms in wavefield updating at each time step, the computational cost is significant, and thereby hampers its prevalence. We propose to use a hybrid pseudospectral (PS) and finite-difference (FD) scheme to solve the pure P-wave equation. In the hybrid solution, most of the cost-consuming wavenumber terms in the equation are replaced by inexpensive FD operators, which in turn accelerates the computation and reduces the computational cost. To demonstrate the benefit in cost saving of the new scheme, 2D and 3D reverse-time migration (RTM) examples using the hybrid solution to the pure P-wave equation are carried out, and respective runtimes are listed and compared. Numerical results show that the hybrid strategy demands less computation time and is faster than using the PS method alone. Furthermore, this new TTI RTM algorithm with the hybrid method is computationally less expensive than that with the FD solution to conventional TTI coupled equations. © 2013 Sinopec Geophysical Research Institute.
Alayon Glazunov, Andrés.
2014-08-01
This paper provides an overview of recent advances in the modeling, analysis, and measurements of interactions between antennas and the propagation channel in multiple antenna systems based on the spherical vector wave mode expansion of the electromagnetic field and the antenna scattering matrix. It demonstrates the importance and usefulness of this approach to gain further insights into a variety of topics such as physics-based propagation channel modeling, mean effective gain, channel correlation, propagation channel measurements, antenna measurements and testing, the number of degrees of freedom of the radio propagation channel, channel throughput, and diversity systems. The paper puts particular emphasis on the unified approach to antenna-channel analysis at the same time as the antenna and the channel influence are separated. Finally, the paper provides the first bibliography on the application of the spherical vector wave mode expansion of the electromagnetic field to antenna-channel interactions.
Directory of Open Access Journals (Sweden)
Mostafa M.A. Khater
2017-09-01
Full Text Available The aim of the article is to construct exact solutions for the time fractional coupled Boussinesq–Burger and approximate long water wave equations by using the generalized Kudryashov method. The fractional differential equation is converted into ordinary differential equations with the help of fractional complex transform and the modified Riemann–Liouville derivative sense. Applying the generalized Kudryashov method through with symbolic computer maple package, numerous new exact solutions are successfully obtained. All calculations in this study have been established and verified back with the aid of the Maple package program. The executed method is powerful, effective and straightforward for solving nonlinear partial differential equations to obtain more and new solutions with the integer and fractional order.
Fast Plane Wave 2-D Vector Flow Imaging Using Transverse Oscillation and Directional Beamforming.
Jensen, Jonas; Villagomez Hoyos, Carlos Armando; Stuart, Matthias Bo; Ewertsen, Caroline; Nielsen, Michael Bachmann; Jensen, Jorgen Arendt
2017-07-01
Several techniques can estimate the 2-D velocity vector in ultrasound. Directional beamforming (DB) estimates blood flow velocities with a higher precision and accuracy than transverse oscillation (TO), but at the cost of a high beamforming load when estimating the flow angle. In this paper, it is proposed to use TO to estimate an initial flow angle, which is then refined in a DB step. Velocity magnitude is estimated along the flow direction using cross correlation. It is shown that the suggested TO-DB method can improve the performance of velocity estimates compared with TO, and with a beamforming load, which is 4.6 times larger than for TO and seven times smaller than for conventional DB. Steered plane wave transmissions are employed for high frame rate imaging, and parabolic flow with a peak velocity of 0.5 m/s is simulated in straight vessels at beam-to-flow angles from 45° to 90°. The TO-DB method estimates the angle with a bias and standard deviation (SD) less than 2°, and the SD of the velocity magnitude is less than 2%. When using only TO, the SD of the angle ranges from 2° to 17° and for the velocity magnitude up to 7%. Bias of the velocity magnitude is within 2% for TO and slightly larger but within 4% for TO-DB. The same trends are observed in measurements although with a slightly larger bias. Simulations of realistic flow in a carotid bifurcation model provide visualization of complex flow, and the spread of velocity magnitude estimates is 7.1 cm/s for TO-DB, while it is 11.8 cm/s using only TO. However, velocities for TO-DB are underestimated at peak systole as indicated by a regression value of 0.97 for TO and 0.85 for TO-DB. An in vivo scanning of the carotid bifurcation is used for vector velocity estimations using TO and TO-DB. The SD of the velocity profile over a cardiac cycle is 4.2% for TO and 3.2% for TO-DB.
Hauser, D.; Tison, C.; Amiot, T.; Delaye, L.; Mouche, A.; Guitton, G.; Aouf, L.; Castillan, P.
2016-05-01
CFOSAT (the China France Oceanography Satellite) is a joint mission from the Chinese and French Space Agencies, devoted to the observation ocean surface wind and waves so as to improve wind and wave forecast for marine meteorology, ocean dynamics modeling and prediction, climate variability knowledge, fundamental knowledge of surface processes. Currently under Phase D (manufacturing phase), the launch is now planned for mid-2018 the later. The CFOSAT will carry two payloads, both Ku-Band radar: the wave scatterometer (SWIM) and the wind scatterometer (SCAT). Both instruments are based on new concepts with respect to existing satellite-borne wind and wave sensors. Indeed, one of the originalities of CFOSAT is that it will provide simultaneously and in the same zone, the directional spectra of ocean waves and the wind vector. The concept used to measure the directional spectra of ocean waves has never been used from space until now: it is based on a near-nadir incidence pointing, rotating fan-beam radar, used in a real-aperture mode. In this paper we present the CFOSAT mission, its objectives and main characteristics. We then focus on the SWIM instrument, the expected geophysical products and performances. Finally, we present ongoing studies based on existing satellite data of directional spectra of ocean waves (Sentinel-1, ..) and carried out in preparation to CAL/VAL activities and to future data exploitation.
Phonon Self-Energy Corrections to Nonzero Wave-Vector Phonon Modes in Single-Layer Graphene
Araujo, P. T.; Mafra, D. L.; Sato, K.; Saito, R.; Kong, J.; Dresselhaus, M. S.
2012-07-01
Phonon self-energy corrections have mostly been studied theoretically and experimentally for phonon modes with zone-center (q=0) wave vectors. Here, gate-modulated Raman scattering is used to study phonons of a single layer of graphene originating from a double-resonant Raman process with q≠0. The observed phonon renormalization effects are different from what is observed for the zone-center q=0 case. To explain our experimental findings, we explored the phonon self-energy for the phonons with nonzero wave vectors (q≠0) in single-layer graphene in which the frequencies and decay widths are expected to behave oppositely to the behavior observed in the corresponding zone-center q=0 processes. Within this framework, we resolve the identification of the phonon modes contributing to the G⋆ Raman feature at 2450cm-1 to include the iTO+LA combination modes with q≠0 and also the 2iTO overtone modes with q=0, showing both to be associated with wave vectors near the high symmetry point K in the Brillouin zone.
Phonon self-energy corrections to nonzero wave-vector phonon modes in single-layer graphene.
Araujo, P T; Mafra, D L; Sato, K; Saito, R; Kong, J; Dresselhaus, M S
2012-07-27
Phonon self-energy corrections have mostly been studied theoretically and experimentally for phonon modes with zone-center (q=0) wave vectors. Here, gate-modulated Raman scattering is used to study phonons of a single layer of graphene originating from a double-resonant Raman process with q≠0. The observed phonon renormalization effects are different from what is observed for the zone-center q=0 case. To explain our experimental findings, we explored the phonon self-energy for the phonons with nonzero wave vectors (q≠0) in single-layer graphene in which the frequencies and decay widths are expected to behave oppositely to the behavior observed in the corresponding zone-center q=0 processes. Within this framework, we resolve the identification of the phonon modes contributing to the G(⋆) Raman feature at 2450 cm(-1) to include the iTO+LA combination modes with q≠0 and also the 2iTO overtone modes with q=0, showing both to be associated with wave vectors near the high symmetry point K in the Brillouin zone.
The Mode Solution of the Wave Equation in Kasner Spacetimes and Redshift
Energy Technology Data Exchange (ETDEWEB)
Petersen, Oliver Lindblad, E-mail: lindblad@uni-potsdam.de [Universität Potsdam, Institut für Mathematik (Germany)
2016-12-15
We study the mode solution to the Cauchy problem of the scalar wave equation □φ = 0 in Kasner spacetimes. As a first result, we give the explicit mode solution in axisymmetric Kasner spacetimes, of which flat Kasner spacetimes are special cases. Furthermore, we give the small and large time asymptotics of the modes in general Kasner spacetimes. Generically, the modes in non-flat Kasner spacetimes grow logarithmically for small times, while the modes in flat Kasner spacetimes stay bounded for small times. For large times, however, the modes in general Kasner spacetimes oscillate with a polynomially decreasing amplitude. This gives a notion of large time frequency of the modes, which we use to model the wavelength of light rays in Kasner spacetimes. We show that the redshift one obtains in this way actually coincides with the usual cosmological redshift.
AN ANALYTICAL SOLUTION OF KINEMATIC WAVE EQUATIONS FOR OVERLAND FLOW UNDER GREEN-AMPT INFILTRATION
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Giorgio Baiamonte
2010-03-01
Full Text Available This paper deals with the analytical solution of kinematic wave equations for overland flow occurring in an infiltrating hillslope. The infiltration process is described by the Green-Ampt model. The solution is derived only for the case of an intermediate flow regime between laminar and turbulent ones. A transitional regime can be considered a reliable flow condition when, to the laminar overland flow, is also associated the effect of the additional resistance due to raindrop impact. With reference to the simple case of an impervious hillslope, a comparison was carried out between the present solution and the non-linear storage model. Some applications of the present solution were performed to investigate the effect of main parameter variability on the hillslope response. Particularly, the effect of hillslope geometry and rainfall intensity on the time to equilibrium is shown.
The new potential for the Weyl tensor in N dimensions: gauge and wave equation
Edgar, S. Brian; Senovilla, J. M. M.
Although the Lanczos potential (a (2,1) form, Lab{}^c) for the Weyl tensor does not exist in dimensions greater than four, a new potential (a (2,3) form, Pab{}cde, which coincides with the double dual of Lab{}c in four dimensions) has recently been shown to exist in all dimensions n≥ 4. In this talk we investigate the question of gauge and discuss the structure of the new potential's wave equation which is obtained from the Bianchi identities; identifying the gauge supplies us with a new direct proof of the existence of Pab{}cde via the Cauchy-Kowaleski theorem, as well as the foundation for more general investigations of the first order symmetric hyperbolic structure.
Existence and asymptotic stability of a viscoelastic wave equation with a delay
Kirane, Mokhtar
2011-07-07
In this paper, we consider the viscoelastic wave equation with a delay term in internal feedbacks; namely, we investigate the following problem, together with initial conditions and boundary conditions of Dirichlet type. Here (x, t) ∈ Ω × (0, ∞), g is a positive real valued decreasing function and μ1, μ2 are positive constants. Under an hypothesis between the weight of the delay term in the feedback and the weight of the term without delay, using the Faedo-Galerkin approximations together with some energy estimates, we prove the global existence of the solutions. Under the same assumptions, general decay results of the energy are established via suitable Lyapunov functionals. © 2011 Springer Basel AG.
Existence and asymptotic behavior of the wave equation with dynamic boundary conditions
Graber, Philip Jameson
2012-03-07
The goal of this work is to study a model of the strongly damped wave equation with dynamic boundary conditions and nonlinear boundary/interior sources and nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. In addition, we show that in the strongly damped case solutions gain additional regularity for positive times t>0. Second, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution grows as an exponential function. Moreover, in the absence of the strong damping term, we prove that the solution ceases to exists and blows up in finite time. © 2012 Springer Science+Business Media, LLC.
Hilditch, David; Bugner, Marcus; Rueter, Hannes; Bruegmann, Bernd
2016-01-01
A long-standing problem in numerical relativity is the satisfactory treatment of future null-infinity. We propose an approach for the evolution of hyperboloidal initial data in which the outer boundary of the computational domain is placed at infinity. The main idea is to apply the `dual foliation' formalism in combination with hyperboloidal coordinates and the generalized harmonic gauge formulation. The strength of the present approach is that, following the ideas of Zenginoglu, a hyperboloidal layer can be naturally attached to a central region using standard coordinates of numerical relativity applications. Employing a generalization of the standard hyperboloidal slices, developed by Calabrese et. al., we find that all formally singular terms take a trivial limit as we head to null-infinity. A byproduct is a numerical approach for hyperboloidal evolution of nonlinear wave equations violating the null-condition. The height-function method, used often for fixed background spacetimes, is generalized in such a...
Wave equation tomography using the unwrapped phase - Analysis of the traveltime sensitivity kernels
Djebbi, Ramzi
2013-01-01
Full waveform inversion suffers from the high non-linearity in the misfit function, which causes the convergence to a local minimum. In the other hand, traveltime tomography has a quasi-linear misfit function but yields low- resolution models. Wave equation tomography (WET) tries to improve on traveltime tomography, by better adhering to the requirements of our finite-frequency data. However, conventional (WET), based on the crosscorelaion lag, yields the popular hallow banana sensitivity kernel indicating that the measured wavefield at a point is insensitive to perturbations along the ray theoretical path at certain finite frequencies. Using the instantaneous traveltime, the sensitivity kernel reflects more the model-data dependency we grown accustom to in seismic inversion (even phase inversion). Demonstrations on synthetic and the Mamousi model support such assertions.
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Yair Zarmi
Full Text Available The (1+1-dimensional Sine-Gordon equation passes integrability tests commonly applied to nonlinear evolution equations. Its kink solutions (one-dimensional fronts are obtained by a Hirota algorithm. In higher space-dimensions, the equation does not pass these tests. Although it has been derived over the years for quite a few physical systems that have nothing to do with Special Relativity, the Sine-Gordon equation emerges as a non-linear relativistic wave equation. This opens the way for exploiting the tools of the Theory of Special Relativity. Using no more than the relativistic kinematics of tachyonic momentum vectors, from which the solutions are constructed through the Hirota algorithm, the existence and classification of N-moving-front solutions of the (1+2- and (1+3-dimensional equations for all N ≥ 1 are presented. In (1+2 dimensions, each multi-front solution propagates rigidly at one velocity. The solutions are divided into two subsets: Solutions whose velocities are lower than a limiting speed, c = 1, or are greater than or equal to c. To connect with concepts of the Theory of Special Relativity, c will be called "the speed of light." In (1+3-dimensions, multi-front solutions are characterized by spatial structure and by velocity composition. The spatial structure is either planar (rotated (1+2-dimensional solutions, or genuinely three-dimensional--branes. Planar solutions, propagate rigidly at one velocity, which is lower than, equal to, or higher than c. Branes must contain clusters of fronts whose speed exceeds c = 1. Some branes are "hybrids": different clusters of fronts propagate at different velocities. Some velocities may be lower than c but some must be equal to, or exceed, c. Finally, the speed of light cannot be approached from within the subset of slower-than-light solutions in both (1+2 and (1+3 dimensions.
Konno, Hidetoshi
2017-06-01
The paper presents the birth-death stochastic process of an optical rogue wave with a long memory described by a fractional master equation. An exact analytic expression for the probability generating function is obtained with an integral representation of the confluent Heun function. This enables a full statistical analysis under any initial condition. It is demonstrated that the present mathematical approach can be utilized for the analysis of birth-death stochastic processes when the generating function can be described by a class of Heun differential equations.
Motional displacements in proteins: The origin of wave-vector-dependent values.
Vural, Derya; Hong, Liang; Smith, Jeremy C; Glyde, Henry R
2015-05-01
The average mean-square displacement, 〈r(2)〉, of H atoms in a protein is frequently determined using incoherent neutron-scattering experiments. 〈r(2)〉 is obtained from the observed elastic incoherent dynamic structure factor, S(i)(Q,ω=0), assuming the form S(i)(Q,ω=0) =exp(-Q(2)〈r(2)〉/3). This is often referred to as the Gaussian approximation (GA) to S(i)(Q,ω=0). 〈r(2)〉 obtained in this way depends on the value of the wave vector, Q considered. Equivalently, the observed S(i)(Q,ω=0) deviates from the GA. We investigate the origin of the Q dependence of 〈r(2)〉 by evaluating the scattering functions in different approximations using molecular dynamics (MD) simulation of the protein lysozyme. We find that keeping only the Gaussian term in a cumulant expansion of S(Q,ω) is an accurate approximation and is not the origin of the Q dependence of 〈r(2)〉. This is demonstrated by showing that the term beyond the Gaussian is negligible and that the GA is valid for an individual atom in the protein. Rather, the Q dependence (deviation from the GA) arises from the dynamical heterogeneity of the H in the protein. Specifically it arises from representing, in the analysis of data, this diverse dynamics by a single average scattering center that has a single, average 〈r(2)〉. The observed Q dependence of 〈r(2)〉 can be used to provide information on the dynamical heterogeneity in proteins.
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H. O. Bakodah
2013-01-01
Full Text Available A method of lines approach to the numerical solution of nonlinear wave equations typified by the regularized long wave (RLW is presented. The method developed uses a finite differences discretization to the space. Solution of the resulting system was obtained by applying fourth Runge-Kutta time discretization method. Using Von Neumann stability analysis, it is shown that the proposed method is marginally stable. To test the accuracy of the method some numerical experiments on test problems are presented. Test problems including solitary wave motion, two-solitary wave interaction, and the temporal evaluation of a Maxwellian initial pulse are studied. The accuracy of the present method is tested with and error norms and the conservation properties of mass, energy, and momentum under the RLW equation.
Zhang, Sanzong
2015-05-26
Full-waveform inversion requires the accurate simulation of the dynamics and kinematics of wave propagation. This is difficult in practice because the amplitudes cannot be precisely reproduced for seismic waves in the earth. Wave-equation reflection traveltime tomography (WT) is proposed to avoid this problem by directly inverting the reflection-traveltime residuals without the use of the high-frequency approximation. We inverted synthetic traces and recorded seismic data for the velocity model by WT. Our results demonstrated that the wave-equation solution overcame the high-frequency approximation of ray-based tomography, was largely insensitive to the accurate modeling of amplitudes, and mitigated problems with ambiguous event identification. The synthetic examples illustrated the effectiveness of the WT method in providing a highly resolved estimate of the velocity model. A real data example from the Gulf of Mexico demonstrated these benefits of WT, but also found the limitations in traveltime residual estimation for complex models.