Improved distorted wave theory with the localized virial conditions

Science.gov (United States)

Hahn, Y. K.; Zerrad, E.

2009-12-01

The distorted wave theory is operationally improved to treat the full collision amplitude, such that the corrections to the distorted wave Born amplitude can be systematically calculated. The localized virial conditions provide the tools necessary to test the quality of successive approximations at each stage and to optimize the solution. The details of the theoretical procedure are explained in concrete terms using a collisional ionization model and variational trial functions. For the first time, adjustable parameters associated with an approximate scattering solution can be fully determined by the theory. A small number of linear parameters are introduced to examine the convergence property and the effectiveness of the new approach.

Travelling wave solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations

Directory of Open Access Journals (Sweden)

M. Arshad

Full Text Available In this manuscript, we constructed different form of new exact solutions of generalized coupled Zakharov–Kuznetsov and dispersive long wave equations by utilizing the modified extended direct algebraic method. New exact traveling wave solutions for both equations are obtained in the form of soliton, periodic, bright, and dark solitary wave solutions. There are many applications of the present traveling wave solutions in physics and furthermore, a wide class of coupled nonlinear evolution equations can be solved by this method. Keywords: Traveling wave solutions, Elliptic solutions, Generalized coupled Zakharov–Kuznetsov equation, Dispersive long wave equation, Modified extended direct algebraic method

Traveling waves and their tails in locally resonant granular systems

International Nuclear Information System (INIS)

Xu, H.; Kevrekidis, P. G.; Stefanov, A.

2015-01-01

In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as mass-in-mass systems. We use three distinct approaches to identify relevant traveling waves. In addition, the first consists of a direct solution of the traveling wave problem. The second one consists of the solution of the Fourier tranformed variant of the problem, or, more precisely, of its convolution reformulation (upon an inverse Fourier transform) in real space. Finally, our third approach will restrict considerations to a finite domain, utilizing the notion of Fourier series for important technical reasons, namely the avoidance of resonances, which will be discussed in detail. All three approaches can be utilized in either the displacement or the strain formulation. Typical resulting computations in finite domains result in the solitary waves bearing symmetric non-vanishing tails at both ends of the computational domain. Importantly, however, a countably infinite set of anti-resonance conditions is identified for which solutions with genuinely rapidly decaying tails arise

Explicit and exact nontraveling wave solutions of the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation

Science.gov (United States)

Yuan, Na

2018-04-01

With the aid of the symbolic computation, we present an improved ( G ‧ / G ) -expansion method, which can be applied to seek more types of exact solutions for certain nonlinear evolution equations. In illustration, we choose the (3 + 1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation to demonstrate the validity and advantages of the method. As a result, abundant explicit and exact nontraveling wave solutions are obtained including two solitary waves solutions, nontraveling wave solutions and dromion soliton solutions. Some particular localized excitations and the interactions between two solitary waves are researched. The method can be also applied to other nonlinear partial differential equations.

Travelling wave solutions to the Kuramoto-Sivashinsky equation

International Nuclear Information System (INIS)

Nickel, J.

2007-01-01

Combining the approaches given by Baldwin [Baldwin D et al. Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs. J Symbol Comput 2004;37:669-705], Peng [Peng YZ. A polynomial expansion method and new general solitary wave solutions to KS equation. Comm Theor Phys 2003;39:641-2] and by Schuermann [Schuermann HW, Serov VS. Weierstrass' solutions to certain nonlinear wave and evolution equations. Proc progress electromagnetics research symposium, 28-31 March 2004, Pisa. p. 651-4; Schuermann HW. Traveling-wave solutions to the cubic-quintic nonlinear Schroedinger equation. Phys Rev E 1996;54:4312-20] leads to a method for finding exact travelling wave solutions of nonlinear wave and evolution equations (NLWEE). The first idea is to generalize ansaetze given by Baldwin and Peng to find elliptic solutions of NLWEEs. Secondly, conditions used by Schuermann to find physical (real and bounded) solutions and to discriminate between periodic and solitary wave solutions are used. The method is shown in detail by evaluating new solutions of the Kuramoto-Sivashinsky equation

Hybrid Numerical-Analytical Scheme for Calculating Elastic Wave Diffraction in Locally Inhomogeneous Waveguides

Science.gov (United States)

Glushkov, E. V.; Glushkova, N. V.; Evdokimov, A. A.

2018-01-01

Numerical simulation of traveling wave excitation, propagation, and diffraction in structures with local inhomogeneities (obstacles) is computationally expensive due to the need for mesh-based approximation of extended domains with the rigorous account for the radiation conditions at infinity. Therefore, hybrid numerical-analytic approaches are being developed based on the conjugation of a numerical solution in a local vicinity of the obstacle and/or source with an explicit analytic representation in the remaining semi-infinite external domain. However, in standard finite-element software, such a coupling with the external field, moreover, in the case of multimode expansion, is generally not provided. This work proposes a hybrid computational scheme that allows realization of such a conjugation using a standard software. The latter is used to construct a set of numerical solutions used as the basis for the sought solution in the local internal domain. The unknown expansion coefficients on this basis and on normal modes in the semi-infinite external domain are then determined from the conditions of displacement and stress continuity at the boundary between the two domains. We describe the implementation of this approach in the scalar and vector cases. To evaluate the reliability of the results and the efficiency of the algorithm, we compare it with a semianalytic solution to the problem of traveling wave diffraction by a horizontal obstacle, as well as with a finite-element solution obtained for a limited domain artificially restricted using absorbing boundaries. As an example, we consider the incidence of a fundamental antisymmetric Lamb wave onto surface and partially submerged elastic obstacles. It is noted that the proposed hybrid scheme can also be used to determine the eigenfrequencies and eigenforms of resonance scattering, as well as the characteristics of traveling waves in embedded waveguides.

Bifurcations of traveling wave solutions for an integrable equation

International Nuclear Information System (INIS)

Li Jibin; Qiao Zhijun

2010-01-01

This paper deals with the following equation m t =(1/2)(1/m k ) xxx -(1/2)(1/m k ) x , which is proposed by Z. J. Qiao [J. Math. Phys. 48, 082701 (2007)] and Qiao and Liu [Chaos, Solitons Fractals 41, 587 (2009)]. By adopting the phase analysis method of planar dynamical systems and the theory of the singular traveling wave systems to the traveling wave solutions of the equation, it is shown that for different k, the equation may have infinitely many solitary wave solutions, periodic wave solutions, kink/antikink wave solutions, cusped solitary wave solutions, and breaking loop solutions. We discuss in a detail the cases of k=-2,-(1/2),(1/2),2, and parametric representations of all possible bounded traveling wave solutions are given in the different (c,g)-parameter regions.

The non-local Fisher–KPP equation: travelling waves and steady states

International Nuclear Information System (INIS)

Berestycki, Henri; Nadin, Grégoire; Perthame, Benoit; Ryzhik, Lenya

2009-01-01

We consider the Fisher–KPP equation with a non-local saturation effect defined through an interaction kernel φ(x) and investigate the possible differences with the standard Fisher–KPP equation. Our first concern is the existence of steady states. We prove that if the Fourier transform φ-circumflex(ξ) is positive or if the length σ of the non-local interaction is short enough, then the only steady states are u ≡ 0 and u ≡ 1. Next, we study existence of the travelling waves. We prove that this equation admits travelling wave solutions that connect u = 0 to an unknown positive steady state u ∞ (x), for all speeds c ≥ c * . The travelling wave connects to the standard state u ∞ (x) ≡ 1 under the aforementioned conditions: φ-circumflex(ξ) > 0 or σ is sufficiently small. However, the wave is not monotonic for σ large

New exact travelling wave solutions of nonlinear physical models

International Nuclear Information System (INIS)

Bekir, Ahmet; Cevikel, Adem C.

2009-01-01

In this work, we established abundant travelling wave solutions for some nonlinear evolution equations. This method was used to construct travelling wave solutions of nonlinear evolution equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The ((G ' )/G )-expansion method presents a wider applicability for handling nonlinear wave equations.

Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets

Directory of Open Access Journals (Sweden)

Ai-Min Yang

2013-01-01

Full Text Available We proposed a local fractional series expansion method to solve the wave and diffusion equations on Cantor sets. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives.

Periodic and solitary-wave solutions of the Degasperis-Procesi equation

International Nuclear Information System (INIS)

Vakhnenko, V.O.; Parkes, E.J.

2004-01-01

Travelling-wave solutions of the Degasperis-Procesi equation are investigated. The solutions are characterized by two parameters. For propagation in the positive x-direction, hump-like, inverted loop-like and coshoidal periodic-wave solutions are found; hump-like, inverted loop-like and peakon solitary-wave solutions are obtained as well. For propagation in the negative x-direction, there are solutions which are just the mirror image in the x-axis of the aforementioned solutions. A transformed version of the Degasperis-Procesi equation, which is a generalization of the Vakhnenko equation, is also considered. For propagation in the positive x-direction, hump-like, loop-like, inverted loop-like, bell-like and coshoidal periodic-wave solutions are found; loop-like, inverted loop-like and kink-like solitary-wave solutions are obtained as well. For propagation in the negative x-direction, well-like and inverted coshoidal periodic-wave solutions are found; well-like and inverted peakon solitary-wave solutions are obtained as well. In an appropriate limit, the previously known solutions of the Vakhnenko equation are recovered

Travelling wave solutions in delayed cooperative systems

International Nuclear Information System (INIS)

Li, Bingtuan; Zhang, Liang

2011-01-01

We establish the existence of travelling wave solutions for delayed cooperative recursions that are allowed to have more than two equilibria. We define an important extended real number that is used to determine the speeds of travelling wave solutions. The results can be applied to a large class of delayed cooperative reaction–diffusion models. We show that for a delayed Lotka–Volterra reaction–diffusion competition model, there exists a finite positive number c * + that can be characterized as the slowest speed of travelling wave solutions connecting two mono-culture equilibria or connecting a mono-culture with the coexistence equilibrium

Solitary wave and periodic wave solutions for Burgers, Fisher ...

Indian Academy of Sciences (India)

Home; Journals; Pramana – Journal of Physics; Volume 85; Issue 1. Solitary wave and periodic wave solutions for Burgers, Fisher, Huxley and combined forms of these equations by the (′/)-expansion method. Jalil Manafian Mehrdad Lakestani. Volume 85 Issue 1 July 2015 pp 31-52 ...

A multimodal wave spectrum-based approach for statistical downscaling of local wave climate

Science.gov (United States)

Hegermiller, Christie; Antolinez, Jose A A; Rueda, Ana C.; Camus, Paula; Perez, Jorge; Erikson, Li; Barnard, Patrick; Mendez, Fernando J.

2017-01-01

Characterization of wave climate by bulk wave parameters is insufficient for many coastal studies, including those focused on assessing coastal hazards and long-term wave climate influences on coastal evolution. This issue is particularly relevant for studies using statistical downscaling of atmospheric fields to local wave conditions, which are often multimodal in large ocean basins (e.g. the Pacific). Swell may be generated in vastly different wave generation regions, yielding complex wave spectra that are inadequately represented by a single set of bulk wave parameters. Furthermore, the relationship between atmospheric systems and local wave conditions is complicated by variations in arrival time of wave groups from different parts of the basin. Here, we address these two challenges by improving upon the spatiotemporal definition of the atmospheric predictor used in statistical downscaling of local wave climate. The improved methodology separates the local wave spectrum into “wave families,” defined by spectral peaks and discrete generation regions, and relates atmospheric conditions in distant regions of the ocean basin to local wave conditions by incorporating travel times computed from effective energy flux across the ocean basin. When applied to locations with multimodal wave spectra, including Southern California and Trujillo, Peru, the new methodology improves the ability of the statistical model to project significant wave height, peak period, and direction for each wave family, retaining more information from the full wave spectrum. This work is the base of statistical downscaling by weather types, which has recently been applied to coastal flooding and morphodynamic applications.

Bifurcations and new exact travelling wave solutions for the ...

Indian Academy of Sciences (India)

By using the method of dynamical system, the bidirectional wave equations are considered. Based on this method, all kinds of phase portraits of the reduced travelling wave system in the parametric space are given. All possible bounded travelling wave solutions such as dark soliton solutions, bright soliton solutions and ...

Exact solution of equations for proton localization in neutron star matter

Science.gov (United States)

Kubis, Sebastian; Wójcik, Włodzimierz

2015-11-01

The rigorous treatment of proton localization phenomenon in asymmetric nuclear matter is presented. The solution of proton wave function and neutron background distribution is found by the use of the extended Thomas-Fermi approach. The minimum of energy is obtained in the Wigner-Seitz approximation of a spherically symmetric cell. The analysis of four different nuclear models suggests that the proton localization is likely to take place in the interior of a neutron star.

Traveling wave solutions for reaction-diffusion systems

DEFF Research Database (Denmark)

Lin, Zhigui; Pedersen, Michael; Tian, Canrong

2010-01-01

This paper is concerned with traveling waves of reaction–diffusion systems. The definition of coupled quasi-upper and quasi-lower solutions is introduced for systems with mixed quasimonotone functions, and the definition of ordered quasi-upper and quasi-lower solutions is also given for systems...... with quasimonotone nondecreasing functions. By the monotone iteration method, it is shown that if the system has a pair of coupled quasi-upper and quasi-lower solutions, then there exists at least a traveling wave solution. Moreover, if the system has a pair of ordered quasi-upper and quasi-lower solutions...

New compacton solutions and solitary wave solutions of fully nonlinear generalized Camassa-Holm equations

International Nuclear Information System (INIS)

Tian Lixin; Yin Jiuli

2004-01-01

In this paper, we introduce the fully nonlinear generalized Camassa-Holm equation C(m,n,p) and by using four direct ansatzs, we obtain abundant solutions: compactons (solutions with the absence of infinite wings), solitary patterns solutions having infinite slopes or cups, solitary waves and singular periodic wave solutions and obtain kink compacton solutions and nonsymmetry compacton solutions. We also study other forms of fully nonlinear generalized Camassa-Holm equation, and their compacton solutions are governed by linear equations

New travelling wave solutions for nonlinear stochastic evolution ...

Indian Academy of Sciences (India)

expansion method to look for travelling wave solutions of nonlinear partial differential equations. It is interesting to mention that, in this method the sign of the parameters can be used to judge the numbers and types of travelling wave solutions.

Interfacial wave theory for dendritic structure of a growing needle crystal. I - Local instability mechanism. II - Wave-emission mechanism at the turning point

Science.gov (United States)

Xu, Jian-Jun

1989-01-01

The complicated dendritic structure of a growing needle crystal is studied on the basis of global interfacial wave theory. The local dispersion relation for normal modes is derived in a paraboloidal coordinate system using the multiple-variable-expansion method. It is shown that the global solution in a dendrite growth process incorporates the morphological instability factor and the traveling wave factor.

Modulation of propagation-invariant Localized Waves for FSO communication systems

KAUST Repository

Salem, Mohamed; Bagci, Hakan

2012-01-01

The novel concept of spatio-Temporal modulation of Nyquist pulses is introduced, and the resulting wave-packets are termed Nyquist Localized Waves (LWs). Ideal Nyquist LWs belong to the generic family of LW solutions and can propagate indefinitely in unbounded media without attenuation or chromatic dispersion. The possibility of modulating Nyquist LWs for free-space optical (FSO) communication systems is demonstrated using two different modulation techniques. The first technique is on-off keying (OOK) with alternate mark inversion (AMI) coding for 1-bit per symbol transmission, and the second one is 16-Ary quadrature amplitude modulation (16-QAM) for 4-bits per symbol transmission. Aspects related to the performance, detection and generation of the spatio-Temporally coupled wave-packets are discussed and future research directions are outlined. © 2012 Optical Society of America.

Band gaps and localization of surface water waves over large-scale sand waves with random fluctuations

Science.gov (United States)

Zhang, Yu; Li, Yan; Shao, Hao; Zhong, Yaozhao; Zhang, Sai; Zhao, Zongxi

2012-06-01

Band structure and wave localization are investigated for sea surface water waves over large-scale sand wave topography. Sand wave height, sand wave width, water depth, and water width between adjacent sand waves have significant impact on band gaps. Random fluctuations of sand wave height, sand wave width, and water depth induce water wave localization. However, random water width produces a perfect transmission tunnel of water waves at a certain frequency so that localization does not occur no matter how large a disorder level is applied. Together with theoretical results, the field experimental observations in the Taiwan Bank suggest band gap and wave localization as the physical mechanism of sea surface water wave propagating over natural large-scale sand waves.

Launching transverse-electric Localized Waves from a circular waveguide

KAUST Repository

Salem, Mohamed

2011-07-01

Axially symmetric transverse electric (TE) modes of a circular waveguide section are used to synthesize the vector TE Localized Wave (LW) field at the open end of the waveguide section. The necessary excitation coefficients of these modes are obtained by the method of matching, taking advantage of the modal power orthogonality relations. The necessary excitation of modes provided by a number of coaxial loop antennas inserted inside the waveguide section. The antennas currents are computed from the solution of the waveguide excitation inverse problem. The accuracy of the synthesized wave field (compared to the mathematical model) and the power efficiency of the generation technique are evaluated in order to practically realize a launcher for LWs in the microwave regime. © 2011 IEEE.

Bifurcations and new exact travelling wave solutions for the ...

Indian Academy of Sciences (India)

2016-10-17

Oct 17, 2016 ... Abstract. By using the method of dynamical system, the bidirectional wave equations are considered. Based on this method, all kinds of phase portraits of the reduced travelling wave system in the parametric space are given. All possible bounded travelling wave solutions such as dark soliton solutions, ...

A third-order KdV solution for internal solitary waves and its application in the numerical wave tank

Directory of Open Access Journals (Sweden)

Qicheng Meng

2016-04-01

Full Text Available A third-order KdV solution to the internal solitary wave is derived by a new method based on the weakly nonlinear assumptions in a rigid-lid two-layer system. The solution corrects an error by Mirie and Su (1984. A two-dimensional numerical wave tank has been established with the help of the open source CFD library OpenFOAM and the third-party software waves2Foam. Various analytical solutions, including the first-order to third-order KdV solutions, the eKdV solution and the MCC solution, have been used to initialise the flow fields in the CFD simulations of internal solitary waves. Two groups including 11 numerical cases have been carried out. In the same group, the initial wave amplitudes are the same but the implemented analytical solutions are different. The simulated wave profiles at different moments have been presented. The relative errors in terms of the wave amplitude between the last time step and the initial input have been analysed quantitatively. It is found that the third-order KdV solution results in the most stable internal solitary wave in the numerical wave tank for both small-amplitude and finite-amplitude cases. The finding is significant for the further simulations involving internal solitary waves.

Jacobian elliptic wave solutions for the Wadati-Segur-Ablowitz equation

International Nuclear Information System (INIS)

Teh, C.G.R.; Koo, W.K.; Lee, B.S.

1996-07-01

Jacobian elliptic travelling wave solutions for a new Hamiltonian amplitude equation determining some instabilities of modulated wave train are obtained. By a mere variation of the Jacobian elliptic parameter k 2 from zero to one, these solutions are transformed from a trivial one to the known solitary wave solutions. (author). 9 refs

Exact traveling wave solutions of the Boussinesq equation

International Nuclear Information System (INIS)

Ding Shuangshuang; Zhao Xiqiang

2006-01-01

The repeated homogeneous balance method is used to construct exact traveling wave solutions of the Boussinesq equation, in which the homogeneous balance method is applied to solve the Riccati equation and the reduced nonlinear ordinary differential equation, respectively. Many new exact traveling wave solutions of the Boussinesq equation are successfully obtained

Path integral for spinning particle in the plane wave field: Global and local projections

International Nuclear Information System (INIS)

Boudiaf, N.; Boudjedaa, T.; Chetouani, L.

2001-01-01

The Green function related to the problem of a Dirac particle interacting with a plane wave is calculated via the path integral formalism proposed recently by Alexandrou et al. according to the two so-called global and local projections. With the help of the incorporation of two simple identities, it is shown that the contribution to the calculation of the integrals comes essentially from classical solutions projected along the direction of wave propagation. (orig.)

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.

Family of electrovac colliding wave solutions of Einstein's equations

International Nuclear Information System (INIS)

Li, W.; Ernst, F.J.

1989-01-01

Beginning with any colliding wave solution of the vacuum Einstein equations, a corresponding electrified colliding wave solution can be generated through the use of a transformation due to Harrison [J. Math. Phys. 9, 1744 (1968)]. The method, long employed in the context of stationary axisymmetric fields, is equally applicable to colliding wave solutions. Here it is applied to a large family of vacuum metrics derived by applying a generalized Ehlers transformation to solutions published recently by Ernst, Garcia, and Hauser (EGH) [J. Math. Phys. 28, 2155, 2951 (1987); 29, 681 (1988)]. Those EGH solutions were themselves a generalization of solutions first derived by Ferrari, Ibanez, and Bruni [Phys. Rev. D 36, 1053 (1987)]. Among the electrovac solutions that are obtained is a charged version of the Nutku--Halil [Phys. Rev. Lett. 39, 1379 (1977)] metric that possesses an arbitrary complex charge parameter

A perturbative solution for gravitational waves in quadratic gravity

International Nuclear Information System (INIS)

Neto, Edgard C de Rey; Aguiar, Odylio D; Araujo, Jose C N de

2003-01-01

We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to Einstein's linearized field equations. We show that only the Ricci-squared quadratic invariant contributes to give a different solution to those found in Einstein's general relativity. The perturbative solution is written as a power series in the β parameter, the coefficient of the Ricci-squared term in the quadratic gravitational action. We also show that, for monochromatic waves of a given angular frequency ω, the perturbative solution can be summed out to give an exact solution to the linearized version of quadratic gravity, for 0 1/2 . This result may lead to implications for the predictions for gravitational wave backgrounds of cosmological origin

Solitary wave and periodic wave solutions for Burgers, Fisher ...

Indian Academy of Sciences (India)

The generalized (G′/G)-expansion method; Burgers equation; Fisher's equation; ... the travelling wave solutions plays an important role in nonlinear sciences. ... Burgers, Fisher, Huxley equations and combined forms of these equations will ...

New exact travelling wave solutions of bidirectional wave equations

Indian Academy of Sciences (India)

Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea. ∗ ... exact travelling wave solutions of system (1) using the modified tanh–coth function method ... The ordinary differential equation is then integrated.

ANALYTICAL SOLUTION FOR WAVES IN PLANETS WITH ATMOSPHERIC SUPERROTATION. II. LAMB, SURFACE, AND CENTRIFUGAL WAVES

International Nuclear Information System (INIS)

Peralta, J.; López-Valverde, M. A.; Imamura, T.; Read, P. L.; Luz, D.; Piccialli, A.

2014-01-01

This paper is the second in a two-part study devoted to developing tools for a systematic classification of the wide variety of atmospheric waves expected on slowly rotating planets with atmospheric superrotation. Starting with the primitive equations for a cyclostrophic regime, we have deduced the analytical solution for the possible waves, simultaneously including the effect of the metric terms for the centrifugal force and the meridional shear of the background wind. In those cases where the conditions for the method of the multiple scales in height are met, these wave solutions are also valid when vertical shear of the background wind is present. A total of six types of waves have been found and their properties were characterized in terms of the corresponding dispersion relations and wave structures. In this second part, we study the waves' solutions when several atmospheric approximations are applied: Lamb, surface, and centrifugal waves. Lamb and surface waves are found to be quite similar to those in a geostrophic regime. By contrast, centrifugal waves turn out to be a special case of Rossby waves that arise in atmospheres in cyclostrophic balance. Finally, we use our results to identify the nature of the waves behind atmospheric periodicities found in polar and lower latitudes of Venus's atmosphere

ANALYTICAL SOLUTION FOR WAVES IN PLANETS WITH ATMOSPHERIC SUPERROTATION. II. LAMB, SURFACE, AND CENTRIFUGAL WAVES

Energy Technology Data Exchange (ETDEWEB)

Peralta, J.; López-Valverde, M. A. [Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía, 18008 Granada (Spain); Imamura, T. [Institute of Space and Astronautical Science-Japan Aerospace Exploration Agency 3-1-1, Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210 (Japan); Read, P. L. [Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford (United Kingdom); Luz, D. [Centro de Astronomia e Astrofísica da Universidade de Lisboa (CAAUL), Observatório Astronómico de Lisboa, Tapada da Ajuda, 1349-018 Lisboa (Portugal); Piccialli, A., E-mail: peralta@iaa.es [LATMOS, UVSQ, 11 bd dAlembert, 78280 Guyancourt (France)

2014-07-01

This paper is the second in a two-part study devoted to developing tools for a systematic classification of the wide variety of atmospheric waves expected on slowly rotating planets with atmospheric superrotation. Starting with the primitive equations for a cyclostrophic regime, we have deduced the analytical solution for the possible waves, simultaneously including the effect of the metric terms for the centrifugal force and the meridional shear of the background wind. In those cases where the conditions for the method of the multiple scales in height are met, these wave solutions are also valid when vertical shear of the background wind is present. A total of six types of waves have been found and their properties were characterized in terms of the corresponding dispersion relations and wave structures. In this second part, we study the waves' solutions when several atmospheric approximations are applied: Lamb, surface, and centrifugal waves. Lamb and surface waves are found to be quite similar to those in a geostrophic regime. By contrast, centrifugal waves turn out to be a special case of Rossby waves that arise in atmospheres in cyclostrophic balance. Finally, we use our results to identify the nature of the waves behind atmospheric periodicities found in polar and lower latitudes of Venus's atmosphere.

Unstable spiral waves and local Euclidean symmetry in a model of cardiac tissue

International Nuclear Information System (INIS)

Marcotte, Christopher D.; Grigoriev, Roman O.

2015-01-01

This paper investigates the properties of unstable single-spiral wave solutions arising in the Karma model of two-dimensional cardiac tissue. In particular, we discuss how such solutions can be computed numerically on domains of arbitrary shape and study how their stability, rotational frequency, and spatial drift depend on the size of the domain as well as the position of the spiral core with respect to the boundaries. We also discuss how the breaking of local Euclidean symmetry due to finite size effects as well as the spatial discretization of the model is reflected in the structure and dynamics of spiral waves. This analysis allows identification of a self-sustaining process responsible for maintaining the state of spiral chaos featuring multiple interacting spirals

Unstable spiral waves and local Euclidean symmetry in a model of cardiac tissue.

Science.gov (United States)

Marcotte, Christopher D; Grigoriev, Roman O

2015-06-01

This paper investigates the properties of unstable single-spiral wave solutions arising in the Karma model of two-dimensional cardiac tissue. In particular, we discuss how such solutions can be computed numerically on domains of arbitrary shape and study how their stability, rotational frequency, and spatial drift depend on the size of the domain as well as the position of the spiral core with respect to the boundaries. We also discuss how the breaking of local Euclidean symmetry due to finite size effects as well as the spatial discretization of the model is reflected in the structure and dynamics of spiral waves. This analysis allows identification of a self-sustaining process responsible for maintaining the state of spiral chaos featuring multiple interacting spirals.

Higher-order rogue wave solutions of the three-wave resonant interaction equation via the generalized Darboux transformation

International Nuclear Information System (INIS)

Wang, Xin; Chen, Yong; Cao, Jianli

2015-01-01

In this paper, we utilize generalized Darboux transformation to study higher-order rogue wave solutions of the three-wave resonant interaction equation, which describes the propagation and mixing of waves with different frequencies in weakly nonlinear dispersive media. A general Nth-order rogue wave solution with two characteristic velocities structural parameters and 3N independent parameters under a determined plane-wave background and a specific parameter condition is derived. As an application, we show that four fundamental rogue waves with fundamental, two kinds of line and quadrilateral patterns, or six fundamental rogue waves with fundamental, triangular, two kinds of quadrilateral and circular patterns can emerge in the second-order rogue waves. Moreover, several important wave characteristics including the maximum values, the corresponding coordinate positions of the humps, and the stability problem for some special higher-order rogue wave solutions such as the fundamental and quadrilateral cases are discussed. (paper)

Full-wave modeling of ICRF waves: global and quasi-local descriptions

International Nuclear Information System (INIS)

Dumont, R. J.

2007-01-01

Waves in the Ion Cyclotron Range of Frequencies (ICRF) undergo significant space dispersion as they propagate in magnetic fusion plasmas, making it necessary to incorporate non-local effects in their physical description. Full-wave codes are routinely employed to simulate ICRF heating experiments in tokamaks. The vast majority of these codes rely on a description of the plasma based on a 'quasi-local' derivation of the dielectric tensor, i.e. assuming that the range of space dispersion remains small compared to the system dimensions. However, non-local effects caused by wide particle orbits are expected to play a significant role in current and future experiments featuring wave-driven fast ions, fusion-born alpha particles... Global formalisms have thus been proposed to include these effects in a more comprehensive fashion. Based on a description of the particle dynamics in terms of action-angle variables, a full-wave code, named EVE, is currently under development. Its first version, presented here, incorporates quasi-local expressions valid to second order in Larmor radius, derived from the more general Hamiltonian formalism. The obtained tool has the advantage of being compatible with the current requirements of integrated modeling, and lends itself to direct comparisons with existing codes

Local Tensor Radiation Conditions For Elastic Waves

DEFF Research Database (Denmark)

Krenk, S.; Kirkegaard, Poul Henning

2001-01-01

A local boundary condition is formulated, representing radiation of elastic waves from an arbitrary point source. The boundary condition takes the form of a tensor relation between the stress at a point on an arbitrarily oriented section and the velocity and displacement vectors at the point....... The tensor relation generalizes the traditional normal incidence impedance condition by accounting for the angle between wave propagation and the surface normal and by including a generalized stiffness term due to spreading of the waves. The effectiveness of the local tensor radiation condition...

Nonlinear localized dust acoustic waves in a charge varying dusty plasma with nonthermal ions

International Nuclear Information System (INIS)

Tribeche, Mouloud; Amour, Rabia

2007-01-01

A numerical investigation is presented to show the existence, formation, and possible realization of large-amplitude dust acoustic (DA) solitary waves in a charge varying dusty plasma with nonthermal ions. These nonlinear localized structures are self-consistent solutions of the collisionless Vlasov equation with a population of fast particles. The spatial patterns of the variable charge DA solitary wave are significantly modified by the nonthermal effects. The results complement and provide new insights into previously published results on this problem

Numerical study of traveling-wave solutions for the Camassa-Holm equation

International Nuclear Information System (INIS)

Kalisch, Henrik; Lenells, Jonatan

2005-01-01

We explore numerically different aspects of periodic traveling-wave solutions of the Camassa-Holm equation. In particular, the time evolution of some recently found new traveling-wave solutions and the interaction of peaked and cusped waves is studied

expansion method and travelling wave solutions for the perturbed ...

Indian Academy of Sciences (India)

Abstract. In this paper, we construct the travelling wave solutions to the perturbed nonlinear. Schrödinger's equation (NLSE) with Kerr law non-linearity by the extended (G /G)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with. Kerr law nonlinearity with arbitrary ...

Solitary wave solution to a singularly perturbed generalized Gardner ...

Indian Academy of Sciences (India)

2017-03-24

Mar 24, 2017 ... Abstract. This paper is concerned with the existence of travelling wave solutions to a singularly perturbed gen- eralized Gardner equation with nonlinear terms of any order. By using geometric singular perturbation theory and based on the relation between solitary wave solution and homoclinic orbits of the ...

ANALYTICAL SOLUTION FOR WAVES IN PLANETS WITH ATMOSPHERIC SUPERROTATION. I. ACOUSTIC AND INERTIA-GRAVITY WAVES

Energy Technology Data Exchange (ETDEWEB)

Peralta, J.; López-Valverde, M. A. [Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía, 18008 Granada (Spain); Imamura, T. [Institute of Space and Astronautical Science-Japan Aerospace Exploration Agency 3-1-1, Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210 (Japan); Read, P. L. [Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford (United Kingdom); Luz, D. [Centro de Astronomia e Astrofísica da Universidade de Lisboa (CAAUL), Observatório Astronómico de Lisboa, Tapada da Ajuda, 1349-018 Lisboa (Portugal); Piccialli, A., E-mail: peralta@iaa.es [LATMOS, UVSQ, 11 bd dAlembert, 78280 Guyancourt (France)

2014-07-01

This paper is the first of a two-part study devoted to developing tools for a systematic classification of the wide variety of atmospheric waves expected on slowly rotating planets with atmospheric superrotation. Starting with the primitive equations for a cyclostrophic regime, we have deduced the analytical solution for the possible waves, simultaneously including the effect of the metric terms for the centrifugal force and the meridional shear of the background wind. In those cases when the conditions for the method of the multiple scales in height are met, these wave solutions are also valid when vertical shear of the background wind is present. A total of six types of waves have been found and their properties were characterized in terms of the corresponding dispersion relations and wave structures. In this first part, only waves that are direct solutions of the generic dispersion relation are studied—acoustic and inertia-gravity waves. Concerning inertia-gravity waves, we found that in the cases of short horizontal wavelengths, null background wind, or propagation in the equatorial region, only pure gravity waves are possible, while for the limit of large horizontal wavelengths and/or null static stability, the waves are inertial. The correspondence between classical atmospheric approximations and wave filtering has been examined too, and we carried out a classification of the mesoscale waves found in the clouds of Venus at different vertical levels of its atmosphere. Finally, the classification of waves in exoplanets is discussed and we provide a list of possible candidates with cyclostrophic regimes.

Enhancing propagation characteristics of truncated localized waves in silica

KAUST Repository

Salem, Mohamed

2011-07-01

The spectral characteristics of truncated Localized Waves propagating in dispersive silica are analyzed. Numerical experiments show that the immunity of the truncated Localized Waves propagating in dispersive silica to decay and distortion is enhanced as the non-linearity of the relation between the transverse spatial spectral components and the wave vector gets stronger, in contrast to free-space propagating waves, which suffer from early decay and distortion. © 2011 IEEE.

Exact solitary and periodic wave solutions for a generalized nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Sun Chengfeng; Gao Hongjun

2009-01-01

The generalized nonlinear Schroedinger equation (GNLS) iu t + u xx + β | u | 2 u + γ | u | 4 u + iα (| u | 2 u) x + iτ(| u | 2 ) x u = 0 is studied. Using the bifurcation of travelling waves of this equation, some exact solitary wave solutions were obtained in [Wang W, Sun J,Chen G, Bifurcation, Exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schroedinger equation. Int J Bifucat Chaos 2005:3295-305.]. In this paper, more explicit exact solitary wave solutions and some new smooth periodic wave solutions are obtained.

Local electromagnetic waves in layered superconductors

International Nuclear Information System (INIS)

Gvozdikov, V.M.; Vega-Monroy, R.

1999-01-01

A dispersion equation for electromagnetic waves localized on a defect layer of a layered superconductor is obtained in the frame of a model which neglects electron hopping between layers but assumes an arbitrary current-current response function within the layers. The defect layer differs from the rest of the layers by density and mass of charge carriers. It is shown that near the critical temperature in the London limit the local mode lies within the superconducting gap and has a wave vector threshold depending on the layered crystal and defect layer parameters. In the case of highly anisotropic layered superconductors, like Bi- or Tl-based high-T c cuprates, the local mode exists within a narrow range of positive variations of the mass and charge carriers. (author)

Model-based dispersive wave processing: A recursive Bayesian solution

International Nuclear Information System (INIS)

Candy, J.V.; Chambers, D.H.

1999-01-01

Wave propagation through dispersive media represents a significant problem in many acoustic applications, especially in ocean acoustics, seismology, and nondestructive evaluation. In this paper we propose a propagation model that can easily represent many classes of dispersive waves and proceed to develop the model-based solution to the wave processing problem. It is shown that the underlying wave system is nonlinear and time-variable requiring a recursive processor. Thus the general solution to the model-based dispersive wave enhancement problem is developed using a Bayesian maximum a posteriori (MAP) approach and shown to lead to the recursive, nonlinear extended Kalman filter (EKF) processor. The problem of internal wave estimation is cast within this framework. The specific processor is developed and applied to data synthesized by a sophisticated simulator demonstrating the feasibility of this approach. copyright 1999 Acoustical Society of America.

The extended hyperbolic function method and exact solutions of the long-short wave resonance equations

International Nuclear Information System (INIS)

Shang Yadong

2008-01-01

The extended hyperbolic functions method for nonlinear wave equations is presented. Based on this method, we obtain a multiple exact explicit solutions for the nonlinear evolution equations which describe the resonance interaction between the long wave and the short wave. The solutions obtained in this paper include (a) the solitary wave solutions of bell-type for S and L, (b) the solitary wave solutions of kink-type for S and bell-type for L, (c) the solitary wave solutions of a compound of the bell-type and the kink-type for S and L, (d) the singular travelling wave solutions, (e) periodic travelling wave solutions of triangle function types, and solitary wave solutions of rational function types. The variety of structure to the exact solutions of the long-short wave equation is illustrated. The methods presented here can also be used to obtain exact solutions of nonlinear wave equations in n dimensions

Stumpons and fractal-like wave solutions to the Dullin-Gottwald-Holm equation

International Nuclear Information System (INIS)

Yin Jiuli; Tian Lixin

2009-01-01

The traveling wave solutions to the Dullin-Gottwald-Holm equation (called DGH equation) are classified by an improved qualitative analysis method. Meanwhile, the influence of the parameters on the traveling wave forms is specifically considered. The equation is shown to admit more traveling wave forms solutions, especially new solutions such as stumpons and fractal-like waves are first given. We also point out that the smooth solutions can converge to non-smooth ones under certain conditions. Furthermore, the new explicit forms of peakons with period are obtained.

Travelling wave solutions of the generalized Benjamin-Bona-Mahony equation

International Nuclear Information System (INIS)

Estevez, P.G.; Kuru, S.; Negro, J.; Nieto, L.M.

2009-01-01

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.

Jacobian elliptic wave solutions in an anharmonic molecular crystal model

International Nuclear Information System (INIS)

Teh, C.G.R.; Lee, B.S.; Koo, W.K.

1997-07-01

Explicit Jacobian elliptic wave solutions are found in the anharmonic molecular crystal model for both the continuum limit and discrete modes. This class of wave solutions include the famous pulse-like and kink-like solitary modes. We would also like to report on the existence of some highly discrete staggered solitary wave modes not found in the continuum limit. (author). 9 refs, 1 fig

Several localized waves induced by linear interference between a nonlinear plane wave and bright solitons

Science.gov (United States)

Qin, Yan-Hong; Zhao, Li-Chen; Yang, Zhan-Ying; Yang, Wen-Li

2018-01-01

We investigate linear interference effects between a nonlinear plane wave and bright solitons, which are admitted by a pair-transition coupled two-component Bose-Einstein condensate. We demonstrate that the interference effects can induce several localized waves possessing distinctive wave structures, mainly including anti-dark solitons, W-shaped solitons, multi-peak solitons, Kuznetsov-Ma like breathers, and multi-peak breathers. Specifically, the explicit conditions for them are clarified by a phase diagram based on the linear interference properties. Furthermore, the interactions between these localized waves are discussed. The detailed analysis indicates that the soliton-soliton interaction induced phase shift brings the collision between these localized waves which can be inelastic for solitons involving collision and can be elastic for breathers. These characters come from the fact that the profile of solitons depends on the relative phase between bright solitons and a plane wave, and the profile of breathers does not depend on the relative phase. These results would motivate more discussions on linear interference between other nonlinear waves. Specifically, the solitons or breathers obtained here are not related to modulational instability. The underlying reasons are discussed in detail. In addition, possibilities to observe these localized waves are discussed in a two species Bose-Einstein condensate.

Global smooth solutions of 3-D null-form wave equations in exterior domains with Neumann boundary conditions

Science.gov (United States)

Jun, Li; Huicheng, Yin

2018-05-01

The paper is devoted to investigating long time behavior of smooth small data solutions to 3-D quasilinear wave equations outside of compact convex obstacles with Neumann boundary conditions. Concretely speaking, when the surface of a 3-D compact convex obstacle is smooth and the quasilinear wave equation fulfills the null condition, we prove that the smooth small data solution exists globally provided that the Neumann boundary condition on the exterior domain is given. One of the main ingredients in the current paper is the establishment of local energy decay estimates of the solution itself. As an application of the main result, the global stability to 3-D static compressible Chaplygin gases in exterior domain is shown under the initial irrotational perturbation with small amplitude.

Travelling wave solutions for a surface wave equation in fluid mechanics

Directory of Open Access Journals (Sweden)

Tian Yi

2016-01-01

Full Text Available This paper considers a non-linear wave equation arising in fluid mechanics. The exact traveling wave solutions of this equation are given by using G'/G-expansion method. This process can be reduced to solve a system of determining equations, which is large and difficult. To reduce this process, we used Wu elimination method. Example shows that this method is effective.

Macroscopic quantum waves in non local theories

International Nuclear Information System (INIS)

Ventura, I.

1979-01-01

By means of an expansion in the density, it is shown that Macroscopic Quantum Waves also appear in non local theories. This result reinforces the conjecture that these waves should exist in liquid 4 He [pt

Asymptotic Behavior of Periodic Wave Solution to the Hirota—Satsuma Equation

International Nuclear Information System (INIS)

Wu Yong-Qi

2011-01-01

The one- and two-periodic wave solutions for the Hirota—Satsuma (HS) equation are presented by using the Hirota derivative and Riemann theta function. The rigorous proofs on asymptotic behaviors of these two solutions are given such that soliton solution can be obtained from the periodic wave solution in an appropriate limiting procedure. (general)

Macroscopic quantum waves in non local theories

International Nuclear Information System (INIS)

Ventura, I.

1979-01-01

By means of an expansion in the density, it is shown that Macroscopic Quantum Waves also apear in non local theories. This result reinforces the conjecture that these waves should exist in liquid 4 He. (Author) [pt

Absolute instabilities of travelling wave solutions in a Keller-Segel model

OpenAIRE

Davis, P. N.; van Heijster, P.; Marangell, R.

2016-01-01

We investigate the spectral stability of travelling wave solutions in a Keller-Segel model of bacterial chemotaxis with a logarithmic chemosensitivity function and a constant, sublinear, and linear consumption rate. Linearising around the travelling wave solutions, we locate the essential and absolute spectrum of the associated linear operators and find that all travelling wave solutions have essential spectrum in the right half plane. However, we show that in the case of constant or sublinea...

Finite-dimensional attractor for a composite system of wave/plate equations with localized damping

International Nuclear Information System (INIS)

Bucci, Francesca; Toundykov, Daniel

2010-01-01

The long-term behaviour of solutions to a model for acoustic–structure interactions is addressed; the system consists of coupled semilinear wave (3D) and plate equations with nonlinear damping and critical sources. The questions of interest are the existence of a global attractor for the dynamics generated by this composite system as well as dimensionality and regularity of the attractor. A distinct and challenging feature of the problem is the geometrically restricted dissipation on the wave component of the system. It is shown that the existence of a global attractor of finite fractal dimension—established in a previous work by Bucci et al (2007 Commun. Pure Appl. Anal. 6 113–40) only in the presence of full-interior acoustic damping—holds even in the case of localized dissipation. This nontrivial generalization is inspired by, and consistent with, the recent advances in the study of wave equations with nonlinear localized damping

Symbolic computation and abundant travelling wave solutions to ...

Indian Academy of Sciences (India)

The method is reliable and useful, and gives more general exact travelling wave solutions than the existing methods. The solutions obtained are in the form of hyperbolic, trigonometricand rational functions including solitary, singular and periodic solutions which have many potential applications in physical science and ...

Covariant interactions of two spinless particles: all local solutions of the angular condition

International Nuclear Information System (INIS)

Leutwyler, H.; Stern, J.

1977-06-01

The solutions of the algebraic problem posed by covariant Hamiltonian quantum mechanics are discussed. If, in the transverse relative coordinates, the mass and spin operators are differential operators of at most second order, the system is shown to be described by a manifestly covariant wave equation supplemented with a covariant constraint. If, in addition, one requires the wave equation and the constraint to be local in the coordinates of both particles, the freedom left in the interaction reduces to four constants. The resulting class of systems represents a generalization of the relativistic oscillator of Feynman, Kislinger and Ravndal

Coherent patterning of matter waves with subwavelength localization

International Nuclear Information System (INIS)

Mompart, J.; Ahufinger, V.; Birkl, G.

2009-01-01

We propose the subwavelength localization via adiabatic passage (SLAP) technique to coherently achieve state-selective patterning of matter waves well beyond the diffraction limit. The SLAP technique consists in coupling two partially overlapping and spatially structured laser fields to three internal levels of the matter wave yielding state-selective localization at those positions where the adiabatic passage process does not occur. We show that by means of this technique matter wave localization down to the single nanometer scale can be achieved. We analyze in detail the potential implementation of the SLAP technique for nanolithography with an atomic beam of metastable Ne* and for coherent patterning of a two-component 87 Rb Bose-Einstein condensate.

New traveling wave solutions to AKNS and SKdV equations

International Nuclear Information System (INIS)

Ozer, Teoman

2009-01-01

We analyze the traveling wave solutions of Ablowitz-Kaup-Newell-Segur (AKNS) and Schwarz-Korteweg-de Vries (SKdV) equations. As the solution method for differential equations we consider the improved tanh approach. This approach provides to transform the partial differential equation into the ordinary differential equation and then obtain the new families of exact solutions based on the solutions of the Riccati equation. The different values of the coefficients of the Riccati equation allow us to obtain new type of traveling wave solutions to AKNS and SKdV equations.

Resonance localization in tokamaks excited with ICRF waves

International Nuclear Information System (INIS)

Kerbel, G.D.; McCoy, M.G.

1985-01-01

Advanced wave models used to evaluate ICRH in tokamaks typically use warm plasma theory and allow inhomogeneity in one dimension. The majority of these calculations neglect the fact that gyrocenters experience the inhomogeneity via their motion parallel to the magnetic field. The non-local effects of rotational transform and toroidicity can play a significant role in both the propagation and the absorption physics. In strongly driven systems, wave damping can distort the particle distribution function supporting the wave and this produces changes in the absorption. The most common approach is to use Maxwellian absorption rates. We have developed a bounce-averaged Fokker-Planck quasilinear computational model which evolves the population of particles on more realistic orbits. Each wave-particle resonance has its own specific interaction amplitude within any given volume element; these data need only be generated once, and appropriately stored for efficient retrieval. The wave-particle resonant interaction then serves as a mechanism by which the diffusion of particle populations can proceed among neighboring orbits. The local specific spectral energy absorption rate is directly calculable once the orbit geometry and populations are determined. The code is constructed in such fashion as to accommodate wave propagation models which provide the wave spectral energy density on a poloidal cross-section. Information provided by the calculation includes the local absorption properties of the medium which can then be exploited to evolve the wave field

Soliton-like solutions to the ordinary Schroedinger equation

International Nuclear Information System (INIS)

Zamboni-Rached, Michel; Recami, Erasmo

2011-01-01

In recent times it has been paid attention to the fact that (linear) wave equations admit of soliton-like solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized Solutions (existing also for K-G or Dirac equations) are a priori suitable, more than Gaussian's, for describing elementary particle motion. In this paper we show that, mutatis mutandis, Localized Solutions exist even for the ordinary Schroedinger equation within standard Quantum Mechanics; and we obtain both approximate and exact solutions, also setting forth for them particular examples. In the ideal case such solutions bear infinite energy, as well as plane or spherical waves: we show therefore how to obtain nite-energy solutions. At last, we briefly consider solutions for a particle moving in the presence of a potential. (author)

Soliton-like solutions to the ordinary Schroedinger equation

Energy Technology Data Exchange (ETDEWEB)

Zamboni-Rached, Michel [Universidade Estadual de Campinas (DMO/FEEC/UNICAMP), Campinas, SP (Brazil). Fac. de Engenharia Eletrica e de Computacao. Dept. de Microondas e Optica; Recami, Erasmo, E-mail: recami@mi.infn.i [Universita Statale di Bergamo, Bergamo (Italy). Facolta di Ingegneria

2011-07-01

In recent times it has been paid attention to the fact that (linear) wave equations admit of soliton-like solutions, known as Localized Waves or Non-diffracting Waves, which propagate without distortion in one direction. Such Localized Solutions (existing also for K-G or Dirac equations) are a priori suitable, more than Gaussian's, for describing elementary particle motion. In this paper we show that, mutatis mutandis, Localized Solutions exist even for the ordinary Schroedinger equation within standard Quantum Mechanics; and we obtain both approximate and exact solutions, also setting forth for them particular examples. In the ideal case such solutions bear infinite energy, as well as plane or spherical waves: we show therefore how to obtain nite-energy solutions. At last, we briefly consider solutions for a particle moving in the presence of a potential. (author)

Supergravity solutions for D-branes in Hpp-wave backgrounds

International Nuclear Information System (INIS)

Bain, P.; Meessen, P.; Zamaklar, M.

2002-05-01

We derive two families of supergravity solutions describing D-branes in the maximally supersymmetric Hpp-wave background. The first family of solutions corresponds to quarter-BPS D-branes. These solutions are delocalised along certain directions transverse to the pp-wave The second family corresponds to the non-supersymmetric D-branes. These solutions are fully localised. A peculiar feature of the nonsupersymmetric solutions is that gravity becomes repulsive close to the core of the D-brane. Both families preserve the amount of supersymmetry predicted by the D-brane probe/CFT analysis. All solutions are written in Brinkman coordinates. To construct these kind of solutions it is crucial to identify the coordinates in which the ansatz looks the simplest. We argue that the natural coordinates to get the supergravity description of the half-BPS branes are the Rosen coordinates. (author)

Bifurcation analysis and the travelling wave solutions of the Klein

Indian Academy of Sciences (India)

In this paper, we investigate the bifurcations and dynamic behaviour of travelling wave solutions of the Klein–Gordon–Zakharov equations given in Shang et al, Comput. Math. Appl. 56, 1441 (2008). Under different parameter conditions, we obtain some exact explicit parametric representations of travelling wave solutions by ...

Applications of exact traveling wave solutions of Modified Liouville and the Symmetric Regularized Long Wave equations via two new techniques

Science.gov (United States)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

In this current work, we employ novel methods to find the exact travelling wave solutions of Modified Liouville equation and the Symmetric Regularized Long Wave equation, which are called extended simple equation and exp(-Ψ(ξ))-expansion methods. By assigning the different values to the parameters, different types of the solitary wave solutions are derived from the exact traveling wave solutions, which shows the efficiency and precision of our methods. Some solutions have been represented by graphical. The obtained results have several applications in physical science.

Impacts of wave energy conversion devices on local wave climate: observations and modelling from the Perth Wave Energy Project

Science.gov (United States)

Hoeke, Ron; Hemer, Mark; Contardo, Stephanie; Symonds, Graham; Mcinnes, Kathy

2016-04-01

As demonstrated by the Australian Wave Energy Atlas (AWavEA), the southern and western margins of the country possess considerable wave energy resources. The Australia Government has made notable investments in pre-commercial wave energy developments in these areas, however little is known about how this technology may impact local wave climate and subsequently affect neighbouring coastal environments, e.g. altering sediment transport, causing shoreline erosion or accretion. In this study, a network of in-situ wave measurement devices have been deployed surrounding the 3 wave energy converters of the Carnegie Wave Energy Limited's Perth Wave Energy Project. This data is being used to develop, calibrate and validate numerical simulations of the project site. Early stage results will be presented and potential simulation strategies for scaling-up the findings to larger arrays of wave energy converters will be discussed. The intended project outcomes are to establish zones of impact defined in terms of changes in local wave energy spectra and to initiate best practice guidelines for the establishment of wave energy conversion sites.

Qualitative analysis and traveling wave solutions for the perturbed nonlinear Schroedinger's equation with Kerr law nonlinearity

International Nuclear Information System (INIS)

Zhang Zaiyun; Liu Zhenhai; Miao Xiujin; Chen Yuezhong

2011-01-01

In this Letter, we investigate the perturbed nonlinear Schroedinger's equation (NLSE) with Kerr law nonlinearity. All explicit expressions of the bounded traveling wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain bell-shaped solitary wave solutions, kink-shaped solitary wave solutions and Jacobi elliptic function periodic solutions. Moreover, we point out the region which these periodic wave solutions lie in. We present the relation between the bounded traveling wave solution and the energy level h. We find that these periodic wave solutions tend to the corresponding solitary wave solutions as h increases or decreases. Finally, for some special selections of the energy level h, it is shown that the exact periodic solutions evolute into solitary wave solution.

Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation

International Nuclear Information System (INIS)

Zhaqilao,

2013-01-01

A simple symbolic computation approach for finding the rogue waves and rational solutions to the nonlinear evolution equation is proposed. It turns out that many rational solutions with real and complex forms of a (3+1)-dimensional nonlinear evolution equation are obtained. Some features of rogue waves and rational solutions are graphically discussed. -- Highlights: •A simple symbolic computation approach for finding the rational solutions to the NEE is proposed. •Some rogue waves and rational solutions with real and complex forms of a (3+1)-D NEE are obtained. •Some features of rogue waves are graphically discussed

Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation

Energy Technology Data Exchange (ETDEWEB)

Zhaqilao,, E-mail: zhaqilao@imnu.edu.cn

2013-12-06

A simple symbolic computation approach for finding the rogue waves and rational solutions to the nonlinear evolution equation is proposed. It turns out that many rational solutions with real and complex forms of a (3+1)-dimensional nonlinear evolution equation are obtained. Some features of rogue waves and rational solutions are graphically discussed. -- Highlights: •A simple symbolic computation approach for finding the rational solutions to the NEE is proposed. •Some rogue waves and rational solutions with real and complex forms of a (3+1)-D NEE are obtained. •Some features of rogue waves are graphically discussed.

Ambipolarons: Solitary wave solutions for the radial electric field in a plasma

International Nuclear Information System (INIS)

Hastings, D.E.; Hazeltine, R.D.; Morrison, P.J.

1986-01-01

The ambipolar radial electric field in a nonaxisymmetric plasma can be described by a nonlinear diffusion equation. This equation is shown to possess solitary wave solutions. A model nonlinear diffusion equation with a cubic nonlinearity is studied. An explicit analytic step-like form for the solitary wave is found. It is shown that the solitary wave solutions are linearly stable against all but translational perturbations. Collisions of these solitary waves are studied and three possible final states are found: two diverging solitary waves, two stationary solitary waves, or two converging solitary waves leading to annihilation

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.

Localized nonlinear waves on quantized superfluid vortex filaments in the presence of mutual friction and a driving normal fluid flow.

Science.gov (United States)

Shah, Rehan; Van Gorder, Robert A

2016-03-01

We demonstrate the existence of localized structures along quantized vortex filaments in superfluid helium under the quantum form of the local induction approximation (LIA), which includes mutual friction and normal fluid effects. For small magnitude normal fluid velocities, the dynamics are dissipative under mutual friction. On the other hand, when normal fluid velocities are sufficiently large, we observe parametric amplification of the localized disturbances along quantized vortex filaments, akin to the Donnelly-Glaberson instability for regular Kelvin waves. As the waves amplify they will eventually cause breakdown of the LIA assumption (and perhaps the vortex filament itself), and we derive a characteristic time for which this breakdown occurs under our model. More complicated localized waves are shown to occur, and we study these asymptotically and through numerical simulations. Such solutions still exhibit parametric amplification for large enough normal fluid velocities, although this amplification may be less uniform than would be seen for more regular filaments such as those corresponding to helical curves. We find that large rotational velocities or large wave speeds of nonlinear waves along the filaments will result in more regular and stable structures, while small rotational velocities and wave speeds will permit far less regular dynamics.

Traveling wave front solutions in lateral-excitatory neuronal networks

Directory of Open Access Journals (Sweden)

Sittipong Ruktamatakul

2008-05-01

Full Text Available In this paper, we discuss the shape of traveling wave front solutions to a neuronal model with the connection function to be of lateral excitation type. This means that close connecting cells have an inhibitory influence, while cells that aremore distant have an excitatory influence. We give results on the shape of the wave fronts solutions, which exhibit different shapes depend ing on the size of a threshold parameter.

Evanescent Wave Absorption Based Fiber Sensor for Measuring Glucose Solution Concentration

Science.gov (United States)

Marzuki, Ahmad; Candra Pratiwi, Arni; Suryanti, Venty

2018-03-01

An optical fiber sensor based on evanescent wave absorption designed for measuring glucose solution consentration was proposed. The sensor was made to detect absorbance of various wavelength in the glucose solution. The sensing element was fabricated by side polishing of multimode polymer optical fiber to form a D-shape. The sensing element was immersed in different concentration of glucoce solution. As light propagated through the optical fiber, the evanescent wave interacted with the glucose solution. Light was absorbed by the glucose solution. The larger concentration the glucose solution has, the more the evanescent wave was absorbed in particular wavelenght. Here in this paper, light absorbtion as function of glucose concentration was measured as function of wavelength (the color of LED). We have shown that the proposed sensor can demonstrated an increase of light absorption as function of glucose concentration.

On Mooring Solutions for Large Wave Energy Converters

DEFF Research Database (Denmark)

Thomsen, Jonas Bjerg; Kofoed, Jens Peter; Ferri, Francesco

2017-01-01

The present paper describes the work carried out in the project ’Mooring Solutions for Large Wave Energy Converters’, which is a Danish research project carried out in a period of three years from September 2014, with the aim of reducing cost of the moorings for four wave energy converters...

The periodic wave solutions for the (2 + 1)-dimensional Konopelchenko-Dubrovsky equations

International Nuclear Information System (INIS)

Sheng Zhang

2006-01-01

More periodic wave solutions expressed by Jacobi elliptic functions for the (2 + 1)-dimensional Konopelchenko-Dubrovsky equations are obtained by using the extended F-expansion method. In the limit cases, the solitary wave solutions and trigonometric function solutions for the equations are also obtained

Global existence and decay of solutions of a nonlinear system of wave equations

KAUST Repository

Said-Houari, Belkacem

2012-01-01

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.

Global existence and decay of solutions of a nonlinear system of wave equations

KAUST Repository

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.

Nondispersive Wave Packets.

Science.gov (United States)

Shaarawi, Amr Mohamed

In this work, nondispersive wavepacket solutions to linear partial differential equations are investigated. These solutions are characterized by infinite energy content; otherwise they are continuous, nonsingular and propagate in free space without spreading out. Examples of such solutions are Berry and Balazs' Airy packet, MacKinnon's wave packet and Brittingham's Focus Wave Mode (FWM). It is demonstrated in this thesis that the infinite energy content is not a basic problem per se and that it can be dealt with in two distinct ways. First these wave packets can be used as bases to construct highly localized, slowly decaying, time-limited pulsed solutions. In the case of the FWMs, this path leads to the formulation of the bidirectional representation, a technique that provides the most natural basis for synthesizing Brittingham-like solutions. This representation is used to derive new exact solutions to the 3-D scalar wave equation. It is also applied to problems involving boundaries, in particular to the propagation of a localized pulse in a infinite acoustic waveguide and to the launchability of such a pulse from the opening of a semi-infinite waveguide. The second approach in dealing with the infinite energy content utilizes the bump-like structure of nondispersive solutions. With an appropriate choice of parameters, these bump fields have very large amplitudes around the centers, in comparison to their tails. In particular, the FWM solutions are used to model massless particles and are capable of providing an interesting interpretation to the results of Young's two slit experiment and to the wave-particle duality of light. The bidirectional representation provides, also, a systematic way of deriving packet solutions to the Klein-Gordon, the Schrodinger and the Dirac equations. Nondispersive solutions of the former two equations are compared to previously derived ones, e.g., the Airy packet and MacKinnon's wave packet.

EXACT TRAVELLING WAVE SOLUTIONS TO BBM EQUATION

Institute of Scientific and Technical Information of China (English)

无

2009-01-01

Abundant new travelling wave solutions to the BBM (Benjamin-Bona-Mahoni) equation are obtained by the generalized Jacobian elliptic function method. This method can be applied to other nonlinear evolution equations.

Localized structures of electromagnetic waves in hot electron-positron plasma

International Nuclear Information System (INIS)

Kartal, S.; Tsintsadze, L.N.; Berezhiani, V.I.

1995-08-01

The dynamics of relatively strong electromagnetic (EM) wave propagation in hot electron-positron plasma is investigated. The possibility of finding localized stationary structures of EM waves is explored. It it shown that under certain conditions the EM wave forms a stable localized soliton-like structures where plasma is completely expelled from the region of EM field location. (author). 9 refs, 2 figs

Square-integrable wave packets from the Volkov solutions

International Nuclear Information System (INIS)

Zakowicz, Stephan

2005-01-01

Rigorous mathematical proofs of some properties of the Volkov solutions are presented, which describe the motion of a relativistic charged Dirac particle in a classical, plane electromagnetic wave. The Volkov solutions are first rewritten in a convenient form, which clearly reveals some of the symmetries of the underlying Dirac equation. Assuming continuity and boundedness of the electromagnetic vector potential, it is shown how one may construct square-integrable wave packets from momentum distributions in the space C 0 ∞ (R 3 ) 4 . If, in addition, the vector potential is C 1 and the derivative is bounded, these wave packets decay in space faster than any polynomial and fulfill the Dirac equation. The mapping which takes momentum distributions into wave packets is shown to be isometric with respect to the L 2 (R 3 ) 4 norm and may therefore be continuously extended to a mapping from L 2 (R 3 ) 4 . For a momentum function in L 1 (R 3 ) 4 intersection L 2 (R 3 ) 4 , an integral representation of this extension is presented

Square-Integrable Wave Packets from the Volkov Solutions

CERN Document Server

Zakowicz, S

2004-01-01

Rigorous mathematical proofs of some properties of the Volkov solutions are presented, which describe the motion of a relativistic charged Dirac particle in a classical, plane electromagnetic wave. The Volkov solutions are first rewritten in a convenient form, which clearly reveals some of the symmetries of the underlying Dirac equation. Assuming continuity and boundedness of the electromagnetic vector potential, it is shown how one may construct square-integrable wave packets from momentum distributions in the space $\\mathcal{C}^{\\infty}_0(\\mathbb{R}^3)^4$. If, in addition, the vector potential is $\\mathcal{C}^1$ and the derivative is bounded, these wave packets decay in space faster than any polynomial and fulfill the Dirac equation. The mapping which takes momentum distributions into wave packets is shown to be isometric with respect to the $L^2(\\mathbb{R}^3)^4$ norm and may therefore be continuously extended to a mapping from $L^2(\\mathbb{R}^3)^4$. For a momen! tum function in $L^1(\\mathbb{R}^3)^4 \\cap L^...

Single-peak solitary wave solutions for the variant Boussinesq ...

Indian Academy of Sciences (India)

ear dispersive waves in shallow water. This equation has attracted a lot of attention ... which is a model for water waves (a = 0), where u(x, t) is the velocity, H(x, t) is the total depth and the subscripts denote partial ... cusped solitary wave solutions of the osmosis K(2, 2) equation. Zhang and Chen [6] obtained new types of ...

Periodic solutions for one dimensional wave equation with bounded nonlinearity

Science.gov (United States)

Ji, Shuguan

2018-05-01

This paper is concerned with the periodic solutions for the one dimensional nonlinear wave equation with either constant or variable coefficients. The constant coefficient model corresponds to the classical wave equation, while the variable coefficient model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. For finding the periodic solutions of variable coefficient wave equation, it is usually required that the coefficient u (x) satisfies ess infηu (x) > 0 with ηu (x) = 1/2 u″/u - 1/4 (u‧/u)2, which actually excludes the classical constant coefficient model. For the case ηu (x) = 0, it is indicated to remain an open problem by Barbu and Pavel (1997) [6]. In this work, for the periods having the form T = 2p-1/q (p , q are positive integers) and some types of boundary value conditions, we find some fundamental properties for the wave operator with either constant or variable coefficients. Based on these properties, we obtain the existence of periodic solutions when the nonlinearity is monotone and bounded. Such nonlinearity may cross multiple eigenvalues of the corresponding wave operator. In particular, we do not require the condition ess infηu (x) > 0.

Explicit Solutions and Bifurcations for a Class of Generalized Boussinesq Wave Equation

International Nuclear Information System (INIS)

Ma Zhi-Min; Sun Yu-Huai; Liu Fu-Sheng

2013-01-01

In this paper, the generalized Boussinesq wave equation u tt — u xx + a(u m ) xx + bu xxxx = 0 is investigated by using the bifurcation theory and the method of phase portraits analysis. Under the different parameter conditions, the exact explicit parametric representations for solitary wave solutions and periodic wave solutions are obtained. (general)

Absolute instabilities of travelling wave solutions in a Keller-Segel model

Science.gov (United States)

Davis, P. N.; van Heijster, P.; Marangell, R.

2017-11-01

We investigate the spectral stability of travelling wave solutions in a Keller-Segel model of bacterial chemotaxis with a logarithmic chemosensitivity function and a constant, sublinear, and linear consumption rate. Linearising around the travelling wave solutions, we locate the essential and absolute spectrum of the associated linear operators and find that all travelling wave solutions have parts of the essential spectrum in the right half plane. However, we show that in the case of constant or sublinear consumption there exists a range of parameters such that the absolute spectrum is contained in the open left half plane and the essential spectrum can thus be weighted into the open left half plane. For the constant and sublinear consumption rate models we also determine critical parameter values for which the absolute spectrum crosses into the right half plane, indicating the onset of an absolute instability of the travelling wave solution. We observe that this crossing always occurs off of the real axis.

New exact travelling wave solutions for the generalized nonlinear Schroedinger equation with a source

International Nuclear Information System (INIS)

Abdou, M.A.

2008-01-01

The generalized F-expansion method with a computerized symbolic computation is used for constructing a new exact travelling wave solutions for the generalized nonlinear Schrodinger equation with a source. As a result, many exact travelling wave solutions are obtained which include new periodic wave solution, trigonometric function solutions and rational solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in physics

A semi-analytical approach towards plane wave analysis of local resonance metamaterials using a multiscale enriched continuum description

NARCIS (Netherlands)

Sridhar, A.; Kouznetsova, V.; Geers, M.G.D.

2017-01-01

This work presents a novel multiscale semi-analytical technique for the acoustic plane wave analysis of (negative) dynamic mass density type local resonance metamaterials with complex micro-structural geometry. A two step solution strategy is adopted, in which the unit cell problem at the

Electromagnetic waves in irregular multilayered spheroidal structures of finite conductivity: full wave solutions

International Nuclear Information System (INIS)

Bahar, E.

1976-01-01

The propagation of electromagnetic waves excited by electric dipoles oriented along the axis of multilayered spheroidal structures of finite conductivity is investigated. The electromagnetic parameters and the thickness of the layers of the structure are assumed to be functions of the latitude. In the analysis, electric and magnetic field transforms that constitute a discrete and a continuous spectrum of spherical waves are used to provide a suitable basis for the expansion of the electromagnetic fields at any point in the irregular spheroidal structure. For spheroidal structures with good conducting cores, the terms in the solutions associated with the continuous part of the wave spectrum vanish. In general, however, when the skin depth for the core is large compared to its dimensions or when the sources are located in the core of the structure and propagation in the core is of special interest, the contribution from the continuous part of the wave spectrum cannot be neglected. At each interface between the layers of the irregular spheroidal structure, exact boundary conditions are imposed. Since the terms of the field expansions in the irregular structure do not individually satisfy the boundary conditions, Maxwell's equations are reduced to sets of coupled ordinary first-order differential equations for the wave amplitudes. The solutions are shown to satisfy the reciprocity relationships in electromagnetic theory. The analysis may be applied to problems of radio wave propagation in a nonuniform model of the earth-ionosphere waveguide, particularly when focusing effects at the antipodes are important

Sub-half-wavelength atom localization via two standing-wave fields

International Nuclear Information System (INIS)

Jin Luling; Sun Hui; Niu Yueping; Gong Shangqing

2008-01-01

We propose a scheme for sub-half-wavelength atom localization in a four-level ladder-type atomic system, which is coupled by two classical standing-wave fields. We find that one of the standing-wave fields can help in enhancing the localization precision, and the other is of crucial importance in increasing the detecting probability and leading sub-half-wavelength localization

Travelling wave solutions and proper solutions to the two-dimensional Burgers-Korteweg-de Vries equation

International Nuclear Information System (INIS)

Feng Zhaosheng

2003-01-01

In this paper, we study the two-dimensional Burgers-Korteweg-de Vries (2D-BKdV) equation by analysing an equivalent two-dimensional autonomous system, which indicates that under some particular conditions, the 2D-BKdV equation has a unique bounded travelling wave solution. Then by using a direct method, a travelling solitary wave solution to the 2D-BKdV equation is expressed explicitly, which appears to be more efficient than the existing methods proposed in the literature. At the end of the paper, the asymptotic behaviour of the proper solutions of the 2D-BKdV equation is established by applying the qualitative theory of differential equations

Stochastic growth of localized plasma waves

International Nuclear Information System (INIS)

Robinson, P.A.; Cairns, Iver H.

2001-01-01

Localized bursty plasma waves are detected by spacecraft in many space plasmas. The large spatiotemporal scales involved imply that beam and other instabilities relax to marginal stability and that mean wave energies are low. Stochastic wave growth occurs when ambient fluctuations perturb the system, causing fluctuations about marginal stability. This yields regions where growth is enhanced and others where damping is increased; bursts are associated with enhanced growth and can occur even when the mean growth rate is negative. In stochastic growth, energy loss from the source is suppressed relative to secular growth, preserving it far longer than otherwise possible. Linear stochastic growth can operate at wave levels below thresholds of nonlinear wave-clumping mechanisms such as strong-turbulence modulational instability and is not subject to their coherence and wavelength limits. These mechanisms can be distinguished by statistics of the fields, whose strengths are lognormally distributed if stochastically growing and power-law distributed in strong turbulence. Recent applications of stochastic growth theory (SGT) are described, involving bursty plasma waves and unstable particle distributions in type III solar radio sources, the Earth's foreshock, magnetosheath, and polar cap regions. It is shown that when combined with wave-wave processes, SGT also accounts for associated radio emissions

Multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method

International Nuclear Information System (INIS)

Fan Engui

2002-01-01

A new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system. Compared with most of the existing tanh methods, the Jacobi elliptic function method or other sophisticated methods, the proposed method not only gives new and more general solutions, but also provides a guideline to classify the various types of the travelling wave solutions according to the values of some parameters. The solutions obtained in this paper include (a) kink-shaped and bell-shaped soliton solutions, (b) rational solutions, (c) triangular periodic solutions and (d) Jacobi and Weierstrass doubly periodic wave solutions. Among them, the Jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition. The efficiency of the method can be demonstrated on a large variety of nonlinear evolution equations such as those considered in this paper, KdV-MKdV, Ito's fifth MKdV, Hirota, Nizhnik-Novikov-Veselov, Broer-Kaup, generalized coupled Hirota-Satsuma, coupled Schroedinger-KdV, (2+1)-dimensional dispersive long wave, (2+1)-dimensional Davey-Stewartson equations. In addition, as an illustrative sample, the properties of the soliton solutions and Jacobi doubly periodic solutions for the Hirota equation are shown by some figures. The links among our proposed method, the tanh method, extended tanh method and the Jacobi elliptic function method are clarified generally. (author)

A third-order asymptotic solution of nonlinear standing water waves in Lagrangian coordinates

International Nuclear Information System (INIS)

Yang-Yih, Chen; Hung-Chu, Hsu

2009-01-01

Asymptotic solutions up to third-order which describe irrotational finite amplitude standing waves are derived in Lagrangian coordinates. The analytical Lagrangian solution that is uniformly valid for large times satisfies the irrotational condition and the pressure p = 0 at the free surface, which is in contrast with the Eulerian solution existing under a residual pressure at the free surface due to Taylor's series expansion. In the third-order Lagrangian approximation, the explicit parametric equation and the Lagrangian wave frequency of water particles could be obtained. In particular, the Lagrangian mean level of a particle motion that is a function of vertical label is found as a part of the solution which is different from that in an Eulerian description. The dynamic properties of nonlinear standing waves in water of a finite depth, including particle trajectory, surface profile and wave pressure are investigated. It is also shown that the Lagrangian solution is superior to an Eulerian solution of the same order for describing the wave shape and the kinematics above the mean water level. (general)

Localization of waves in a fluctuating plasma

International Nuclear Information System (INIS)

Escande, D.F.; Souillard, B.

1984-01-01

We present the first application of localization theory to plasma physics: Density fluctuations induce exponential localization of longitudinal and transverse electron plasma waves, i.e., the eigenmodes have an amplitude decreasing exponentially for large distances without any dissipative mechanism in the plasma. This introduces a new mechanism for converting a convective instability into an absolute one. Localization should be observable in clear-cut experiments

Colliding almost-plane gravitational waves: Colliding plane waves and general properties of almost-plane-wave spacetimes

International Nuclear Information System (INIS)

Yurtsever, U.

1988-01-01

It is well known that when two precisely plane-symmetric gravitational waves propagating in an otherwise flat background collide, they focus each other so strongly as to produce a curvature singularity. This paper is the first of several devoted to almost-plane gravitational waves and their collisions. Such waves are more realistic than plane waves in having a finite but very large transverse size. In this paper we review some crucial features of the well-known exact solutions for colliding plane waves and we argue that one of these features, the breakdown of ''local inextendibility'' can be regarded as nongeneric. We then introduce a new framework for analyzing general colliding plane-wave spacetimes; we give an alternative proof of a theorem due to Tipler implying the existence of singularities in all generic colliding plane-wave solutions; and we discuss the fact that the recently constructed Chandrasekhar-Xanthopoulos colliding plane-wave solutions are not strictly plane symmetric and thus do not satisfy the conditions and the conclusion of Tipler's theorem

Localized nonlinear waves and dynamical stability in spinor Bose–Einstein condensates with time–space modulation

Science.gov (United States)

Yao, Yu-Qin; Han, Wei; Li, Ji; Liu, Wu-Ming

2018-05-01

Nonlinearity is one of the most remarkable characteristics of Bose–Einstein condensates (BECs). Much work has been done on one- and two-component BECs with time- or space-modulated nonlinearities, while there is little work on spinor BECs with space–time-modulated nonlinearities. In the present paper we investigate localized nonlinear waves and dynamical stability in spinor Bose–Einstein condensates with nonlinearities dependent on time and space. We solve the three coupled Gross–Pitaevskii equations by similarity transformation and obtain two families of exact matter wave solutions in terms of Jacobi elliptic functions and the Mathieu equation. The localized states of the spinor matter wave describe the dynamics of vector breathing solitons, moving breathing solitons, quasi-breathing solitons and resonant solitons. The results show that one-order vector breathing solitons, quasi-breathing solitons, resonant solitons and the moving breathing solitons ψ ±1 are all stable, but the moving breathing soliton ψ 0 is unstable. We also present the experimental parameters to realize these phenomena in future experiments.

Localized excitations in a nonlinearly coupled magnetic drift wave-zonal flow system

International Nuclear Information System (INIS)

Shukla, Nitin; Shukla, P.K.

2010-01-01

We consider the amplitude modulation of the magnetic drift wave (MDW) by zonal flows (ZFs) in a nonuniform magnetoplasma. For this purpose, we use the two-fluid model to derive a nonlinear Schroedinger equation for the amplitude modulated MDWs in the presence of the ZF potential, and an evolution equation for the ZF potential which is reinforced by the nonlinear Lorentz force of the MDWs. Our nonlinearly coupled MDW-ZFs system of equations admits stationary solutions in the form of a localized MDW envelope and a shock-like ZF potential profile.

The classification of the single travelling wave solutions to the ...

Indian Academy of Sciences (India)

The discrimination system for the polynomial method is applied to variant Boussinesq equations to classify single travelling wave solutions. In particular, we construct corresponding solutions to the concrete parameters to show that each solution in the classification can be realized.

Travelling Solitary Wave Solutions for Generalized Time-delayed Burgers-Fisher Equation

International Nuclear Information System (INIS)

Deng Xijun; Han Libo; Li Xi

2009-01-01

In this paper, travelling wave solutions for the generalized time-delayed Burgers-Fisher equation are studied. By using the first-integral method, which is based on the ring theory of commutative algebra, we obtain a class of travelling solitary wave solutions for the generalized time-delayed Burgers-Fisher equation. A minor error in the previous article is clarified. (general)

Local full-wave energy and quasilinear analysis in nonuniform plasmas

International Nuclear Information System (INIS)

Smithe, D.N.

1989-01-01

The subject of local wave energy in plasmas is treated via quasilinear theory from the dual perspectives of the action-angle formalism and gyrokinetic analysis. An extension is presented to all orders in the gyroradius of the self-consistent wave-propagation/quasilinear-absorption problem using gyrokinetics. Questions of when and under what conditions local energy should be of definite sign are answered using the action-angle formalism. An important result is that the ''dielectric operators'' of the linearized wave equation and of the local energy are not the same, a fact which is obscured when the eikonal or WKB assumption is invoked. Even though the two dielectrics are very different in character, it is demonstrated that they are nevertheless related by a simple mathematical statement. This study was originally motivated by concern over the question of local energy for r.f.-heating of plasmas, where in certain instances, full-wave effects such as refraction, strong absorption, and mode conversion are of primary importance. Fundamentally, the r.f.-absorption must equate with the energy moment of the quasilinear term to achieve a correct energy balance. This fact governs the derivation (as opposed to postulation) of the local absorption. The troublesome ''kinetic flux'' may then be chosen (it is not unique) to satisfy a wave-energy balance relation with the Poynting flux and local absorption. It is shown that at least one such choice reduces asymptotically to the Stix form away from nonuniformities. (author)

The Evolution and Revival Structure of Localized Quantum Wave Packets

OpenAIRE

Bluhm, Robert; Kostelecky, Alan; Porter, James

1995-01-01

Localized quantum wave packets can be produced in a variety of physical systems and are the subject of much current research in atomic, molecular, chemical, and condensed-matter physics. They are particularly well suited for studying the classical limit of a quantum-mechanical system. The motion of a localized quantum wave packet initially follows the corresponding classical motion. However, in most cases the quantum wave packet spreads and undergoes a series of collapses and revivals. We pre...

Exact Solutions of a High-Order Nonlinear Wave Equation of Korteweg-de Vries Type under Newly Solvable Conditions

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.

Classification of homoclinic rogue wave solutions of the nonlinear Schrödinger equation

Science.gov (United States)

Osborne, A. R.

2014-01-01

Certain homoclinic solutions of the nonlinear Schrödinger (NLS) equation, with spatially periodic boundary conditions, are the most common unstable wave packets associated with the phenomenon of oceanic rogue waves. Indeed the homoclinic solutions due to Akhmediev, Peregrine and Kuznetsov-Ma are almost exclusively used in scientific and engineering applications. Herein I investigate an infinite number of other homoclinic solutions of NLS and show that they reduce to the above three classical homoclinic solutions for particular spectral values in the periodic inverse scattering transform. Furthermore, I discuss another infinity of solutions to the NLS equation that are not classifiable as homoclinic solutions. These latter are the genus-2N theta function solutions of the NLS equation: they are the most general unstable spectral solutions for periodic boundary conditions. I further describe how the homoclinic solutions of the NLS equation, for N = 1, can be derived directly from the theta functions in a particular limit. The solutions I address herein are actual spectral components in the nonlinear Fourier transform theory for the NLS equation: The periodic inverse scattering transform. The main purpose of this paper is to discuss a broader class of rogue wave packets1 for ship design, as defined in the Extreme Seas program. The spirit of this research came from D. Faulkner (2000) who many years ago suggested that ship design procedures, in order to take rogue waves into account, should progress beyond the use of simple sine waves. 1An overview of other work in the field of rogue waves is given elsewhere: Osborne 2010, 2012 and 2013. See the books by Olagnon and colleagues 2000, 2004 and 2008 for the Brest meetings. The books by Kharif et al. (2008) and Pelinovsky et al. (2010) are excellent references.

A new auxiliary equation and exact travelling wave solutions of nonlinear equations

International Nuclear Information System (INIS)

Sirendaoreji

2006-01-01

A new auxiliary ordinary differential equation and its solutions are used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the auxiliary equation which has more new exact solutions. More new exact travelling wave solutions are obtained for the quadratic nonlinear Klein-Gordon equation, the combined KdV and mKdV equation, the sine-Gordon equation and the Whitham-Broer-Kaup equations

Certain Solutions Of Shock-Waves In Non-Ideal Gases

Directory of Open Access Journals (Sweden)

Kanti Pandey

2016-05-01

Full Text Available In present paper non similar solutions for plane, cylindrical and spherical unsteady flows of non-ideal gas behind shock wave of arbitrary strength initiated by the instantaneous release of finite energy and propagating in a non-ideal gas is investigated. Asymptotic analysis is applied to obtain a solution up to second order. Solution for numerical calculation Runga-Kutta method of fourth order is applied and is concluded that for non-ideal case there is a decrease in velocity, pressure and density for 0th and IInd order in comparison to ideal gas but a increasing tendency in velocity, pressure and density for Ist order in comparison to ideal gas. The energy of explosion J0 for ideal gas is greater in comparison to non-ideal gas for plane, cylindrical and spherical waves.

Evidence of localized wave transmission

International Nuclear Information System (INIS)

Anon.

1988-01-01

LLNL [Lawrence Livermore National Lab.] experiments to test the feasibility of launching an acoustic, directed-energy pulse train (ADEPT) in water have demonstrated localized transmission of wave energy far beyond the classical Rayleigh length that defines the boundary between near-field and far-field transmission for Gaussian (diffraction-limited) pulses. The results of the experiments are in excellent agreement with computer simulations

Weak localization of seismic waves

International Nuclear Information System (INIS)

Larose, E.; Margerin, L.; Tiggelen, B.A. van; Campillo, M.

2004-01-01

We report the observation of weak localization of seismic waves in a natural environment. It emerges as a doubling of the seismic energy around the source within a spot of the width of a wavelength, which is several tens of meters in our case. The characteristic time for its onset is the scattering mean-free time that quantifies the internal heterogeneity

Travelling wave solutions to nonlinear physical models by means

Indian Academy of Sciences (India)

This paper presents the first integral method to carry out the integration of nonlinear partial differential equations in terms of travelling wave solutions. For illustration, three important equations of mathematical physics are analytically investigated. Through the established first integrals, exact solutions are successfully ...

Travelling wave solutions for some time-delayed equations through factorizations

International Nuclear Information System (INIS)

Fahmy, E.S.

2008-01-01

In this work, we use factorization method to find explicit particular travelling wave solutions for the following important nonlinear second-order partial differential equations: The generalized time-delayed Burgers-Huxley, time-delayed convective Fishers, and the generalized time-delayed Burgers-Fisher. Using the particular solutions for these equations we find the general solutions, two-parameter solution, as special cases

An Analytical Method of Auxiliary Sources Solution for Plane Wave Scattering by Impedance Cylinders

DEFF Research Database (Denmark)

Larsen, Niels Vesterdal; Breinbjerg, Olav

2004-01-01

Analytical Method of Auxiliary Sources solutions for plane wave scattering by circular impedance cylinders are derived by transformation of the exact eigenfunction series solutions employing the Hankel function wave transformation. The analytical Method of Auxiliary Sources solution thus obtained...

Exact traveling wave solutions of modified KdV-Zakharov-Kuznetsov equation and viscous Burgers equation.

Science.gov (United States)

Islam, Md Hamidul; Khan, Kamruzzaman; Akbar, M Ali; Salam, Md Abdus

2014-01-01

Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters. 35C07; 35C08; 35P99.

The Multi-Wave Method for Exact Solutions of Nonlinear Partial Differential Equations

Directory of Open Access Journals (Sweden)

Yusuf Pandir

2018-02-01

Full Text Available In this research, we use the multi-wave method to obtain new exact solutions for generalized forms of 5th order KdV equation and fth order KdV (fKdV equation with power law nonlinearity. Computations are performed with the help of the mathematics software Mathematica. Then, periodic wave solutions, bright soliton solutions and rational function solutions with free parameters are obtained by this approach. It is shown that this method is very useful and effective.

Analytical solution for the transient wave propagation of a buried cylindrical P-wave line source in a semi-infinite elastic medium with a fluid surface layer

Science.gov (United States)

Shan, Zhendong; Ling, Daosheng

2018-02-01

This article develops an analytical solution for the transient wave propagation of a cylindrical P-wave line source in a semi-infinite elastic solid with a fluid layer. The analytical solution is presented in a simple closed form in which each term represents a transient physical wave. The Scholte equation is derived, through which the Scholte wave velocity can be determined. The Scholte wave is the wave that propagates along the interface between the fluid and solid. To develop the analytical solution, the wave fields in the fluid and solid are defined, their analytical solutions in the Laplace domain are derived using the boundary and interface conditions, and the solutions are then decomposed into series form according to the power series expansion method. Each item of the series solution has a clear physical meaning and represents a transient wave path. Finally, by applying Cagniard's method and the convolution theorem, the analytical solutions are transformed into the time domain. Numerical examples are provided to illustrate some interesting features in the fluid layer, the interface and the semi-infinite solid. When the P-wave velocity in the fluid is higher than that in the solid, two head waves in the solid, one head wave in the fluid and a Scholte wave at the interface are observed for the cylindrical P-wave line source.

Time-Reversal Generation of Rogue Waves

Science.gov (United States)

Chabchoub, Amin; Fink, Mathias

2014-03-01

The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schrödinger equation (NLS). Within the class of exact NLS breather solutions on a finite background, which describe the modulational instability of monochromatic wave trains, the hierarchy of rational solutions localized in both time and space is considered to provide appropriate prototypes to model rogue wave dynamics. Here, we use the time-reversal invariance of the NLS to propose and experimentally demonstrate a new approach to constructing strongly nonlinear localized waves focused in both time and space. The potential applications of this time-reversal approach include remote sensing and motivated analogous experimental analysis in other nonlinear dispersive media, such as optics, Bose-Einstein condensates, and plasma, where the wave motion dynamics is governed by the NLS.

The collision of multimode dromions and a firewall in the two-component long-wave-short-wave resonance interaction equation

International Nuclear Information System (INIS)

Radha, R; Kumar, C Senthil; Lakshmanan, M; Gilson, C R

2009-01-01

In this communication, we investigate the two-component long-wave-short-wave resonance interaction equation and show that it admits the Painleve property. We then suitably exploit the recently developed truncated Painleve approach to generate exponentially localized solutions for the short-wave components S (1) and S (2) while the long wave L admits a line soliton only. The exponentially localized solutions driving the short waves S (1) and S (2) in the y-direction are endowed with different energies (intensities) and are called 'multimode dromions'. We also observe that the multimode dromions suffer from intramodal inelastic collision while the existence of a firewall across the modes prevents the switching of energy between the modes. (fast track communication)

New Exact Travelling Wave and Periodic Solutions of Discrete Nonlinear Schroedinger Equation

International Nuclear Information System (INIS)

Yang Qin; Dai Chaoqing; Zhang Jiefang

2005-01-01

Some new exact travelling wave and period solutions of discrete nonlinear Schroedinger equation are found by using a hyperbolic tangent function approach, which was usually presented to find exact travelling wave solutions of certain nonlinear partial differential models. Now we can further extend the new algorithm to other nonlinear differential-different models.

Asymptotic solutions and spectral theory of linear wave equations

International Nuclear Information System (INIS)

Adam, J.A.

1982-01-01

This review contains two closely related strands. Firstly the asymptotic solution of systems of linear partial differential equations is discussed, with particular reference to Lighthill's method for obtaining the asymptotic functional form of the solution of a scalar wave equation with constant coefficients. Many of the applications of this technique are highlighted. Secondly, the methods and applications of the theory of the reduced (one-dimensional) wave equation - particularly spectral theory - are discussed. While the breadth of application and power of the techniques is emphasised throughout, the opportunity is taken to present to a wider readership, developments of the methods which have occured in some aspects of astrophysical (particularly solar) and geophysical fluid dynamics. It is believed that the topics contained herein may be of relevance to the applied mathematician or theoretical physicist interest in problems of linear wave propagation in these areas. (orig./HSI)

A local adaptive method for the numerical approximation in seismic wave modelling

Directory of Open Access Journals (Sweden)

Galuzzi Bruno G.

2017-12-01

Full Text Available We propose a new numerical approach for the solution of the 2D acoustic wave equation to model the predicted data in the field of active-source seismic inverse problems. This method consists in using an explicit finite difference technique with an adaptive order of approximation of the spatial derivatives that takes into account the local velocity at the grid nodes. Testing our method to simulate the recorded seismograms in a marine seismic acquisition, we found that the low computational time and the low approximation error of the proposed approach make it suitable in the context of seismic inversion problems.

Explicit and exact solutions for a generalized long-short wave resonance equations with strong nonlinear term

International Nuclear Information System (INIS)

Shang Yadong

2005-01-01

In this paper, the evolution equations with strong nonlinear term describing the resonance interaction between the long wave and the short wave are studied. Firstly, based on the qualitative theory and bifurcation theory of planar dynamical systems, all of the explicit and exact solutions of solitary waves are obtained by qualitative seeking the homoclinic and heteroclinic orbits for a class of Lienard equations. Then the singular travelling wave solutions, periodic travelling wave solutions of triangle functions type are also obtained on the basis of the relationships between the hyperbolic functions and that between the hyperbolic functions with the triangle functions. The varieties of structure of exact solutions of the generalized long-short wave equation with strong nonlinear term are illustrated. The methods presented here also suitable for obtaining exact solutions of nonlinear wave equations in multidimensions

Travelling wave solutions in a class of generalized Korteweg-de Vries equation

International Nuclear Information System (INIS)

Shen Jianwei; Xu Wei

2007-01-01

In this paper, we consider a new generalization of KdV equation u t = u x u l-2 + α[2u xxx u p + 4pu p-1 u x u xx + p(p - 1)u p-2 (u x ) 3 ] and investigate its bifurcation of travelling wave solutions. From the above analysis, we know that there exists compacton and cusp waves in the system. We explain the reason that these non-smooth travelling wave solution arise by using the bifurcation theory

Source localization with an advanced gravitational wave detector network

International Nuclear Information System (INIS)

Fairhurst, Stephen

2011-01-01

We derive an expression for the accuracy with which sources can be localized using a network of gravitational wave detectors. The result is obtained via triangulation, using timing accuracies at each detector and is applicable to a network with any number of detectors. We use this result to investigate the ability of advanced gravitational wave detector networks to accurately localize signals from compact binary coalescences. We demonstrate that additional detectors can significantly improve localization results and illustrate our findings with networks comprised of the advanced LIGO, advanced Virgo and LCGT. In addition, we evaluate the benefits of relocating one of the advanced LIGO detectors to Australia.

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.

Local Dynamics of Baroclinic Waves in the Martian Atmosphere

KAUST Repository

Kavulich, Michael J.

2013-11-01

The paper investigates the processes that drive the spatiotemporal evolution of baroclinic transient waves in the Martian atmosphere by a simulation experiment with the Geophysical Fluid Dynamics Laboratory (GFDL) Mars general circulation model (GCM). The main diagnostic tool of the study is the (local) eddy kinetic energy equation. Results are shown for a prewinter season of the Northern Hemisphere, in which a deep baroclinic wave of zonal wavenumber 2 circles the planet at an eastward phase speed of about 70° Sol-1 (Sol is a Martian day). The regular structure of the wave gives the impression that the classical models of baroclinic instability, which describe the underlying process by a temporally unstable global wave (e.g., Eady model and Charney model), may have a direct relevance for the description of the Martian baroclinic waves. The results of the diagnostic calculations show, however, that while the Martian waves remain zonally global features at all times, there are large spatiotemporal changes in their amplitude. The most intense episodes of baroclinic energy conversion, which take place in the two great plain regions (Acidalia Planitia and Utopia Planitia), are strongly localized in both space and time. In addition, similar to the situation for terrestrial baroclinic waves, geopotential flux convergence plays an important role in the dynamics of the downstream-propagating unstable waves. © 2013 American Meteorological Society.

Local Dynamics of Baroclinic Waves in the Martian Atmosphere

KAUST Repository

Kavulich, Michael J.; Szunyogh, Istvan; Gyarmati, Gyorgyi; Wilson, R. John

2013-01-01

The paper investigates the processes that drive the spatiotemporal evolution of baroclinic transient waves in the Martian atmosphere by a simulation experiment with the Geophysical Fluid Dynamics Laboratory (GFDL) Mars general circulation model (GCM). The main diagnostic tool of the study is the (local) eddy kinetic energy equation. Results are shown for a prewinter season of the Northern Hemisphere, in which a deep baroclinic wave of zonal wavenumber 2 circles the planet at an eastward phase speed of about 70° Sol-1 (Sol is a Martian day). The regular structure of the wave gives the impression that the classical models of baroclinic instability, which describe the underlying process by a temporally unstable global wave (e.g., Eady model and Charney model), may have a direct relevance for the description of the Martian baroclinic waves. The results of the diagnostic calculations show, however, that while the Martian waves remain zonally global features at all times, there are large spatiotemporal changes in their amplitude. The most intense episodes of baroclinic energy conversion, which take place in the two great plain regions (Acidalia Planitia and Utopia Planitia), are strongly localized in both space and time. In addition, similar to the situation for terrestrial baroclinic waves, geopotential flux convergence plays an important role in the dynamics of the downstream-propagating unstable waves. © 2013 American Meteorological Society.

New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod

Directory of Open Access Journals (Sweden)

Aly R. Seadawy

2018-03-01

Full Text Available This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM in exactly solving a well-known nonlinear equation of partial differential equations (PDEs. In this respect, the longitudinal wave equation (LWE that arises in mathematical physics with dispersion caused by the transverse Poisson’s effect in a magneto-electro-elastic (MEE circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method. Keywords: Extended trial equation method, Longitudinal wave equation in a MEE circular rod, Dark solitons, Bright solitons, Solitary wave, Periodic solitary wave

Bifurcations of Exact Traveling Wave Solutions for (2+1)-Dimensional HNLS Equation

International Nuclear Information System (INIS)

Xu Yuanfen

2012-01-01

For the (2+1)-Dimensional HNLS equation, what are the dynamical behavior of its traveling wave solutions and how do they depend on the parameters of the systems? This paper will answer these questions by using the methods of dynamical systems. Ten exact explicit parametric representations of the traveling wave solutions are given. (general)

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.

Soliton and periodic solutions for higher order wave equations of KdV type (I)

International Nuclear Information System (INIS)

Khuri, S.A.

2005-01-01

The aim of the paper is twofold. First, a new ansaetze is introduced for the construction of exact solutions for higher order wave equations of KdV type (I). We show the existence of a class of discontinuous soliton solutions with infinite spikes. Second, the projective Riccati technique is implemented as an alternate approach for obtaining new exact solutions, solitary solutions, and periodic wave solutions

Exact solution of planar and nonplanar weak shock wave problem in gasdynamics

International Nuclear Information System (INIS)

Singh, L.P.; Ram, S.D.; Singh, D.B.

2011-01-01

Highlights: → An exact solution is derived for a problem of weak shock wave in adiabatic gas dynamics. → The density ahead of the shock is taken as a power of the position from the origin of the shock wave. → For a planar and non-planar motion, the total energy carried by the wave varies with respect to time. → The solution obtained for the planer, and cylindrically symmetric flow is new one. → The results obtained are also presented graphically for different Mach numbers. - Abstract: In the present paper, an analytical approach is used to determine a new exact solution of the problem of one dimensional unsteady adiabatic flow of planer and non-planer weak shock waves in an inviscid ideal fluid. Here it is assumed that the density ahead of the shock front varies according to the power law of the distance from the source of disturbance. The solution of the problem is presented in the form of a power in the distance and the time.

Stochastic growth of localized plasma waves

International Nuclear Information System (INIS)

Robinson, P.A.; Cairns, I.H.

2000-01-01

Full text: Localized bursty plasma waves occur in many natural systems, where they are detected by spacecraft. The large spatiotemporal scales involved imply that beam and other instabilities relax to marginal stability and that mean wave energies are low. Stochastic wave growth occurs when ambient fluctuations perturb the wave-driver interaction, causing fluctuations about marginal stability. This yields regions where growth is enhanced and others where damping is increased; observed bursts are associated with enhanced growth and can occur even when the mean growth rate is negative. In stochastic growth, energy loss from the source is suppressed relative to secular growth, preserving it for much longer times and distances than otherwise possible. Linear stochastic growth can operate at wave levels below thresholds of nonlinear wave-clumping mechanisms such as strong-turbulence modulational instability and is not subject to their coherence and wavelength limits. Growth mechanisms can be distinguished by statistics of the fields, whose strengths are lognormally distributed if stochastically growing, power-law distributed in strong turbulence, and uniformly distributed in log under secular growth. After delineating stochastic growth and strong-turbulence regimes, recent applications of stochastic growth theory (SGT) are described, involving bursty plasma waves and unstable particle distributions in type II and III solar radio sources, foreshock regions upstream of the bow shocks of Earth and planets, and Earth's magnetosheath, auroras, and polar-caps. It is shown that when combined with wave-wave processes, SGT accounts for type II and III solar radio emissions. SGT thus removes longstanding problems in understanding persistent unstable distributions, bursty fields, and radio emissions observed in space

Exponential decay for solutions to semilinear damped wave equation

KAUST Repository

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].

Stability of plane wave solutions of the two-space-dimensional nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Martin, D.U.; Yuen, H.C.; Saffman, P.G.

1980-01-01

The stability of plane, periodic solutions of the two-dimensional nonlinear Schroedinger equation to infinitesimal, two-dimensional perturbation has been calculated and verified numerically. For standing wave disturbances, instability is found for both odd and even modes; as the period of the unperturbed solution increases, the instability associated with the odd modes remains but that associated with the even mode disappears, which is consistent with the results of Zakharov and Rubenchik, Saffman and Yuen and Ablowitz and Segur on the stability of solitons. In addition, we have identified travelling wave instabilities for the even mode perturbations which are absent in the long-wave limit. Extrapolation to the case of an unperturbed solution with infinite period suggests that these instabilities may also be present for the soliton. In other words, the soliton is unstable to odd, standing-wave perturbations, and very likely also to even, travelling-wave perturbations. (orig.)

On the solution of the equations for nonlinear interaction of three damped waves

International Nuclear Information System (INIS)

1976-01-01

Three-wave interactions are analyzed in a coherent wave description assuming different linear damping (or growth) of the individual waves. It is demonstrated that when two of the coefficients of dissipation are equal, the set of equations can be reduced to a single equivalent equation, which in the nonlinearly unstable case, where one wave is undamped, asymptotically takes the form of an equation defining the third Painleve transcendent. It is then possible to find an asymptotic expansion near the time of explosion. This solution is of principal interest since it indicates that the solution of the general three-wave system, where the waves undergo different individual dissipations, belongs to a higher class of functions, which reduces to Jacobian elliptic functions only in the case where all waves suffer the same damping [fr

A Study on Scattered Wave Amplitude Closed-Form Solution Calculation of Torsional Wave Mode by Reciprocity Theorem

International Nuclear Information System (INIS)

Lee, Jaesun; Cho, Younho; Achenbach, Jan D.

2016-01-01

Guided waves can be used for the inspection of long range pipelines. Surface corrosion is often found as a major defect type in pipelines. The reciprocity relation is a well-established theorem by which one can simplify complicated mathematical expressions. The approach has been already applied to plate and half-space structures to obtain the closed-form solutions of scattered amplitude. However, results for the case of cylindrical structures have not been reported yet. In this paper, the scattering of torsional waves, which is widely used in commercial applications, is explored by the reciprocity theorem approach. Obtaining closed-form solutions of the amplitudes of propagating waves is much simplified by using the reciprocal relation. The scattered amplitudes for elliptical and rectangular defect shapes are calculated with respect to defect depth and width, at frequencies between 0 and 500 kHz. The amplitude shows the periodic result as a function of frequency. The derived closed-form solutions can play a significant role in quantitative signal interpretation

A Study on Scattered Wave Amplitude Closed-Form Solution Calculation of Torsional Wave Mode by Reciprocity Theorem

Energy Technology Data Exchange (ETDEWEB)

Lee, Jaesun; Cho, Younho [Pusan National Univ., Pusan (Korea, Republic of); Achenbach, Jan D. [Northwestern Univ., Everston (United States)

2016-07-15

Guided waves can be used for the inspection of long range pipelines. Surface corrosion is often found as a major defect type in pipelines. The reciprocity relation is a well-established theorem by which one can simplify complicated mathematical expressions. The approach has been already applied to plate and half-space structures to obtain the closed-form solutions of scattered amplitude. However, results for the case of cylindrical structures have not been reported yet. In this paper, the scattering of torsional waves, which is widely used in commercial applications, is explored by the reciprocity theorem approach. Obtaining closed-form solutions of the amplitudes of propagating waves is much simplified by using the reciprocal relation. The scattered amplitudes for elliptical and rectangular defect shapes are calculated with respect to defect depth and width, at frequencies between 0 and 500 kHz. The amplitude shows the periodic result as a function of frequency. The derived closed-form solutions can play a significant role in quantitative signal interpretation.

Multicomponent long-wave-short-wave resonance interaction system: Bright solitons, energy-sharing collisions, and resonant solitons.

Science.gov (United States)

Sakkaravarthi, K; Kanna, T; Vijayajayanthi, M; Lakshmanan, M

2014-11-01

We consider a general multicomponent (2+1)-dimensional long-wave-short-wave resonance interaction (LSRI) system with arbitrary nonlinearity coefficients, which describes the nonlinear resonance interaction of multiple short waves with a long wave in two spatial dimensions. The general multicomponent LSRI system is shown to be integrable by performing the Painlevé analysis. Then we construct the exact bright multisoliton solutions by applying the Hirota's bilinearization method and study the propagation and collision dynamics of bright solitons in detail. Particularly, we investigate the head-on and overtaking collisions of bright solitons and explore two types of energy-sharing collisions as well as standard elastic collision. We have also corroborated the obtained analytical one-soliton solution by direct numerical simulation. Also, we discuss the formation and dynamics of resonant solitons. Interestingly, we demonstrate the formation of resonant solitons admitting breather-like (localized periodic pulse train) structure and also large amplitude localized structures akin to rogue waves coexisting with solitons. For completeness, we have also obtained dark one- and two-soliton solutions and studied their dynamics briefly.

Asymmetric rogue waves, breather-to-soliton conversion, and nonlinear wave interactions in the Hirota–Maxwell–Bloch system

International Nuclear Information System (INIS)

Wang Lei; Zhu Yujie; Wang Ziqi; Xu Tao; Qi Fenghua; Xue Yushan

2016-01-01

We study the nonlinear localized waves on constant backgrounds of the Hirota–Maxwell–Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons. (author)

Asymmetric Rogue Waves, Breather-to-Soliton Conversion, and Nonlinear Wave Interactions in the Hirota-Maxwell-Bloch System

Science.gov (United States)

Wang, Lei; Zhu, Yu-Jie; Wang, Zi-Qi; Xu, Tao; Qi, Feng-Hua; Xue, Yu-Shan

2016-02-01

We study the nonlinear localized waves on constant backgrounds of the Hirota-Maxwell-Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons.

Introduction to wave scattering, localization, and mesoscopic phenomena

CERN Document Server

Sheng, Ping

1995-01-01

This book gives readers a coherent picture of waves in disordered media, including multiple scattered waves. The book is intended to be self-contained, with illustrated problems and solutions at the end of each chapter to serve the double purpose of filling out the technical and mathematical details and giving the students exercises if used as a course textbook.The study of wave behavior in disordered media has applications in:Condensed matter physics (semi and superconductor nanostructures and mesoscopic phenomena)Materials science/analytical chemistry (analysis of composite and crystalline structures and properties)Optics and electronics (microelectronic and optoelectronic devices)Geology (seismic exploration of Earths subsurface)

Localized vortices in ηi-modes

International Nuclear Information System (INIS)

Nycander, J.; Lynov, J.P.; Juul Rasmussen, J.

1992-01-01

For a wide variety of nonlinear wave equations necessary conditions for the existence of localized, stationary structures can be found by applying a simple procedure, involving two steps: First the linear dispersion relation is obtained and the regions of the phase velocity of linear waves found. Secondly, assuming that localized solutions exist, their velocities are determined by using integral relations. The obtained velocity takes the form of a ''center of mass velocity''. If this velocity falls outside the regions of phase velocities for linear waves then nonlinear localized vortices may exist. Otherwise, the structure will couple to the linear waves and gradually disperse. Applying this method we have shown that monopole vortex solutions exist for drift waves driven by the ion temperature gradient in a magnetized plasma, the so-called η i -modes. Numerical solutions show that such vortices are steadily propagating and stable and they generally emerge from localized initial conditions. Our study is motivated by recent high resolution simulations of η i -turbulence, where it was observed that coherent vortices developed spontaneously. These had a dominating influence on the evolution of the turbulence, and the associated anomalous transport was found to be significantly reduced as compared with the predictions from quasilinear theory. (author) 8 refs., 3 figs

Introduction to wave scattering, localization, and mesoscopic phenomena

National Research Council Canada - National Science Library

Sheng, Ping

1995-01-01

... Extension of the CPA to the Intermediate Frequency Regime Problems and Solutions References 73 77 82 84 85 87 113 4. Diffusive Waves 115 4.1 Beyond the Effective Medium 4.2 Pulse Intensity Evolution...

New exact travelling wave solutions for two potential coupled KdV equations with symbolic computation

International Nuclear Information System (INIS)

Yang Zonghang

2007-01-01

We find new exact travelling wave solutions for two potential KdV equations which are presented by Foursov [Foursov MV. J Math Phys 2000;41:6173-85]. Compared with the extended tanh-function method, the algorithm used in our paper can obtain some new kinds of exact travelling wave solutions. With the aid of symbolic computation, some novel exact travelling wave solutions of the potential KdV equations are constructed

Smooth and non-smooth traveling wave solutions of a class of nonlinear dispersive equation

International Nuclear Information System (INIS)

Zhao Xiaoshan; Wu Aidi; He Wenzhang

2009-01-01

There is the widespread existence of wave phenomena in physics, mechanics. This clearly necessitates a study of traveling waves in depth and of the modeling and analysis involved. In this paper, we study a nonlinear dispersive K(n,-n,2n) equation, which can be regarded as a generalized K(n,n) equation. Applying the bifurcation theory and the method of phase portraits analysis, we obtain the dynamical behavior and special exact solutions of the K(n,-n,2n) equation. As a result, the conditions under which peakon and compacton solutions appear are also given and the analytic expressions of peakon solutions, compacton and periodic cusp wave solutions are obtained.

New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod

Science.gov (United States)

Seadawy, Aly R.; Manafian, Jalil

2018-03-01

This paper examines the effectiveness of an integration scheme which called the extended trial equation method (ETEM) in exactly solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the longitudinal wave equation (LWE) that arises in mathematical physics with dispersion caused by the transverse Poisson's effect in a magneto-electro-elastic (MEE) circular rod, which a series of exact traveling wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this longitudinal wave equation. Many other such types of nonlinear equations arising in non-destructive evaluation of structures made of the advanced MEE material can also be solved by this method.

Statistical lamb wave localization based on extreme value theory

Science.gov (United States)

Harley, Joel B.

2018-04-01

Guided wave localization methods based on delay-and-sum imaging, matched field processing, and other techniques have been designed and researched to create images that locate and describe structural damage. The maximum value of these images typically represent an estimated damage location. Yet, it is often unclear if this maximum value, or any other value in the image, is a statistically significant indicator of damage. Furthermore, there are currently few, if any, approaches to assess the statistical significance of guided wave localization images. As a result, we present statistical delay-and-sum and statistical matched field processing localization methods to create statistically significant images of damage. Our framework uses constant rate of false alarm statistics and extreme value theory to detect damage with little prior information. We demonstrate our methods with in situ guided wave data from an aluminum plate to detect two 0.75 cm diameter holes. Our results show an expected improvement in statistical significance as the number of sensors increase. With seventeen sensors, both methods successfully detect damage with statistical significance.

Joint Inversion of Earthquake Source Parameters with local and teleseismic body waves

Science.gov (United States)

Chen, W.; Ni, S.; Wang, Z.

2011-12-01

In the classical source parameter inversion algorithm of CAP (Cut and Paste method, by Zhao and Helmberger), waveform data at near distances (typically less than 500km) are partitioned into Pnl and surface waves to account for uncertainties in the crustal models and different amplitude weight of body and surface waves. The classical CAP algorithms have proven effective for resolving source parameters (focal mechanisms, depth and moment) for earthquakes well recorded on relatively dense seismic network. However for regions covered with sparse stations, it is challenging to achieve precise source parameters . In this case, a moderate earthquake of ~M6 is usually recorded on only one or two local stations with epicentral distances less than 500 km. Fortunately, an earthquake of ~M6 can be well recorded on global seismic networks. Since the ray paths for teleseismic and local body waves sample different portions of the focal sphere, combination of teleseismic and local body wave data helps constrain source parameters better. Here we present a new CAP mothod (CAPjoint), which emploits both teleseismic body waveforms (P and SH waves) and local waveforms (Pnl, Rayleigh and Love waves) to determine source parameters. For an earthquake in Nevada that is well recorded with dense local network (USArray stations), we compare the results from CAPjoint with those from the traditional CAP method involving only of local waveforms , and explore the efficiency with bootstraping statistics to prove the results derived by CAPjoint are stable and reliable. Even with one local station included in joint inversion, accuracy of source parameters such as moment and strike can be much better improved.

New binary travelling-wave periodic solutions for the modified KdV equation

International Nuclear Information System (INIS)

Yan Zhenya

2008-01-01

In this Letter, the modified Korteweg-de Vries (mKdV) equations with the focusing (+) and defocusing (-) branches are investigated, respectively. Many new types of binary travelling-wave periodic solutions are obtained for the mKdV equation in terms of Jacobi elliptic functions such as sn(ξ,m)cn(ξ,m)dn(ξ,m) and their extensions. Moreover, we analyze asymptotic properties of some solutions. In addition, with the aid of the Miura transformation, we also give the corresponding binary travelling-wave periodic solutions of KdV equation

Travelling wave solutions to the perturbed Π4 equation

International Nuclear Information System (INIS)

Geicke, J.

1985-01-01

Exact travelling wave solutions to the Π 4 equation, perturbed by a dissipative force and a constant external field η, are presented. For |η| 3 -λ 2 and λ 2 -λ 1 where λ 1 2 3 are the real roots of λ 3 -λ+η=O. The class with |v/ 3 -λ 1 . The stability of the solutions is discussed. (author) [pt

Extended Long Wave Hindcast inside Port Solutions to Minimize Resonance

Directory of Open Access Journals (Sweden)

Gabriel Diaz-Hernandez

2016-02-01

Full Text Available The present study shows a methodology to carry out a comprehensive study of port agitation and resonance analysis in Geraldton Harbor (Western Australia. The methodology described and applied here extends the short and long wave hindcast outside the harbor and towards the main basin. To perform such an analysis, and as the first stage of the methodology, it is necessary to determine, in detail, both the long and short wave characteristics, through a comprehensive methodology to obtain and to hindcast the full spectral data (short waves + long waves, for frequencies between 0.005 and 1 Hz. Twelve-year spectral hindcast wave data, at a location before the reef, have been modified analytically to include the energy input associated with infragravity waves. A decomposition technique based on the energy balance of the radiation stress of short waves is followed. Predictions for long wave heights and periods at different harbor locations are predicted and validated with data recorded during 2004 to 2009. This new database will ensure an accurate and reliable assessment of long wave hourly data (height, period and currents in any area within the main basin of the Port of Geraldton, for its present geometry. With this information, two main task will be completed: (1 undertake a forensic diagnosis of the present response of the harbor, identifying those forcing characteristics related to inoperability events; and (2 propose any layout solutions to minimize, change, dissipate/fade/vanish or positively modify the effects of long waves in the harbor, proposing different harbor geometry modifications. The goal is to identify all possible combinations of solutions that would minimize the current inoperability in the harbor. Different pre-designs are assessed in this preliminary study in order to exemplify the potential of the methodology.

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.

New Families of Rational Form Solitary Wave Solutions to (2+1)-Dimensional Broer-Kaup-Kupershmidt System

International Nuclear Information System (INIS)

Wang Qi; Li Biao; Zhang Hongqing; Chen Yong

2005-01-01

Taking the (2+1)-dimensional Broer-Kaup-Kupershmidt system as a simple example, some families of rational form solitary wave solutions, triangular periodic wave solutions, and rational wave solutions are constructed by using the Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations.

Surface/state correspondence and bulk local operators in pp-wave holography

Directory of Open Access Journals (Sweden)

Nakwoo Kim

2015-12-01

Full Text Available We apply the surface/state correspondence proposal of Miyaji et al. to IIB pp-waves and propose that the bulk local operators should be instantonic D-branes. In line with ordinary AdS/CFT correspondence, the bulk local operators in pp-waves also create a hole, or a boundary, in the dual gauge theory as pointed out by H. Verlinde, and by Y. Nakayama and H. Ooguri. We also present simple calculations which illustrate how to extract the spacetime metric of pp-waves from instantonic D-branes in boundary state formalism.

Exact travelling wave solutions of the (3+1)-dimensional mKdV-ZK ...

Indian Academy of Sciences (India)

In this paper, the new generalized (′/)-expansion method is executed to find the travelling wave solutions of the (3+1)-dimensional mKdV-ZK equation and the (1+1)-dimensional compound KdVB equation. The efficiency of this method for finding exact and travelling wave solutions has been demonstrated. It is shown ...

Electromagnetic pulses, localized and causal

Science.gov (United States)

Lekner, John

2018-01-01

We show that pulse solutions of the wave equation can be expressed as time Fourier superpositions of scalar monochromatic beam wave functions (solutions of the Helmholtz equation). This formulation is shown to be equivalent to Bateman's integral expression for solutions of the wave equation, for axially symmetric solutions. A closed-form one-parameter solution of the wave equation, containing no backward-propagating parts, is constructed from a beam which is the tight-focus limit of two families of beams. Application is made to transverse electric and transverse magnetic pulses, with evaluation of the energy, momentum and angular momentum for a pulse based on the general localized and causal form. Such pulses can be represented as superpositions of photons. Explicit total energy and total momentum values are given for the one-parameter closed-form pulse.

Exact bidirectional X -wave solutions in fiber Bragg gratings

Science.gov (United States)

Efremidis, Nikolaos K.; Nye, Nicholas S.; Christodoulides, Demetrios N.

2017-10-01

We find exact solutions describing bidirectional pulses propagating in fiber Bragg gratings. They are derived by solving the coupled-mode theory equations and are expressed in terms of products of modified Bessel functions with algebraic functions. Depending on the values of the two free parameters, the general bidirectional X -wave solution can also take the form of a unidirectional pulse. We analyze the symmetries and the asymptotic properties of the solutions and also discuss additional waveforms that are obtained by interference of more than one solution. Depending on their parameters, such pulses can create a sharp focus with high contrast.

Localization of Waves in Fractals : Spatial Behavior

NARCIS (Netherlands)

Vries, Pedro de; Raedt, Hans De; Lagendijk, Ad

1989-01-01

Localization of a quantum particle on two-dimensional percolating networks is investigated numerically. Solving the time-dependent Schrödinger equation for particular initial wave packets we study the spatial behavior of eigenstates for two tight-binding models: the quantum percolation model and the

Interference of Locally Forced Internal Waves in Non-Uniform Stratifications

Science.gov (United States)

Supekar, Rohit; Peacock, Thomas

2017-11-01

Several studies have investigated the effect of constructive or destructive interference on the transmission of internal waves propagating through non-uniform stratifications. Such studies have been performed for internal waves that are spatiotemporally harmonic. To understand the effect of localization, we perform a theoretical and experimental study of the transmission of two-dimensional internal waves that are generated by a spatiotemporally localized boundary forcing. This is done by considering an idealized problem and applying a weakly viscous semi-analytic linear model. Parametric studies using this model show that localization leads to the disappearance of transmission peaks and troughs that would otherwise be present for a harmonic forcing. Laboratory experiments that we perform provide a clear indication of this physical effect. Based on the group velocity and angle of propagation of the internal waves, a practical criteria that assesses when the transmission peaks or troughs are evident, is obtained. It is found that there is a significant difference in the predicted energy transfer due to a harmonic and non-harmonic forcing which has direct implications to various physical forcings such as a storm over the ocean.

New travelling wave solutions for nonlinear stochastic evolution

Indian Academy of Sciences (India)

The nonlinear stochastic evolution equations have a wide range of applications in physics, chemistry, biology, economics and finance from various points of view. In this paper, the (′/)-expansion method is implemented for obtaining new travelling wave solutions of the nonlinear (2 + 1)-dimensional stochastic ...

Collision broadened resonance localization in tokamaks excited with ICRF waves

International Nuclear Information System (INIS)

Kerbel, G.D.; McCoy, M.G.

1985-08-01

Advanced wave models used to evaluate ICRH in tokamaks typically use warm plasma theory and allow inhomogeneity in one dimension. The authors have developed a bounce-averaged Fokker-Planck quasilinear computational model which evolves the population of particles on more realistic orbits. Each wave-particle resonance has its own specific interaction amplitude within any given volume element. These data need only be generated once, and appropriately stored for efficient retrieval. The wave-particle resonant interaction then serves as a mechanism by which the diffusion of particle populations can proceed among neighboring orbits. Collisions affect the absorption of rf energy by two quite distinct processes: In addition to the usual relaxation towards the Maxwellian distribution creating velocity gradients which drive quasilinear diffusion, collisions also affect the wave-particle resonance through the mechanism of gyro-phase diffusion. The local specific spectral energy absorption rate is directly calculable once the orbit geometry and populations are determined. The code is constructed in such fashion as to accommodate wave propagation models which provide the wave spectral energy density on a poloidal cross-section. Information provided by the calculation includes the local absorption properties of the medium which can then be exploited to evolve the wave field

Periodic and solitary wave solutions of cubic–quintic nonlinear ...

Indian Academy of Sciences (India)

Hence, most of the real nonlinear physical equations possess variable ... evolution of the system with time and second term represents the convective flux term. The ... Travelling wave solutions of nonlinear reaction-diffusion equations are.

Travelling wave solutions to the K-P-P equation at supercritical wave speeds: a parallel to Simon Harris' probabilistic analysis

NARCIS (Netherlands)

Kyprianou, A.E.

2000-01-01

Recently Harris using probabilistic methods alone has given new proofs for the known existence asymptotics and unique ness of travelling wave solutions to the KPP equation Following in this vein we outline alternative probabilistic proofs for wave speeds exceeding the critical minimal wave speed

Analytical Time-Domain Solution of Plane Wave Propagation Across a Viscoelastic Rock Joint

Science.gov (United States)

Zou, Yang; Li, Jianchun; Laloui, Lyesse; Zhao, Jian

2017-10-01

The effects of viscoelastic filled rock joints on wave propagation are of great significance in rock engineering. The solutions in time domain for plane longitudinal ( P-) and transverse ( S-) waves propagation across a viscoelastic rock joint are derived based on Maxwell and Kelvin models which are, respectively, applied to describe the viscoelastic deformational behaviour of the rock joint and incorporated into the displacement discontinuity model (DDM). The proposed solutions are verified by comparing with the previous studies on harmonic waves, which are simulated by sinusoidal incident P- and S-waves. Comparison between the predicted transmitted waves and the experimental data for P-wave propagation across a joint filled with clay is conducted. The Maxwell is found to be more appropriate to describe the filled joint. The parametric studies show that wave propagation is affected by many factors, such as the stiffness and the viscosity of joints, the incident angle and the duration of incident waves. Furthermore, the dependences of the transmission and reflection coefficients on the specific joint stiffness and viscosity are different for the joints with Maxwell and Kelvin behaviours. The alternation of the reflected and transmitted waveforms is discussed, and the application scope of this study is demonstrated by an illustration of the effects of the joint thickness. The solutions are also extended for multiple parallel joints with the virtual wave source method and the time-domain recursive method. For an incident wave with arbitrary waveform, it is convenient to adopt the present approach to directly calculate wave propagation across a viscoelastic rock joint without additional mathematical methods such as the Fourier and inverse Fourier transforms.

The Role of Localized Compressional Ultra-low Frequency Waves in Energetic Electron Precipitation

Science.gov (United States)

Rae, I. Jonathan; Murphy, Kyle R.; Watt, Clare E. J.; Halford, Alexa J.; Mann, Ian R.; Ozeke, Louis G.; Sibeck, David G.; Clilverd, Mark A.; Rodger, Craig J.; Degeling, Alex W.; Forsyth, Colin; Singer, Howard J.

2018-03-01

Typically, ultra-low frequency (ULF) waves have historically been invoked for radial diffusive transport leading to acceleration and loss of outer radiation belt electrons. At higher frequencies, very low frequency waves are generally thought to provide a mechanism for localized acceleration and loss through precipitation into the ionosphere of radiation belt electrons. In this study we present a new mechanism for electron loss through precipitation into the ionosphere due to a direct modulation of the loss cone via localized compressional ULF waves. We present a case study of compressional wave activity in tandem with riometer and balloon-borne electron precipitation across keV-MeV energies to demonstrate that the experimental measurements can be explained by our new enhanced loss cone mechanism. Observational evidence is presented demonstrating that modulation of the equatorial loss cone can occur via localized compressional wave activity, which greatly exceeds the change in pitch angle through conservation of the first and second adiabatic invariants. The precipitation response can be a complex interplay between electron energy, the localization of the waves, the shape of the phase space density profile at low pitch angles, ionospheric decay time scales, and the time dependence of the electron source; we show that two pivotal components not usually considered are localized ULF wave fields and ionospheric decay time scales. We conclude that enhanced precipitation driven by compressional ULF wave modulation of the loss cone is a viable candidate for direct precipitation of radiation belt electrons without any additional requirement for gyroresonant wave-particle interaction. Additional mechanisms would be complementary and additive in providing means to precipitate electrons from the radiation belts during storm times.

Rayleigh-wave phase-velocity maps and three-dimensional shear velocity structure of the western US from local non-plane surface wave tomography

Science.gov (United States)

Pollitz, F.F.; Snoke, J. Arthur

2010-01-01

We utilize two-and-three-quarter years of vertical-component recordings made by the Transportable Array (TA) component of Earthscope to constrain three-dimensional (3-D) seismic shear wave velocity structure in the upper 200 km of the western United States. Single-taper spectral estimation is used to compile measurements of complex spectral amplitudes from 44 317 seismograms generated by 123 teleseismic events. In the first step employed to determine the Rayleigh-wave phase-velocity structure, we implement a new tomographic method, which is simpler and more robust than scattering-based methods (e.g. multi-plane surface wave tomography). The TA is effectively implemented as a large number of local arrays by defining a horizontal Gaussian smoothing distance that weights observations near a given target point. The complex spectral-amplitude measurements are interpreted with the spherical Helmholtz equation using local observations about a succession of target points, resulting in Rayleigh-wave phase-velocity maps at periods over the range of 18–125 s. The derived maps depend on the form of local fits to the Helmholtz equation, which generally involve the nonplane-wave solutions of Friederich et al. In a second step, the phase-velocity maps are used to derive 3-D shear velocity structure. The 3-D velocity images confirm details witnessed in prior body-wave and surface-wave studies and reveal new structures, including a deep (>100 km deep) high-velocity lineament, of width ∼200 km, stretching from the southern Great Valley to northern Utah that may be a relic of plate subduction or, alternatively, either a remnant of the Mojave Precambrian Province or a mantle downwelling. Mantle seismic velocity is highly correlated with heat flow, Holocene volcanism, elastic plate thickness and seismicity. This suggests that shallow mantle structure provides the heat source for associated magmatism, as well as thinning of the thermal lithosphere, leading to relatively high

Nonlinear Dispersive Elastic Waves in Solids: Exact, Approximate, and Numerical Solutions

Science.gov (United States)

Khajehtourian, Romik

Wave motion lies at the heart of many disciplines in the physical sciences and engineering. For example, problems and applications involving light, sound, heat, or fluid flow are all likely to involve wave dynamics at some level. A particular class of problems is concerned with the propagation of elastic waves in a solid medium, such as a fiber-reinforced composite material responding to vibratory excitations, or soil and rock admitting seismic waves moments after the onset of an earthquake, or phonon transport in a semiconducting crystal like silicon. Regardless of the type of wave, the dispersion relation provides a fundamental characterization of the elastodynamic properties of the medium. The first part of the dissertation examines the propagation of a large-amplitude elastic wave in a one-dimensional homogeneous medium with a focus on the effects of inherent nonlinearities on the dispersion relation. Considering a thin rod, where the thickness is small compared to the wavelength, an exact, closed-form formulation is presented for the treatment of two types of nonlinearity in the strain-displacement gradient relation: Green-Lagrange and Hencky. The derived relation is then verified by direct time-domain simulations, examining both instantaneous dispersion (by direct observation) and short-term, pre-breaking dispersion (by Fourier transformation). A high-order perturbation analysis is also conducted yielding an explicit analytical space-time solution, which is shown to be spectrally accurate. The results establish a perfect match between theory and simulation and reveal that regardless of the strength of the nonlinearity, the dispersion relation fully embodies all information pertaining to the nonlinear harmonic generation mechanism that unfolds as an arbitrary-profiled wave evolves in the medium. In the second part of the dissertation, the analysis is extended to a continuous periodic thin rod exhibiting multiple phases or embedded local resonators. The

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 ... rating a noise-sensitive nonlinear process in which extremely broadband radiations are ..... Based on [21,24], the higher-order rational solution of eq. (15) are.

Deltons, peakons and other traveling-wave solutions of a Camassa-Holm hierarchy

International Nuclear Information System (INIS)

Peng Xiaochun; Dai Huihui

2009-01-01

In this letter, we study an integrable Camassa-Holm hierarchy whose high-frequency limit is the Camassa-Holm equation. Phase plane analysis is employed to investigate bounded traveling wave solutions. An important feature is that there exists a singular line on the phase plane. By considering the properties of the equilibrium points and the relative position of the singular line, we find that there are in total three types of phase planes. Those paths in phase planes which represented bounded solutions are discussed one-by-one. Besides solitary, peaked and periodic waves, the equations are shown to admit a new type of traveling waves, which concentrate all their energy in one point, and we name them deltons as they can be expressed as some constant multiplied by a delta function. There also exists a type of traveling waves we name periodic deltons, which concentrate their energy in periodic points. The explicit expressions for them and all the other traveling waves are given.

Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method

Directory of Open Access Journals (Sweden)

Rahmatullah

2018-03-01

Full Text Available We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses. Keywords: Exp-function method, New exact traveling wave solutions, Modified Riemann-Liouville derivative, Fractional complex transformation, Fractional order Boussinesq-like equations, Symbolic computation

Localized solutions for a nonlocal discrete NLS equation

International Nuclear Information System (INIS)

Ben, Roberto I.; Cisneros Ake, Luís; Minzoni, A.A.; Panayotaros, Panayotis

2015-01-01

We study spatially localized time-periodic solutions of breather type for a cubic discrete NLS equation with a nonlocal nonlinearity that models light propagation in a liquid crystal waveguide array. We show the existence of breather solutions in the limit where both linear and nonlinear intersite couplings vanish, and in the limit where the linear coupling vanishes with arbitrary nonlinear intersite coupling. Breathers of this nonlocal regime exhibit some interesting features that depart from what is seen in the NLS breathers with power nonlinearity. One property we see theoretically is the presence of higher amplitude at interfaces between sites with zero and nonzero amplitude in the vanishing linear coupling limit. A numerical study also suggests the presence of internal modes of orbitally stable localized modes. - Highlights: • Show existence of spatially localized solutions in nonlocal discrete NLS model. • Study spatial properties of localized solutions for arbitrary nonlinear nonlocal coupling. • Present numerical evidence that nonlocality leads to internal modes around stable breathers. • Present theoretical and numerical evidence for amplitude maxima at interfaces

Localized solutions for a nonlocal discrete NLS equation

Energy Technology Data Exchange (ETDEWEB)

Ben, Roberto I. [Instituto de Desarrollo Humano, Universidad Nacional de General Sarmiento, J.M. Gutiérrez 1150, 1613 Los Polvorines (Argentina); Cisneros Ake, Luís [Department of Mathematics, ESFM, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos Edificio 9, 07738 México D.F. (Mexico); Minzoni, A.A. [Depto. Matemáticas y Mecánica, I.I.M.A.S.-U.N.A.M., Apdo. Postal 20-726, 01000 México D.F. (Mexico); Panayotaros, Panayotis, E-mail: panos@mym.iimas.unam.mx [Depto. Matemáticas y Mecánica, I.I.M.A.S.-U.N.A.M., Apdo. Postal 20-726, 01000 México D.F. (Mexico)

2015-09-04

We study spatially localized time-periodic solutions of breather type for a cubic discrete NLS equation with a nonlocal nonlinearity that models light propagation in a liquid crystal waveguide array. We show the existence of breather solutions in the limit where both linear and nonlinear intersite couplings vanish, and in the limit where the linear coupling vanishes with arbitrary nonlinear intersite coupling. Breathers of this nonlocal regime exhibit some interesting features that depart from what is seen in the NLS breathers with power nonlinearity. One property we see theoretically is the presence of higher amplitude at interfaces between sites with zero and nonzero amplitude in the vanishing linear coupling limit. A numerical study also suggests the presence of internal modes of orbitally stable localized modes. - Highlights: • Show existence of spatially localized solutions in nonlocal discrete NLS model. • Study spatial properties of localized solutions for arbitrary nonlinear nonlocal coupling. • Present numerical evidence that nonlocality leads to internal modes around stable breathers. • Present theoretical and numerical evidence for amplitude maxima at interfaces.

Simulation study of localization of electromagnetic waves in two-dimensional random dipolar systems

International Nuclear Information System (INIS)

Wang, Ken Kang-Hsin; Ye Zhen

2003-01-01

We study the propagation and scattering of electromagnetic waves by random arrays of dipolar cylinders in a uniform medium. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is derived from first principles and then solved numerically for electromagnetic fields. For certain ranges of frequencies, spatially localized electromagnetic waves appear in such a simple but realistic disordered system. Dependence of localization on the frequency, radiation damping, and filling factor is shown. The spatial behavior of the total, coherent, and diffusive waves is explored in detail, and found to comply with a physical intuitive picture. A phase diagram characterizing localization is presented, in agreement with previous investigations on other systems

Simulation study of localization of electromagnetic waves in two-dimensional random dipolar systems.

Science.gov (United States)

Wang, Ken Kang-Hsin; Ye, Zhen

2003-12-01

We study the propagation and scattering of electromagnetic waves by random arrays of dipolar cylinders in a uniform medium. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is derived from first principles and then solved numerically for electromagnetic fields. For certain ranges of frequencies, spatially localized electromagnetic waves appear in such a simple but realistic disordered system. Dependence of localization on the frequency, radiation damping, and filling factor is shown. The spatial behavior of the total, coherent, and diffusive waves is explored in detail, and found to comply with a physical intuitive picture. A phase diagram characterizing localization is presented, in agreement with previous investigations on other systems.

A generic travelling wave solution in dissipative laser cavity

Indian Academy of Sciences (India)

2016-09-09

Sep 9, 2016 ... Abstract. A large family of cosh-Gaussian travelling wave solution of a complex Ginzburg–Landau equation ... pling, wherein the real part represents diffusive coupling ... knowledge, this is the first time that cosh-Gaussian pro-.

Exact travelling wave solutions for some important nonlinear

Indian Academy of Sciences (India)

The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical ...

EXACT SOLITARY WAVE SOLUTIONS TO A CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS USING DIRECT ALGEBRAIC METHOD

Institute of Scientific and Technical Information of China (English)

无

2008-01-01

Using direct algebraic method,exact solitary wave solutions are performed for a class of third order nonlinear dispersive disipative partial differential equations. These solutions are obtained under certain conditions for the relationship between the coefficients of the equation. The exact solitary waves of this class are rational functions of real exponentials of kink-type solutions.

Periodic travelling and non-travelling wave solutions of the nonlinear Klein-Gordon equation with imaginary mass

International Nuclear Information System (INIS)

Tang Xiaoyan; Shukla, Padma Kant

2008-01-01

Exact solutions, including the periodic travelling and non-travelling wave solutions, are presented for the nonlinear Klein-Gordon equation with imaginary mass. Some arbitrary functions are permitted in the periodic non-travelling wave solutions, which contribute to various high dimensional nonlinear structures

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.

Explicit solution for a wave equation with nonlocal condition

Science.gov (United States)

Bazhlekova, Emilia; Dimovski, Ivan

2012-11-01

An initial-boundary value problem with a nonlocal boundary condition for one-dimensional wave equation is studied. Applying spectral projections, we find a series solution of the problem. The character of the solution found shows that the oscillation amplitude of the system described by this equation increases with time at any fixed x in absence of external forces. To find a representation of the solution more convenient for numerical calculation we develop a two-dimensional operational calculus for the problem. The solution is expressed as a sum of non-classical convolution products of particular solutions and the arbitrary initial functions. This result is an extension of the classical Duhamel principle for the space variable. The representation is used successfully for numerical computation and visualization of the solution. Numerical results obtained for specific test problems with known exact solutions indicate that the present technique provides accurate numerical solutions.

Exponential decay for solutions to semilinear damped wave equation

KAUST Repository

Gerbi, Sté phane; Said-Houari, Belkacem

2011-01-01

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

Mean field effects for counterpropagating traveling wave solutions of reaction-diffusion systems

International Nuclear Information System (INIS)

Bernoff, A.J.; Kuske, R.; Matkowsky, B.J.; Volpert, V.

1995-01-01

In many problems, one observes traveling waves that propagate with constant velocity and shape in the χ direction, say, are independent of y, and z and describe transitions between two equilibrium states. As parameters of the system are varied, these traveling waves can become unstable and give rise to waves having additional structure, such as traveling waves in the y and z directions, which can themselves be subject to instabilities as parameters are further varied. To investigate this scenario the authors consider a system of reaction-diffusion equations with a traveling wave solution as a basic state. They determine solutions bifurcating from the basic state that describe counterpropagating traveling wave in directions orthogonal to the direction of propagation of the basic state and determine their stability. Specifically, they derive long wave modulation equations for the amplitudes of the counterpropagating traveling waves that are coupled to an equation for a mean field, generated by the translation of the basic state in the direction of its propagation. The modulation equations are then employed to determine stability boundaries to long wave perturbations for both unidirectional and counterpropagating traveling waves. The stability analysis is delicate because the results depend on the order in which transverse and longitudinal perturbation wavenumbers are taken to zero. For the unidirectional wave they demonstrate that it is sufficient to consider the cases of (1) purely transverse perturbations, (2) purely longitudinal perturbations, and (3) longitudinal perturbations with a small transverse component. These yield Eckhaus type, zigzag type, and skew type instabilities, respectively

Localization and solitary waves in solid mechanics

CERN Document Server

Champneys, A R; Thompson, J M T

1999-01-01

This book is a collection of recent reprints and new material on fundamentally nonlinear problems in structural systems which demonstrate localized responses to continuous inputs. It has two intended audiences. For mathematicians and physicists it should provide useful new insights into a classical yet rapidly developing area of application of the rich subject of dynamical systems theory. For workers in structural and solid mechanics it introduces a new methodology for dealing with structural localization and the related topic of the generation of solitary waves. Applications range from classi

Representations and Classification of Traveling Wave Solutions to sinh-Goerdon Equation

International Nuclear Information System (INIS)

Liu Chengshi

2008-01-01

Two concepts named atom solution and combinatory solution are defined. The classification of all single traveling wave atom solutions to sinh-Goerdon equation is obtained, and qualitative properties of solutions are discussed. In particular, we point out that some qualitative properties derived intuitively from dynamic system method are not true. Finally, we prove that our solutions to sinh-Goerdon equation include all solutions obtained in the paper [Z.T. Fu, et al., Commun. Theor. Phys. (Beijing, China) 45 (2006) 55]. Through an example, we show how to give some new identities on Jacobian elliptic functions.

Algebraic method for constructing singular steady solitary waves: a case study

Science.gov (United States)

Clamond, Didier; Dutykh, Denys; Galligo, André

2016-07-01

This article describes the use of algebraic methods in a phase plane analysis of ordinary differential equations. The method is illustrated by the study of capillary-gravity steady surface waves propagating in shallow water. We consider the (fully nonlinear, weakly dispersive) Serre-Green-Naghdi equation with surface tension, because it provides a tractable model that, at the same time, is not too simple, so interest in the method can be emphasized. In particular, we analyse a special class of solutions, the solitary waves, which play an important role in many fields of physics. In capillary-gravity regime, there are two kinds of localized infinitely smooth travelling wave solutions-solitary waves of elevation and of depression. However, if we allow the solitary waves to have an angular point, then the `zoology' of solutions becomes much richer, and the main goal of this study is to provide a complete classification of such singular localized solutions using the methods of the effective algebraic geometry.

Full-wave solution of short impulses in inhomogeneous plasma

International Nuclear Information System (INIS)

Ferencz, Orsolya E.

2005-01-01

In this paper the problem of real impulse propagation in arbitrarily inhomogeneous media will be presented on a fundamentally new, general, theoretical way. The general problem of wave propagation of monochromatic signals in inhomogeneous media was enlightened. The earlier theoretical models for spatial inhomogeneities have some errors regarding the structure of the resultant signal originated from backward and forward propagating parts. The application of the method of inhomogeneous basic modes (MIBM) and the complete full-wave solution of arbitrarily shaped non-monochromatic plane waves in plasmas made it possible to obtain a better description of the problem, on a fully analytical way, directly from Maxwell's equations. The model investigated in this paper is inhomogeneous of arbitrary order (while the wave pattern can exist), anisotropic (magnetized), linear, cold plasma, in which the gradient of the one-dimensional spatial inhomogeneity is parallel to the direction of propagation. (author)

Two general classes of self dual, Minkowski propagating wave solutions in Yang Mills gauge theory

International Nuclear Information System (INIS)

Kovacs, E.; Lo, S.Y.

1979-01-01

Two classes of self dual propogating wave solutions to the sourceless field equations in Minkowski space are presented. Some of these solutions can be linearly superposed. These waves can propogate at either the speed of light or at a speed less than that of light

Symbolic computation and abundant travelling wave solutions to ...

Indian Academy of Sciences (India)

2016-12-09

Dec 9, 2016 ... Abstract. In this article, the novel (G /G)-expansion method is successfully applied to construct the abundant travelling wave solutions to the KdV–mKdV equation with the aid of symbolic computation. This equation is one of the most popular equation in soliton physics and appear in many practical scenarios ...

Travelling Wave Solutions in Multigroup Age-Structured Epidemic Models

Science.gov (United States)

Ducrot, Arnaut; Magal, Pierre; Ruan, Shigui

2010-01-01

Age-structured epidemic models have been used to describe either the age of individuals or the age of infection of certain diseases and to determine how these characteristics affect the outcomes and consequences of epidemiological processes. Most results on age-structured epidemic models focus on the existence, uniqueness, and convergence to disease equilibria of solutions. In this paper we investigate the existence of travelling wave solutions in a deterministic age-structured model describing the circulation of a disease within a population of multigroups. Individuals of each group are able to move with a random walk which is modelled by the classical Fickian diffusion and are classified into two subclasses, susceptible and infective. A susceptible individual in a given group can be crisscross infected by direct contact with infective individuals of possibly any group. This process of transmission can depend upon the age of the disease of infected individuals. The goal of this paper is to provide sufficient conditions that ensure the existence of travelling wave solutions for the age-structured epidemic model. The case of two population groups is numerically investigated which applies to the crisscross transmission of feline immunodeficiency virus (FIV) and some sexual transmission diseases.

Analytic Approximations for Soliton Solutions of Short-Wave Models for Camassa-Holm and Degasperis-Procesi Equations

International Nuclear Information System (INIS)

Yang Pei; Li Zhibin; Chen Yong

2010-01-01

In this paper, the short-wave model equations are investigated, which are associated with the Camassa-Holm (CH) and Degasperis-Procesi (DP) shallow-water wave equations. Firstly, by means of the transformation of the independent variables and the travelling wave transformation, the partial differential equation is reduced to an ordinary differential equation. Secondly, the equation is solved by homotopy analysis method. Lastly, by the transformations back to the original independent variables, the solution of the original partial differential equation is obtained. The two types of solutions of the short-wave models are obtained in parametric form, one is one-cusp soliton for the CH equation while the other one is one-loop soliton for the DP equation. The approximate analytic solutions expressed by a series of exponential functions agree well with the exact solutions. It demonstrates the validity and great potential of homotopy analysis method for complicated nonlinear solitary wave problems. (general)

Super rogue wave in plasma

International Nuclear Information System (INIS)

Pathak, Pallabi; Sharma, Sumita Kumari; Bailung, Heremba

2015-01-01

The evolution of super rogue wave having amplitude ∼5 times the background wave has been observed in multicomponent plasma with critical concentration of negative ions in a double plasma device. In normal electron-ion plasma the ion acoustic solitons are described by the Korteweg-de Vries (KdV) equation. At a critical concentration of negative ions, the ion acoustic modified KdV solitons are found to propagate. Multicomponent plasma also supports the propagation of a special kind of soliton namely 'Peregrine soliton' at critical concentration of negative ions. Peregrine soliton is a doubly localized solution of the nonlinear Schrodinger equation (NLSE) having amplitude 3 times the background carrier wave. In a double plasma device, ion-acoustic Peregrine soliton is excited by applying slowly varying amplitude modulated continuous sinusoidal signal to the source anode and described by the rational solution of NLSE. The ion acoustic wave is modulationally unstable in multicomponent plasma with critical concentration of negative ions and an initial modulated wave perturbation is found to undergo self-modulation to form localized structures by balancing the nonlinearity with the dispersion. In presence of higher order nonlinearity, propagation of a high amplitude (∼5 times of background carrier wave) ion acoustic Peregrine soliton has been observed experimentally. The existence of such types of higher order wave has been reported in other dispersive media. These are considered to be the prototype of super rogue wave in deep water. In this work, experimental results on the evolution of super rogue wave in a double plasma device are presented and compared with the numerical solution of NLSE. (author)

Abundant general solitary wave solutions to the family of KdV type equations

Directory of Open Access Journals (Sweden)

Md. Azmol Huda

2017-03-01

Full Text Available This work explores the construction of more general exact traveling wave solutions of some nonlinear evolution equations (NLEEs through the application of the (G′/G, 1/G-expansion method. This method is allied to the widely used (G′/G-method initiated by Wang et al. and can be considered as an extension of the (G′/G-expansion method. For effectiveness, the method is applied to the family of KdV type equations. Abundant general form solitary wave solutions as well as periodic solutions are successfully obtained through this method. Moreover, in the obtained wider set of solutions, if we set special values of the parameters, some previously known solutions are revived. The approach of this method is simple and elegantly standard. Having been computerized it is also powerful, reliable and effective.

A set of exact two soliton wave solutions to Einstein field equations

International Nuclear Information System (INIS)

Wang Youtang; He Zhixian

1991-09-01

A set of exact solutions of Einstein equations in vacuum is obtained. Taking this set of solutions as seed solutions and making use of the Belinsky-Zakharov generation technique a set of generated solutions is constructed. Both set of exact solutions and a set of generated solutions describe two solition waves, which propagate in opposite directions and collide with each other, and then recover their original shapes. The singularities of the two set of solutions are analyzed. The relationship between our solutions and other solutions is also discussed. (author). 11 refs, 4 figs

Application of Modified G'/G-Expansion Method to Traveling Wave Solutions for Whitham-Broer-Kaup-Like Equations

International Nuclear Information System (INIS)

Zhou Yubin; Li Chao

2009-01-01

A modified G'/G-expansion method is presented to derive traveling wave solutions for a class of nonlinear partial differential equations called Whitham-Broer-Kaup-Like equations. As a result, the hyperbolic function solutions, trigonometric function solutions, and rational solutions with parameters to the equations are obtained. When the parameters are taken as special values the solitary wave solutions can be obtained. (general)

Asymmetric systems described by a pair of local covariant wave equations

Energy Technology Data Exchange (ETDEWEB)

Mallik, S [Bern Univ. (Switzerland). Inst. fuer Theoretische Physik

1979-07-16

A class of asymmetric solutions of the integrability conditions for systems obeying the Leutwyler-Stern pair of covariant wave equations is obtained. The class of unequal-mass systems described by these solutions does not embed the particle-antiparticle system behaving as a relativistic harmonic oscillator.

Sustainable Cities : Local Solutions in the Global South | CRDI ...

International Development Research Centre (IDRC) Digital Library (Canada)

Sustainable Cities : Local Solutions in the Global South. Couverture du livre Sustainable Cities: Local Solutions in the Global South. Directeur(s):. Mélanie Robertson. Maison(s) d'édition: Practical Action Publishing, CRDI. 6 avril 2012. ISBN : 9781853397233. 178 pages. e-ISBN : 9781552505366. Téléchargez le PDF.

On "new travelling wave solutions" of the KdV and the KdV-Burgers equations

NARCIS (Netherlands)

Kudryashov, Nikolai A.

The Korteweg-de Vries and the Korteweg-de Vries-Burgers equations are considered. Using the travelling wave the general solutions of these equations are presented. "New travelling wave solutions" of the KdV and the KdV-Burgers equations by Wazzan [Wazzan L Commun Nonlinear Sci Numer Simulat

Localization of Ultra-Low Frequency Waves in Multi-Ion Plasmas of the Planetary Magnetosphere

Directory of Open Access Journals (Sweden)

Eun-Hwa Kim

2015-12-01

Full Text Available By adopting a 2D time-dependent wave code, we investigate how mode-converted waves at the Ion-Ion Hybrid (IIH resonance and compressional waves propagate in 2D density structures with a wide range of field-aligned wavenumbers to background magnetic fields. The simulation results show that the mode-converted waves have continuous bands across the field line consistent with previous numerical studies. These waves also have harmonic structures in frequency domain and are localized in the field-aligned heavy ion density well. Our results thus emphasize the importance of a field-aligned heavy ion density structure for ultra-low frequency wave propagation, and suggest that IIH waves can be localized in different locations along the field line.

The magnetic particle in a box: Analytic and micromagnetic analysis of probe-localized spin wave modes

Science.gov (United States)

Adur, Rohan; Du, Chunhui; Manuilov, Sergei A.; Wang, Hailong; Yang, Fengyuan; Pelekhov, Denis V.; Hammel, P. Chris

2015-05-01

The dipole field from a probe magnet can be used to localize a discrete spectrum of standing spin wave modes in a continuous ferromagnetic thin film without lithographic modification to the film. Obtaining the resonance field for a localized mode is not trivial due to the effect of the confined and inhomogeneous magnetization precession. We compare the results of micromagnetic and analytic methods to find the resonance field of localized modes in a ferromagnetic thin film, and investigate the accuracy of these methods by comparing with a numerical minimization technique that assumes Bessel function modes with pinned boundary conditions. We find that the micromagnetic technique, while computationally more intensive, reveals that the true magnetization profiles of localized modes are similar to Bessel functions with gradually decaying dynamic magnetization at the mode edges. We also find that an analytic solution, which is simple to implement and computationally much faster than other methods, accurately describes the resonance field of localized modes when exchange fields are negligible, and demonstrating the accessibility of localized mode analysis.

A new sub-equation method applied to obtain exact travelling wave solutions of some complex nonlinear equations

International Nuclear Information System (INIS)

Zhang Huiqun

2009-01-01

By using a new coupled Riccati equations, a direct algebraic method, which was applied to obtain exact travelling wave solutions of some complex nonlinear equations, is improved. And the exact travelling wave solutions of the complex KdV equation, Boussinesq equation and Klein-Gordon equation are investigated using the improved method. The method presented in this paper can also be applied to construct exact travelling wave solutions for other nonlinear complex equations.

Periodic and solitary wave solutions of cubic–quintic nonlinear ...

Indian Academy of Sciences (India)

Home; Journals; Pramana – Journal of Physics; Volume 86; Issue 6. Periodic and solitary wave solutions of cubic–quintic nonlinear reaction-diffusion equation with variable convection coefficients. BHARDWAJ S B SINGH RAM MEHAR SHARMA KUSHAL MISHRA S C. Regular Volume 86 Issue 6 June 2016 pp 1253-1258 ...

Solutions to Time-Fractional Diffusion-Wave Equation in Cylindrical Coordinates

Directory of Open Access Journals (Sweden)

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.

Dynamic Sensing of Localized Corrosion at the Metal/Solution Interface

Directory of Open Access Journals (Sweden)

Shenhao Chen

2012-04-01

Full Text Available A Mach-Zehnder interferometer is employed to detect localized corrosion at the metal/solution interface in the potentiodynamic sweep of the iron electrode in solutions. During the electrochemical reactions, local variations of the electrolyte’s refractive index, which correlate with the concentration of dissolved species, change the optical path length (OPL of the object beam when the beam passes through the electrolyte. The distribution of the OPL difference was obtained to present the concentration change of the metal ions visually, which enable direct evidence of corrosion processes. The OPL difference distribution shows localized and general corrosion during the anodic dissolution of the iron electrode in solutions with and without chloride ions, respectively. This method provides an approach for dynamic detection of localized corrosion at the metal/solution interface.

Millimetre-Wave Backhaul for 5G Networks: Challenges and Solutions

Directory of Open Access Journals (Sweden)

Wei Feng

2016-06-01

Full Text Available The trend for dense deployment in future 5G mobile communication networks makes current wired backhaul infeasible owing to the high cost. Millimetre-wave (mm-wave communication, a promising technique with the capability of providing a multi-gigabit transmission rate, offers a flexible and cost-effective candidate for 5G backhauling. By exploiting highly directional antennas, it becomes practical to cope with explosive traffic demands and to deal with interference problems. Several advancements in physical layer technology, such as hybrid beamforming and full duplexing, bring new challenges and opportunities for mm-wave backhaul. This article introduces a design framework for 5G mm-wave backhaul, including routing, spatial reuse scheduling and physical layer techniques. The associated optimization model, open problems and potential solutions are discussed to fully exploit the throughput gain of the backhaul network. Extensive simulations are conducted to verify the potential benefits of the proposed method for the 5G mm-wave backhaul design.

A phase-plane analysis of localized frictional waves

Science.gov (United States)

Putelat, T.; Dawes, J. H. P.; Champneys, A. R.

2017-07-01

Sliding frictional interfaces at a range of length scales are observed to generate travelling waves; these are considered relevant, for example, to both earthquake ground surface movements and the performance of mechanical brakes and dampers. We propose an explanation of the origins of these waves through the study of an idealized mechanical model: a thin elastic plate subject to uniform shear stress held in frictional contact with a rigid flat surface. We construct a nonlinear wave equation for the deformation of the plate, and couple it to a spinodal rate-and-state friction law which leads to a mathematically well-posed problem that is capable of capturing many effects not accessible in a Coulomb friction model. Our model sustains a rich variety of solutions, including periodic stick-slip wave trains, isolated slip and stick pulses, and detachment and attachment fronts. Analytical and numerical bifurcation analysis is used to show how these states are organized in a two-parameter state diagram. We discuss briefly the possible physical interpretation of each of these states, and remark also that our spinodal friction law, though more complicated than other classical rate-and-state laws, is required in order to capture the full richness of wave types.

Effect of laser beam filamentation on plasma wave localization and stimulated Raman scattering

International Nuclear Information System (INIS)

Purohit, Gunjan; Sharma, R. P.

2013-01-01

This paper presents the effect of laser beam filamentation on the localization of electron plasma wave (EPW) and stimulated Raman scattering (SRS) in unmagnitized plasma when both relativistic and ponderomotive nonlinearities are operative. The filamentary dynamics of laser beam is studied and the splitted profile of the laser beam is obtained due to uneven focusing of the off-axial rays. The localization of electron plasma wave takes place due to nonlinear coupling between the laser beam and EPW. Stimulated Raman scattering of this EPW is studied and backreflectivity has been calculated. The localization of EPW also affects the eigenfrequency and damping of plasma wave; consequently, mismatch and modified enhanced Landau damping lead to the disruption of SRS process and a substantial reduction in the backreflectivity. The new enhanced damping of the plasma wave has been calculated and it is found that the SRS process gets suppressed due to the localization of plasma wave in laser beam filamentary structures. For typical laser beam and plasma parameters with wavelength λ (=1064 nm), power flux (=10 16 W/cm 2 ) and plasma density (n/n cr ) = 0.2; the SRS back reflectivity is found to be suppressed by a factor of around 5%. (author)

On the exact solutions of high order wave equations of KdV type (I)

Science.gov (United States)

Bulut, Hasan; Pandir, Yusuf; Baskonus, Haci Mehmet

2014-12-01

In this paper, by means of a proper transformation and symbolic computation, we study high order wave equations of KdV type (I). We obtained classification of exact solutions that contain soliton, rational, trigonometric and elliptic function solutions by using the extended trial equation method. As a result, the motivation of this paper is to utilize the extended trial equation method to explore new solutions of high order wave equation of KdV type (I). This method is confirmed by applying it to this kind of selected nonlinear equations.

New solutions of the generalized ellipsoidal wave equation

Directory of Open Access Journals (Sweden)

Harold Exton

1999-10-01

Full Text Available Certain aspects and a contribution to the theory of new forms of solutions of an algebraic form of the generalized ellipsoidal wave equation are deduced by considering the Laplace transform of a soluble system of linear differential equations. An ensuing system of non-linear algebraic equations is shown to be consistent and is numerically implemented by means of the computer algebra package MAPLE V. The main results are presented as series of hypergeometric type of there and four variables which readily lend themselves to numerical handling although this does not indicate all of the detailedanalytic properties of the solutions under consideration.

Multi-wave solutions of the space–time fractional Burgers and Sharma–Tasso–Olver equations

OpenAIRE

Emad A.-B. Abdel-Salam; Gamal F. Hassan

2016-01-01

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.

Smooth, cusped, and discontinuous traveling waves in the periodic fluid resonance equation

Science.gov (United States)

Kruse, Matthew Thomas

The principal motivation for this dissertation is to extend the study of small amplitude high frequency wave propagation in solutions for hyperbolic conservation laws begun by A. Majda and R. Rosales in 1984. It was then that Majda and Rosales obtained equations governing the leading order wave amplitudes of resonantly interacting weakly nonlinear high frequency wave trains in the compressible Euler equations. The equations were obtained through systematic application of multiple scales and result in a pair of nonlinear acoustic wave equations coupled through a convolution operator. The extended solutions satisfy a pair of inviscid Burgers' equations coupled via a spatial convolution operator. Since then, many mathematicians have used this technique to extend the time validity of solutions to systems of equations other than the Euler equations and have arrived at similar nonlinear non-local systems. This work attempts to look at some of the basic features of the linear and nonlinear coupled and decoupled non- local equations, offering some analytic solutions and numerical insight into the phenomena associated with these equations. We do so by examining a single non-local linear equation, and then a single equation coupling a Burgers' nonlinearity with a linear convolution operator. The linear case is completely solvable. Analytic solutions are provided along with numerical results showing the fundamental properties of the linear non- local equations. In the nonlinear case some analytic solutions, including steady state profiles and traveling wave solutions, are provided along with a battery of numerical simulations. Evidence indicates the existence of attractors for solutions of the single equation with a single mode kernel. Provided resonant interaction takes place, the profile of the attractor is uniquely dependent on the kernel alone. Hamiltonian equations are obtained for both the linear and nonlinear equations with the condition that the resonant kernel must

High-resolution seismic wave propagation using local time stepping

KAUST Repository

Peter, Daniel; Rietmann, Max; Galvez, Percy; Ampuero, Jean Paul

2017-01-01

High-resolution seismic wave simulations often require local refinements in numerical meshes to accurately capture e.g. steep topography or complex fault geometry. Together with explicit time schemes, this dramatically reduces the global time step

Extending the D’alembert solution to space–time Modified Riemann–Liouville fractional wave equations

International Nuclear Information System (INIS)

Godinho, Cresus F.L.; Weberszpil, J.; Helayël-Neto, J.A.

2012-01-01

In the realm of complexity, it is argued that adequate modeling of TeV-physics demands an approach based on fractal operators and fractional calculus (FC). Non-local theories and memory effects are connected to complexity and the FC. The non-differentiable nature of the microscopic dynamics may be connected with time scales. Based on the Modified Riemann–Liouville definition of fractional derivatives, we have worked out explicit solutions to a fractional wave equation with suitable initial conditions to carefully understand the time evolution of classical fields with a fractional dynamics. First, by considering space–time partial fractional derivatives of the same order in time and space, a generalized fractional D’alembertian is introduced and by means of a transformation of variables to light-cone coordinates, an explicit analytical solution is obtained. To address the situation of different orders in the time and space derivatives, we adopt different approaches, as it will become clear throughout this paper. Aspects connected to Lorentz symmetry are analyzed in both approaches.

A class of periodic solutions of nonlinear wave and evolution equations

International Nuclear Information System (INIS)

Kashcheev, V.N.

1987-01-01

For the case of 1+1 dimensions a new heuristic method is proposed for deriving dels-similar solutions to nonlinear autonomous differential equations. If the differential function f is a polynomial, then: (i) in the case of even derivatives in f the solution is the ratio of two polynomials from the Weierstrass elliptic functions; (ii) in the case of any order derivatives in f the solution is the ratio of two polynomials from simple exponents. Numerous examples are given constructing such periodic solutions to the wave and evolution equations

Exact traveling wave solutions of fractional order Boussinesq-like equations by applying Exp-function method

Science.gov (United States)

Rahmatullah; Ellahi, Rahmat; Mohyud-Din, Syed Tauseef; Khan, Umar

2018-03-01

We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses.

ANTENNA RADIATION NEAR THE LOCAL PLASMA FREQUENCY BY LANGMUIR WAVE EIGENMODES

International Nuclear Information System (INIS)

Malaspina, David M.; Cairns, Iver H.; Ergun, Robert E.

2012-01-01

Langmuir waves (LWs) in the solar wind are generated by electron beams associated with solar flares, interplanetary shock fronts, planetary bow shocks, and magnetic holes. In principle, LWs localized as eigenmodes of density fluctuations can emit electromagnetic (EM) radiation by an antenna mechanism near the local plasma frequency f p and twice the local plasma frequency. In this work, analytic expressions are derived for the radiated electric and magnetic fields and power generated near f p by LW eigenmodes. The EM wave power emitted near f p is predicted as a function of the eigenmode length scale L, maximum electric field, driving electron beam speed, and the ambient plasma density and temperature. The escape to a distant observer of f p radiation from a localized Langmuir eigenmode is also briefly explored as a function of the plasma conditions.

Non-local coexistence of multiple spiral waves with independent frequencies

International Nuclear Information System (INIS)

Zhan Meng; Luo Jinming

2009-01-01

The interactions of several spiral waves with different independent rotation frequencies are studied in a model of two-dimensional complex Ginzburg-Laudau equation. We find a general coexistence phenomenon, non-local non-phase-locking-invasion coexistence, that is, the non-slowest spiral wave can survive and not be killed by the fastest spiral wave as it is insulated from the fastest one with the sacrifice of the slowest one, which stays in the spatial position between the fastest spiral and the non-slowest one. Both the parameter non-monotonicity and the non-phase-locking invasion between the fastest and the slowest spiral waves play key roles in this phenomenon. Importantly, the results could give a general idea for extensively observed coexistence of spiral waves in various inhomogeneous circumstances.

Localization of Matter Waves in Two-Dimensional Disordered Optical Potentials

International Nuclear Information System (INIS)

Kuhn, R.C.; Miniatura, C.; Delande, D.; Sigwarth, O.; Mueller, C.A.

2005-01-01

We consider ultracold atoms in 2D disordered optical potentials and calculate microscopic quantities characterizing matter wave quantum transport in the noninteracting regime. We derive the diffusion constant as a function of all relevant microscopic parameters and show that coherent multiple scattering induces significant weak localization effects. In particular, we find that even the strong localization regime is accessible with current experimental techniques and calculate the corresponding localization length

MEASUREMENTS OF ABSORPTION, EMISSIVITY REDUCTION, AND LOCAL SUPPRESSION OF SOLAR ACOUSTIC WAVES IN SUNSPOTS

International Nuclear Information System (INIS)

Chou, D.-Y.; Liang, Z.-C.; Yang, M.-H.; Zhao Hui; Sun, M.-T.

2009-01-01

The power of solar acoustic waves in magnetic regions is lower relative to the quiet Sun. Absorption, emissivity reduction, and local suppression of acoustic waves contribute to the observed power reduction in magnetic regions. We propose a model for the energy budget of acoustic waves propagating through a sunspot in terms of the coefficients of absorption, emissivity reduction, and local suppression of the sunspot. Using the property that the waves emitted along the wave path between two points have no correlation with the signal at the starting point, we can separate the effects of these three mechanisms. Applying this method to helioseismic data filtered with direction and phase-velocity filters, we measure the fraction of the contribution of each mechanism to the power deficit in the umbra of the leading sunspot of NOAA 9057. The contribution from absorption is 23.3 ± 1.3%, emissivity reduction 8.2 ± 1.4%, and local suppression 68.5 ± 1.5%, for a wave packet corresponding to a phase velocity of 6.98 x 10 -5 rad s -1 .

Multi-wave solutions of the space–time fractional Burgers and Sharma–Tasso–Olver equations

Directory of Open Access Journals (Sweden)

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.

Launching transverse-electric Localized Waves from a circular waveguide

KAUST Repository

Salem, Mohamed; Niver, Edip

2011-01-01

Axially symmetric transverse electric (TE) modes of a circular waveguide section are used to synthesize the vector TE Localized Wave (LW) field at the open end of the waveguide section. The necessary excitation coefficients of these modes

Instantaneous local wave vector estimation from multi-spacecraft measurements using few spatial points

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.

Investigating The Travelling Wave Solution For an SIR Endemic ...

African Journals Online (AJOL)

This paper presents the travelling wave solution for an SIR endemic disease model with no disease related death when the spatial spread of the susceptible is not negligible. In this case the disease is driven by both the susceptible and the infective classes. The population is open since the disease is habitually prevalent in ...

Strip waves in vibrated shear-thickening wormlike micellar solutions

Science.gov (United States)

Epstein, T.; Deegan, R. D.

2010-06-01

We present an instability in vertically vibrated dilute wormlike micellar solutions. Above a critical driving acceleration the fluid forms elongated solitary domains of high amplitude waves. We model this instability using a Mathieu equation modified to account for the non-Newtonian character of the fluid. We find that our model successfully reproduces the observed transitions.

Traveling wave solutions of the Boussinesq equation via the new approach of generalized (G'/G)-expansion method.

Science.gov (United States)

Alam, Md Nur; Akbar, M Ali; Roshid, Harun-Or-

2014-01-01

Exact solutions of nonlinear evolution equations (NLEEs) play a vital role to reveal the internal mechanism of complex physical phenomena. In this work, the exact traveling wave solutions of the Boussinesq equation is studied by using the new generalized (G'/G)-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, trigonometric, and rational functions. It is shown that the new approach of generalized (G'/G)-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations in mathematical physics and engineering. 05.45.Yv, 02.30.Jr, 02.30.Ik.

Exact solution to the Coulomb wave using the linearized phase-amplitude method

Directory of Open Access Journals (Sweden)

Shuji Kiyokawa

2015-08-01

Full Text Available The author shows that the amplitude equation from the phase-amplitude method of calculating continuum wave functions can be linearized into a 3rd-order differential equation. Using this linearized equation, in the case of the Coulomb potential, the author also shows that the amplitude function has an analytically exact solution represented by means of an irregular confluent hypergeometric function. Furthermore, it is shown that the exact solution for the Coulomb potential reproduces the wave function for free space expressed by the spherical Bessel function. The amplitude equation for the large component of the Dirac spinor is also shown to be the linearized 3rd-order differential equation.

Quantitative study of two- and three-dimensional strong localization of matter waves by atomic scatterers

International Nuclear Information System (INIS)

Antezza, Mauro; Castin, Yvan; Hutchinson, David A. W.

2010-01-01

We study the strong localization of atomic matter waves in a disordered potential created by atoms pinned at the nodes of a lattice, for both three-dimensional (3D) and two-dimensional (2D) systems. The localization length of the matter wave, the density of localized states, and the occurrence of energy mobility edges (for the 3D system), are numerically investigated as a function of the effective scattering length between the atomic matter wave and the pinned atoms. Both positive and negative matter wave energies are explored. Interesting features of the density of states are discovered at negative energies, where maxima in the density of bound states for the system can be interpreted in terms of bound states of a matter wave atom with a few pinned atomic scatterers. In 3D we found evidence of up to three mobility edges, one at positive energies, and two at negative energies, the latter corresponding to transitions between extended and localized bound states. In 2D, no mobility edge is found, and a rapid exponential-like increase of the localization length is observed at high energy.

Local increase of anticyclonic wave activity over northern Eurasia under amplified Arctic warming: WAVE ACTIVITY RESPONSE TO ARCTIC MELTING

Energy Technology Data Exchange (ETDEWEB)

Xue, Daokai [School of Atmospheric Sciences, Nanjing University, Nanjing China; Lu, Jian [Atmospheric Sciences and Global Change Division, Pacific Northwest National Laboratory, Richland Washington USA; Sun, Lantao [CIRES, University of Colorado Boulder, Boulder Colorado USA; PSD, ESRL, NOAA, Boulder Colorado USA; Chen, Gang [Department of Earth and Atmospheric Sciences, UCLA, Los Angeles California USA; Zhang, Yaocun [School of Atmospheric Sciences, Nanjing University, Nanjing China

2017-04-10

In an attempt to resolve the controversy as to whether Arctic sea ice loss leads to more mid-latitude extremes, a metric of finite-amplitude wave activity is adopted to quantify the midlatitude wave activity and its change during the observed period of the drastic Arctic sea ice decline in both ERA Interim reanalysis data and a set of AMIP-type of atmospheric model experiments. Neither the experiment with the trend in the SST or that with the declining trend of Arctic sea ice can simulate the sizable midlatitude-wide reduction in the total wave activity (Ae) observed in the reanalysis, leaving its explanation to the atmospheric internal variability. On the other hand, both the diagnostics of the flux of the local wave activity and the model experiments lend evidence to a possible linkage between the sea ice loss near the Barents and Kara seas and the increasing trend of anticyclonic local wave activity over the northern part of the central Eurasia and the associated impacts on the frequency of temperature extremes.

On the Painleve integrability, periodic wave solutions and soliton solutions of generalized coupled higher-order nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Xu Guiqiong; Li Zhibin

2005-01-01

It is proven that generalized coupled higher-order nonlinear Schroedinger equations possess the Painleve property for two particular choices of parameters, using the Weiss-Tabor-Carnevale method and Kruskal's simplification. Abundant families of periodic wave solutions are obtained by using the Jacobi elliptic function expansion method with the assistance of symbolic manipulation system, Maple. It is also shown that these solutions exactly degenerate to bright soliton, dark soliton and mixed dark and bright soliton solutions with physical interests

The classification of the single travelling wave solutions to the ...

Indian Academy of Sciences (India)

a large number of methods for finding exact solutions have been established and devel ... Painleve method [1] and transformed rational function method for finding ... travelling wave transformation and integrating it, the nonlinear differential ...... The project is supported by Scientific Research Fund of Education Department of.

Dispersive solitary wave solutions of Kadomtsev-Petviashvili and modified Kadomtsev-Petviashvili dynamical equations in unmagnetized dust plasma

Science.gov (United States)

Seadawy, A. R.; El-Rashidy, K.

2018-03-01

The Kadomtsev-Petviashvili (KP) and modified KP equations are two of the most universal models in nonlinear wave theory, which arises as a reduction of system with quadratic nonlinearity which admit weakly dispersive waves. The generalized extended tanh method and the F-expansion method are used to derive exact solitary waves solutions of KP and modified KP equations. The region of solutions are displayed graphically.

Shock wave emission from laser-induced cavitation bubbles in polymer solutions.

Science.gov (United States)

Brujan, Emil-Alexandru

2008-09-01

The role of extensional viscosity on the acoustic emission from laser-induced cavitation bubbles in polymer solutions and near a rigid boundary is investigated by acoustic measurements. The polymer solutions consist of a 0.5% polyacrylamide (PAM) aqueous solution with a strong elastic component and a 0.5% carboxymethylcellulose (CMC) aqueous solution with a weak elastic component. A reduction of the maximum amplitude of the shock wave pressure and a prolongation of the oscillation period of the bubble were found in the elastic PAM solution. It might be caused by an increased resistance to extensional flow which is conferred upon the liquid by the polymer additive. In both polymer solutions, however, the shock pressure decays proportionally to r(-1) with increasing distance r from the emission centre.

Exact explicit travelling wave solutions for (n + 1)-dimensional Klein-Gordon-Zakharov equations

International Nuclear Information System (INIS)

Li Jibin

2007-01-01

Using the methods of dynamical systems for the (n + 1)-dimensional KGS nonlinear wave equations, five classes of exact explicit parametric representations of the bounded travelling solutions are obtained. To guarantee the existence of the above solutions, all parameter conditions are given

The classification of single travelling wave solutions to the Camassa ...

Indian Academy of Sciences (India)

Introduction. Classifications of single travelling wave solutions to some nonlinear differential equations have been obtained extensively by the complete discrimination system for polynomial method proposed by Liu [1–7]. Furthermore, Wang and Li [8] used Liu's method and factorization method proposed by Cornejo-Pérez ...

Travelling wave solutions for a singularly perturbed Burgers–KdV ...

Indian Academy of Sciences (India)

This paper concerns with the existence problem of travelling wave solutions to a singularly perturbed Burgers–KdV equation. For this, we use the dynamical systems approach, specifically, the geometric singular perturbation theory and centre manifold theory. We also numerically show approximations, in particular, for ...

A time-localized response of wave growth process under turbulent winds

Directory of Open Access Journals (Sweden)

Z. Ge

2007-06-01

Full Text Available Very short time series (with lengths of approximately 40 s or 5~7 wave periods of wind velocity fluctuations and wave elevation were recorded simultaneously and investigated using the wavelet bispectral analysis. Rapid changes in the wave and wind spectra were detected, which were found to be intimately related to significant energy transfers through transient quadratic wind-wave and wave-wave interactions. A possible pattern of energy exchange between the wind and wave fields was further deduced. In particular, the generation and variation of the strong wave-induced perturbation velocity in the wind can be explained by the strengthening and diminishing of the associated quadratic interactions, which cannot be unveiled by linear theories. On small time scales, the wave-wave quadratic interactions were as active and effective in transferring energy as the wind-wave interactions. The results also showed that the wind turbulence was occasionally effective in transferring energy between the wind and the wave fields, so that the background turbulence in the wind cannot be completely neglected. Although these effects are all possibly significant over short times, the time-localized growth of the wave spectrum may not considerably affect the long-term process of wave development.

Localizing gravitational wave sources with single-baseline atom interferometers

Science.gov (United States)

Graham, Peter W.; Jung, Sunghoon

2018-02-01

Localizing sources on the sky is crucial for realizing the full potential of gravitational waves for astronomy, astrophysics, and cosmology. We show that the midfrequency band, roughly 0.03 to 10 Hz, has significant potential for angular localization. The angular location is measured through the changing Doppler shift as the detector orbits the Sun. This band maximizes the effect since these are the highest frequencies in which sources live for several months. Atom interferometer detectors can observe in the midfrequency band, and even with just a single baseline they can exploit this effect for sensitive angular localization. The single-baseline orbits around the Earth and the Sun, causing it to reorient and change position significantly during the lifetime of the source, and making it similar to having multiple baselines/detectors. For example, atomic detectors could predict the location of upcoming black hole or neutron star merger events with sufficient accuracy to allow optical and other electromagnetic telescopes to observe these events simultaneously. Thus, midband atomic detectors are complementary to other gravitational wave detectors and will help complete the observation of a broad range of the gravitational spectrum.

Solitary wave solutions of the fourth order Boussinesq equation through the exp(-Ф(η))-expansion method.

Science.gov (United States)

Akbar, M Ali; Hj Mohd Ali, Norhashidah

2014-01-01

The exp(-Ф(η))-expansion method is an ascending method for obtaining exact and solitary wave solutions for nonlinear evolution equations. In this article, we implement the exp(-Ф(η))-expansion method to build solitary wave solutions to the fourth order Boussinesq equation. The procedure is simple, direct and useful with the help of computer algebra. By using this method, we obtain solitary wave solutions in terms of the hyperbolic functions, the trigonometric functions and elementary functions. The results show that the exp(-Ф(η))-expansion method is straightforward and effective mathematical tool for the treatment of nonlinear evolution equations in mathematical physics and engineering. 35C07; 35C08; 35P99.

On waves below the local proton gyrofrequency in auroral acceleration regions

International Nuclear Information System (INIS)

Gustafsson, G.; Andre, M.; Matson, L.; Koskinen, H.

1990-01-01

The Viking wave electric field and density fluctuation measurements together with simultaneous particle observations are used to study waves at frequencies below the local proton gyrofrequency. Such waves were observed during about 20% of nightside auroral field line crossings by Viking at altitudes between 2,000 and 10,000 km. The observations are different from earlier spacecraft observations of similar waves in such a way that the center frequency in about one out of four of the observed events was below the gyrofrequency of singly charged helium, which has not been reported previously. The waves were well correlated with precipitating electrons of energies of a few keV and with VLF auroral hiss. Detailed investigations of simultaneously observed wave emissions, particles, and total densities strongly suggest that secondary peaks at keV energies in the distributions of downgoing electrons can cause the emissions

Higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials

Science.gov (United States)

Liu, Lei; Tian, Bo; Wu, Xiao-Yu; Sun, Yan

2018-02-01

Under investigation in this paper is the higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials which can be applied in the nonlinear optics, hydrodynamics, plasma physics and Bose-Einstein condensation. Based on the Kadomtsev-Petviashvili hierarchy reduction, we construct the Nth order rogue wave-like solutions in terms of the Gramian under the integrable constraint. With the help of the analytic and graphic analysis, we exhibit the first-, second- and third-order rogue wave-like solutions through the different dispersion, nonlinearity and linear potential coefficients. We find that only if the dispersion and nonlinearity coefficients are proportional to each other, heights of the background of those rogue waves maintain unchanged with time increasing. Due to the existence of complex parameters, such nonautonomous rogue waves in the higher-order cases have more complex features than those in the lower.

The classification of the single travelling wave solutions to the ...

Indian Academy of Sciences (India)

2016-09-21

Sep 21, 2016 ... For example,. Fan used Liu's method [11,12] to invest the generalized equal width equation and Pochhammer–Chree equa- tion, and she obtained all the possible travelling wave solutions including elliptic functions and hyperelliptic functions. In this paper, we consider the variant Boussinesq equations [13].

Transition, coexistence, and interaction of vector localized waves arising from higher-order effects

International Nuclear Information System (INIS)

Liu, Chong; Yang, Zhan-Ying; Zhao, Li-Chen; Yang, Wen-Li

2015-01-01

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.

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.

Rogue waves, rational solutions, the patterns of their zeros and integral relations

International Nuclear Information System (INIS)

Ankiewicz, Adrian; Akhmediev, Nail; Clarkson, Peter A

2010-01-01

The focusing nonlinear Schroedinger equation, which describes generic nonlinear phenomena, including waves in the deep ocean and light pulses in optical fibres, supports a whole hierarchy of recently discovered rational solutions. We present recurrence relations for the hierarchy, the pattern of zeros for each solution and a set of integral relations which characterizes them. (fast track communication)

Singular solitons and other solutions to a couple of nonlinear wave equations

International Nuclear Information System (INIS)

Inc Mustafa; Ulutaş Esma; Biswas Anjan

2013-01-01

This paper addresses the extended (G'/G)-expansion method and applies it to a couple of nonlinear wave equations. These equations are modified the Benjamin—Bona—Mahoney equation and the Boussinesq equation. This extended method reveals several solutions to these equations. Additionally, the singular soliton solutions are revealed, for these two equations, with the aid of the ansatz method

Rational solutions to two- and one-dimensional multicomponent Yajima–Oikawa systems

International Nuclear Information System (INIS)

Chen, Junchao; Chen, Yong; Feng, Bao-Feng; Maruno, Ken-ichi

2015-01-01

Exact explicit rational solutions of two- and one-dimensional multicomponent Yajima–Oikawa (YO) systems, which contain multi-short-wave components and single long-wave one, are presented by using the bilinear method. For two-dimensional system, the fundamental rational solution first describes the localized lumps, which have three different patterns: bright, intermediate and dark states. Then, rogue waves can be obtained under certain parameter conditions and their behaviors are also classified to above three patterns with different definition. It is shown that the simplest (fundamental) rogue waves are line localized waves which arise from the constant background with a line profile and then disappear into the constant background again. In particular, two-dimensional intermediate and dark counterparts of rogue wave are found with the different parameter requirements. We demonstrate that multirogue waves describe the interaction of several fundamental rogue waves, in which interesting curvy wave patterns appear in the intermediate times. Different curvy wave patterns form in the interaction of different types fundamental rogue waves. Higher-order rogue waves exhibit the dynamic behaviors that the wave structures start from lump and then retreat back to it, and this transient wave possesses the patterns such as parabolas. Furthermore, different states of higher-order rogue wave result in completely distinguishing lumps and parabolas. Moreover, one-dimensional rogue wave solutions with three states are constructed through the further reduction. Specifically, higher-order rogue wave in one-dimensional case is derived under the parameter constraints. - Highlights: • Exact explicit rational solutions of two-and one-dimensional multicomponent Yajima–Oikawa systems. • Two-dimensional rogue wave contains three different patterns: bright, intermediate and dark states. • Multi- and higher-order rogue waves exhibit distinct dynamic behaviors in two-dimensional case

Investigation of Solitary wave solutions for Vakhnenko-Parkes equation via exp-function and Exp(-ϕ(ξ))-expansion method.

Science.gov (United States)

Roshid, Harun-Or; Kabir, Md Rashed; Bhowmik, Rajandra Chadra; Datta, Bimal Kumar

2014-01-01

In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(-ϕ(ξ)) -expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko- Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.

On the propagation of truncated localized waves in dispersive silica

KAUST Repository

Salem, Mohamed; Bagci, Hakan

2010-01-01

Propagation characteristics of truncated Localized Waves propagating in dispersive silica and free space are numerically analyzed. It is shown that those characteristics are affected by the changes in the relation between the transverse spatial

Long-range traveling waves of activity triggered by local dichoptic stimulation in V1 of behaving monkeys

Science.gov (United States)

Yang, Zhiyong; Heeger, David J.; Blake, Randolph

2014-01-01

Traveling waves of cortical activity, in which local stimulation triggers lateral spread of activity to distal locations, have been hypothesized to play an important role in cortical function. However, there is conflicting physiological evidence for the existence of spreading traveling waves of neural activity triggered locally. Dichoptic stimulation, in which the two eyes view dissimilar monocular patterns, can lead to dynamic wave-like fluctuations in visual perception and therefore, provides a promising means for identifying and studying cortical traveling waves. Here, we used voltage-sensitive dye imaging to test for the existence of traveling waves of activity in the primary visual cortex of awake, fixating monkeys viewing dichoptic stimuli. We find clear traveling waves that are initiated by brief, localized contrast increments in one of the monocular patterns and then, propagate at speeds of ∼30 mm/s. These results demonstrate that under an appropriate visual context, circuitry in visual cortex in alert animals is capable of supporting long-range traveling waves triggered by local stimulation. PMID:25343785

Covariant two-particle wave functions for model quasipotential allowing exact solutions

International Nuclear Information System (INIS)

Kapshaj, V.N.; Skachkov, N.B.

1982-01-01

Two formulations of quasipotential equations in the relativistic configurational representation are considered for the wave function of relative motion of a bound state of two relativistic particles. Exact solutions of these equations are found for some model quasipotentials

On The Travelling Wave Solution For An SEIR Epidemic Disease ...

African Journals Online (AJOL)

We present the travelling wave solution for a Susceptible, Exposed, Infective and Removed (SEIR) epidemic disease model. For this SEIR model, the disease is driven by both the latent and infective class (the diffusion term is included in both classes). The population is closed. Keywords: Epidemic model, spatial spread, ...

Classification of All Single Travelling Wave Solutions to Calogero-Degasperis-Focas Equation

International Nuclear Information System (INIS)

Liu Chengshi

2007-01-01

Under the travelling wave transformation, Calogero-Degasperis-Focas equation is reduced to an ordinary differential equation. Using a symmetry group of one parameter, this ODE is reduced to a second-order linear inhomogeneous ODE. Furthermore, we apply the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtained the classification of all single travelling wave solutions to Calogero-Degasperis-Focas equation.

Covariant two-particle wave functions for model quasipotentials admitting exact solutions

International Nuclear Information System (INIS)

Kapshaj, V.N.; Skachkov, N.B.

1983-01-01

Two formulations of quasipotential equations in the relativistic configurational representation are considered for the wave function of the internal motion of the bound system of two relativistic particles. Exact solutions of these equations are found for some model quasipotentials

Geometrical optics in the near field: local plane-interface approach with evanescent waves.

Science.gov (United States)

Bose, Gaurav; Hyvärinen, Heikki J; Tervo, Jani; Turunen, Jari

2015-01-12

We show that geometrical models may provide useful information on light propagation in wavelength-scale structures even if evanescent fields are present. We apply a so-called local plane-wave and local plane-interface methods to study a geometry that resembles a scanning near-field microscope. We show that fair agreement between the geometrical approach and rigorous electromagnetic theory can be achieved in the case where evanescent waves are required to predict any transmission through the structure.

Nonlocal symmetry and explicit solutions from the CRE method of the Boussinesq equation

Science.gov (United States)

Zhao, Zhonglong; Han, Bo

2018-04-01

In this paper, we analyze the integrability of the Boussinesq equation by using the truncated Painlevé expansion and the CRE method. Based on the truncated Painlevé expansion, the nonlocal symmetry and Bäcklund transformation of this equation are obtained. A prolonged system is introduced to localize the nonlocal symmetry to the local Lie point symmetry. It is proved that the Boussinesq equation is CRE solvable. The two-solitary-wave fusion solutions, single soliton solutions and soliton-cnoidal wave solutions are presented by means of the Bäcklund transformations.

Abundant families of new traveling wave solutions for the coupled Drinfel'd-Sokolov-Wilson equation

International Nuclear Information System (INIS)

Yao Yuqin

2005-01-01

The generalized Jacobi elliptic function method is further improved by introducing an elliptic function φ(ξ) as a new independent variable and it is easy to calculate the over-determined equations. Abundant new traveling wave solutions of the coupled Drinfel'd-Sokolov-Wilson equation are obtained. The solutions obtained include the kink-shaped solutions, bell-shaped solutions, singular solutions and periodic solutions

Stability of a family of travelling wave solutions in a feedforward chain of phase oscillators

International Nuclear Information System (INIS)

Lanford, O E III; Mintchev, S M

2015-01-01

Travelling waves are an important class of signal propagation phenomena in extended systems with a preferred direction of information flow. We study the generation of travelling waves in unidirectional chains of coupled oscillators communicating via a phase-dependent pulse-response interaction borrowed from mathematical neuroscience. Within the context of such systems, we develop a widely applicable, jointly numerical and analytical methodology for deducing existence and stability of periodic travelling waves. We provide careful numerical studies that support the existence of a periodic travelling wave solution as well as the asymptotic relaxation of a single oscillator to the wave when it is forced with the wave profile. Using this evidence as an assumption, we analytically prove global stability of waves in the infinite chain, with respect to initial perturbations of downstream sites. This rigorous stability result suggests that asymptotic relaxation to the travelling wave occurs even when the forcing is perturbed from the wave profile, a property of the motivating system that is supported by previous work as well as the convergence of the more sophisticated numerical algorithm that we propose in order to compute a high-precision approximation to the solution. We provide additional numerical studies that show that the wave is part of a one-parameter family, and we illustrate the structural robustness of this family with respect to changes in the coupling strength. (paper)

Solitary ionizing surface waves on low-temperature plasmas

International Nuclear Information System (INIS)

Vladimirov, S.V.; Yu, M.Y.

1993-01-01

It is demonstrated that at the boundary of semi-infinite low-temperature plasma new types of localized ionizing surface wave structures can propagate. The solitary waves are described by an evolution equation similar to the KdV equation, but the solutions differ considerably from that of the latter

Exact traveling wave solutions for a new nonlinear heat transfer equation

Directory of Open Access Journals (Sweden)

Gao Feng

2017-01-01

Full Text Available In this paper, we propose a new non-linear partial differential equation to de-scribe the heat transfer problems at the extreme excess temperatures. Its exact traveling wave solutions are obtained by using Cornejo-Perez and Rosu method.

Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators

Directory of Open Access Journals (Sweden)

Dumitru Baleanu

2014-01-01

Full Text Available We perform a comparison between the fractional iteration and decomposition methods applied to the wave equation on Cantor set. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.

Hanbury Brown and Twiss correlations of Anderson localized waves

International Nuclear Information System (INIS)

Lahini, Y.; Bromberg, Y.; Silberberg, Y.; Shechtman, Y.; Szameit, A.; Christodoulides, D. N.; Morandotti, R.

2011-01-01

When light waves propagate through disordered photonic lattices, they can eventually become localized due to multiple scattering effects. Here we show experimentally that while the evolution and localization of the photon density distribution is similar in the two cases of diagonal and off-diagonal disorder, the density-density correlation carries a distinct signature of the type of disorder. We show that these differences reflect a symmetry in the spectrum and eigenmodes that exists in off-diagonally disordered lattices but is absent in lattices with diagonal disorder.

High-resolution seismic wave propagation using local time stepping

KAUST Repository

Peter, Daniel

2017-03-13

High-resolution seismic wave simulations often require local refinements in numerical meshes to accurately capture e.g. steep topography or complex fault geometry. Together with explicit time schemes, this dramatically reduces the global time step size for ground-motion simulations due to numerical stability conditions. To alleviate this problem, local time stepping (LTS) algorithms allow an explicit time stepping scheme to adapt the time step to the element size, allowing nearoptimal time steps everywhere in the mesh. This can potentially lead to significantly faster simulation runtimes.

Useful Solutions for Plane Wave Diffraction by Dielectric Slabs and Wedges

Directory of Open Access Journals (Sweden)

Gianluca Gennarelli

2012-01-01

Full Text Available This work presents an overview of available uniform asymptotic physical optics solutions for evaluating the plane wave diffraction by some canonical geometries of large interest: dielectric slabs and wedges. Such solutions are based on a physical optics approximation of the electric and magnetic equivalent surface currents in the involved scattering integrals. The resulting diffraction coefficients are expressed in terms of the geometrical optics response of the considered structure and the standard transition function of the Uniform Geometrical Theory of Diffraction. Numerical tests and comparisons make evident the effectiveness and reliability of the presented solutions.

A novel method for the extraction of local gravity wave parameters from gridded three-dimensional data: description, validation, and application

Directory of Open Access Journals (Sweden)

L. Schoon

2018-05-01

Full Text Available For the local diagnosis of wave properties, we develop, validate, and apply a novel method which is based on the Hilbert transform. It is called Unified Wave Diagnostics (UWaDi. It provides the wave amplitude and three-dimensional wave number at any grid point for gridded three-dimensional data. UWaDi is validated for a synthetic test case comprising two different wave packets. In comparison with other methods, the performance of UWaDi is very good with respect to wave properties and their location. For a first practical application of UWaDi, a minor sudden stratospheric warming on 30 January 2016 is chosen. Specifying the diagnostics for hydrostatic inertia–gravity waves in analyses from the European Centre for Medium-Range Weather Forecasts, we detect the local occurrence of gravity waves throughout the middle atmosphere. The local wave characteristics are discussed in terms of vertical propagation using the diagnosed local amplitudes and wave numbers. We also note some hints on local inertia–gravity wave generation by the stratospheric jet from the detection of shallow slow waves in the vicinity of its exit region.

The focusing effect of P-wave in the Moon's and Earth's low-velocity core. Analytical solution

Science.gov (United States)

Fatyanov, A. G.; Burmin, V. Yu

2018-04-01

The important aspect in the study of the structure of the interiors of planets is the question of the presence and state of core inside them. While for the Earth this task was solved long ago, the question of whether the core of the Moon is in a liquid or solid state up to the present is debatable up to present. If the core of the Moon is liquid, then the velocity of longitudinal waves in it should be lower than in the surrounding mantle. If the core is solid, then most likely, the velocity of longitudinal waves in it is higher than in the mantle. Numerical calculations of the wave field allow us to identify the criteria for drawing conclusions about the state of the lunar core. In this paper we consider the problem of constructing an analytical solution for wave fields in a layered sphere of arbitrary radius. A stable analytic solution is obtained for the wave fields of longitudinal waves in a three-layer sphere. Calculations of the total wave fields and rays for simplified models of the Earth and the Moon with real parameters are presented. The analytical solution and the ray pattern showed that the low-velocity cores of the Earth and the Moon possess the properties of a collecting lens. This leads to the emergence of a wave field focusing area. As a result, focused waves of considerable amplitude appear on the surface of the Earth and the Moon. In the Earth case, they appear before the first PKP-wave arrival. These are so-called "precursors", which continue in the subsequent arrivals of waves. At the same time, for the simplified model of the Earth, the maximum amplitude growth is observed in the 147-degree region. For the Moon model, the maximum amplitude growth is around 180°.

Localization of fluctuation measurement by wave scattering close to a cut off layer

International Nuclear Information System (INIS)

Zou, X.L.; Laurent, L.; Rax, J.M.; Lehner, T.

1990-01-01

The diagnostic of plasma fluctuations in tokamaks based on the scattering of an electromagnetic wave close to a cut off layer is investigated. A linear density profile is considered. An one-dimensional exact analysis is performed. Spatial and spectral localization of scattering process close to the cut off layer is studied and a modified Bragg rule is derived. The structure of pump and of scattered waves is analyzed. The diagnostic seems to be local and sensitive for low R fluctuations

A series of new soliton-like solutions and double-like periodic solutions of a (2 + 1)-dimensional dispersive long wave equation

International Nuclear Information System (INIS)

Yong Chen; Qi Wang

2005-01-01

In this paper, we extend the algebraic method proposed by Fan (Chaos, Solitons and Fractals 20 (2004) 609) and the improved extended tanh method by Yomba (Chaos, Solitons and Fractals 20 (2004) 1135) to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations (NPDE). Some new soliton-like solutions and double-like periodic solutions of a (2 + 1)-dimensional dispersive long wave equation are obtained

Rational homoclinic solution and rogue wave solution for the ...

Indian Academy of Sciences (India)

–4]. Rogue waves were first observed in deep ocean [5]. A wave can be called a rogue wave when its height and steepness is much greater than the average crest, and appears from nowhere and disappears without a trace [6]. Rogue waves ...

Turbulent Spot Pressure Fluctuation Wave Packet Model

Energy Technology Data Exchange (ETDEWEB)

Dechant, Lawrence J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-05-01

Wave packet analysis provides a connection between linear small disturbance theory and subsequent nonlinear turbulent spot flow behavior. The traditional association between linear stability analysis and nonlinear wave form is developed via the method of stationary phase whereby asymptotic (simplified) mean flow solutions are used to estimate dispersion behavior and stationary phase approximation are used to invert the associated Fourier transform. The resulting process typically requires nonlinear algebraic equations inversions that can be best performed numerically, which partially mitigates the value of the approximation as compared to a more complete, e.g. DNS or linear/nonlinear adjoint methods. To obtain a simpler, closed-form analytical result, the complete packet solution is modeled via approximate amplitude (linear convected kinematic wave initial value problem) and local sinusoidal (wave equation) expressions. Significantly, the initial value for the kinematic wave transport expression follows from a separable variable coefficient approximation to the linearized pressure fluctuation Poisson expression. The resulting amplitude solution, while approximate in nature, nonetheless, appears to mimic many of the global features, e.g. transitional flow intermittency and pressure fluctuation magnitude behavior. A low wave number wave packet models also recover meaningful auto-correlation and low frequency spectral behaviors.

Streamwise-Localized Solutions with natural 1-fold symmetry

Science.gov (United States)

Altmeyer, Sebastian; Willis, Ashley; Hof, Björn

2014-11-01

It has been proposed in recent years that turbulence is organized around unstable invariant solutions, which provide the building blocks of the chaotic dynamics. In direct numerical simulations of pipe flow we show that when imposing a minimal symmetry constraint (reflection in an axial plane only) the formation of turbulence can indeed be explained by dynamical systems concepts. The hypersurface separating laminar from turbulent motion, the edge of turbulence, is spanned by the stable manifolds of an exact invariant solution, a periodic orbit of a spatially localized structure. The turbulent states themselves (turbulent puffs in this case) are shown to arise in a bifurcation sequence from a related localized solution (the upper branch orbit). The rather complex bifurcation sequence involves secondary Hopf bifurcations, frequency locking and a period doubling cascade until eventually turbulent puffs arise. In addition we report preliminary results of the transition sequence for pipe flow without symmetry constraints.

Local Open Innovation: How to Go from Ideas to Solutions

Directory of Open Access Journals (Sweden)

Oscar Smulders

2013-03-01

Full Text Available Local open innovation can be used to create a powerful dynamic within a local multi-stakeholder environment. This article shares the experiences of setting up a collaborative innovation process in a regional initiative in the Netherlands. In the first phase of the process, a couple of interactive idea generating sessions have been organized. These so called Quest for Solutions sessions have not only generated a rich set of useful solutions, but they also created a positive vibe within the local community. Factors that have contributed to the success of the idea generation sessions are working around real-life problems involving people who are directly affected by the problem. The structure of the sessions with alternating phases of divergence, exploration, and convergence allowed for broad understanding of the problems, exploration of potential solutions, and working towards result-oriented value statements. Key challenges in translating the ideas into solutions have been determining the value case and dealing with intellectual property. Special attention is given to the notion of innovative contract design as a means of dealing with intellectual property in an environment of local open innovation.

The theory of magnetohydrodynamic wave generation by localized sources. I - General asymptotic theory

Science.gov (United States)

Collins, William

1989-01-01

The magnetohydrodynamic wave emission from several localized, periodic, kinematically specified fluid velocity fields are calculated using Lighthill's method for finding the far-field wave forms. The waves propagate through an isothermal and uniform plasma with a constant B field. General properties of the energy flux are illustrated with models of pulsating flux tubes and convective rolls. Interference theory from geometrical optics is used to find the direction of minimum fast-wave emission from multipole sources and slow-wave emission from discontinuous sources. The distribution of total flux in fast and slow waves varies with the ratios of the source dimensions l to the acoustic and Alfven wavelengths.

On the propagation of truncated localized waves in dispersive silica

KAUST Repository

Salem, Mohamed

2010-01-01

Propagation characteristics of truncated Localized Waves propagating in dispersive silica and free space are numerically analyzed. It is shown that those characteristics are affected by the changes in the relation between the transverse spatial spectral components and the wave vector. Numerical experiments demonstrate that as the non-linearity of this relation gets stronger, the pulses propagating in silica become more immune to decay and distortion whereas the pulses propagating in free-space suffer from early decay and distortion. © 2010 Optical Society of America.

The evolution of a localized nonlinear wave of the Kelvin-Helmholtz instability with gravity

Science.gov (United States)

Orazzo, Annagrazia; Hoepffner, Jérôme

2012-11-01

At the interface between two fluids of different density and in the presence of gravity, there are well known periodic surface waves which can propagate for long distances with little attenuation, as it is for instance the case at the surface of the sea. If wind is present, these waves progressively accumulate energy as they propagate and grow to large sizes—this is the Kelvin-Helmholtz instability. On the other hand, we show in this paper that for a given wind strength, there is potential for the growth of a localized nonlinear wave. This wave can reach a size such that the hydrostatic pressure drop from top to bottom equals the stagnation pressure of the wind. This process for the disruption of the flat interface is localized and nonlinear. We study the properties of this wave using numerical simulations of the Navier-Stokes equations.

The wave attenuation mechanism of the periodic local resonant metamaterial

Science.gov (United States)

Chang, I.-Ling; Liang, Zhen-Xian; Kao, Hao-Wei; Chang, Shih-Hsiang; Yang, Chih-Ying

2018-01-01

This research discusses the wave propagation behavior and attenuation mechanism of the elastic metamaterial with locally resonant sub-structure. The dispersion relation of the single resonance system, i.e., periodic spring mass system with sub-structure, could be derived based on lattice dynamics and the band gap could be easily identified. The dynamically equivalent properties, i.e., mass and elastic property, of the single resonance system are derived and found to be frequency dependent. Negative effective properties are found in the vicinity of the local resonance. It is examined whether the band gap always coincides with the frequency range of negative effective properties. The wave attenuation mechanism and the characteristic dynamic behavior of the elastic metamaterial are also studied from the energy point of view. From the analysis, it is clarified that the coupled Bragg-resonance band gap is much wider than the narrow-banded local resonance and the corresponding effective material properties at band gap could be either positive or negative. However, the band gap is totally overlapping with the frequency range of negative effective properties for the metamaterial with band gap purely caused by local resonance. The presented analysis can be extended to other forms of elastic metamaterials involving periodic resonator structures.

Matter-wave solitons and finite-amplitude Bloch waves in optical lattices with spatially modulated nonlinearity

Science.gov (United States)

Zhang, Jie-Fang; Li, Yi-Shen; Meng, Jianping; Wu, Lei; Malomed, Boris A.

2010-09-01

We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices (OLs). By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite set of exact soliton solutions in terms of Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite gap of the OL-induced spectrum. Starting from the particular exact solutions, we employ the relaxation method to construct generic families of soliton solutions in a numerical form. The stability of the solitons is investigated through the computation of the eigenvalues for small perturbations, and also by direct simulations. Finally, we demonstrate a virtually exact (in the numerical sense) composition relation between nonlinear Bloch waves and solitons.

Matter-wave solitons and finite-amplitude Bloch waves in optical lattices with spatially modulated nonlinearity

International Nuclear Information System (INIS)

Zhang Jiefang; Meng Jianping; Wu Lei; Li Yishen; Malomed, Boris A.

2010-01-01

We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices (OLs). By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite set of exact soliton solutions in terms of Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite gap of the OL-induced spectrum. Starting from the particular exact solutions, we employ the relaxation method to construct generic families of soliton solutions in a numerical form. The stability of the solitons is investigated through the computation of the eigenvalues for small perturbations, and also by direct simulations. Finally, we demonstrate a virtually exact (in the numerical sense) composition relation between nonlinear Bloch waves and solitons.

Impact localization in dispersive waveguides based on energy-attenuation of waves with the traveled distance

Science.gov (United States)

Alajlouni, Sa'ed; Albakri, Mohammad; Tarazaga, Pablo

2018-05-01

An algorithm is introduced to solve the general multilateration (source localization) problem in a dispersive waveguide. The algorithm is designed with the intention of localizing impact forces in a dispersive floor, and can potentially be used to localize and track occupants in a building using vibration sensors connected to the lower surface of the walking floor. The lower the wave frequencies generated by the impact force, the more accurate the localization is expected to be. An impact force acting on a floor, generates a seismic wave that gets distorted as it travels away from the source. This distortion is noticeable even over relatively short traveled distances, and is mainly caused by the dispersion phenomenon among other reasons, therefore using conventional localization/multilateration methods will produce localization error values that are highly variable and occasionally large. The proposed localization approach is based on the fact that the wave's energy, calculated over some time window, decays exponentially as the wave travels away from the source. Although localization methods that assume exponential decay exist in the literature (in the field of wireless communications), these methods have only been considered for wave propagation in non-dispersive media, in addition to the limiting assumption required by these methods that the source must not coincide with a sensor location. As a result, these methods cannot be applied to the indoor localization problem in their current form. We show how our proposed method is different from the other methods, and that it overcomes the source-sensor location coincidence limitation. Theoretical analysis and experimental data will be used to motivate and justify the pursuit of the proposed approach for localization in a dispersive medium. Additionally, hammer impacts on an instrumented floor section inside an operational building, as well as finite element model simulations, are used to evaluate the performance of

Stability analysis of the soliton solutions for the generalized quintic derivative nonlinear Schrödinger equation

Directory of Open Access Journals (Sweden)

Chen Yue

Full Text Available The propagation of hydrodynamic wave packets and media with negative refractive index is studied in a quintic derivative nonlinear Schrödinger (DNLS equation. The quintic DNLS equation describe the wave propagation on a discrete electrical transmission line. We obtain a Lagrangian and the invariant variational principle for quintic DNLS equation. By using a class of ordinary differential equation, we found four types of exact solutions of the quintic DNLS equation, which are kink-type solitary wave solution, antikink-type solitary wave solution, sinusoidal solitary wave solution, bell-type solitary wave solution. By applying the modulation instability to discuss stability analysis of the obtained solutions. Modulation instabilities of continuous waves and localized solutions on a zero background have been investigated. Keywords: Quintic derivative NLS equation, Solitary wave solutions, Mathematical physics methods, 2000 MR Subject Classification: 35G20, 35Q53, 37K10, 49S05, 76A60

Solitary wave solutions to the modified form of Camassa-Holm equation by means of the homotopy analysis method

International Nuclear Information System (INIS)

Abbasbandy, S.

2009-01-01

Solitary wave solutions to the modified form of Camassa-Holm (CH) equation are sought. In this work, the homotopy analysis method (HAM), one of the most effective method, is applied to obtain the soliton wave solutions with and without continuity of first derivatives at crest

Interpeace: local solutions, lasting peace | IDRC - International ...

International Development Research Centre (IDRC) Digital Library (Canada)

2010-10-27

Oct 27, 2010 ... With funding from IDRC, a UN pilot initiative, the War-torn Societies Project, sought durable, locally rooted solutions to the conflicts in four test countries: Somalia ... "The issues the projects were working on were defined by the ...

Quasitravelling waves

International Nuclear Information System (INIS)

Beklaryan, Leva A

2011-01-01

A finite difference analogue of the wave equation with potential perturbation is investigated, which simulates the behaviour of an infinite rod under the action of an external longitudinal force field. For a homogeneous rod, describing solutions of travelling wave type is equivalent to describing the full space of classical solutions to an induced one-parameter family of functional differential equations of point type, with the characteristic of the travelling wave as parameter. For an inhomogeneous rod, the space of solutions of travelling wave type is trivial, and their 'proper' extension is defined as solutions of 'quasitravelling' wave type. By contrast to the case of a homogeneous rod, describing the solutions of quasitravelling wave type is equivalent to describing the quotient of the full space of impulsive solutions to an induced one-parameter family of point-type functional differential equations by an equivalence relation connected with the definition of solutions of quasitravelling wave type. Stability of stationary solutions is analyzed. Bibliography: 9 titles.

Localization of binary neutron star mergers with second and third generation gravitational-wave detectors

Science.gov (United States)

Mills, Cameron; Tiwari, Vaibhav; Fairhurst, Stephen

2018-05-01

The observation of gravitational wave signals from binary black hole and binary neutron star mergers has established the field of gravitational wave astronomy. It is expected that future networks of gravitational wave detectors will possess great potential in probing various aspects of astronomy. An important consideration for successive improvement of current detectors or establishment on new sites is knowledge of the minimum number of detectors required to perform precision astronomy. We attempt to answer this question by assessing the ability of future detector networks to detect and localize binary neutron stars mergers on the sky. Good localization ability is crucial for many of the scientific goals of gravitational wave astronomy, such as electromagnetic follow-up, measuring the properties of compact binaries throughout cosmic history, and cosmology. We find that although two detectors at improved sensitivity are sufficient to get a substantial increase in the number of observed signals, at least three detectors of comparable sensitivity are required to localize majority of the signals, typically to within around 10 deg2 —adequate for follow-up with most wide field of view optical telescopes.

Conditional Stability of Solitary-Wave Solutions for Generalized Compound KdV Equation and Generalized Compound KdV-Burgers Equation

International Nuclear Information System (INIS)

Zhang Weiguo; Dong Chunyan; Fan Engui

2006-01-01

In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the exact solitary-wave solutions is proved for the above two types of equations when the small disturbance of travelling wave form satisfies some special conditions.

Holographic magnetisation density waves

Energy Technology Data Exchange (ETDEWEB)

Donos, Aristomenis [Centre for Particle Theory and Department of Mathematical Sciences, Durham University,Stockton Road, Durham, DH1 3LE (United Kingdom); Pantelidou, Christiana [Departament de Fisica Quantica i Astrofisica & Institut de Ciencies del Cosmos (ICC),Universitat de Barcelona,Marti i Franques 1, 08028 Barcelona (Spain)

2016-10-10

We numerically construct asymptotically AdS black brane solutions of D=4 Einstein theory coupled to a scalar and two U(1) gauge fields. The solutions are holographically dual to d=3 CFTs in a constant external magnetic field along one of the U(1)’s. Below a critical temperature the system’s magnetisation density becomes inhomogeneous, leading to spontaneous formation of current density waves. We find that the transition can be of second order and that the solutions which minimise the free energy locally in the parameter space of solutions have averaged stressed tensor of a perfect fluid.

Local fields for asymptotic matching in multidimensional mode conversion

International Nuclear Information System (INIS)

Tracy, E. R.; Kaufman, A. N.; Jaun, A.

2007-01-01

The problem of resonant mode conversion in multiple spatial dimensions is considered. Using phase space methods, a complete theory is developed for constructing matched asymptotic expansions that fit incoming and outgoing WKB solutions. These results provide, for the first time, a complete and practical method for including multidimensional conversion in ray tracing algorithms. The paper provides a self-contained description of the following topics: (1) how to use eikonal (also known as ray tracing or WKB) methods to solve vector wave equations and how to detect conversion regions while following rays; (2) once conversion is detected, how to fit to a generic saddle structure in ray phase space associated with the most common type of conversion; (3) given the saddle structure, how to carry out a local projection of the full vector wave equation onto a local two-component normal form that governs the two resonantly interacting waves. This determines both the uncoupled dispersion functions and the coupling constant, which in turn determine the uncoupled WKB solutions; (4) given the normal form of the local two-component wave equation, how to find the particular solution that matches the amplitude, phase, and polarization of the incoming ray, to the amplitude, phase, and polarization of the two outgoing rays: the transmitted and converted rays

Localization Problem in the 5D Standing Wave Braneworld

OpenAIRE

Gogberashvili, Merab; Midodashvili, Pavle; Midodashvili, Levan

2012-01-01

We investigate the problem of pure gravitational localization of matter fields within the 5D standing wave braneworld generated by gravity coupled to a phantom-like scalar field. We show that in the case of increasing warp factor there exist normalizable zero modes of spin-0, -1/2, -1, and -2 fields on the brane.

Localized atomic basis set in the projector augmented wave method

DEFF Research Database (Denmark)

Larsen, Ask Hjorth; Vanin, Marco; Mortensen, Jens Jørgen

2009-01-01

We present an implementation of localized atomic-orbital basis sets in the projector augmented wave (PAW) formalism within the density-functional theory. The implementation in the real-space GPAW code provides a complementary basis set to the accurate but computationally more demanding grid...

Fusion an annihilation of solitary waves for a (2+1)-dimensional nonlinear system

Energy Technology Data Exchange (ETDEWEB)

Qiang, Ji-Ye [Nanjing Agricultural Univ. (China). Agronomy College; Lishui Univ., Zhejiang (China). College of Mathematics and Physics; Yunnan Agricultural Univ., Kunming (China). Tobacco College; Ma, Song-Hua; Ren, Qing-Bao [Lishui Univ., Zhejiang (China). College of Mathematics and Physics; Wang, Shao-Hua [Nanjing Agricultural Univ. (China). Agronomy College

2010-12-15

In this paper, a new projective equation is used to obtain the variable separation solutions with two arbitrary functions of the (2+1)-dimensional Broek-Kaup system (BKK). Based on the derived solitary wave solutions and by selecting appropriate functions, some novel localized excitations such as fusion and annihilation of solitary waves are investigated. (orig.)

An Operator Method for Field Moments from the Extended Parabolic Wave Equation and Analytical Solutions of the First and Second Moments for Atmospheric Electromagnetic Wave Propagation

Science.gov (United States)

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.

Stability of nonlinear waves and patterns and related topics

Science.gov (United States)

Ghazaryan, Anna; Lafortune, Stephane; Manukian, Vahagn

2018-04-01

Periodic and localized travelling waves such as wave trains, pulses, fronts and patterns of more complex structure often occur in natural and experimentally built systems. In mathematics, these objects are realized as solutions of nonlinear partial differential equations. The existence, dynamic properties and bifurcations of those solutions are of interest. In particular, their stability is important for applications, as the waves that are observable are usually stable. When the waves are unstable, further investigation is warranted of the way the instability is exhibited, i.e. the nature of the instability, and also coherent structures that appear as a result of an instability of travelling waves. A variety of analytical, numerical and hybrid techniques are used to study travelling waves and their properties. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.

Multidimensional behavior of an electrostatic ion wave in a magnetized plasma

International Nuclear Information System (INIS)

Nishinari, K.; Abe, K.; Satsuma, J.

1994-01-01

Three-dimensional nonlinear evolution equations of an electrostatic ion wave in the short wave region in a magnetized plasma are derived by means of the reductive perturbation method. It is shown that, in some cases, the evolution equations reduce to the Davey--Stewartson 1 equations, which are known to admit solutions with localized structure in higher dimension. It is also shown that there is a possibility of collapse of localized structure in the case of wave propagation parallel to a magnetic field

Exact traveling wave solutions of the KP-BBM equation by using the new approach of generalized (G'/G)-expansion method.

Science.gov (United States)

Alam, Md Nur; Akbar, M Ali

2013-01-01

The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. By means of this scheme, we found some new traveling wave solutions of the above mentioned equation.

Kinetic Alfvén wave turbulence and formation of localized structures

Energy Technology Data Exchange (ETDEWEB)

Sharma, R. P. [Centre for Energy Studies, Indian Institute of Technology Delhi, Delhi 110016 (India); Modi, K. V. [Centre for Energy Studies, Indian Institute of Technology Delhi, Delhi 110016 (India); Mechanical Engineering Department, Government Engineering College Valsad, Gujarat 396001 (India)

2013-08-15

This work presents non-linear interaction of magnetosonic wave with kinetic Alfvén wave for intermediate β-plasma (m{sub e}/m{sub i}≪β≪1). A set of dimensionless equations have been developed for analysis by considering ponderomotive force due to pump kinetic Alfvén wave in the dynamics of magnetosonic wave. Stability analysis has been done to study modulational instability or linear growth rate. Further, numerical simulation has been carried out to study the nonlinear stage of instability and resulting power spectrum applicable to solar wind around 1 AU. Due to the nonlinearity, background density of magnetosonic wave gets modified which results in localization of kinetic Alfvén wave. From the obtained results, we observed that spectral index follows k{sup −3.0}, consistent with observation received by Cluster spacecraft for the solar wind around 1 AU. The result shows the steepening of power spectrum which may be responsible for heating and acceleration of plasma particles in solar wind.

Global paths of time-periodic solutions of the Benjamin-Ono equation connecting arbitrary traveling waves

Energy Technology Data Exchange (ETDEWEB)

Ambrose, David M.; Wilkening, Jon

2008-12-11

We classify all bifurcations from traveling waves to non-trivial time-periodic solutions of the Benjamin-Ono equation that are predicted by linearization. We use a spectrally accurate numerical continuation method to study several paths of non-trivial solutions beyond the realm of linear theory. These paths are found to either re-connect with a different traveling wave or to blow up. In the latter case, as the bifurcation parameter approaches a critical value, the amplitude of the initial condition grows without bound and the period approaches zero. We propose a conjecture that gives the mapping from one bifurcation to its counterpart on the other side of the path of non-trivial solutions. By experimentation with data fitting, we identify the form of the exact solutions on the path connecting two traveling waves, which represents the Fourier coefficients of the solution as power sums of a finite number of particle positions whose elementary symmetric functions execute simple orbits in the complex plane (circles or epicycles). We then solve a system of algebraic equations to express the unknown constants in the new representation in terms of the mean, a spatial phase, a temporal phase, four integers (enumerating the bifurcation at each end of the path) and one additional bifurcation parameter. We also find examples of interior bifurcations from these paths of already non-trivial solutions, but we do not attempt to analyze their algebraic structure.

Exact solution for the reflection and diffraction of atomic de Broglie waves by a travelling evanescent laser wave

International Nuclear Information System (INIS)

Witte, N.S.

1997-01-01

The exact solution to the problem of reflection and diffraction of atomic de Broglie waves by a travelling evanescent wave is found starting with a bare-state formulation. The solution for the wavefunctions, the tunnelling losses and the non-adiabatic losses are given exactly in terms of hyper-Bessel functions, and are valid for all detuning and Rabi frequencies, thus generalizing previous approximate methods. Furthermore we give the limiting cases of all amplitudes in the uniform semiclassical limit, which is valid in all regions including near the classical turning points, and in the large and weak coupling cases. Exact results for the zero detuning case are obtained in terms of Bessel functions. We find our uniform semiclassical limit to be closer to the exact result over the full range of parameter values than the previously reported calculations. The current knowledge of hyper-Bessel function properties is reviewed in order to apply this to the physical problems imposed

Travelling-wave amplitudes as solutions of the phase-field crystal equation

Science.gov (United States)

Nizovtseva, I. G.; Galenko, P. K.

2018-01-01

The dynamics of the diffuse interface between liquid and solid states is analysed. The diffuse interface is considered as an envelope of atomic density amplitudes as predicted by the phase-field crystal model (Elder et al. 2004 Phys. Rev. E 70, 051605 (doi:10.1103/PhysRevE.70.051605); Elder et al. 2007 Phys. Rev. B 75, 064107 (doi:10.1103/PhysRevB.75.064107)). The propagation of crystalline amplitudes into metastable liquid is described by the hyperbolic equation of an extended Allen-Cahn type (Galenko & Jou 2005 Phys. Rev. E 71, 046125 (doi:10.1103/PhysRevE.71.046125)) for which the complete set of analytical travelling-wave solutions is obtained by the method (Malfliet & Hereman 1996 Phys. Scr. 15, 563-568 (doi:10.1088/0031-8949/54/6/003); Wazwaz 2004 Appl. Math. Comput. 154, 713-723 (doi:10.1016/S0096-3003(03)00745-8)). The general solution of travelling waves is based on the function of hyperbolic tangent. Together with its set of particular solutions, the general solution is analysed within an example of specific task about the crystal front invading metastable liquid (Galenko et al. 2015 Phys. D 308, 1-10 (doi:10.1016/j.physd.2015.06.002)). The influence of the driving force on the phase-field profile, amplitude velocity and correlation length is investigated for various relaxation times of the gradient flow. This article is part of the theme issue `From atomistic interfaces to dendritic patterns'.

δ- and δ'-shock wave types of singular solutions of systems of conservation laws and transport and concentration processes

International Nuclear Information System (INIS)

Shelkovich, V M

2008-01-01

This is a survey of some results and problems connected with the theory of generalized solutions of quasi-linear conservation law systems which can admit delta-shaped singularities. They are the so-called δ-shock wave type solutions and the recently introduced δ (n) -shock wave type solutions, n=1,2,..., which cannot be included in the classical Lax-Glimm theory. The case of δ- and δ'-shock waves is analyzed in detail. A specific analytical technique is developed to deal with such solutions. In order to define them, some special integral identities are introduced which extend the concept of weak solution, and the Rankine-Hugoniot conditions are derived. Solutions of Cauchy problems are constructed for some typical systems of conservation laws. Also investigated are multidimensional systems of conservation laws (in particular, zero-pressure gas dynamics systems) which admit δ-shock wave type solutions. A geometric aspect of such solutions is considered: they are connected with transport and concentration processes, and the balance laws of transport of 'volume' and 'area' to δ- and δ'-shock fronts are derived for them. For a 'zero-pressure gas dynamics' system these laws are the mass and momentum transport laws. An algebraic aspect of these solutions is also considered: flux-functions are constructed for them which, being non-linear, are nevertheless uniquely defined Schwartz distributions. Thus, a singular solution of the Cauchy problem generates algebraic relations between its components (distributions).

Numerical analysis of quasiperiodic perturbations for the Alfven wave

International Nuclear Information System (INIS)

Yamakoshi, Y.; Muto, K.; Yoshida, Z.

1994-01-01

The Alfven wave may have a localized eigenfunction when it propagates on a chaotic magnetic field. The Arnold-Beltrami-Childress (ABC) flow is a paradigm of chaotic stream lines and is a simple exact solution to the three-dimensional force-free plasma equilibrium equations. The three-dimensional structure of the magnetic field is represented by sinusoidal quasiperiodic modulation. The short wavelength Alfven wave equation for the ABC-flow magnetic field has a quasiperiodic potential term, which induces interference among ''Bragg-reflected'' waves with irregular phases. Then the eigenfunction decays at long distance and a point spectrum occurs. Two different types of short wavelength modes have numerically analyzed to demonstrate the existence of localized Alfven wave eigenmodes

Traveling wave solutions to some nonlinear fractional partial differential equations through the rational (G′/G-expansion method

Directory of Open Access Journals (Sweden)

Tarikul Islam

2018-03-01

Full Text Available In this article, the analytical solutions to the space-time fractional foam drainage equation and the space-time fractional symmetric regularized long wave (SRLW equation are successfully examined by the recently established rational (G′/G-expansion method. The suggested equations are reduced into the nonlinear ordinary differential equations with the aid of the fractional complex transform. Consequently, the theories of the ordinary differential equations are implemented effectively. Three types closed form traveling wave solutions, such as hyperbolic function, trigonometric function and rational, are constructed by using the suggested method in the sense of conformable fractional derivative. The obtained solutions might be significant to analyze the depth and spacing of parallel subsurface drain and small-amplitude long wave on the surface of the water in a channel. It is observed that the performance of the rational (G′/G-expansion method is reliable and will be used to establish new general closed form solutions for any other NPDEs of fractional order.

Initial-Boundary Value Problem Solution of the Nonlinear Shallow-water Wave Equations

Science.gov (United States)

Kanoglu, U.; Aydin, B.

2014-12-01

The hodograph transformation solutions of the one-dimensional nonlinear shallow-water wave (NSW) equations are usually obtained through integral transform techniques such as Fourier-Bessel transforms. However, the original formulation of Carrier and Greenspan (1958 J Fluid Mech) and its variant Carrier et al. (2003 J Fluid Mech) involve evaluation integrals. Since elliptic integrals are highly singular as discussed in Carrier et al. (2003), this solution methodology requires either approximation of the associated integrands by smooth functions or selection of regular initial/boundary data. It should be noted that Kanoglu (2004 J Fluid Mech) partly resolves this issue by simplifying the resulting integrals in closed form. Here, the hodograph transform approach is coupled with the classical eigenfunction expansion method rather than integral transform techniques and a new analytical model for nonlinear long wave propagation over a plane beach is derived. This approach is based on the solution methodology used in Aydın & Kanoglu (2007 CMES-Comp Model Eng) for wind set-down relaxation problem. In contrast to classical initial- or boundary-value problem solutions, here, the NSW equations are formulated to yield an initial-boundary value problem (IBVP) solution. In general, initial wave profile with nonzero initial velocity distribution is assumed and the flow variables are given in the form of Fourier-Bessel series. The results reveal that the developed method allows accurate estimation of the spatial and temporal variation of the flow quantities, i.e., free-surface height and depth-averaged velocity, with much less computational effort compared to the integral transform techniques such as Carrier et al. (2003), Kanoglu (2004), Tinti & Tonini (2005 J Fluid Mech), and Kanoglu & Synolakis (2006 Phys Rev Lett). Acknowledgments: This work is funded by project ASTARTE- Assessment, STrategy And Risk Reduction for Tsunamis in Europe. Grant 603839, 7th FP (ENV.2013.6.4-3 ENV

The Method of Lines Solution of the Regularized Long-Wave Equation Using Runge-Kutta Time Discretization Method

Directory of Open Access Journals (Sweden)

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.

A non-differentiable solution for the local fractional telegraph equation

Directory of Open Access Journals (Sweden)

Li Jie

2017-01-01

Full Text Available In this paper, we consider the linear telegraph equations with local fractional derivative. The local fractional Laplace series expansion method is used to handle the local fractional telegraph equation. The analytical solution with the non-differentiable graphs is discussed in detail. The proposed method is efficient and accurate.

A numerical solution to the radial equation of the tidal wave propagation

International Nuclear Information System (INIS)

Makarious, S.H.

1981-08-01

The tidal wave function y(x) is a solution to an inhomogeneous, linear, second-order differential equation with variable coefficient. Numerical values for the height-dependence terms, in the observed tides, have been utilized in finding y(x) as a solution to an initial-value problem. Complex Fast Fourier Transform technique is also used to obtain the solution in a complex form. Based on a realistic temperature structure, the atmosphere - below 110 km - has been divided into layers with distinct characteristics, and thus the technique of propagation in stratified media has been applied. The reduced homogeneous equation assumes the form of Helmholtz equation and with initial conditions the general solution is obtained. (author)

Localization of small arms fire using acoustic measurements of muzzle blast and/or ballistic shock wave arrivals.

Science.gov (United States)

Lo, Kam W; Ferguson, Brian G

2012-11-01

The accurate localization of small arms fire using fixed acoustic sensors is considered. First, the conventional wavefront-curvature passive ranging method, which requires only differential time-of-arrival (DTOA) measurements of the muzzle blast wave to estimate the source position, is modified to account for sensor positions that are not strictly collinear (bowed array). Second, an existing single-sensor-node ballistic model-based localization method, which requires both DTOA and differential angle-of-arrival (DAOA) measurements of the muzzle blast wave and ballistic shock wave, is improved by replacing the basic external ballistics model (which describes the bullet's deceleration along its trajectory) with a more rigorous model and replacing the look-up table ranging procedure with a nonlinear (or polynomial) equation-based ranging procedure. Third, a new multiple-sensor-node ballistic model-based localization method, which requires only DTOA measurements of the ballistic shock wave to localize the point of fire, is formulated. The first method is applicable to situations when only the muzzle blast wave is received, whereas the third method applies when only the ballistic shock wave is received. The effectiveness of each of these methods is verified using an extensive set of real data recorded during a 7 day field experiment.

Symmetries, Traveling Wave Solutions, and Conservation Laws of a (3+1-Dimensional Boussinesq Equation

Directory of Open Access Journals (Sweden)

Letlhogonolo Daddy Moleleki

2014-01-01

Full Text Available We analyze the (3+1-dimensional Boussinesq equation, which has applications in fluid mechanics. We find exact solutions of the (3+1-dimensional Boussinesq equation by utilizing the Lie symmetry method along with the simplest equation method. The solutions obtained are traveling wave solutions. Moreover, we construct the conservation laws of the (3+1-dimensional Boussinesq equation using the new conservation theorem, which is due to Ibragimov.

Periodic and solitary wave solutions of Kawahara and modified Kawahara equations by using Sine-Cosine method

International Nuclear Information System (INIS)

Yusufoglu, E.; Bekir, A.; Alp, M.

2008-01-01

In this paper, we establish exact solutions for nonlinear evolution equations. The sine-cosine method is used to construct periodic and solitary wave solutions of the Kawahara and modified Kawahara equations. These solutions may be important of significance for the explanation of some practical physical problems

Stability of time-dependent particle-like solutions of some wave equations

International Nuclear Information System (INIS)

Voronov, N.A.

1978-01-01

The proof of the nonstability of the one-dimensional periodical localized solutions of the equation with a spontaneously broken symmetry is given. The stability of the one-dimensional oscillating solutions of the sine-Gordon equation was also considered with regard to such perturbations. As it was expected these solutions proved to be stable

THE EXPONENTIAL STABILIZATION FOR A SEMILINEAR WAVE EQUATION WITH LOCALLY DISTRIBUTED FEEDBACK

Institute of Scientific and Technical Information of China (English)

JIA CHAOHUA; FENG DEXING

2005-01-01

This paper considers the exponential decay of the solution to a damped semilinear wave equation with variable coefficients in the principal part by Riemannian multiplier method. A differential geometric condition that ensures the exponential decay is obtained.

Traveling wave solution of the Reggeon field theory

International Nuclear Information System (INIS)

Peschanski, Robi

2009-01-01

We identify the nonlinear evolution equation in impact-parameter space for the 'Supercritical Pomeron' in Reggeon field theory as a two-dimensional stochastic Fisher-Kolmogorov-Petrovski-Piscounov equation. It exactly preserves unitarity and leads in its radial form to a high-energy traveling wave solution corresponding to a 'universal' behavior of the impact-parameter front profile of the elastic amplitude; its rapidity dependence and form depend only on one parameter, the noise strength, independently of the initial conditions and of the nonlinear terms restoring unitarity. Theoretical predictions are presented for the three typical distinct regimes corresponding to zero, weak, and strong noise.

THE NEW SOLUTION OF TIME FRACTIONAL WAVE EQUATION WITH CONFORMABLE FRACTIONAL DERIVATIVE DEFINITION

OpenAIRE

Çenesiz, Yücel; Kurt, Ali

2015-01-01

– In this paper, we used new fractional derivative definition, the conformable fractional derivative, for solving two and three dimensional time fractional wave equation. This definition is simple and very effective in the solution procedures of the fractional differential equations that have complicated solutions with classical fractional derivative definitions like Caputo, Riemann-Liouville and etc. The results show that conformable fractional derivative definition is usable and convenient ...

Generalized Bilinear Differential Operators, Binary Bell Polynomials, and Exact Periodic Wave Solution of Boiti-Leon-Manna-Pempinelli Equation

Directory of Open Access Journals (Sweden)

Huanhe Dong

2014-01-01

Full Text Available We introduce how to obtain the bilinear form and the exact periodic wave solutions of a class of (2+1-dimensional nonlinear integrable differential equations directly and quickly with the help of the generalized Dp-operators, binary Bell polynomials, and a general Riemann theta function in terms of the Hirota method. As applications, we solve the periodic wave solution of BLMP equation and it can be reduced to soliton solution via asymptotic analysis when the value of p is 5.

Soliton solutions to the fifth-order Korteweg-de Vries equation and their applications to surface and internal water waves

Science.gov (United States)

Khusnutdinova, K. R.; Stepanyants, Y. A.; Tranter, M. R.

2018-02-01

We study solitary wave solutions of the fifth-order Korteweg-de Vries equation which contains, besides the traditional quadratic nonlinearity and third-order dispersion, additional terms including cubic nonlinearity and fifth order linear dispersion, as well as two nonlinear dispersive terms. An exact solitary wave solution to this equation is derived, and the dependence of its amplitude, width, and speed on the parameters of the governing equation is studied. It is shown that the derived solution can represent either an embedded or regular soliton depending on the equation parameters. The nonlinear dispersive terms can drastically influence the existence of solitary waves, their nature (regular or embedded), profile, polarity, and stability with respect to small perturbations. We show, in particular, that in some cases embedded solitons can be stable even with respect to interactions with regular solitons. The results obtained are applicable to surface and internal waves in fluids, as well as to waves in other media (plasma, solid waveguides, elastic media with microstructure, etc.).

Adjoint eigenfunctions of temporally recurrent single-spiral solutions in a simple model of atrial fibrillation.

Science.gov (United States)

Marcotte, Christopher D; Grigoriev, Roman O

2016-09-01

This paper introduces a numerical method for computing the spectrum of adjoint (left) eigenfunctions of spiral wave solutions to reaction-diffusion systems in arbitrary geometries. The method is illustrated by computing over a hundred eigenfunctions associated with an unstable time-periodic single-spiral solution of the Karma model on a square domain. We show that all leading adjoint eigenfunctions are exponentially localized in the vicinity of the spiral tip, although the marginal modes (response functions) demonstrate the strongest localization. We also discuss the implications of the localization for the dynamics and control of unstable spiral waves. In particular, the interaction with no-flux boundaries leads to a drift of spiral waves which can be understood with the help of the response functions.

Numerical solutions of several reflected shock-wave flow fields with nonequilibrium chemical reactions

Science.gov (United States)

Hanson, R. K.; Presley, L. L.; Williams, E. V.

1972-01-01

The method of characteristics for a chemically reacting gas is used in the construction of the time-dependent, one-dimensional flow field resulting from the normal reflection of an incident shock wave at the end wall of a shock tube. Nonequilibrium chemical reactions are allowed behind both the incident and reflected shock waves. All the solutions are evaluated for oxygen, but the results are generally representative of any inviscid, nonconducting, and nonradiating diatomic gas. The solutions clearly show that: (1) both the incident- and reflected-shock chemical relaxation times are important in governing the time to attain steady state thermodynamic properties; and (2) adjacent to the end wall, an excess-entropy layer develops wherein the steady state values of all the thermodynamic variables except pressure differ significantly from their corresponding Rankine-Hugoniot equilibrium values.

INTEGRATED DOCUMENT MANAGEMENT SOLUTION FOR THE LOCAL GOVERNMENT

Directory of Open Access Journals (Sweden)

Nistor Razvan

2013-07-01

Full Text Available In this paper we present system analysis and design elements for the integrated document management solution at local governing authorities in the rural areas. While specifically dealing with the actual management of the Agricultural Register, an important primary unitary evidence document, we also keep a general character of the discussion, in order to argue for the generality of the proposed solution. Hence, for the identified and described problem space we propose an administrative and software infrastructure solution. This work is an empirical research in which our aim is primarily to identify key problems within the local governing authorities from several perspectives concerning the management of the Agricultural Register then to address those problems with an integrated document management system. For the proposed solution we give and argue the general system architecture and describe the key-mechanisms that support quality requirements. The relevance of this research concern is given by the impact of the actual Agricultural Register management on important stakeholders. This can be measured as the satisfaction felt by taxpayers and the performance of the local governing authorities, the Financial Administration, the Agency of Payments and Intervention in Agriculture and the Ministry of Agriculture and Rural Development. This work is also intended as a start-point for a new, modern thinking of the governing authorities in their pursue to improve public services. For this, in our work we highlight the importance of complete system analysis at all administrative levels as a main priority concern for all public managers. Our aim is the improvement of the public service by rising the awareness of the decision makers on the necessity of using integrated document management solutions for the provided services. Also, our work aims at increasing the efficiency with which nowadays, governing authorities invest public funds in various IT projects

Traveling waves in lattice differential equations with distributed maturation delay

Directory of Open Access Journals (Sweden)

Hui-Ling Niu

2013-07-01

Full Text Available In this paper we derive a lattice model with infinite distributed delay to describe the growth of a single-species population in a 2D patchy environment with infinite number of patches connected locally by diffusion and global interaction. We consider the existence of traveling wave solutions when the birth rate is large enough that each patch can sustain a positive equilibrium. When the birth function is monotone, we prove that there exists a traveling wave solution connecting two equilibria with wave speed $c>c^*(\\theta$ by using the monotone iterative method and super and subsolution technique, where $\\theta\\in [0,2\\pi]$ is any fixed direction of propagation. When the birth function is non-monotone, we prove the existence of non-trivial traveling wave solutions by constructing two auxiliary systems satisfying quasi-monotonicity.

Cnoidal waves as solutions of the nonlinear liquid drop model

International Nuclear Information System (INIS)

Ludu, Andrei; Sandulescu, Aureliu; Greiner Walter

1997-01-01

By introducing in the hydrodynamic model, i.e. in the hydrodynamic equation and the corresponding boundary conditions, the higher order terms in the deviation of the shape, we obtain in the second order the Korteweg de Vries equations (KdV). The same equation is obtained by introducing in the liquid drop model (LDM), i.e. in the kinetic, surface and Coulomb terms, the higher terms in the second order. The KdV equation has the cnoidal waves as steady-state solutions. These waves could describe the small anharmonic vibrations of spherical nuclei up to the solitary waves. The solitons could describe the preformation of clusters on the nuclear surface. We apply this nonlinear liquid drop model to the alpha formation in heavy nuclei. We find an additional minimum in the total energy of such systems, corresponding to the solitons as clusters on the nuclear surface. By introducing the shell effects we choose this minimum to be degenerated with the ground state. The spectroscopic factor is given by ratio of the square amplitudes in the two minima. (authors)

Prospects for Observing and Localizing Gravitational-Wave Transients with Advanced LIGO and Advanced Virgo

Science.gov (United States)

Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M. R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R. X.;

Prospects for Observing and Localizing Gravitational-Wave Transients with Advanced LIGO and Advanced Virgo

Science.gov (United States)

Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M. R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R. X.; Adya, V. B.; Affeldt, C.; Agathos, M.; Agatsuma, K.; Aggarwal, N.; Aguiar, O. D.; Ain, A.; Ajith, P.; Allen, B.; Allocca, A.; Altin, P. A.; Amariutei, D. V.; Anderson, S. B.; Anderson, W. G.; Arai, K.; Araya, M. C.; Arceneaux, C. C.; Areeda, J. S.; Arnaud, N.; Arun, K. G.; Ashton, G.; Ast, M.; Aston, S. M.; Astone, P.; Aufmuth, P.; Aulbert, C.; Babak, S.; Baker, P. T.; Baldaccini, F.; Ballardin, G.; Ballmer, S. W.; Barayoga, J. C.; Barclay, S. E.; Barish, B. C.; Barker, D.; Barone, F.; Barr, B.; Barsotti, L.; Barsuglia, M.; Barta, D.; Bartlett, J.; Bartos, I.; Bassiri, R.; Basti, A.; Batch, J. C.; Baune, C.; Bavigadda, V.; Bazzan, M.; Behnke, B.; Bejger, M.; Belczynski, C.; Bell, A. S.; Bell, C. J.; Berger, B. K.; Bergman, J.; Bergmann, G.; Berry, C. P. L.; Bersanetti, D.; Bertolini, A.; Betzwieser, J.; Bhagwat, S.; Bhandare, R.; Bilenko, I. A.; Billingsley, G.; Birch, J.; Birney, R.; Biscans, S.; Bisht, A.; Bitossi, M.; Biwer, C.; Bizouard, M. A.; Blackburn, J. K.; Blair, C. D.; Blair, D.; Blair, R. M.; Bloemen, S.; Bock, O.; Bodiya, T. P.; Boer, M.; Bogaert, G.; Bogan, C.; Bohe, A.; Bojtos, P.; Bond, C.; Bondu, F.; Bonnand, R.; Bork, R.; Boschi, V.; Bose, S.; Bozzi, A.; Bradaschia, C.; Brady, P. R.; Braginsky, V. B.; Branchesi, M.; Brau, J. E.; Briant, T.; Brillet, A.; Brinkmann, M.; Brisson, V.; Brockill, P.; Brooks, A. F.; Brown, D. A.; Brown, D. D.; Brown, N. M.; Buchanan, C. C.; Buikema, A.; Bulik, T.; Bulten, H. J.; Buonanno, A.; Buskulic, D.; Buy, C.; Byer, R. L.; Cadonati, L.; Cagnoli, G.; Cahillane, C.; Calderón Bustillo, J.; Callister, T.; Calloni, E.; Camp, J. B.; Cannon, K. C.; Cao, J.; Capano, C. D.; Capocasa, E.; Carbognani, F.; Caride, S.; Casanueva Diaz, J.; Casentini, C.; Caudill, S.; Cavaglià, M.; Cavalier, F.; Cavalieri, R.; Cella, G.; Cepeda, C.; Cerboni Baiardi, L.; Cerretani, G.; Cesarini, E.; Chakraborty, R.; Chalermsongsak, T.; Chamberlin, S. J.; Chan, M.; Chao, S.; Charlton, P.; Chassande-Mottin, E.; Chen, H. Y.; Chen, Y.; Cheng, C.; Chincarini, A.; Chiummo, A.; Cho, H. S.; Cho, M.; Chow, J. H.; Christensen, N.; Chu, Q.; Chua, S.; Chung, S.; Ciani, G.; Clara, F.; Clark, J. A.; Cleva, F.; Coccia, E.; Cohadon, P.-F.; Colla, A.; Collette, C. G.; Constancio, M.; Conte, A.; Conti, L.; Cook, D.; Corbitt, T. R.; Cornish, N.; Corsi, A.; Cortese, S.; Costa, C. A.; Coughlin, M. W.; Coughlin, S. B.; Coulon, J.-P.; Countryman, S. T.; Couvares, P.; Coward, D. M.; Cowart, M. J.; Coyne, D. C.; Coyne, R.; Craig, K.; Creighton, J. D. E.; Cripe, J.; Crowder, S. G.; Cumming, A.; Cunningham, L.; Cuoco, E.; Dal Canton, T.; Danilishin, S. L.; D'Antonio, S.; Danzmann, K.; Darman, N. S.; Dattilo, V.; Dave, I.; Daveloza, H. P.; Davier, M.; Davies, G. S.; Daw, E. J.; Day, R.; DeBra, D.; Debreczeni, G.; Degallaix, J.; De Laurentis, M.; Deléglise, S.; Del Pozzo, W.; Denker, T.; Dent, T.; Dereli, H.; Dergachev, V.; DeRosa, R.; De Rosa, R.; DeSalvo, R.; Dhurandhar, S.; Díaz, M. C.; Di Fiore, L.; Di Giovanni, M.; Di Lieto, A.; Di Palma, I.; Di Virgilio, A.; Dojcinoski, G.; Dolique, V.; Donovan, F.; Dooley, K. L.; Doravari, S.; Douglas, R.; Downes, T. P.; Drago, M.; Drever, R. W. P.; Driggers, J. C.; Du, Z.; Ducrot, M.; Dwyer, S. E.; Edo, T. B.; Edwards, M. C.; Effler, A.; Eggenstein, H.-B.; Ehrens, P.; Eichholz, J. M.; Eikenberry, S. S.; Engels, W.; Essick, R. C.; Etzel, T.; Evans, M.; Evans, T. M.; Everett, R.; Factourovich, M.; Fafone, V.; Fair, H.; Fairhurst, S.; Fan, X.; Fang, Q.; Farinon, S.; Farr, B.; Farr, W. M.; Favata, M.; Fays, M.; Fehrmann, H.; Fejer, M. M.; Ferrante, I.; Ferreira, E. C.; Ferrini, F.; Fidecaro, F.; Fiori, I.; Fisher, R. P.; Flaminio, R.; Fletcher, M.; Fournier, J.-D.; Franco, S.; Frasca, S.; Frasconi, F.; Frei, Z.; Freise, A.; Frey, R.; Fricke, T. T.; Fritschel, P.; Frolov, V. V.; Fulda, P.; Fyffe, M.; Gabbard, H. A. G.; Gair, J. R.; Gammaitoni, L.; Gaonkar, S. G.; Garufi, F.; Gatto, A.; Gaur, G.; Gehrels, N.; Gemme, G.; Gendre, B.; Genin, E.; Gennai, A.; George, J.; Gergely, L.; Germain, V.; Ghosh, A.; Ghosh, S.; Giaime, J. A.; Giardina, K. D.; Giazotto, A.; Gill, K.; Glaefke, A.; Goetz, E.; Goetz, R.; Gondan, L.; González, G.; Gonzalez Castro, J. M.; Gopakumar, A.; Gordon, N. A.; Gorodetsky, M. L.; Gossan, S. E.; Gosselin, M.; Gouaty, R.; Graef, C.; Graff, P. B.; Granata, M.; Grant, A.; Gras, S.; Gray, C.; Greco, G.; Green, A. C.; Groot, P.; Grote, H.; Grunewald, S.; Guidi, G. M.; Guo, X.; Gupta, A.; Gupta, M. K.; Gushwa, K. E.; Gustafson, E. K.; Gustafson, R.; Hacker, J. J.; Hall, B. R.; Hall, E. D.; Hammond, G.; Haney, M.; Hanke, M. M.; Hanks, J.; Hanna, C.; Hannam, M. D.; Hanson, J.; Hardwick, T.; Harms, J.; Harry, G. M.; Harry, I. W.; Hart, M. J.; Hartman, M. T.; Haster, C.-J.; Haughian, K.; Heidmann, A.; Heintze, M. C.; Heitmann, H.; Hello, P.; Hemming, G.; Hendry, M.; Heng, I. S.; Hennig, J.; Heptonstall, A. W.; Heurs, M.; Hild, S.; Hoak, D.; Hodge, K. A.; Hofman, D.; Hollitt, S. E.; Holt, K.; Holz, D. E.; Hopkins, P.; Hosken, D. J.; Hough, J.; Houston, E. A.; Howell, E. J.; Hu, Y. M.; Huang, S.; Huerta, E. A.; Huet, D.; Hughey, B.; Husa, S.; Huttner, S. H.; Huynh-Dinh, T.; Idrisy, A.; Indik, N.; Ingram, D. R.; Inta, R.; Isa, H. N.; Isac, J.-M.; Isi, M.; Islas, G.; Isogai, T.; Iyer, B. R.; Izumi, K.; Jacqmin, T.; Jang, H.; Jani, K.; Jaranowski, P.; Jawahar, S.; Jiménez-Forteza, F.; Johnson, W. W.; Jones, D. I.; Jones, R.; Jonker, R. J. G.; Ju, L.; K, Haris; Kalaghatgi, C. V.; Kalogera, V.; Kandhasamy, S.; Kang, G.; Kanner, J. B.; Karki, S.; Kasprzack, M.; Katsavounidis, E.; Katzman, W.; Kaufer, S.; Kaur, T.; Kawabe, K.; Kawazoe, F.; Kéfélian, F.; Kehl, M. S.; Keitel, D.; Kelley, D. B.; Kells, W.; Kennedy, R.; Key, J. S.; Khalaidovski, A.; Khalili, F. Y.; Khan, S.; Khan, Z.; Khazanov, E. A.; Kijbunchoo, N.; Kim, C.; Kim, J.; Kim, K.; Kim, N.; Kim, N.; Kim, Y.-M.; King, E. J.; King, P. J.; Kinzel, D. L.; Kissel, J. S.; Kleybolte, L.; Klimenko, S.; Koehlenbeck, S. M.; Kokeyama, K.; Koley, S.; Kondrashov, V.; Kontos, A.; Korobko, M.; Korth, W. Z.; Kowalska, I.; Kozak, D. B.; Kringel, V.; Krishnan, B.; Królak, A.; Krueger, C.; Kuehn, G.; Kumar, P.; Kuo, L.; Kutynia, A.; Lackey, B. D.; Landry, M.; Lange, J.; Lantz, B.; Lasky, P. D.; Lazzarini, A.; Lazzaro, C.; Leaci, P.; Leavey, S.; Lebigot, E.; Lee, C. H.; Lee, H. K.; Lee, H. M.; Lee, K.; Lenon, A.; Leonardi, M.; Leong, J. R.; Leroy, N.; Letendre, N.; Levin, Y.; Levine, B. M.; Li, T. G. F.; Libson, A.; Littenberg, T. B.; Lockerbie, N. A.; Logue, J.; Lombardi, A. L.; Lord, J. E.; Lorenzini, M.; Loriette, V.; Lormand, M.; Losurdo, G.; Lough, J. D.; Lück, H.; Lundgren, A. P.; Luo, J.; Lynch, R.; Ma, Y.; MacDonald, T.; Machenschalk, B.; MacInnis, M.; Macleod, D. M.; Magana-Sandoval, F.; Magee, R. M.; Mageswaran, M.; Majorana, E.; Maksimovic, I.; Malvezzi, V.; Man, N.; Mandel, I.; Mandic, V.; Mangano, V.; Mansell, G. L.; Manske, M.; Mantovani, M.; Marchesoni, F.; Marion, F.; Márka, S.; Márka, Z.; Markosyan, A. S.; Maros, E.; Martelli, F.; Martellini, L.; Martin, I. W.; Martin, R. M.; Martynov, D. V.; Marx, J. N.; Mason, K.; Masserot, A.; Massinger, T. J.; Masso-Reid, M.; Matichard, F.; Matone, L.; Mavalvala, N.; Mazumder, N.; Mazzolo, G.; McCarthy, R.; McClelland, D. E.; McCormick, S.; McGuire, S. C.; McIntyre, G.; McIver, J.; McManus, D. J.; McWilliams, S. T.; Meacher, D.; Meadors, G. D.; Meidam, J.; Melatos, A.; Mendell, G.; Mendoza-Gandara, D.; Mercer, R. A.; Merilh, E.; Merzougui, M.; Meshkov, S.; Messenger, C.; Messick, C.; Meyers, P. M.; Mezzani, F.; Miao, H.; Michel, C.; Middleton, H.; Mikhailov, E. E.; Milano, L.; Miller, J.; Millhouse, M.; Minenkov, Y.; Ming, J.; Mirshekari, S.; Mishra, C.; Mitra, S.; Mitrofanov, V. P.; Mitselmakher, G.; Mittleman, R.; Moggi, A.; Mohan, M.; Mohapatra, S. R. P.; Montani, M.; Moore, B. C.; Moore, C. J.; Moraru, D.; Moreno, G.; Morriss, S. R.; Mossavi, K.; Mours, B.; Mow-Lowry, C. M.; Mueller, C. L.; Mueller, G.; Muir, A. W.; Mukherjee, Arunava; Mukherjee, D.; Mukherjee, S.; Mullavey, A.; Munch, J.; Murphy, D. J.; Murray, P. G.; Mytidis, A.; Nardecchia, I.; Naticchioni, L.; Nayak, R. K.; Necula, V.; Nedkova, K.; Nelemans, G.; Neri, M.; Neunzert, A.; Newton, G.; Nguyen, T. T.; Nielsen, A. B.; Nissanke, S.; Nitz, A.; Nocera, F.; Nolting, D.; Normandin, M. E. N.; Nuttall, L. K.; Oberling, J.; Ochsner, E.; O'Dell, J.; Oelker, E.; Ogin, G. H.; Oh, J. J.; Oh, S. H.; Ohme, F.; Oliver, M.; Oppermann, P.; Oram, Richard J.; O'Reilly, B.; O'Shaughnessy, R.; Ott, C. D.; Ottaway, D. J.; Ottens, R. S.; Overmier, H.; Owen, B. J.; Pai, A.; Pai, S. A.; Palamos, J. R.; Palashov, O.; Palomba, C.; Pal-Singh, A.; Pan, H.; Pankow, C.; Pannarale, F.; Pant, B. C.; Paoletti, F.; Paoli, A.; Papa, M. A.; Paris, H. R.; Parker, W.; Pascucci, D.; Pasqualetti, A.; Passaquieti, R.; Passuello, D.; Patrick, Z.; Pearlstone, B. L.; Pedraza, M.; Pedurand, R.; Pekowsky, L.; Pele, A.; Penn, S.; Pereira, R.; Perreca, A.; Phelps, M.; Piccinni, O.; Pichot, M.; Piergiovanni, F.; Pierro, V.; Pillant, G.; Pinard, L.; Pinto, I. M.; Pitkin, M.; Poggiani, R.; Post, A.; Powell, J.; Prasad, J.; Predoi, V.; Premachandra, S. S.; Prestegard, T.; Price, L. R.; Prijatelj, M.; Principe, M.; Privitera, S.; Prodi, G. A.; Prokhorov, L.; Punturo, M.; Puppo, P.; Pürrer, M.; Qi, H.; Qin, J.; Quetschke, V.; Quintero, E. A.; Quitzow-James, R.; Raab, F. J.; Rabeling, D. S.; Radkins, H.; Raffai, P.; Raja, S.; Rakhmanov, M.; Rapagnani, P.; Raymond, V.; Razzano, M.; Re, V.; Read, J.; Reed, C. M.; Regimbau, T.; Rei, L.; Reid, S.; Reitze, D. H.; Rew, H.; Ricci, F.; Riles, K.; Robertson, N. A.; Robie, R.; Robinet, F.; Rocchi, A.; Rolland, L.; Rollins, J. G.; Roma, V. J.; Romano, J. D.; Romano, R.; Romanov, G.; Romie, J. H.; Rosińska, D.; Rowan, S.; Rüdiger, A.; Ruggi, P.; Ryan, K.; Sachdev, S.; Sadecki, T.; Sadeghian, L.; Saleem, M.; Salemi, F.; Samajdar, A.; Sammut, L.; Sanchez, E. J.; Sandberg, V.; Sandeen, B.; Sanders, J. R.; Sassolas, B.; Sathyaprakash, B. S.; Saulson, P. R.; Sauter, O.; Savage, R. L.; Sawadsky, A.; Schale, P.; Schilling, R.; Schmidt, J.; Schmidt, P.; Schnabel, R.; Schofield, R. M. S.; Schönbeck, A.; Schreiber, E.; Schuette, D.; Schutz, B. F.; Scott, J.; Scott, S. M.; Sellers, D.; Sentenac, D.; Sequino, V.; Sergeev, A.; Serna, G.; Setyawati, Y.; Sevigny, A.; Shaddock, D. A.; Shah, S.; Shahriar, M. S.; Shaltev, M.; Shao, Z.; Shapiro, B.; Shawhan, P.; Sheperd, A.; Shoemaker, D. H.; Shoemaker, D. M.; Siellez, K.; Siemens, X.; Sigg, D.; Silva, A. D.; Simakov, D.; Singer, A.; Singer, L. P.; Singh, A.; Singh, R.; Sintes, A. M.; Slagmolen, B. J. J.; Smith, J. R.; Smith, N. D.; Smith, R. J. E.; Son, E. J.; Sorazu, B.; Sorrentino, F.; Souradeep, T.; Srivastava, A. K.; Staley, A.; Steinke, M.; Steinlechner, J.; Steinlechner, S.; Steinmeyer, D.; Stephens, B. C.; Stone, R.; Strain, K. A.; Straniero, N.; Stratta, G.; Strauss, N. A.; Strigin, S.; Sturani, R.; Stuver, A. L.; Summerscales, T. Z.; Sun, L.; Sutton, P. J.; Swinkels, B. L.; Szczepanczyk, M. J.; Tacca, M.; Talukder, D.; Tanner, D. B.; Tápai, M.; Tarabrin, S. P.; Taracchini, A.; Taylor, R.; Theeg, T.; Thirugnanasambandam, M. P.; Thomas, E. G.; Thomas, M.; Thomas, P.; Thorne, K. A.; Thorne, K. S.; Thrane, E.; Tiwari, S.; Tiwari, V.; Tokmakov, K. V.; Tomlinson, C.; Tonelli, M.; Torres, C. V.; Torrie, C. I.; Töyrä, D.; Travasso, F.; Traylor, G.; Trifirò, D.; Tringali, M. C.; Trozzo, L.; Tse, M.; Turconi, M.; Tuyenbayev, D.; Ugolini, D.; Unnikrishnan, C. S.; Urban, A. L.; Usman, S. A.; Vahlbruch, H.; Vajente, G.; Valdes, G.; van Bakel, N.; van Beuzekom, M.; van den Brand, J. F. J.; van den Broeck, C.; Vander-Hyde, D. C.; van der Schaaf, L.; van der Sluys, M. V.; van Heijningen, J. V.; van Veggel, A. A.; Vardaro, M.; Vass, S.; Vasúth, M.; Vaulin, R.; Vecchio, A.; Vedovato, G.; Veitch, J.; Veitch, P. J.; Venkateswara, K.; Verkindt, D.; Vetrano, F.; Viceré, A.; Vinciguerra, S.; Vine, D. J.; Vinet, J.-Y.; Vitale, S.; Vo, T.; Vocca, H.; Vorvick, C.; Vousden, W. D.; Vyatchanin, S. P.; Wade, A. R.; Wade, L. E.; Wade, M.; Walker, M.; Wallace, L.; Walsh, S.; Wang, G.; Wang, H.; Wang, M.; Wang, X.; Wang, Y.; Ward, R. L.; Warner, J.; Was, M.; Weaver, B.; Wei, L.-W.; Weinert, M.; Weinstein, A. J.; Weiss, R.; Welborn, T.; Wen, L.; Weßels, P.; Westphal, T.; Wette, K.; Whelan, J. T.; White, D. J.; Whiting, B. F.; Williams, R. D.; Williamson, A. R.; Willis, J. L.; Willke, B.; Wimmer, M. H.; Winkler, W.; Wipf, C. C.; Wittel, H.; Woan, G.; Worden, J.; Wright, J. L.; Wu, G.; Yablon, J.; Yam, W.; Yamamoto, H.; Yancey, C. C.; Yap, M. J.; Yu, H.; Yvert, M.; Zadrożny, A.; Zangrando, L.; Zanolin, M.; Zendri, J.-P.; Zevin, M.; Zhang, F.; Zhang, L.; Zhang, M.; Zhang, Y.; Zhao, C.; Zhou, M.; Zhou, Z.; Zhu, X. J.; Zucker, M. E.; Zuraw, S. E.; Zweizig, J.; LIGO Scientific Collaboration; Virgo Collaboration

2016-02-01

We present a possible observing scenario for the Advanced LIGO and Advanced Virgo gravitational-wave detectors over the next decade, with the intention of providing information to the astronomy community to facilitate planning for multi-messenger astronomy with gravitational waves. We determine the expected sensitivity of the network to transient gravitational-wave signals, and study the capability of the network to determine the sky location of the source. We report our findings for gravitational-wave transients, with particular focus on gravitational-wave signals from the inspiral of binary neutron-star systems, which are considered the most promising for multi-messenger astronomy. The ability to localize the sources of the detected signals depends on the geographical distribution of the detectors and their relative sensitivity, and 90% credible regions can be as large as thousands of square degrees when only two sensitive detectors are operational. Determining the sky position of a significant fraction of detected signals to areas of 5 deg2 to 20 deg2 will require at least three detectors of sensitivity within a factor of ˜ 2 of each other and with a broad frequency bandwidth. Should the third LIGO detector be relocated to India as expected, a significant fraction of gravitational-wave signals will be localized to a few square degrees by gravitational-wave observations alone.

Travelling wave solutions of the Schamel–Korteweg–de Vries and the Schamel equations

Directory of Open Access Journals (Sweden)

Figen Kangalgil

2016-10-01

Full Text Available In this paper, the extended (G′/G-expansion method has been suggested for constructing travelling wave solutions of the Schamel–Korteweg–de Vries (s-KdV and the Schamel equations with aid of computer systems like Maple or Mathematica. The hyperbolic function solutions and the trigonometric function solutions with free parameters of these equations have been obtained. Moreover, it has been shown that the suggested method is elementary, effective and has been used to solve nonlinear evolution equations in applied mathematics, engineering and mathematical physics.

Solution of wave-like equation based on Haar wavelet

Directory of Open Access Journals (Sweden)

Naresh Berwal

2012-11-01

Full Text Available Wavelet transform and wavelet analysis are powerful mathematical tools for many problems. Wavelet also can be applied in numerical analysis. In this paper, we apply Haar wavelet method to solve wave-like equation with initial and boundary conditions known. The fundamental idea of Haar wavelet method is to convert the differential equations into a group of algebraic equations, which involves a finite number or variables. The results and graph show that the proposed way is quite reasonable when compared to exact solution.

Shock formation in small-data solutions to 3D quasilinear wave equations

CERN Document Server

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...

Methylparaben concentration in commercial Brazilian local anesthetics solutions

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Gustavo Henrique Rodriguez da Silva

2012-08-01

Full Text Available OBJECTIVE: To detect the presence and concentration of methylparaben in cartridges of commercial Brazilian local anesthetics. MATERIAL AND METHODS: Twelve commercial brands (4 in glass and 8 in plastic cartridges of local anesthetic solutions for use in dentistry were purchased from the Brazilian market and analyzed. Different lots of the commercial brands were obtained in different Brazilian cities (Piracicaba, Campinas and São Paulo. Separation was performed using high performance liquid chromatography (HPLC with UV-Vis detector. The mobile phase used was acetonitrile:water (75:25 - v/v, pH 4.5, adjusted with acetic acid at a flow rate of 1.0 ml.min-1. RESULTS: When detected in the solutions, the methylparaben concentration ranged from 0.01% (m/v to 0.16% (m/v. One glass and all plastic cartridges presented methylparaben. CONCLUSION: 1. Methylparaben concentration varied among solutions from different manufacturers, and it was not indicated in the drug package inserts; 2. Since the presence of methylparaben in dental anesthetics is not regulated by the Brazilian National Health Surveillance Agency (ANVISA and this substance could cause allergic reactions, it is important to alert dentists about its possible presence.

A high-order discontinuous Galerkin method for wave propagation through coupled elastic-acoustic media

International Nuclear Information System (INIS)

Wilcox, Lucas C.; Stadler, Georg; Burstedde, Carsten; Ghattas, Omar

2010-01-01

We introduce a high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in coupled elastic-acoustic media. A velocity-strain formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same unified framework. Careful attention is directed at the derivation of a numerical flux that preserves high-order accuracy in the presence of material discontinuities, including elastic-acoustic interfaces. Explicit expressions for the 3D upwind numerical flux, derived as an exact solution for the relevant Riemann problem, are provided. The method supports h-non-conforming meshes, which are particularly effective at allowing local adaptation of the mesh size to resolve strong contrasts in the local wavelength, as well as dynamic adaptivity to track solution features. The use of high-order elements controls numerical dispersion, enabling propagation over many wave periods. We prove consistency and stability of the proposed dG scheme. To study the numerical accuracy and convergence of the proposed method, we compare against analytical solutions for wave propagation problems with interfaces, including Rayleigh, Lamb, Scholte, and Stoneley waves as well as plane waves impinging on an elastic-acoustic interface. Spectral rates of convergence are demonstrated for these problems, which include a non-conforming mesh case. Finally, we present scalability results for a parallel implementation of the proposed high-order dG scheme for large-scale seismic wave propagation in a simplified earth model, demonstrating high parallel efficiency for strong scaling to the full size of the Jaguar Cray XT5 supercomputer.

Electromagnetic Waves with Frequencies Near the Local Proton Gryofrequency: ISEF-3 1 AU Observations

Science.gov (United States)

Tsurutani, B.

1993-01-01

Low Frequency electromagnetic waves with periods near the local proton gyrofrequency have been detected near 1 AU by the magnetometer onboard ISEE-3. For these 1 AU waves two physical processes are possible: solar wind pickup of nuetral (interstellar?) particles and generation by relativistic electron beams propagating from the Sun.

Drift waves in a stellarator

International Nuclear Information System (INIS)

Bhattacharjee, A.; Sedlak, J.E.; Similon, P.L.; Rosenbluth, M.N.; Ross, D.W.

1982-11-01

We investigate the eigenmode structure of drift waves in a straight stellarator using the ballooning mode formalism. The electrons are assumed to be adiabatic and the ions constitute a cold, magnetized fluid. The effective potential has an overall parabolic envelope but is modulated strongly by helical ripples along B. We have found two classes of solutions: those that are strongly localized in local helical wells, and those that are weakly localized and have broad spatial extent. The weakly localized modes decay spatially due to the existence of Mathieu resonances between the periods of the eigenfunction and the effective potential

Multi-soliton and rogue-wave solutions of the higher-order Hirota system for an erbium-doped nonlinear fiber

Energy Technology Data Exchange (ETDEWEB)

Zuo, Da-Wei [Beijing University of Aeronautics and Astronautics, Beijing (China). State Key Laboratory of Software Development Environment; Ministry of Education, Beijing (China). Key Laboratory of Fluid Mechanics; Shijiazhuang Tiedao University (China). Dept. of Mathematics and Physics; Gao, Yi-Tian; Sun, Yu-Hao; Feng, Yu-Jie; Xue, Long [Beijing University of Aeronautics and Astronautics, Beijing (China). State Key Laboratory of Software Development Environment; Ministry of Education, Beijing (China). Key Laboratory of Fluid Mechanics

2014-10-15

The nonlinear Schroedinger (NLS) equation appears in fluid mechanics, plasma physics, etc., while the Hirota equation, a higher-order NLS equation, has been introduced. In this paper, a higher-order Hirota system is investigated, which describes the wave propagation in an erbium-doped nonlinear fiber with higher-order dispersion. By virtue of the Darboux transformation and generalized Darboux transformation, multi-soliton solutions and higher-order rogue-wave solutions are derived, beyond the published first-order consideration. Wave propagation and interaction are analyzed: (i) Bell-shape solitons, bright- and dark-rogue waves are found; (ii) the two-soliton interaction is elastic, i.e., the amplitude and velocity of each soliton remain unchanged after the interaction; (iii) the coefficient in the system affects the direction of the soliton propagation, patterns of the soliton interaction, distance, and direction of the first-order rogue-wave propagation, as well as the range and direction of the second-order rogue-wave interaction.

The Peano-series solution for modeling shear horizontal waves in piezoelectric plates

Directory of Open Access Journals (Sweden)

Ben Ghozlen M.H.

2012-06-01

Full Text Available The shear horizontal (SH wave devices have been widely used in electroacoustic. To improve their performance, the phase velocity dispersion and the electromechanical coupling coefficient of the Lamb wave should be calculated exactly in the design. Therefore, this work is to analyze exactly the Lamb waves polarized in the SH direction in homogeneous plate pie.zoelectric material (PZT-5H. An alternative method is proposed to solve the wave equation in such a structure without using the standard method based on the electromechanical partial waves. This method is based on an analytical solution, the matricant explicitly expressed under the Peano series expansion form. Two types of configuration have been addressed, namely the open circuited and the short circuited. Results confirm that the SH wave provides a number of attractive properties for use in sensing and signal processing applications. It has been found that the phase velocity remains nearly constant for all values of h/λ (h is the plate thickness, λ the acoustic wavelength. Secondly the SH0 wave mode can provide very high electromechanical coupling. Graphical representations of electrical and mechanical amounts function of depth are made, they are in agreement with the continuity rules. The developed Peano technique is in agreement with the classical approach, and can be suitable with cylindrical geometry.

Matter-wave solitons and finite-amplitude Bloch waves in optical lattices with a spatially modulated nonlinearity

OpenAIRE

Zhang, Jie-Fang; Li, Yi-Shen; Meng, Jianping; Wu, Lei; Malomed, Boris A.

2010-01-01

We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices. By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite number of exact soliton solutions in terms of the Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite bandgap of the optical-lattice-induced spectrum. Starting from the exact solutions, we employ the relaxation met...

Gravitational-wave localization alone can probe origin of stellar-mass black hole mergers.

Science.gov (United States)

Bartos, I; Haiman, Z; Marka, Z; Metzger, B D; Stone, N C; Marka, S

2017-10-10

The recent discovery of gravitational waves from stellar-mass binary black hole mergers by the Laser Interferometer Gravitational-wave Observatory opened the door to alternative probes of stellar and galactic evolution, cosmology and fundamental physics. Probing the origin of binary black hole mergers will be difficult due to the expected lack of electromagnetic emission and limited localization accuracy. Associations with rare host galaxy types-such as active galactic nuclei-can nevertheless be identified statistically through spatial correlation. Here we establish the feasibility of statistically proving the connection between binary black hole mergers and active galactic nuclei as hosts, even if only a sub-population of mergers originate from active galactic nuclei. Our results are the demonstration that the limited localization of gravitational waves, previously written off as not useful to distinguish progenitor channels, can in fact contribute key information, broadening the range of astrophysical questions probed by binary black hole observations.Binary black hole mergers have recently been observed through the detection of gravitational wave signatures. The authors demonstrate that their association with active galactic nuclei can be made through a statistical spatial correlation.

Travelling wave solutions for an infection-age structured epidemic model with external supplies

International Nuclear Information System (INIS)

Ducrot, Arnaud; Magal, Pierre

2011-01-01

The aim of this paper is to investigate the spatial invasion of some infectious disease. The contamination process is described by the age since infection. Compared with the classical Kermack and McKendrick's model, the vital dynamic is not omitted, and we allow some constant input flux into the population. This problem is rather natural in the context of epidemic problems and it has not been studied. Here we prove an existence and non-existence result for travelling wave solutions. We also describe the minimal wave speed. We are able to construct a suitable Lyapunov like functional decreasing along the travelling wave allowing to derive some qualitative properties, namely their convergence towards equilibrium points at x = ±∞

High frequency asymptotic solutions of the reduced wave equation on infinite regions with non-convex boundaries

Directory of Open Access Journals (Sweden)

Bloom Clifford O.

1996-01-01

Full Text Available The asymptotic behavior as λ → ∞ of the function U ( x , λ that satisfies the reduced wave equation L λ [ U ] = ∇ ⋅ ( E ( x ∇ U + λ 2 N 2 ( x U = 0 on an infinite 3-dimensional region, a Dirichlet condition on ∂ V , and an outgoing radiation condition is investigated. A function U N ( x , λ is constructed that is a global approximate solution as λ → ∞ of the problem satisfied by U ( x , λ . An estimate for W N ( x , λ = U ( x , λ − U N ( x , λ on V is obtained, which implies that U N ( x , λ is a uniform asymptotic approximation of U ( x , λ as λ → ∞ , with an error that tends to zero as rapidly as λ − N ( N = 1 , 2 , 3 , ... . This is done by applying a priori estimates of the function W N ( x , λ in terms of its boundary values, and the L 2 norm of r L λ [ W N ( x , λ ] on V . It is assumed that E ( x , N ( x , ∂ V and the boundary data are smooth, that E ( x − I and N ( x − 1 tend to zero algebraically fast as r → ∞ , and finally that E ( x and N ( x are slowly varying; ∂ V may be finite or infinite. The solution U ( x , λ can be interpreted as a scalar potential of a high frequency acoustic or electromagnetic field radiating from the boundary of an impenetrable object of general shape. The energy of the field propagates through an inhomogeneous, anisotropic medium; the rays along which it propagates may form caustics. The approximate solution (potential derived in this paper is defined on and in a neighborhood of any such caustic, and can be used to connect local “geometrical optics” type approximate solutions that hold on caustic free subsets of V .The result of this paper generalizes previous work of Bloom and Kazarinoff [C. O. BLOOM and N. D. KAZARINOFF, Short Wave Radiation Problems in Inhomogeneous Media: Asymptotic Solutions, SPRINGER VERLAG, NEW YORK, NY, 1976].

Atom localization and center-of-mass wave-function determination via multiple simultaneous quadrature measurements

International Nuclear Information System (INIS)

Evers, Joerg; Qamar, Shahid; Zubairy, M. Suhail

2007-01-01

We discuss localization and center-of-mass wave-function measurement of a quantum particle using multiple simultaneous dispersive interactions of the particle with different standing-wave fields. In particular, we consider objects with an internal structure consisting of a single ground state and several excited states. The transitions between ground and the corresponding excited states are coupled to the light fields in the dispersive limit, thus giving rise to a phase shift of the light field during the interaction. We show that multiple simultaneous measurements allow both an increase in the measurement or localization precision in a single direction and the performance of multidimensional measurements or localization. Further, we show that multiple measurements may relax the experimental requirements for each individual measurement

Solution of inverse localization problem associated to multistatic radar system

Directory of Open Access Journals (Sweden)

Boutkhil M.

2016-01-01

Full Text Available This work deals with the problem of inverse localization by a target with the aim to retrieve the position of the target, given the intensity and phase of the electromagnetic waves scattered by this object. Assuming the surface cross section to be known as well as the intensity and phase of the scattered waves, the target position was reconstructed through the echo signals scattered of each bistatic. We develop in the same time a multistatic ambiguity function trough bistatic ambiguity function to investigate several fundamental aspects that determine multistatic radar performance. We used a multistatic radar constructed of two bistatic radars, two transmitters and one receiver.

Exact solitary wave solution for higher order nonlinear Schrodinger equation using He's variational iteration method

Science.gov (United States)

Rani, Monika; Bhatti, Harbax S.; Singh, Vikramjeet

2017-11-01

In optical communication, the behavior of the ultrashort pulses of optical solitons can be described through nonlinear Schrodinger equation. This partial differential equation is widely used to contemplate a number of physically important phenomena, including optical shock waves, laser and plasma physics, quantum mechanics, elastic media, etc. The exact analytical solution of (1+n)-dimensional higher order nonlinear Schrodinger equation by He's variational iteration method has been presented. Our proposed solutions are very helpful in studying the solitary wave phenomena and ensure rapid convergent series and avoid round off errors. Different examples with graphical representations have been given to justify the capability of the method.

Solution of the nonrelativistic wave equation using the tridiagonal representation approach

Science.gov (United States)

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.

Nonlinear Waves in the Terrestrial Quasiparallel Foreshock.

Science.gov (United States)

Hnat, B; Kolotkov, D Y; O'Connell, D; Nakariakov, V M; Rowlands, G

2016-12-02

We provide strongly conclusive evidence that the cubic nonlinearity plays an important part in the evolution of the large amplitude magnetic structures in the terrestrial foreshock. Large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency are identified after nonharmonic slow variations are filtered out by applying the empirical mode decomposition. Numerical solutions of the derivative nonlinear Schrödinger equation, predicted analytically by the use of a pseudopotential approach, are found to be consistent with the observed wave forms. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfvén speed. We suggest that the feedback of the large amplitude fluctuations on background plasma is reflected in the evolution of the pseudopotential.

On exact solitary wave solutions of the nonlinear Schroedinger equation with a source

International Nuclear Information System (INIS)

Raju, T Solomon; Kumar, C Nagaraja; Panigrahi, Prasanta K

2005-01-01

We use a fractional transformation to connect the travelling wave solutions of the nonlinear Schroedinger equation (NLSE), phase locked with a source, to the elliptic equations satisfying, f-Prime ± af ± λf 3 = 0. The solutions are necessarily of rational form, containing both trigonometric and hyperbolic types as special cases. Bright and dark solitons, as well as singular solitons, are obtained in a suitable range of parameter values. (letter to the editor)

Construction of localized atomic wave packets

International Nuclear Information System (INIS)

Ranjani, S Sree; Kapoor, A K; Panigrahi, P K

2010-01-01

It is shown that highly localized solitons can be created in lower dimensional Bose-Einstein condensates (BECs), trapped in a regular harmonic trap, by temporally varying the trap frequency. A BEC confined in such a trap can be effectively used to construct a pulsed atomic laser emitting coherent atomic wave packets. In addition to having a complete control over the spatio-temporal dynamics of the solitons, we can separate the equation governing the Kohn mode (centre of mass motion). We investigate the effect of the temporal modulation of the trap frequency on the spatio-temporal dynamics of the bright solitons and also on the Kohn mode. The dynamics of the solitons and the variations in the Kohn mode with time are compared with those in a BEC confined in a trap with unmodulated trap frequency.

Wind wave source functions in opposing seas

KAUST Repository

Langodan, Sabique; Cavaleri, Luigi; Viswanadhapalli, Yesubabu; Hoteit, Ibrahim

2015-01-01

that the currently available wave model source functions may not properly represent the evolution of the local fields that appear to be characterized by a less effective wind input and an enhanced white-capping. We propose and test a possible simple solution

Elastic wave localization in two-dimensional phononic crystals with one-dimensional random disorder and aperiodicity

International Nuclear Information System (INIS)

Yan Zhizhong; Zhang Chuanzeng; Wang Yuesheng

2011-01-01

The band structures of in-plane elastic waves propagating in two-dimensional phononic crystals with one-dimensional random disorder and aperiodicity are analyzed in this paper. The localization of wave propagation is discussed by introducing the concept of the localization factor, which is calculated by the plane-wave-based transfer-matrix method. By treating the random disorder and aperiodicity as the deviation from the periodicity in a special way, three kinds of aperiodic phononic crystals that have normally distributed random disorder, Thue-Morse and Rudin-Shapiro sequence in one direction and translational symmetry in the other direction are considered and the band structures are characterized using localization factors. Besides, as a special case, we analyze the band gap properties of a periodic planar layered composite containing a periodic array of square inclusions. The transmission coefficients based on eigen-mode matching theory are also calculated and the results show the same behaviors as the localization factor does. In the case of random disorders, the localization degree of the normally distributed random disorder is larger than that of the uniformly distributed random disorder although the eigenstates are both localized no matter what types of random disorders, whereas, for the case of Thue-Morse and Rudin-Shapiro structures, the band structures of Thue-Morse sequence exhibit similarities with the quasi-periodic (Fibonacci) sequence not present in the results of the Rudin-Shapiro sequence.

Computing wave functions in multichannel collisions with non-local potentials using the R-matrix method

Science.gov (United States)

Bonitati, Joey; Slimmer, Ben; Li, Weichuan; Potel, Gregory; Nunes, Filomena

2017-09-01

The calculable form of the R-matrix method has been previously shown to be a useful tool in approximately solving the Schrodinger equation in nuclear scattering problems. We use this technique combined with the Gauss quadrature for the Lagrange-mesh method to efficiently solve for the wave functions of projectile nuclei in low energy collisions (1-100 MeV) involving an arbitrary number of channels. We include the local Woods-Saxon potential, the non-local potential of Perey and Buck, a Coulomb potential, and a coupling potential to computationally solve for the wave function of two nuclei at short distances. Object oriented programming is used to increase modularity, and parallel programming techniques are introduced to reduce computation time. We conclude that the R-matrix method is an effective method to predict the wave functions of nuclei in scattering problems involving both multiple channels and non-local potentials. Michigan State University iCER ACRES REU.

Localization of gravitational wave sources with networks of advanced detectors

International Nuclear Information System (INIS)

Klimenko, S.; Mitselmakher, G.; Pankow, C.; Vedovato, G.; Drago, M.; Prodi, G.; Mazzolo, G.; Salemi, F.; Re, V.; Yakushin, I.

2011-01-01

Coincident observations with gravitational wave (GW) detectors and other astronomical instruments are among the main objectives of the experiments with the network of LIGO, Virgo, and GEO detectors. They will become a necessary part of the future GW astronomy as the next generation of advanced detectors comes online. The success of such joint observations directly depends on the source localization capabilities of the GW detectors. In this paper we present studies of the sky localization of transient GW sources with the future advanced detector networks and describe their fundamental properties. By reconstructing sky coordinates of ad hoc signals injected into simulated detector noise, we study the accuracy of the source localization and its dependence on the strength of injected signals, waveforms, and network configurations.

A non-local computational boundary condition for duct acoustics

Science.gov (United States)

Zorumski, William E.; Watson, Willie R.; Hodge, Steve L.

1994-01-01

A non-local boundary condition is formulated for acoustic waves in ducts without flow. The ducts are two dimensional with constant area, but with variable impedance wall lining. Extension of the formulation to three dimensional and variable area ducts is straightforward in principle, but requires significantly more computation. The boundary condition simulates a nonreflecting wave field in an infinite duct. It is implemented by a constant matrix operator which is applied at the boundary of the computational domain. An efficient computational solution scheme is developed which allows calculations for high frequencies and long duct lengths. This computational solution utilizes the boundary condition to limit the computational space while preserving the radiation boundary condition. The boundary condition is tested for several sources. It is demonstrated that the boundary condition can be applied close to the sound sources, rendering the computational domain small. Computational solutions with the new non-local boundary condition are shown to be consistent with the known solutions for nonreflecting wavefields in an infinite uniform duct.

Asymptotic behaviors of solutions for viscoelastic wave equation with space-time dependent damping term

KAUST Repository

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.

Asymptotic behaviors of solutions for viscoelastic wave equation with space-time dependent damping term

KAUST Repository

Said-Houari, Belkacem

2012-01-01

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.

Computation of High-Frequency Waves with Random Uncertainty

KAUST Repository

Malenova, Gabriela

2016-01-06

We consider the forward propagation of uncertainty in high-frequency waves, described by the second order wave equation with highly oscillatory initial data. The main sources of uncertainty are the wave speed and/or the initial phase and amplitude, described by a finite number of random variables with known joint probability distribution. We propose a stochastic spectral asymptotic method [1] for computing the statistics of uncertain output quantities of interest (QoIs), which are often linear or nonlinear functionals of the wave solution and its spatial/temporal derivatives. The numerical scheme combines two techniques: a high-frequency method based on Gaussian beams [2, 3], a sparse stochastic collocation method [4]. The fast spectral convergence of the proposed method depends crucially on the presence of high stochastic regularity of the QoI independent of the wave frequency. In general, the high-frequency wave solutions to parametric hyperbolic equations are highly oscillatory and non-smooth in both physical and stochastic spaces. Consequently, the stochastic regularity of the QoI, which is a functional of the wave solution, may in principle below and depend on frequency. In the present work, we provide theoretical arguments and numerical evidence that physically motivated QoIs based on local averages of |uE|2 are smooth, with derivatives in the stochastic space uniformly bounded in E, where uE and E denote the highly oscillatory wave solution and the short wavelength, respectively. This observable related regularity makes the proposed approach more efficient than current asymptotic approaches based on Monte Carlo sampling techniques.

Drift wave coherent vortex structures in inhomogeneous plasmas

International Nuclear Information System (INIS)

Su, X.N.

1992-01-01

Nonlinear drift wave vortex structures in magnetized plasmas are studied theoretically and numerically in the various physical environments. The effects of density and temperature gradients on drift wave vortex dynamics are analyzed using a fully nonlinear model with the Boltzmann density distribution. The equation, based on the full Boltzmann relation, possess no localized monopole solution in the short wavelength (∼ρ s ) region, while in the longer wavelength (∼(ρ s (r) n ) 1/2 ) region the density profile governs the existence of monopole-like solutions. In the longer wavelength regime, however, the monopoles cannot be localized sufficiently to avoid coupling to propagating drift waves due to the inhomogeneity of the plasma. Thus, the monopole vortex is a long lived coherent structure, but it is not precisely a stationary structure since the coupling results in a open-quote flapping close-quote tail. The tail causes energy of the vortex to leak out, but the effect of the temperature gradient is to reduce the leaking of this energy. Nonlinear coherent structures governing by the coupled drift wave-ion acoustic mode equations in sheared magnetic field are studied analytically and numerically. A solitary vortex equation that includes the effects of density and temperature gradients and magnetic shear is derived and analyzed. The results show that for a plasma in a sheared magnetic field, there exist the solitary vortex solutions. The new vortex structures are dipole-like in their symmetry, but not the modon type of dipoles. The numerical simulations are performed in 2-D with the coupled vorticity and parallel mass flow equations. The vortex structures in an unstable drift wave system driven by parallel shear flow are studied. The nonlinear solitary vortex solutions are given and the formation of the vortices from a turbulent state is observed from the numerical simulations

Group Velocity for Leaky Waves

Science.gov (United States)

Rzeznik, Andrew; Chumakova, Lyubov; Rosales, Rodolfo

2017-11-01

In many linear dispersive/conservative wave problems one considers solutions in an infinite medium which is uniform everywhere except for a bounded region. In general, localized inhomogeneities of the medium cause partial internal reflection, and some waves leak out of the domain. Often one only desires the solution in the inhomogeneous region, with the exterior accounted for by radiation boundary conditions. Formulating such conditions requires definition of the direction of energy propagation for leaky waves in multiple dimensions. In uniform media such waves have the form exp (d . x + st) where d and s are complex and related by a dispersion relation. A complex s is required since these waves decay via radiation to infinity, even though the medium is conservative. We present a modified form of Whitham's Averaged Lagrangian Theory along with modulation theory to extend the classical idea of group velocity to leaky waves. This allows for solving on the bounded region by representing the waves as a linear combination of leaky modes, each exponentially decaying in time. This presentation is part of a joint project, and applications of these results to example GFD problems will be presented by L. Chumakova in the talk ``Leaky GFD Problems''. This work is partially supported by NSF Grants DMS-1614043, DMS-1719637, and 1122374, and by the Hertz Foundation.

A self-similar solution of a curved shock wave and its time-dependent force variation for a starting flat plate airfoil in supersonic flow

Directory of Open Access Journals (Sweden)

Zijun CHEN

2018-02-01

Full Text Available The problem of aeroelasticity and maneuvering of command surface and gust wing interaction involves a starting flow period which can be seen as the flow of an airfoil attaining suddenly an angle of attack. In the linear or nonlinear case, compressive Mach or shock waves are generated on the windward side and expansive Mach or rarefaction waves are generated on the leeward side. On each side, these waves are composed of an oblique steady state wave, a vertically-moving one-dimensional unsteady wave, and a secondary wave resulting from the interaction between the steady and unsteady ones. An analytical solution in the secondary wave has been obtained by Heaslet and Lomax in the linear case, and this linear solution has been borrowed to give an approximate solution by Bai and Wu for the nonlinear case. The structure of the secondary shock wave and the appearance of various force stages are two issues not yet considered in previous studies and has been studied in the present paper. A self-similar solution is obtained for the secondary shock wave, and the reason to have an initial force plateau as observed numerically is identified. Moreover, six theoretical characteristic time scales for pressure load variation are determined which explain the slope changes of the time-dependent force curve. Keywords: Force, Self-similar solution, Shock-shock interaction, Shock waves, Unsteady flow

New travelling wave solutions of the (1 + 1-dimensional cubic nonlinear Schrodinger equation using novel (G′/G-expansion method

Directory of Open Access Journals (Sweden)

M.G. Hafez

2016-06-01

Full Text Available In this paper, the novel (G′/G-expansion method is applied to construct exact travelling wave solutions of the cubic nonlinear Schrodinger equation. This technique is straightforward and simple to use, and gives more new general solutions than the other existing methods. Various types of solitary and periodic wave solutions of this equation are derived. The obtained results may be helpful to describe the wave propagation in soliton physics, such as soliton propagation in optical fibers, modulus instability in plasma physics, etc. and provided us the firm mathematical foundation in soliton physics or any varied instances. Furthermore, three-dimensional modules plot of the solutions are also given to visualize the dynamics of the equation.

Wave propagation in a non-isothermal atmosphere and the solar five-minute oscillations. [Acoustic waves

Energy Technology Data Exchange (ETDEWEB)

Chiuderi, C; Giovanardi, C [Florence Univ. (Italy). Istituto di Astronomia

1979-11-01

This paper presents a detailed discussion of the properties of linear, periodic acoustic waves that propagate vertically in a non-isothermal atmosphere. In order to retain the basic feature of the solar atmosphere we have chosen a temperature profile presenting a minimum. An analytical solution of the problem is possible if T/..mu.., ..mu.. being the mean molecular weight, varies parabolically with height. The purpose of this study is to point out the qualitative differences existing between the case treated here and the customary analysis based on a locally isothermal treatment. The computed velocity amplitude and the temperature-perturbation as functions of the wave period exhibit a sharp peak in the region between 180 and 300 s, thus showing the possibility of interpreting the five-minute oscillations as a resonant phenomenon. The propagating or stationary nature of the waves is investigated by a study of the phase of the proposed analytical solution.

Travelling wave solutions of the homogeneous one-dimensional FREFLO model

Science.gov (United States)

Huang, B.; Hong, J. Y.; Jing, G. Q.; Niu, W.; Fang, L.

2018-01-01

Presently there is quite few analytical studies in traffic flows due to the non-linearity of the governing equations. In the present paper we introduce travelling wave solutions for the homogeneous one-dimensional FREFLO model, which are expressed in the form of series and describe the procedure that vehicles/pedestrians move with a negative velocity and decelerate until rest, then accelerate inversely to positive velocities. This method is expect to be extended to more complex situations in the future.

Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains

Science.gov (United States)

Przedborski, Michelle; Anco, Stephen C.

2017-09-01

A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.

Propagation of a linear wave created by a spatially localized perturbation in a regular lattice and punctured Lagrangian manifolds

Science.gov (United States)

Dobrokhotov, S. Yu.; Nazaikinskii, V. E.

2017-01-01

The following results are obtained for the Cauchy problem with localized initial data for the crystal lattice vibration equations with continuous and discrete time: (i) the asymptotics of the solution is determined by Lagrangian manifolds with singularities ("punctured" Lagrangian manifolds); (ii) Maslov's canonical operator is defined on such manifolds as a modification of a new representation recently obtained for the canonical operator by the present authors together with A. I. Shafarevich (Dokl. Ross. Akad. Nauk 46 (6), 641-644 (2016)); (iii) the projection of the Lagrangian manifold onto the configuration plane specifies a bounded oscillation region, whose boundary (which is naturally referred to as the leading edge front) is determined by the Hamiltonians corresponding to the limit wave equations; (iv) the leading edge front is a special caustic, which possibly contains stronger focal points. These observations, together with earlier results, lead to efficient formulas for the wave field in a neighborhood of the leading edge front.

Exact density functional and wave function embedding schemes based on orbital localization

International Nuclear Information System (INIS)

Hégely, Bence; Nagy, Péter R.; Kállay, Mihály; Ferenczy, György G.

2016-01-01

Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.

Exact density functional and wave function embedding schemes based on orbital localization

Science.gov (United States)

Hégely, Bence; Nagy, Péter R.; Ferenczy, György G.; Kállay, Mihály

2016-08-01

Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.

Exact density functional and wave function embedding schemes based on orbital localization

Energy Technology Data Exchange (ETDEWEB)

Hégely, Bence; Nagy, Péter R.; Kállay, Mihály, E-mail: kallay@mail.bme.hu [MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest (Hungary); Ferenczy, György G. [Medicinal Chemistry Research Group, Research Centre for Natural Sciences, Hungarian Academy of Sciences, Magyar tudósok körútja 2, H-1117 Budapest (Hungary); Department of Biophysics and Radiation Biology, Semmelweis University, Tűzoltó u. 37-47, H-1094 Budapest (Hungary)

2016-08-14

Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.

Six-dimensional localized black holes: Numerical solutions

International Nuclear Information System (INIS)

Kudoh, Hideaki

2004-01-01

To test the strong-gravity regime in Randall-Sundrum braneworlds, we consider black holes bound to a brane. In a previous paper, we studied numerical solutions of localized black holes whose horizon radii are smaller than the AdS curvature radius. In this paper, we improve the numerical method and discuss properties of the six-dimensional (6D) localized black holes whose horizon radii are larger than the AdS curvature radius. At a horizon temperature T≅1/2πl, the thermodynamics of the localized black hole undergo a transition with its character changing from a 6D Schwarzschild black hole type to a 6D black string type. The specific heat of the localized black holes is negative, and the entropy is greater than or nearly equal to that of the 6D black strings with the same thermodynamic mass. The large localized black holes show flattened horizon geometries, and the intrinsic curvature of the horizon four-geometry becomes negative near the brane. Our results indicate that the recovery mechanism of lower-dimensional Einstein gravity on the brane works even in the presence of the black holes

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

Energy Technology Data Exchange (ETDEWEB)

Arevalo, Edward, E-mail: arevalo@temf.tu-darmstadt.d [Technische Universitaet Darmstadt, Institut fuer Theorie elektromagnetischer Felder, TEMF, Schlossgartenstr. 8, D-64289 Darmstadt (Germany)

2009-09-21

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

Traveling Wave Solutions of Reaction-Diffusion Equations Arising in Atherosclerosis Models

Directory of Open Access Journals (Sweden)

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.

Two-dimensional interaction of a shear flow with a free surface in a stratified fluid and its solitary-wave solutions via mathematical methods

Science.gov (United States)

Seadawy, Aly R.

2017-12-01

In this study, we presented the problem formulations of models for internal solitary waves in a stratified shear flow with a free surface. The nonlinear higher order of extended KdV equations for the free surface displacement is generated. We derived the coefficients of the nonlinear higher-order extended KdV equation in terms of integrals of the modal function for the linear long-wave theory. The wave amplitude potential and the fluid pressure of the extended KdV equation in the form of solitary-wave solutions are deduced. We discussed and analyzed the stability of the obtained solutions and the movement role of the waves by making graphs of the exact solutions.

Exact traveling wave solutions of the bbm and kdv equations using (G'/G)-expansion method

International Nuclear Information System (INIS)

Saddique, I.; Nazar, K.

2009-01-01

In this paper, we construct the traveling wave solutions involving parameters of the Benjamin Bona-Mahony (BBM) and KdV equations in terms of the hyperbolic, trigonometric and rational functions by using the (G'/G)-expansion method, where G = G(zeta) satisfies a second order linear ordinary differential equation. When the parameters are taken special values, the Solitary was are derived from the traveling waves. (author)

Scattering of lower-hybrid waves by drift-wave density fluctuations: solutions of the radiative transfer equation

International Nuclear Information System (INIS)

Andrews, P.L.; Perkins, F.W.

1983-01-01

The investigation of the scattering of lower-hybrid waves by density fluctuations arising from drift waves in tokamaks is distinguished by the presence in the wave equation of a large, random, derivative-coupling term. The propagation of the lower-hybrid waves is well represented by a radiative transfer equation when the scale size of the density fluctuations is small compared to the overall plasma size. The radiative transfer equation is solved in two limits: first, the forward scattering limit, where the scale size of density fluctuations is large compared to the lower-hybrid perpendicular wavelength, and second, the large-angle scattering limit, where this inequality is reversed. The most important features of these solutions are well represented by analytical formulas derived by simple arguments. Based on conventional estimates for density fluctuations arising from drift waves and a parabolic density profile, the optical depth tau for scattering through a significant angle, is given by tauroughly-equal(2/N 2 /sub parallel/) (#betta#/sub p/i0/#betta#) 2 (m/sub e/c 2 /2T/sub i/)/sup 1/2/ [c/α(Ω/sub i/Ω/sub e/)/sup 1/2/ ], where #betta#/sub p/i0 is the central ion plasma frequency and T/sub i/ denotes the ion temperature near the edge of the plasma. Most of the scattering occurs near the surface. The transmission through the scattering region scales as tau - 1 and the emerging intensity has an angular spectrum proportional to cos theta, where sin theta = k/sub perpendicular/xB/sub p//(k/sub perpendicular/B/sub p/), and B/sub p/ is the poloidal field

Prospects for observing and localizing gravitational-wave transients with Advanced LIGO, Advanced Virgo and KAGRA.

Science.gov (United States)

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2018-01-01

We present possible observing scenarios for the Advanced LIGO, Advanced Virgo and KAGRA gravitational-wave detectors over the next decade, with the intention of providing information to the astronomy community to facilitate planning for multi-messenger astronomy with gravitational waves. We estimate the sensitivity of the network to transient gravitational-wave signals, and study the capability of the network to determine the sky location of the source. We report our findings for gravitational-wave transients, with particular focus on gravitational-wave signals from the inspiral of binary neutron star systems, which are the most promising targets for multi-messenger astronomy. The ability to localize the sources of the detected signals depends on the geographical distribution of the detectors and their relative sensitivity, and [Formula: see text] credible regions can be as large as thousands of square degrees when only two sensitive detectors are operational. Determining the sky position of a significant fraction of detected signals to areas of 5-[Formula: see text] requires at least three detectors of sensitivity within a factor of [Formula: see text] of each other and with a broad frequency bandwidth. When all detectors, including KAGRA and the third LIGO detector in India, reach design sensitivity, a significant fraction of gravitational-wave signals will be localized to a few square degrees by gravitational-wave observations alone.

Prospects for observing and localizing gravitational-wave transients with Advanced LIGO, Advanced Virgo and KAGRA

Science.gov (United States)

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S.; Wu, G.; Yam, W.; Yamamoto, H.; Yamamoto, K.; Yamamoto, T.; Yancey, C. C.; Yano, K.; Yap, M. J.; Yokoyama, J.; Yokozawa, T.; Yoon, T. H.; Yu, Hang; Yu, Haocun; Yuzurihara, H.; Yvert, M.; Zadrożny, A.; Zangrando, L.; Zanolin, M.; Zeidler, S.; Zendri, J.-P.; Zevin, M.; Zhang, L.; Zhang, M.; Zhang, T.; Zhang, Y.; Zhao, C.; Zhou, M.; Zhou, Z.; Zhu, S. J.; Zhu, X. J.; Zucker, M. E.; Zweizig, J.

2018-04-01

We present possible observing scenarios for the Advanced LIGO, Advanced Virgo and KAGRA gravitational-wave detectors over the next decade, with the intention of providing information to the astronomy community to facilitate planning for multi-messenger astronomy with gravitational waves. We estimate the sensitivity of the network to transient gravitational-wave signals, and study the capability of the network to determine the sky location of the source. We report our findings for gravitational-wave transients, with particular focus on gravitational-wave signals from the inspiral of binary neutron star systems, which are the most promising targets for multi-messenger astronomy. The ability to localize the sources of the detected signals depends on the geographical distribution of the detectors and their relative sensitivity, and 90% credible regions can be as large as thousands of square degrees when only two sensitive detectors are operational. Determining the sky position of a significant fraction of detected signals to areas of 5-20 deg^2 requires at least three detectors of sensitivity within a factor of ˜ 2 of each other and with a broad frequency bandwidth. When all detectors, including KAGRA and the third LIGO detector in India, reach design sensitivity, a significant fraction of gravitational-wave signals will be localized to a few square degrees by gravitational-wave observations alone.

Using wave intensity analysis to determine local reflection coefficient in flexible tubes.

Science.gov (United States)

Li, Ye; Parker, Kim H; Khir, Ashraf W

2016-09-06

It has been shown that reflected waves affect the shape and magnitude of the arterial pressure waveform, and that reflected waves have physiological and clinical prognostic values. In general the reflection coefficient is defined as the ratio of the energy of the reflected to the incident wave. Since pressure has the units of energy per unit volume, arterial reflection coefficient are traditionally defined as the ratio of reflected to the incident pressure. We demonstrate that this approach maybe prone to inaccuracies when applied locally. One of the main objectives of this work is to examine the possibility of using wave intensity, which has units of energy flux per unit area, to determine the reflection coefficient. We used an in vitro experimental setting with a single inlet tube joined to a second tube with different properties to form a single reflection site. The second tube was long enough to ensure that reflections from its outlet did not obscure the interactions of the initial wave. We generated an approximately half sinusoidal wave at the inlet of the tube and took measurements of pressure and flow along the tube. We calculated the reflection coefficient using wave intensity (R dI and R dI 0.5 ) and wave energy (R I and R I 0.5 ) as well as the measured pressure (R dP ) and compared these results with the reflection coefficient calculated theoretically based on the mechanical properties of the tubes. The experimental results show that the reflection coefficients determined by all the techniques we studied increased or decreased with distance from the reflection site, depending on the type of reflection. In our experiments, R dP , R dI 0.5 and R I 0.5 are the most reliable parameters to measure the mean reflection coefficient, whilst R dI and R I provide the best measure of the local reflection coefficient, closest to the reflection site. Additional work with bifurcations, tapered tubes and in vivo experiments are needed to further understand, validate the

High-efficiency one-dimensional atom localization via two parallel standing-wave fields

International Nuclear Information System (INIS)

Wang, Zhiping; Wu, Xuqiang; Lu, Liang; Yu, Benli

2014-01-01

We present a new scheme of high-efficiency one-dimensional (1D) atom localization via measurement of upper state population or the probe absorption in a four-level N-type atomic system. By applying two classical standing-wave fields, the localization peak position and number, as well as the conditional position probability, can be easily controlled by the system parameters, and the sub-half-wavelength atom localization is also observed. More importantly, there is 100% detecting probability of the atom in the subwavelength domain when the corresponding conditions are satisfied. The proposed scheme may open up a promising way to achieve high-precision and high-efficiency 1D atom localization. (paper)

Green function iterative solution of ground state wave function for Yukawa potential

International Nuclear Information System (INIS)

Zhang Zhao

2003-01-01

The newly developed single trajectory quadrature method is applied to solve central potentials. First, based on the series expansion method an exact analytic solution of the ground state for Hulthen potential and an approximate solution for Yukawa potential are obtained respectively. Second, the newly developed iterative method based on Green function defined by quadratures along the single trajectory is applied to solve Yukawa potential using the Coulomb solution and Hulthen solution as the trial functions respectively. The results show that a more proper choice of the trial function will give a better convergence. To further improve the convergence the iterative method is combined with the variational method to solve the ground state wave function for Yukawa potential, using variational solutions of the Coulomb and Hulthen potentials as the trial functions. The results give much better convergence. Finally, the obtained critical screen coefficient is applied to discuss the dissociate temperature of J/ψ in high temperature QGP

New exact travelling wave solutions of generalised sinh- Gordon and (2 + 1-dimensional ZK-BBM equations

Directory of Open Access Journals (Sweden)

Sachin Kumar

2012-10-01

Full Text Available Exact travelling wave solutions have been established for generalised sinh-Gordon andgeneralised (2+1 dimensional ZK-BBM equations by using GG      expansion method whereG  G( satisfies a second-order linear ordinary differential equation. The travelling wave solutionsare expressed by hyperbolic, trigonometric and rational functions.

Simultaneous large band gaps and localization of electromagnetic and elastic waves in defect-free quasicrystals.

Science.gov (United States)

Yu, Tianbao; Wang, Zhong; Liu, Wenxing; Wang, Tongbiao; Liu, Nianhua; Liao, Qinghua

2016-04-18

We report numerically large and complete photonic and phononic band gaps that simultaneously exist in eight-fold phoxonic quasicrystals (PhXQCs). PhXQCs can possess simultaneous photonic and phononic band gaps over a wide range of geometric parameters. Abundant localized modes can be achieved in defect-free PhXQCs for all photonic and phononic polarizations. These defect-free localized modes exhibit multiform spatial distributions and can confine simultaneously electromagnetic and elastic waves in a large area, thereby providing rich selectivity and enlarging the interaction space of optical and elastic waves. The simulated results based on finite element method show that quasiperiodic structures formed of both solid rods in air and holes in solid materials can simultaneously confine and tailor electromagnetic and elastic waves; these structures showed advantages over the periodic counterparts.

On Some New Properties of the Fundamental Solution to the Multi-Dimensional Space- and Time-Fractional Diffusion-Wave Equation

Directory of Open Access Journals (Sweden)

Yuri Luchko

2017-12-01

Full Text Available In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the previous publications of the author. The Mellin-Barnes integral is used to obtain two new representations of the fundamental solution in the form of the Mellin convolution of the special functions of the Wright type. Moreover, some new closed-form formulas for particular cases of the fundamental solution are derived. In particular, we solve the open problem of the representation of the fundamental solution to the two-dimensional neutral-fractional diffusion-wave equation in terms of the known special functions.

Is wave-particle objectivity compatible with determinism and locality?

Science.gov (United States)

Ionicioiu, Radu; Jennewein, Thomas; Mann, Robert B; Terno, Daniel R

2014-09-26

Wave-particle duality, superposition and entanglement are among the most counterintuitive features of quantum theory. Their clash with our classical expectations motivated hidden-variable (HV) theories. With the emergence of quantum technologies, we can test experimentally the predictions of quantum theory versus HV theories and put strong restrictions on their key assumptions. Here, we study an entanglement-assisted version of the quantum delayed-choice experiment and show that the extension of HV to the controlling devices only exacerbates the contradiction. We compare HV theories that satisfy the conditions of objectivity (a property of photons being either particles or waves, but not both), determinism and local independence of hidden variables with quantum mechanics. Any two of the above conditions are compatible with it. The conflict becomes manifest when all three conditions are imposed and persists for any non-zero value of entanglement. We propose an experiment to test our conclusions.

The linear stability of the Schwarzschild solution to gravitational perturbations in the generalised wave gauge

OpenAIRE

Johnson, Thomas

2018-01-01

In a recent seminal paper \\cite{D--H--R} of Dafermos, Holzegel and Rodnianski the linear stability of the Schwarzschild family of black hole solutions to the Einstein vacuum equations was established by imposing a double null gauge. In this paper we shall prove that the Schwarzschild family is linearly stable as solutions to the Einstein vacuum equations by imposing instead a generalised wave gauge: all sufficiently regular solutions to the system of equations that result from linearising the...

Combined solitary-wave solution for coupled higher-order nonlinear Schroedinger equations