one-dimensional wave equation: Topics by Science.gov

Sample records for one-dimensional wave equation

Classifying bilinear differential equations by linear superposition principle

NASA Astrophysics Data System (ADS)

Zhang, Lijun; Khalique, Chaudry Masood; Ma, Wen-Xiu

2016-09-01

In this paper, we investigate the linear superposition principle of exponential traveling waves to construct a sub-class of N-wave solutions of Hirota bilinear equations. A necessary and sufficient condition for Hirota bilinear equations possessing this specific sub-class of N-wave solutions is presented. We apply this result to find N-wave solutions to the (2+1)-dimensional KP equation, a (3+1)-dimensional generalized Kadomtsev-Petviashvili (KP) equation, a (3+1)-dimensional generalized BKP equation and the (2+1)-dimensional BKP equation. The inverse question, i.e., constructing Hirota Bilinear equations possessing N-wave solutions, is considered and a refined 3-step algorithm is proposed. As examples, we construct two very general kinds of Hirota bilinear equations of order 4 possessing N-wave solutions among which one satisfies dispersion relation and another does not satisfy dispersion relation.
One- and Two-dimensional Solitary Wave States in the Nonlinear Kramers Equation with Movement Direction as a Variable

NASA Astrophysics Data System (ADS)

Sakaguchi, Hidetsugu; Ishibashi, Kazuya

2018-06-01

We study self-propelled particles by direct numerical simulation of the nonlinear Kramers equation for self-propelled particles. In our previous paper, we studied self-propelled particles with velocity variables in one dimension. In this paper, we consider another model in which each particle exhibits directional motion. The movement direction is expressed with a variable ϕ. We show that one-dimensional solitary wave states appear in direct numerical simulations of the nonlinear Kramers equation in one- and two-dimensional systems, which is a generalization of our previous result. Furthermore, we find two-dimensionally localized states in the case that each self-propelled particle exhibits rotational motion. The center of mass of the two-dimensionally localized state exhibits circular motion, which implies collective rotating motion. Finally, we consider a simple one-dimensional model equation to qualitatively understand the formation of the solitary wave state.
Uniform high order spectral methods for one and two dimensional Euler equations

NASA Technical Reports Server (NTRS)

Cai, Wei; Shu, Chi-Wang

1991-01-01

Uniform high order spectral methods to solve multi-dimensional Euler equations for gas dynamics are discussed. Uniform high order spectral approximations with spectral accuracy in smooth regions of solutions are constructed by introducing the idea of the Essentially Non-Oscillatory (ENO) polynomial interpolations into the spectral methods. The authors present numerical results for the inviscid Burgers' equation, and for the one dimensional Euler equations including the interactions between a shock wave and density disturbance, Sod's and Lax's shock tube problems, and the blast wave problem. The interaction between a Mach 3 two dimensional shock wave and a rotating vortex is simulated.
Solitary wave solutions of two-dimensional nonlinear Kadomtsev-Petviashvili dynamic equation in dust-acoustic plasmas

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-09-01

Nonlinear two-dimensional Kadomtsev-Petviashvili (KP) equation governs the behaviour of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions. By using the reductive perturbation method, the two-dimensional dust-acoustic solitary waves (DASWs) in unmagnetized cold plasma consisting of dust fluid, ions and electrons lead to a KP equation. We derived the solitary travelling wave solutions of the two-dimensional nonlinear KP equation by implementing sech-tanh, sinh-cosh, extended direct algebraic and fraction direct algebraic methods. We found the electrostatic field potential and electric field in the form travelling wave solutions for two-dimensional nonlinear KP equation. The solutions for the KP equation obtained by using these methods can be demonstrated precisely and efficiency. As an illustration, we used the readymade package of Mathematica program 10.1 to solve the original problem. These solutions are in good agreement with the analytical one.
Newton's method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion.

PubMed

Leszczynski, Henryk; Wrzosek, Monika

2017-02-01

We consider nonlinear stochastic wave equations driven by one-dimensional white noise with respect to time. The existence of solutions is proved by means of Picard iterations. Next we apply Newton's method. Moreover, a second-order convergence in a probabilistic sense is demonstrated.
Symmetry Reductions and Group-Invariant Radial Solutions to the n-Dimensional Wave Equation

NASA Astrophysics Data System (ADS)

Feng, Wei; Zhao, Songlin

2018-01-01

In this paper, we derive explicit group-invariant radial solutions to a class of wave equation via symmetry group method. The optimal systems of one-dimensional subalgebras for the corresponding radial wave equation are presented in terms of the known point symmetries. The reductions of the radial wave equation into second-order ordinary differential equations (ODEs) with respect to each symmetry in the optimal systems are shown. Then we solve the corresponding reduced ODEs explicitly in order to write out the group-invariant radial solutions for the wave equation. Finally, several analytical behaviours and smoothness of the resulting solutions are discussed.
Modeling digital pulse waveforms by solving one-dimensional Navier-stokes equations.

PubMed

Fedotov, Aleksandr A; Akulova, Anna S; Akulov, Sergey A

2016-08-01

Mathematical modeling for composition distal arterial pulse wave in the blood vessels of the upper limbs was considered. Formation of distal arterial pulse wave is represented as a composition of forward and reflected pulse waves propagating along the arterial vessels. The formal analogy between pulse waves propagation along the human arterial system and the propagation of electrical oscillations in electrical transmission lines with distributed parameters was proposed. Dependencies of pulse wave propagation along the human arterial system were obtained by solving the one-dimensional Navier-Stokes equations for a few special cases.
A Numerical Investigation of the Burnett Equations Based on the Second Law

NASA Technical Reports Server (NTRS)

Comeaux, Keith A.; Chapman, Dean R.; MacCormack, Robert W.; Edwards, Thomas A. (Technical Monitor)

1995-01-01

The Burnett equations have been shown to potentially violate the second law of thermodynamics. The objective of this investigation is to correlate the numerical problems experienced by the Burnett equations to the negative production of entropy. The equations have had a long history of numerical instability to small wavelength disturbances. Recently, Zhong corrected the instability problem and made solutions attainable for one dimensional shock waves and hypersonic blunt bodies. Difficulties still exist when attempting to solve hypersonic flat plate boundary layers and blunt body wake flows, however. Numerical experiments will include one-dimensional shock waves, quasi-one dimensional nozzles, and expanding Prandlt-Meyer flows and specifically examine the entropy production for these cases.
Long-Time Numerical Integration of the Three-Dimensional Wave Equation in the Vicinity of a Moving Source

NASA Technical Reports Server (NTRS)

Ryabenkii, V. S.; Turchaninov, V. I.; Tsynkov, S. V.

1999-01-01

We propose a family of algorithms for solving numerically a Cauchy problem for the three-dimensional wave equation. The sources that drive the equation (i.e., the right-hand side) are compactly supported in space for any given time; they, however, may actually move in space with a subsonic speed. The solution is calculated inside a finite domain (e.g., sphere) that also moves with a subsonic speed and always contains the support of the right-hand side. The algorithms employ a standard consistent and stable explicit finite-difference scheme for the wave equation. They allow one to calculate tile solution for arbitrarily long time intervals without error accumulation and with the fixed non-growing amount of tile CPU time and memory required for advancing one time step. The algorithms are inherently three-dimensional; they rely on the presence of lacunae in the solutions of the wave equation in oddly dimensional spaces. The methodology presented in the paper is, in fact, a building block for constructing the nonlocal highly accurate unsteady artificial boundary conditions to be used for the numerical simulation of waves propagating with finite speed over unbounded domains.
Global and blowup solutions of a mixed problem with nonlinear boundary conditions for a one-dimensional semilinear wave equation

NASA Astrophysics Data System (ADS)

Kharibegashvili, S. S.; Jokhadze, O. M.

2014-04-01

A mixed problem for a one-dimensional semilinear wave equation with nonlinear boundary conditions is considered. Conditions of this type occur, for example, in the description of the longitudinal oscillations of a spring fastened elastically at one end, but not in accordance with Hooke's linear law. Uniqueness and existence questions are investigated for global and blowup solutions to this problem, in particular how they depend on the nature of the nonlinearities involved in the equation and the boundary conditions. Bibliography: 14 titles.
On an Acoustic Wave Equation Arising in Non-Equilibrium Gasdynamics. Classroom Notes

ERIC Educational Resources Information Center

Chandran, Pallath

2004-01-01

The sixth-order wave equation governing the propagation of one-dimensional acoustic waves in a viscous, heat conducting gaseous medium subject to relaxation effects has been considered. It has been reduced to a system of lower order equations corresponding to the finite speeds occurring in the equation, following a method due to Whitham. The lower…
Nonlinear excited waves on the interventricular septum

NASA Astrophysics Data System (ADS)

Bekki, Naoaki; Harada, Yoshifumi; Kanai, Hiroshi

2012-11-01

Using a novel ultrasonic noninvasive imaging method, we observe some phase singularities in propagating excited waves on a human cardiac interventricular septum (IVS) for a healthy young male. We present a possible physical model explaining one-dimensional dynamics of phase singularities in nonlinearly excited waves on the IVS. We show that at least one of the observed phase singularities in the excited waves on the IVS can be explained by the Bekki-Nozaki hole solution of the complex Ginzburg-Landau equation without any adjustable parameters. We conclude that the complex Ginzburg-Landau equation is such a suitable model for one-dimensional dynamics of cardiac phase singularities in nonlinearly excited waves on the IVS.
Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

NASA Astrophysics Data System (ADS)

Ye, H.; Liu, F.; Turner, I.; Anh, V.; Burrage, K.

2013-09-01

Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0, m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.
A quasi-one-dimensional theory of sound propagation in lined ducts with mean flow

NASA Astrophysics Data System (ADS)

Dokumaci, Erkan

2018-04-01

Sound propagation in ducts with locally-reacting liners has received the attention of many authors proposing two- and three-dimensional solutions of the convected wave equation and of the Pridmore-Brown equation. One-dimensional lined duct models appear to have received less attention. The present paper proposes a quasi-one-dimensional theory for lined uniform ducts with parallel sheared mean flow. The basic assumption of the theory is that the effects of refraction and wall compliance on the fundamental mode remain within ranges in which the acoustic fluctuations are essentially uniform over a duct section. This restricts the model to subsonic low Mach numbers and Helmholtz numbers of less than about unity. The axial propagation constants and the wave transfer matrix of the duct are given by simple explicit expressions and can be applied with no-slip, full-slip or partial slip boundary conditions. The limitations of the theory are discussed and its predictions are compared with the fundamental mode solutions of the convected wave equation, the Pridmore-Brown equation and measurements where available.
Statistics of extreme waves in the framework of one-dimensional Nonlinear Schrodinger Equation

NASA Astrophysics Data System (ADS)

Agafontsev, Dmitry; Zakharov, Vladimir

2013-04-01

We examine the statistics of extreme waves for one-dimensional classical focusing Nonlinear Schrodinger (NLS) equation, iÎ¨t + Î¨xx + |Î¨ |2Î¨ = 0, (1) as well as the influence of the first nonlinear term beyond Eq. (1) - the six-wave interactions - on the statistics of waves in the framework of generalized NLS equation accounting for six-wave interactions, dumping (linear dissipation, two- and three-photon absorption) and pumping terms, We solve these equations numerically in the box with periodically boundary conditions starting from the initial data Î¨t=0 = F(x) + ?(x), where F(x) is an exact modulationally unstable solution of Eq. (1) seeded by stochastic noise ?(x) with fixed statistical properties. We examine two types of initial conditions F(x): (a) condensate state F(x) = 1 for Eq. (1)-(2) and (b) cnoidal wave for Eq. (1). The development of modulation instability in Eq. (1)-(2) leads to formation of one-dimensional wave turbulence. In the integrable case the turbulence is called integrable and relaxes to one of infinite possible stationary states. Addition of six-wave interactions term leads to appearance of collapses that eventually are regularized by the dumping terms. The energy lost during regularization of collapses in (2) is restored by the pumping term. In the latter case the system does not demonstrate relaxation-like behavior. We measure evolution of spectra Ik =< |Î¨k|2 >, spatial correlation functions and the PDFs for waves amplitudes |Î¨|, concentrating special attention on formation of "fat tails" on the PDFs. For the classical integrable NLS equation (1) with condensate initial condition we observe Rayleigh tails for extremely large waves and a "breathing region" for middle waves with oscillations of the frequency of waves appearance with time, while nonintegrable NLS equation with dumping and pumping terms (2) with the absence of six-wave interactions α = 0 demonstrates perfectly Rayleigh PDFs without any oscillations with time. In case of the cnoidal wave initial condition we observe severely non-Rayleigh PDFs for the classical NLS equation (1) with the regions corresponding to 2-, 3- and so on soliton collisions clearly seen of the PDFs. Addition of six-wave interactions in Eq. (2) for condensate initial condition results in appearance of non-Rayleigh addition to the PDFs that increase with six-wave interaction constant α and disappears with the absence of six-wave interactions α = 0. References: [1] D.S. Agafontsev, V.E. Zakharov, Rogue waves statistics in the framework of one-dimensional Generalized Nonlinear Schrodinger Equation, arXiv:1202.5763v3.
On the dispersionless Kadomtsev-Petviashvili equation with arbitrary nonlinearity and dimensionality: exact solutions, longtime asymptotics of the Cauchy problem, wave breaking and shocks

NASA Astrophysics Data System (ADS)

Santucci, F.; Santini, P. M.

2016-10-01

We study the generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation in n+1 dimensions and with nonlinearity of degree m+1, a model equation describing the propagation of weakly nonlinear, quasi one-dimensional waves in the absence of dispersion and dissipation, and arising in several physical contexts, like acoustics, plasma physics, hydrodynamics and nonlinear optics. In 2 + 1 dimensions and with quadratic nonlinearity, this equation is integrable through a novel inverse scattering transform, and it has been recently shown to be a prototype model equation in the description of the two-dimensional wave breaking of localized initial data. In higher dimensions and with higher nonlinearity, the generalized dKP equations are not integrable, but their invariance under motions on the paraboloid allows one to construct in this paper a family of exact solutions describing waves constant on their paraboloidal wave front and breaking simultaneously in all points of it, developing after breaking either multivaluedness or single-valued discontinuous profiles (shocks). Then such exact solutions are used to build the longtime behavior of the solutions of the Cauchy problem, for small and localized initial data, showing that wave breaking of small initial data takes place in the longtime regime if and only if m(n-1)≤slant 2. Lastly, the analytic aspects of such wave breaking are investigated in detail in terms of the small initial data, in both cases in which the solution becomes multivalued after breaking or it develops a shock. These results, contained in the 2012 master’s thesis of one of the authors (FS) [1], generalize those obtained in [2] for the dKP equation in n+1 dimensions with quadratic nonlinearity, and are obtained following the same strategy.
Stability of Planar Rarefaction Wave to 3D Full Compressible Navier-Stokes Equations

NASA Astrophysics Data System (ADS)

Li, Lin-an; Wang, Teng; Wang, Yi

2018-05-01

We prove time-asymptotic stability toward the planar rarefaction wave for the three-dimensional full, compressible Navier-Stokes equations with the heat-conductivities in an infinite long flat nozzle domain {R × T^2} . Compared with one-dimensional case, the proof here is based on our new observations on the cancellations on the flux terms and viscous terms due to the underlying wave structures, which are crucial for overcoming the difficulties due to the wave propagation in the transverse directions x 2 and x 3 and its interactions with the planar rarefaction wave in x 1 direction.
Benchmark problems in computational aeroacoustics

NASA Technical Reports Server (NTRS)

Porter-Locklear, Freda

1994-01-01

A recent directive at NASA Langley is aimed at numerically predicting principal noise sources. During my summer stay, I worked with high-order ENO code, developed by Dr. Harold Atkins, for solving the unsteady compressible Navier-Stokes equations, as it applies to computational aeroacoustics (CAA). A CAA workshop, composed of six categories of benchmark problems, has been organized to test various numerical properties of code. My task was to determine the robustness of Atkins' code for these test problems. In one category, we tested the nonlinear wave propagation of the code for the one-dimensional Euler equations, with initial pressure, density, and velocity conditions. Using freestream boundary conditions, our results were plausible. In another category, we solved the linearized two-dimensional Euler equations to test the effectiveness of radiation boundary conditions. Here we utilized MAPLE to compute eigenvalues and eigenvectors of the Jacobian given variable and flux vectors. We experienced a minor problem with inflow and outflow boundary conditions. Next, we solved the quasi one dimensional unsteady flow equations with an incoming acoustic wave of amplitude 10(exp -6). The small amplitude sound wave was incident on a convergent-divergent nozzle. After finding a steady-state solution and then marching forward, our solution indicated that after 30 periods the acoustic wave had dissipated (a period is time required for sound wave to traverse one end of nozzle to other end).
Simulations and analysis of asteroid-generated tsunamis using the shallow water equations

NASA Astrophysics Data System (ADS)

Berger, M. J.; LeVeque, R. J.; Weiss, R.

2016-12-01

We discuss tsunami propagation for asteroid-generated air bursts and water impacts. We present simulations for a range of conditions using the GeoClaw simulation software. Examples include meteors that span 5 to 250 MT of kinetic energy, and use bathymetry from the U.S. coastline. We also study radially symmetric one-dimensional equations to better explore the nature and decay rate of waves generated by air burst pressure disturbances traveling at the speed of sound in air, which is much greater than the gravity wave speed of the tsunami generated. One-dimensional simulations along a transect of bathymetry are also used to explore the resolution needed for the full two-dimensional simulations, which are much more expensive even with the use of adaptive mesh refinement due to the short wave lengths of these tsunamis. For this same reason, shallow water equations may be inadequate and we also discuss dispersive effects.
Breathers, quasi-periodic and travelling waves for a generalized ?-dimensional Yu-Toda-Sasa-Fukayama equation in fluids

NASA Astrophysics Data System (ADS)

Hu, Wen-Qiang; Gao, Yi-Tian; Zhao, Chen; Jia, Shu-Liang; Lan, Zhong-Zhou

2017-07-01

Under investigation in this paper is a generalized ?-dimensional Yu-Toda-Sasa-Fukayama equation for the interfacial wave in a two-layer fluid or the elastic quasi-plane wave in a liquid lattice. By virtue of the binary Bell polynomials, bilinear form of this equation is obtained. With the help of the bilinear form, N-soliton solutions are obtained via the Hirota method, and a bilinear Bäcklund transformation is derived to verify the integrability. Homoclinic breather waves are obtained according to the homoclinic test approach, which is not only the space-periodic breather but also the time-periodic breather via the graphic analysis. Via the Riemann theta function, quasi one-periodic waves are constructed, which can be viewed as a superposition of the overlapping solitary waves, placed one period apart. Finally, soliton-like, periodical triangle-type, rational-type and solitary bell-type travelling waves are obtained by means of the polynomial expansion method.

An approximate Riemann solver for magnetohydrodynamics (that works in more than one dimension)

NASA Technical Reports Server (NTRS)

Powell, Kenneth G.

1994-01-01

An approximate Riemann solver is developed for the governing equations of ideal magnetohydrodynamics (MHD). The Riemann solver has an eight-wave structure, where seven of the waves are those used in previous work on upwind schemes for MHD, and the eighth wave is related to the divergence of the magnetic field. The structure of the eighth wave is not immediately obvious from the governing equations as they are usually written, but arises from a modification of the equations that is presented in this paper. The addition of the eighth wave allows multidimensional MHD problems to be solved without the use of staggered grids or a projection scheme, one or the other of which was necessary in previous work on upwind schemes for MHD. A test problem made up of a shock tube with rotated initial conditions is solved to show that the two-dimensional code yields answers consistent with the one-dimensional methods developed previously.
Progress in multi-dimensional upwind differencing

NASA Technical Reports Server (NTRS)

Vanleer, Bram

1992-01-01

Multi-dimensional upwind-differencing schemes for the Euler equations are reviewed. On the basis of the first-order upwind scheme for a one-dimensional convection equation, the two approaches to upwind differencing are discussed: the fluctuation approach and the finite-volume approach. The usual extension of the finite-volume method to the multi-dimensional Euler equations is not entirely satisfactory, because the direction of wave propagation is always assumed to be normal to the cell faces. This leads to smearing of shock and shear waves when these are not grid-aligned. Multi-directional methods, in which upwind-biased fluxes are computed in a frame aligned with a dominant wave, overcome this problem, but at the expense of robustness. The same is true for the schemes incorporating a multi-dimensional wave model not based on multi-dimensional data but on an 'educated guess' of what they could be. The fluctuation approach offers the best possibilities for the development of genuinely multi-dimensional upwind schemes. Three building blocks are needed for such schemes: a wave model, a way to achieve conservation, and a compact convection scheme. Recent advances in each of these components are discussed; putting them all together is the present focus of a worldwide research effort. Some numerical results are presented, illustrating the potential of the new multi-dimensional schemes.
Exact solutions to three-dimensional generalized nonlinear Schrödinger equations with varying potential and nonlinearities.

PubMed

Yan, Zhenya; Konotop, V V

2009-09-01

It is shown that using the similarity transformations, a set of three-dimensional p-q nonlinear Schrödinger (NLS) equations with inhomogeneous coefficients can be reduced to one-dimensional stationary NLS equation with constant or varying coefficients, thus allowing for obtaining exact localized and periodic wave solutions. In the suggested reduction the original coordinates in the (1+3) space are mapped into a set of one-parametric coordinate surfaces, whose parameter plays the role of the coordinate of the one-dimensional equation. We describe the algorithm of finding solutions and concentrate on power (linear and nonlinear) potentials presenting a number of case examples. Generalizations of the method are also discussed.
Numerical modeling of surface wave development under the action of wind

NASA Astrophysics Data System (ADS)

Chalikov, Dmitry

2018-06-01

The numerical modeling of two-dimensional surface wave development under the action of wind is performed. The model is based on three-dimensional equations of potential motion with a free surface written in a surface-following nonorthogonal curvilinear coordinate system in which depth is counted from a moving surface. A three-dimensional Poisson equation for the velocity potential is solved iteratively. A Fourier transform method, a second-order accuracy approximation of vertical derivatives on a stretched vertical grid and fourth-order Runge-Kutta time stepping are used. Both the input energy to waves and dissipation of wave energy are calculated on the basis of earlier developed and validated algorithms. A one-processor version of the model for PC allows us to simulate an evolution of the wave field with thousands of degrees of freedom over thousands of wave periods. A long-time evolution of a two-dimensional wave structure is illustrated by the spectra of wave surface and the input and output of energy.
KAM Tori for 1D Nonlinear Wave Equationswith Periodic Boundary Conditions

NASA Astrophysics Data System (ADS)

Chierchia, Luigi; You, Jiangong

In this paper, one-dimensional (1D) nonlinear wave equations with periodic boundary conditions are considered; V is a periodic smooth or analytic function and the nonlinearity f is an analytic function vanishing together with its derivative at u≡0. It is proved that for ``most'' potentials V(x), the above equation admits small-amplitude periodic or quasi-periodic solutions corresponding to finite dimensional invariant tori for an associated infinite dimensional dynamical system. The proof is based on an infinite dimensional KAM theorem which allows for multiple normal frequencies.
Exact Analytical Solutions for Elastodynamic Impact

DTIC Science & Technology

2015-11-30

corroborated by derivation of exact discrete solutions from recursive equations for the impact problems. 15. SUBJECT TERMS One-dimensional impact; Elastic...wave propagation; Laplace transform; Floor function; Discrete solutions 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18...impact Elastic wave propagation Laplace transform Floor function Discrete solutionsWe consider the one-dimensional impact problem in which a semi
Simulation Of Wave Function And Probability Density Of Modified Poschl Teller Potential Derived Using Supersymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

Angraini, Lily Maysari; Suparmi, Variani, Viska Inda

2010-12-01

SUSY quantum mechanics can be applied to solve Schrodinger equation for high dimensional system that can be reduced into one dimensional system and represented in lowering and raising operators. Lowering and raising operators can be obtained using relationship between original Hamiltonian equation and the (super) potential equation. In this paper SUSY quantum mechanics is used as a method to obtain the wave function and the energy level of the Modified Poschl Teller potential. The graph of wave function equation and probability density is simulated by using Delphi 7.0 programming language. Finally, the expectation value of quantum mechanics operator could be calculated analytically using integral form or probability density graph resulted by the programming.
Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-01-01

The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.
On the dimensionally correct kinetic theory of turbulence for parallel propagation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gaelzer, R., E-mail: rudi.gaelzer@ufrgs.br, E-mail: yoonp@umd.edu, E-mail: 007gasun@khu.ac.kr, E-mail: luiz.ziebell@ufrgs.br; Ziebell, L. F., E-mail: rudi.gaelzer@ufrgs.br, E-mail: yoonp@umd.edu, E-mail: 007gasun@khu.ac.kr, E-mail: luiz.ziebell@ufrgs.br; Yoon, P. H., E-mail: rudi.gaelzer@ufrgs.br, E-mail: yoonp@umd.edu, E-mail: 007gasun@khu.ac.kr, E-mail: luiz.ziebell@ufrgs.br

2015-03-15

Yoon and Fang [Phys. Plasmas 15, 122312 (2008)] formulated a second-order nonlinear kinetic theory that describes the turbulence propagating in directions parallel/anti-parallel to the ambient magnetic field. Their theory also includes discrete-particle effects, or the effects due to spontaneously emitted thermal fluctuations. However, terms associated with the spontaneous fluctuations in particle and wave kinetic equations in their theory contain proper dimensionality only for an artificial one-dimensional situation. The present paper extends the analysis and re-derives the dimensionally correct kinetic equations for three-dimensional case. The new formalism properly describes the effects of spontaneous fluctuations emitted in three-dimensional space, while the collectivelymore » emitted turbulence propagates predominantly in directions parallel/anti-parallel to the ambient magnetic field. As a first step, the present investigation focuses on linear wave-particle interaction terms only. A subsequent paper will include the dimensionally correct nonlinear wave-particle interaction terms.« less
Fully three-dimensional direct numerical simulation of a plunging breaker

NASA Astrophysics Data System (ADS)

Lubin, Pierre; Vincent, Stéphane; Caltagirone, Jean-Paul; Abadie, Stéphane

2003-07-01

The scope of this paper is to show the results obtained for simulating three-dimensional breaking waves by solving the Navier-Stokes equations in air and water. The interface tracking is achieved by a Lax-Wendroff TVD scheme (Total Variation Diminishing), which is able to handle interface reconnections. We first present the equations and the numerical methods used in this work. We then proceed to the study of a three-dimensional plunging breaking wave, using initial conditions corresponding to unstable periodic sinusoidal waves of large amplitudes. We compare the results obtained for two simulations, a longshore depth perturbation has been introduced in the solution of the flow equations in order to see the transition from a two-dimensional velocity field to a fully three-dimensional one after plunging. Breaking processes including overturning, splash-up and breaking induced vortex-like motion beneath the surface are presented and discussed. To cite this article: P. Lubin et al., C. R. Mecanique 331 (2003).
Bäcklund transformation, infinitely-many conservation laws, solitary and periodic waves of an extended (3 + 1)-dimensional Jimbo-Miwa equation with time-dependent coefficients

NASA Astrophysics Data System (ADS)

Deng, Gao-Fu; Gao, Yi-Tian; Gao, Xin-Yi

2018-07-01

In this paper, an extended (3+1)-dimensional Jimbo-Miwa equation with time-dependent coefficients is investigated, which comes from the second member of the Kadomtsev-Petviashvili hierarchy and is shown to be conditionally integrable. Bilinear form, Bäcklund transformation, Lax pair and infinitely-many conservation laws are derived via the binary Bell polynomials and symbolic computation. With the help of the bilinear form, one-, two- and three-soliton solutions are obtained via the Hirota method, one-periodic wave solutions are constructed via the Riemann theta function. Additionally, propagation and interaction of the solitons are investigated analytically and graphically, from which we find that the interaction between the solitons is elastic and the time-dependent coefficients can affect the soliton velocities, but the soliton amplitudes remain unchanged. One-periodic waves approach the one-solitary waves with the amplitudes vanishing and can be viewed as a superposition of the overlapping solitary waves, placed one period apart.
Solitary waves, rogue waves and homoclinic breather waves for a (2 + 1)-dimensional generalized Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Dong, Min-Jie; Tian, Shou-Fu; Yan, Xue-Wei; Zou, Li; Li, Jin

2017-10-01

We study a (2 + 1)-dimensional generalized Kadomtsev-Petviashvili (gKP) equation, which characterizes the formation of patterns in liquid drops. By using Bell’s polynomials, an effective way is employed to succinctly construct the bilinear form of the gKP equation. Based on the resulting bilinear equation, we derive its solitary waves, rogue waves and homoclinic breather waves, respectively. Our results can help enrich the dynamical behavior of the KP-type equations.
Three-Dimensional Shallow Water Acoustics

DTIC Science & Technology

2015-09-30

converts the Helmholtz wave equation of elliptic type to a one-way wave equation of parabolic type. The conversion allows efficient marching solution ...algorithms for 2 solving the boundary value problem posed by the Helmholtz equation . This can reduce significantly the requirement for computational...Fourier parabolic- equation sound propagation solution scheme," J. Acoust. Soc. Am, vol. 132, pp. EL61-EL67 (2012). [6] Y.-T. Lin, J.M. Collis and T.F
Study on longitudinal dispersion relation in one-dimensional relativistic plasma: Linear theory and Vlasov simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, H.; Wu, S. Z.; Zhou, C. T.

2013-09-15

The dispersion relation of one-dimensional longitudinal plasma waves in relativistic homogeneous plasmas is investigated with both linear theory and Vlasov simulation in this paper. From the Vlasov-Poisson equations, the linear dispersion relation is derived for the proper one-dimensional Jüttner distribution. Numerically obtained linear dispersion relation as well as an approximate formula for plasma wave frequency in the long wavelength limit is given. The dispersion of longitudinal wave is also simulated with a relativistic Vlasov code. The real and imaginary parts of dispersion relation are well studied by varying wave number and plasma temperature. Simulation results are in agreement with establishedmore » linear theory.« less
Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents.

PubMed

Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan

2014-04-08

Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves.
Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents

PubMed Central

Kundu, Anjan; Mukherjee, Abhik; Naskar, Tapan

2014-01-01

Rogue waves are extraordinarily high and steep isolated waves, which appear suddenly in a calm sea and disappear equally fast. However, though the rogue waves are localized surface waves, their theoretical models and experimental observations are available mostly in one dimension, with the majority of them admitting only limited and fixed amplitude and modular inclination of the wave. We propose two dimensions, exactly solvable nonlinear Schrödinger (NLS) equation derivable from the basic hydrodynamic equations and endowed with integrable structures. The proposed two-dimensional equation exhibits modulation instability and frequency correction induced by the nonlinear effect, with a directional preference, all of which can be determined through precise analytic result. The two-dimensional NLS equation allows also an exact lump soliton which can model a full-grown surface rogue wave with adjustable height and modular inclination. The lump soliton under the influence of an ocean current appears and disappears preceded by a hole state, with its dynamics controlled by the current term. These desirable properties make our exact model promising for describing ocean rogue waves. PMID:24711719
Nonlinear Ocean Waves

DTIC Science & Technology

1994-01-06

for all of this work is the fact that the Kadomtsev - Petviashvili equation , a1(atu + ui)xU + a.3u) + ay2u = 0, (KP) describes approximately the evolution...the contents of these two papers. (a) Numerically induced chaos The cubic-nonlinear Schrtdinger equation in one dimension, iatA +,2V + 21i,1 =0, (NLS...arises in several physical contexts, including the evolution of nearly monochromatic, one-dimensional waves in deep water. The equation is known to be
Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Demirci, Ali; Ma, Yi-Ping

2016-10-01

Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and two dimensional Benjamin-Ono (2DBO) equation are considered using step like initial data along a parabolic front. Employing a parabolic similarity reduction exactly reduces the study of such DSWs in two space one time (2 + 1) dimensions to finding DSW solutions of (1 + 1) dimensional equations. With this ansatz, the KP and 2DBO equations can be exactly reduced to the cylindrical Korteweg-de Vries (cKdV) and cylindrical Benjamin-Ono (cBO) equations, respectively. Whitham modulation equations which describe DSW evolution in the cKdV and cBO equations are derived and Riemann type variables are introduced. DSWs obtained from the numerical solutions of the corresponding Whitham systems and direct numerical simulations of the cKdV and cBO equations are compared with very good agreement obtained. In turn, DSWs obtained from direct numerical simulations of the KP and 2DBO equations are compared with the cKdV and cBO equations, again with good agreement. It is concluded that the (2 + 1) DSW behavior along self similar parabolic fronts can be effectively described by the DSW solutions of the reduced (1 + 1) dimensional equations.
Two-dimensional evolution equation of finite-amplitude internal gravity waves in a uniformly stratified fluid

PubMed

Kataoka; Tsutahara; Akuzawa

2000-02-14

We derive a fully nonlinear evolution equation that can describe the two-dimensional motion of finite-amplitude long internal waves in a uniformly stratified three-dimensional fluid of finite depth. The derived equation is the two-dimensional counterpart of the evolution equation obtained by Grimshaw and Yi [J. Fluid Mech. 229, 603 (1991)]. In the small-amplitude limit, our equation is reduced to the celebrated Kadomtsev-Petviashvili equation.
Solution of the Burnett equations for hypersonic flows near the continuum limit

NASA Technical Reports Server (NTRS)

Imlay, Scott T.

1992-01-01

The INCA code, a three-dimensional Navier-Stokes code for analysis of hypersonic flowfields, was modified to analyze the lower reaches of the continuum transition regime, where the Navier-Stokes equations become inaccurate and Monte Carlo methods become too computationally expensive. The two-dimensional Burnett equations and the three-dimensional rotational energy transport equation were added to the code and one- and two-dimensional calculations were performed. For the structure of normal shock waves, the Burnett equations give consistently better results than Navier-Stokes equations and compare reasonably well with Monte Carlo methods. For two-dimensional flow of Nitrogen past a circular cylinder the Burnett equations predict the total drag reasonably well. Care must be taken, however, not to exceed the range of validity of the Burnett equations.

On the existence of solutions to a one-dimensional degenerate nonlinear wave equation

NASA Astrophysics Data System (ADS)

Hu, Yanbo

2018-07-01

This paper is concerned with the degenerate initial-boundary value problem to the one-dimensional nonlinear wave equation utt =((1 + u) aux) x which arises in a number of various physical contexts. The global existence of smooth solutions to the degenerate problem was established under relaxed conditions on the initial-boundary data by the characteristic decomposition method. Moreover, we show that the solution is uniformly C 1 , α continuous up to the degenerate boundary and the degenerate curve is C 1 , α continuous for α ∈ (0 , min ⁡ a/1+a, 1/1+a).
On the three dimensional structure of stratospheric material transport associated with various types of waves

NASA Astrophysics Data System (ADS)

Kinoshita, T.; Sato, K.

2016-12-01

The Transformed Eulerian-Mean (TEM) equations were derived by Andrews and McIntyre (1976, 1978) and have been widely used to examine wave-mean flow interaction in the meridional cross section. According to previous studies, the Brewer-Dobson circulation in the stratosphere is driven by planetary waves, baroclinic waves, and inertia-gravity waves, and that the meridional circulation from the summer hemisphere to the winter hemisphere in the mesosphere is mainly driven by gravity waves (e.g., Garcia and Boville 1994; Plumb and Semeniuk 2003; Watanabe et al. 2008; Okamoto et al. 2011). However, the TEM equations do not provide the three-dimensional view of the transport, so that the three dimensional TEM equations have been formulated (Hoskins et al. 1983, Trenberth 1986, Plumb 1985, 1986, Takaya and Nakamura 1997, 2001, Miyahara 2006, Kinoshita et al. 2010, Noda 2010, Kinoshita and Sato 2013a, b, and Noda 2014). On the other hand, the TEM equations cannot properly treat the lower boundary and unstable waves. The Mass-weighted Isentropic Mean (MIM) equations derived by Iwasaki (1989, 1990) are the equations that overcome those problems and the formulation of three-dimensional MIM equations have been studied. The present study applies the three-dimensional TEM and MIM equations to the ERA-Interim reanalysis data and examines the climatological character of three-dimensional structure of Stratospheric Brewer-Dobson circulation. Next, we will discuss how to treat the flow associated with spatial structure of stationary waves.
Periodic solutions for one dimensional wave equation with bounded nonlinearity

NASA Astrophysics Data System (ADS)

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.
Wave Transformation Over Reefs: Evaluation of One-Dimensional Numerical Models

DTIC Science & Technology

2009-01-01

equations on an unstructured grid. Proceedings International Conference on Coastal Engineering ‘06 V1. San Diego, CA, 73-85. Baldock, T. E., P. Holmes , S...equations. Monthly Weather Review 91:99-164. Smith, J. M, A. R. Sherlock , and D. T. Resio. 2001. Steady state spectral wave model user’s manual
One-Dimensional Fokker-Planck Equation with Quadratically Nonlinear Quasilocal Drift

NASA Astrophysics Data System (ADS)

Shapovalov, A. V.

2018-04-01

The Fokker-Planck equation in one-dimensional spacetime with quadratically nonlinear nonlocal drift in the quasilocal approximation is reduced with the help of scaling of the coordinates and time to a partial differential equation with a third derivative in the spatial variable. Determining equations for the symmetries of the reduced equation are derived and the Lie symmetries are found. A group invariant solution having the form of a traveling wave is found. Within the framework of Adomian's iterative method, the first iterations of an approximate solution of the Cauchy problem are obtained. Two illustrative examples of exact solutions are found.
Exact Lyapunov exponent of the harmonic magnon modes of one-dimensional Heisenberg-Mattis spin glasses

NASA Astrophysics Data System (ADS)

Sepehrinia, Reza; Niry, M. D.; Bozorg, B.; Tabar, M. Reza Rahimi; Sahimi, Muhammad

2008-03-01

A mapping is developed between the linearized equation of motion for the dynamics of the transverse modes at T=0 of the Heisenberg-Mattis model of one-dimensional (1D) spin glasses and the (discretized) random wave equation. The mapping is used to derive an exact expression for the Lyapunov exponent (LE) of the magnon modes of spin glasses and to show that it follows anomalous scaling at low magnon frequencies. In addition, through numerical simulations, the differences between the LE and the density of states of the wave equation in a discrete 1D model of randomly disordered media (those with a finite correlation length) and that of continuous media (with a zero correlation length) are demonstrated and emphasized.
Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applications

NASA Astrophysics Data System (ADS)

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

2018-06-01

The Equal-Width and Modified Equal-Width equations are used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. In this article we have employed extend simple equation method and the exp(-varphi(ξ)) expansion method to construct the exact traveling wave solutions of equal width and modified equal width equations. The obtained results are novel and have numerous applications in current areas of research in mathematical physics. It is exposed that our method, with the help of symbolic computation, provides a effective and powerful mathematical tool for solving different kind nonlinear wave problems.
Splash singularity for water waves.

PubMed

Castro, Angel; Córdoba, Diego; Fefferman, Charles L; Gancedo, Francisco; Gómez-Serrano, Javier

2012-01-17

We exhibit smooth initial data for the two-dimensional (2D) water-wave equation for which we prove that smoothness of the interface breaks down in finite time. Moreover, we show a stability result together with numerical evidence that there exist solutions of the 2D water-wave equation that start from a graph, turn over, and collapse in a splash singularity (self-intersecting curve in one point) in finite time.
Splash singularity for water waves

PubMed Central

Castro, Angel; Córdoba, Diego; Fefferman, Charles L.; Gancedo, Francisco; Gómez-Serrano, Javier

2012-01-01

We exhibit smooth initial data for the two-dimensional (2D) water-wave equation for which we prove that smoothness of the interface breaks down in finite time. Moreover, we show a stability result together with numerical evidence that there exist solutions of the 2D water-wave equation that start from a graph, turn over, and collapse in a splash singularity (self-intersecting curve in one point) in finite time. PMID:22219372
Dispersion relations of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with functionally graded interlayers.

PubMed

Guo, Xiao; Wei, Peijun; Lan, Man; Li, Li

2016-08-01

The effects of functionally graded interlayers on dispersion relations of elastic waves in a one-dimensional piezoelectric/piezomagnetic phononic crystal are studied in this paper. First, the state transfer equation of the functionally graded interlayer is derived from the motion equation by the reduction of order (from second order to first order). The transfer matrix of the functionally graded interlayer is obtained by solving the state transfer equation with the spatial-varying coefficient. Based on the transfer matrixes of the piezoelectric slab, the piezomagnetic slab and the functionally graded interlayers, the total transfer matrix of a single cell is obtained. Further, the Bloch theorem is used to obtain the resultant dispersion equations of in-plane and anti-plane Bloch waves. The dispersion equations are solved numerically and the numerical results are shown graphically. Five kinds of profiles of functionally graded interlayers between a piezoelectric slab and a piezomagnetic slab are considered. It is shown that the functionally graded interlayers have evident influences on the dispersion curves and the band gaps. Copyright © 2016 Elsevier B.V. All rights reserved.
Chirped or time modulated excitation compared to short pulses for photoacoustic imaging in acoustic attenuating media

NASA Astrophysics Data System (ADS)

Burgholzer, P.; Motz, C.; Lang, O.; Berer, T.; Huemer, M.

2018-02-01

In photoacoustic imaging, optically generated acoustic waves transport the information about embedded structures to the sample surface. Usually, short laser pulses are used for the acoustic excitation. Acoustic attenuation increases for higher frequencies, which reduces the bandwidth and limits the spatial resolution. One could think of more efficient waveforms than single short pulses, such as pseudo noise codes, chirped, or harmonic excitation, which could enable a higher information-transfer from the samples interior to its surface by acoustic waves. We used a linear state space model to discretize the wave equation, such as the Stoke's equation, but this method could be used for any other linear wave equation. Linear estimators and a non-linear function inversion were applied to the measured surface data, for onedimensional image reconstruction. The proposed estimation method allows optimizing the temporal modulation of the excitation laser such that the accuracy and spatial resolution of the reconstructed image is maximized. We have restricted ourselves to one-dimensional models, as for higher dimensions the one-dimensional reconstruction, which corresponds to the acoustic wave without attenuation, can be used as input for any ultrasound imaging method, such as back-projection or time-reversal method.
Hamiltonian structures for systems of hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Olver, Peter J.; Nutku, Yavuz

1988-07-01

The bi-Hamiltonian structure for a large class of one-dimensional hyberbolic systems of conservation laws in two field variables, including the equations of gas dynamics, shallow water waves, one-dimensional elastic media, and the Born-Infeld equation from nonlinear electrodynamics, is exhibited. For polytropic gas dynamics, these results lead to a quadri-Hamiltonian structure. New higher-order entropy-flux pairs (conservation laws) and higher-order symmetries are exhibited.
Rogue waves for a discrete (2+1)-dimensional Ablowitz-Ladik equation in the nonlinear optics and Bose-Einstein condensation

NASA Astrophysics Data System (ADS)

Wu, Xiao-Yu; Tian, Bo; Chai, Han-Peng; Du, Zhong

2018-03-01

Under investigation in this paper is a discrete (2+1)-dimensional Ablowitz-Ladik equation, which is used to model the nonlinear waves in the nonlinear optics and Bose-Einstein condensation. Employing the Kadomtsev-Petviashvili hierarchy reduction, we obtain the rogue wave solutions in terms of the Gramian. We graphically study the first-, second- and third-order rogue waves with the influence of the focusing coefficient and coupling strength. When the value of the focusing coefficient increases, both the peak of the rogue wave and background decrease. When the value of the coupling strength increases, the rogue wave raises and decays in a shorter time. High-order rogue waves are exhibited as one single highest peak and some lower humps, and such lower humps are shown as the triangular and circular patterns.
Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation.

PubMed

Liu, Wei; Zhang, Jing; Li, Xiliang

2018-01-01

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota's bilinear method. Like the nonlocal NLS equation, these solutions may have singularities. However, by suitable constraints of parameters, nonsingular breather solutions are generated. Besides, by taking a long wave limit of these obtained soliton solutions, rogue wave solutions and semi-rational solutions are derived. For the two dimensional NLS equation, rogue wave solutions are line rogue waves, which arise from a constant background with a line profile and then disappear into the same background. The semi-rational solutions shows intriguing dynamical behaviours: line rogue wave and line breather arise from a constant background together and then disappear into the constant background again uniformly. For the coupled nonlocal Klein-Gordon equation, rogue waves are localized in both space and time, semi-rational solutions are composed of rogue waves, breathers and periodic line waves. These solutions are demonstrated analytically to exist for special classes of nonlocal equations relevant to optical waveguides.
Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation

PubMed Central

Zhang, Jing; Li, Xiliang

2018-01-01

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota’s bilinear method. Like the nonlocal NLS equation, these solutions may have singularities. However, by suitable constraints of parameters, nonsingular breather solutions are generated. Besides, by taking a long wave limit of these obtained soliton solutions, rogue wave solutions and semi-rational solutions are derived. For the two dimensional NLS equation, rogue wave solutions are line rogue waves, which arise from a constant background with a line profile and then disappear into the same background. The semi-rational solutions shows intriguing dynamical behaviours: line rogue wave and line breather arise from a constant background together and then disappear into the constant background again uniformly. For the coupled nonlocal Klein-Gordon equation, rogue waves are localized in both space and time, semi-rational solutions are composed of rogue waves, breathers and periodic line waves. These solutions are demonstrated analytically to exist for special classes of nonlocal equations relevant to optical waveguides. PMID:29432495
Fast Neural Solution Of A Nonlinear Wave Equation

NASA Technical Reports Server (NTRS)

Barhen, Jacob; Toomarian, Nikzad

1996-01-01

Neural algorithm for simulation of class of nonlinear wave phenomena devised. Numerically solves special one-dimensional case of Korteweg-deVries equation. Intended to be executed rapidly by neural network implemented as charge-coupled-device/charge-injection device, very-large-scale integrated-circuit analog data processor of type described in "CCD/CID Processors Would Offer Greater Precision" (NPO-18972).
On the modeling of the bottom particles segregation with non-linear diffusion equations: application to the marine sand ripples

NASA Astrophysics Data System (ADS)

Tiguercha, Djlalli; Bennis, Anne-claire; Ezersky, Alexander

2015-04-01

The elliptical motion in surface waves causes an oscillating motion of the sand grains leading to the formation of ripple patterns on the bottom. Investigation how the grains with different properties are distributed inside the ripples is a difficult task because of the segration of particle. The work of Fernandez et al. (2003) was extended from one-dimensional to two-dimensional case. A new numerical model, based on these non-linear diffusion equations, was developed to simulate the grain distribution inside the marine sand ripples. The one and two-dimensional models are validated on several test cases where segregation appears. Starting from an homogeneous mixture of grains, the two-dimensional simulations demonstrate different segregation patterns: a) formation of zones with high concentration of light and heavy particles, b) formation of «cat's eye» patterns, c) appearance of inverse Brazil nut effect. Comparisons of numerical results with the new set of field data and wave flume experiments show that the two-dimensional non-linear diffusion equations allow us to reproduce qualitatively experimental results on particles segregation.
Unsteady free surface flow in porous media: One-dimensional model equations including vertical effects and seepage face

NASA Astrophysics Data System (ADS)

Di Nucci, Carmine

2018-05-01

This note examines the two-dimensional unsteady isothermal free surface flow of an incompressible fluid in a non-deformable, homogeneous, isotropic, and saturated porous medium (with zero recharge and neglecting capillary effects). Coupling a Boussinesq-type model for nonlinear water waves with Darcy's law, the two-dimensional flow problem is solved using one-dimensional model equations including vertical effects and seepage face. In order to take into account the seepage face development, the system equations (given by the continuity and momentum equations) are completed by an integral relation (deduced from the Cauchy theorem). After testing the model against data sets available in the literature, some numerical simulations, concerning the unsteady flow through a rectangular dam (with an impermeable horizontal bottom), are presented and discussed.
A Model for Measured Traveling Waves at End-Diastole in Human Heart Wall by Ultrasonic Imaging Method

NASA Astrophysics Data System (ADS)

Bekki, Naoaki; Shintani, Seine A.; Ishiwata, Shin'ichi; Kanai, Hiroshi

2016-04-01

We observe traveling waves, measured by the ultrasonic noninvasive imaging method, in a longitudinal beam direction from the apex to the base side on the interventricular septum (IVS) during the period from the end-diastole to the beginning of systole for a healthy human heart wall. We present a possible phenomenological model to explain part of one-dimensional cardiac behaviors for the observed traveling waves around the time of R-wave of echocardiography (ECG) in the human heart. Although the observed two-dimensional patterns of traveling waves are extremely complex and no one knows yet the exact solutions for the traveling homoclinic plane wave in the one-dimensional complex Ginzburg-Landau equation (CGLE), we numerically find that part of the one-dimensional homoclinic dynamics of the phase and amplitude patterns in the observed traveling waves is similar to that of the numerical homoclinic plane-wave solutions in the CGLE with periodic boundary condition in a certain parameter space. It is suggested that part of the cardiac dynamics of the traveling waves on the IVS can be qualitatively described by the CGLE model as a paradigm for understanding biophysical nonlinear phenomena.
Controlled formation and reflection of a bright solitary matter-wave

PubMed Central

Marchant, A. L.; Billam, T. P.; Wiles, T. P.; Yu, M. M. H.; Gardiner, S. A.; Cornish, S. L.

2013-01-01

Bright solitons are non-dispersive wave solutions, arising in a diverse range of nonlinear, one-dimensional systems, including atomic Bose–Einstein condensates with attractive interactions. In reality, cold-atom experiments can only approach the idealized one-dimensional limit necessary for the realization of true solitons. Nevertheless, it remains possible to create bright solitary waves, the three-dimensional analogue of solitons, which maintain many of the key properties of their one-dimensional counterparts. Such solitary waves offer many potential applications and provide a rich testing ground for theoretical treatments of many-body quantum systems. Here we report the controlled formation of a bright solitary matter-wave from a Bose–Einstein condensate of 85Rb, which is observed to propagate over a distance of ∼1.1 mm in 150 ms with no observable dispersion. We demonstrate the reflection of a solitary wave from a repulsive Gaussian barrier and contrast this to the case of a repulsive condensate, in both cases finding excellent agreement with theoretical simulations using the three-dimensional Gross–Pitaevskii equation. PMID:23673650

Rogue wave and a pair of resonance stripe solitons to a reduced (3+1)-dimensional Jimbo-Miwa equation

NASA Astrophysics Data System (ADS)

Zhang, Xiaoen; Chen, Yong

2017-11-01

In this paper, a combination of stripe soliton and lump soliton is discussed to a reduced (3+1)-dimensional Jimbo-Miwa equation, in which such solution gives rise to two different excitation phenomena: fusion and fission. Particularly, a new combination of positive quadratic functions and hyperbolic functions is considered, and then a novel nonlinear phenomenon is explored. Via this method, a pair of resonance kink stripe solitons and rogue wave is studied. Rogue wave is triggered by the interaction between lump soliton and a pair of resonance kink stripe solitons. It is exciting that rogue wave must be attached to the stripe solitons from its appearing to disappearing. The whole progress is completely symmetry, the rogue wave starts itself from one stripe soliton and lose itself in another stripe soliton. The dynamic properties of the interaction between one stripe soliton and lump soliton, rogue wave are discussed by choosing appropriate parameters.
Mixed lump-kink and rogue wave-kink solutions for a (3 + 1) -dimensional B-type Kadomtsev-Petviashvili equation in fluid mechanics

NASA Astrophysics Data System (ADS)

Hu, Cong-Cong; Tian, Bo; Wu, Xiao-Yu; Yuan, Yu-Qiang; Du, Zhong

2018-02-01

Under investigation is a (3 + 1) -dimensional B-type Kadomtsev-Petviashvili equation, which describes the weakly dispersive waves in a fluid. Via the Hirota method and symbolic computation, we obtain the mixed lump-kink and mixed rogue wave-kink solutions. Through the mixed lump-kink solutions, we observe three different phenomena between a lump and one kink. For the fusion phenomenon, a lump and a kink are merged with the lump's energy transferring into the kink gradually, until the lump merges into the kink completely. Fission phenomenon displays that a lump separates from a kink. The last phenomenon shows that a lump travels together with a kink with their amplitudes unchanged. In addition, we graphically study the interaction between a rogue wave and a pair of the kinks. It can be observed that the rogue wave arises from one kink and disappears into the other kink. At certain time, the amplitude of the rogue wave reaches the maximum.
Using Global Invariant Manifolds to Understand Metastability in the Burgers Equation With Small Viscosity

NASA Astrophysics Data System (ADS)

Beck, Margaret; Wayne, C. Eugene

2009-01-01

The large-time behavior of solutions to the Burgers equation with small viscosity is described using invariant manifolds. In particular, a geometric explanation is provided for a phenomenon known as metastability, which in the present context means that solutions spend a very long time near the family of solutions known as diffusive N-waves before finally converging to a stable self-similar diffusion wave. More precisely, it is shown that in terms of similarity, or scaling, variables in an algebraically weighted L^2 space, the self-similar diffusion waves correspond to a one-dimensional global center manifold of stationary solutions. Through each of these fixed points there exists a one-dimensional, global, attractive, invariant manifold corresponding to the diffusive N-waves. Thus, metastability corresponds to a fast transient in which solutions approach this metastable manifold of diffusive N-waves, followed by a slow decay along this manifold, and, finally, convergence to the self-similar diffusion wave.
The effect of dissipative inhomogeneous medium on the statistics of the wave intensity

NASA Technical Reports Server (NTRS)

Saatchi, Sasan S.

1993-01-01

One of the main theoretical points in the theory of wave propagation in random medium is the derivation of closed form equations to describe the statistics of the propagating waves. In particular, in one dimensional problems, the closed form representation of the multiple scattering effects is important since it contributes in understanding such problems like wave localization, backscattering enhancement, and intensity fluctuations. In this the propagation of plane waves in a layer of one-dimensional dissipative random medium is considered. The medium is modeled by a complex permittivity whose real part is a constant representing the absorption. The one dimensional problem is mathematically equivalent to the analysis of a transmission line with randomly perturbed distributed parameters and a single mode lossy waveguide and the results can be used to study the propagation of radio waves through atmosphere and the remote sensing of geophysical media. It is assumed the scattering medium consists of an ensemble of one-dimensional point scatterers randomly positioned in a layer of thickness L with diffuse boundaries. A Poisson impulse process with density lambda is used to model the position of scatterers in the medium. By employing the Markov properties of this process an exact closed form equation of Kolmogorov-Feller type was obtained for the probability density of the reflection coefficient. This equation was solved by combining two limiting cases: (1) when the density of scatterers is small; and (2) when the medium is weakly dissipative. A two variable perturbation method for small lambda was used to obtain solutions valid for thick layers. These solutions are then asymptotically evaluated for small dissipation. To show the effect of dissipation, the mean and fluctuations of the reflected power are obtained. The results were compared with a lossy homogeneous medium and with a lossless inhomogeneous medium and the regions where the effect of absorption is not essential were discussed.
Explicit mathematical construction of relativistic nonlinear de Broglie waves described by three-dimensional (wave and electromagnetic) solitons ``piloted'' (controlled) by corresponding solutions of associated linear Klein-Gordon and Schrödinger equations

NASA Astrophysics Data System (ADS)

Vigier, Jean-Pierre

1991-02-01

Starting from a nonlinear relativistic Klein-Gordon equation derived from the stochastic interpretation of quantum mechanics (proposed by Bohm-Vigier, (1) Nelson, (2) de Broglie, (3) Guerra et al. (4) ), one can construct joint wave and particle, soliton-like solutions, which follow the average de Broglie-Bohm (5) real trajectories associated with linear solutions of the usual Schrödinger and Klein-Gordon equations.
Guided solitary waves.

PubMed

Miles, J

1980-04-01

Transversely periodic solitary-wave solutions of the Boussinesq equations (which govern wave propagation in a weakly dispersive, weakly nonlinear physical system) are determined. The solutions for negative dispersion (e.g., gravity waves) are singular and therefore physically unacceptable. The solutions for positive dispersion (e.g., capillary waves or magnetosonic waves in a plasma) are physically acceptable except in a limited parametric interval, in which they are complex. The two end points of this interval are associated with (two different) resonant interactions among three basic solitary waves, two of which are two-dimensional complex conjugates and the third of which is one-dimensional and real.
Comparison between results of solution of Burgers' equation and Laplace's equation by Galerkin and least-square finite element methods

NASA Astrophysics Data System (ADS)

Adib, Arash; Poorveis, Davood; Mehraban, Farid

2018-03-01

In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.
True amplitude wave equation migration arising from true amplitude one-way wave equations

NASA Astrophysics Data System (ADS)

Zhang, Yu; Zhang, Guanquan; Bleistein, Norman

2003-10-01

One-way wave operators are powerful tools for use in forward modelling and inversion. Their implementation, however, involves introduction of the square root of an operator as a pseudo-differential operator. Furthermore, a simple factoring of the wave operator produces one-way wave equations that yield the same travel times as the full wave equation, but do not yield accurate amplitudes except for homogeneous media and for almost all points in heterogeneous media. Here, we present augmented one-way wave equations. We show that these equations yield solutions for which the leading order asymptotic amplitude as well as the travel time satisfy the same differential equations as the corresponding functions for the full wave equation. Exact representations of the square-root operator appearing in these differential equations are elusive, except in cases in which the heterogeneity of the medium is independent of the transverse spatial variables. Here, we address the fully heterogeneous case. Singling out depth as the preferred direction of propagation, we introduce a representation of the square-root operator as an integral in which a rational function of the transverse Laplacian appears in the integrand. This allows us to carry out explicit asymptotic analysis of the resulting one-way wave equations. To do this, we introduce an auxiliary function that satisfies a lower dimensional wave equation in transverse spatial variables only. We prove that ray theory for these one-way wave equations leads to one-way eikonal equations and the correct leading order transport equation for the full wave equation. We then introduce appropriate boundary conditions at z = 0 to generate waves at depth whose quotient leads to a reflector map and an estimate of the ray theoretical reflection coefficient on the reflector. Thus, these true amplitude one-way wave equations lead to a 'true amplitude wave equation migration' (WEM) method. In fact, we prove that applying the WEM imaging condition to these newly defined wavefields in heterogeneous media leads to the Kirchhoff inversion formula for common-shot data when the one-way wavefields are replaced by their ray theoretic approximations. This extension enhances the original WEM method. The objective of that technique was a reflector map, only. The underlying theory did not address amplitude issues. Computer output obtained using numerically generated data confirms the accuracy of this inversion method. However, there are practical limitations. The observed data must be a solution of the wave equation. Therefore, the data over the entire survey area must be collected from a single common-shot experiment. Multi-experiment data, such as common-offset data, cannot be used with this method as currently formulated. Research on extending the method is ongoing at this time.
New exact periodic solitary-wave solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in multi-temperature electron plasmas

NASA Astrophysics Data System (ADS)

Liu, Jian-Guo; Tian, Yu; Zeng, Zhi-Fang

2017-10-01

In this paper, we aim to introduce a new form of the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation for the long waves of small amplitude with slow dependence on the transverse coordinate. By using the Hirota's bilinear form and the extended homoclinic test approach, new exact periodic solitary-wave solutions for the new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation are presented. Moreover, the properties and characteristics for these new exact periodic solitary-wave solutions are discussed with some figures.
Nonlocal symmetries, solitary waves and cnoidal periodic waves of the (2+1)-dimensional breaking soliton equation

NASA Astrophysics Data System (ADS)

Zou, Li; Tian, Shou-Fu; Feng, Lian-Li

2017-12-01

In this paper, we consider the (2+1)-dimensional breaking soliton equation, which describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis. By virtue of the truncated Painlevé expansion method, we obtain the nonlocal symmetry, Bäcklund transformation and Schwarzian form of the equation. Furthermore, by using the consistent Riccati expansion (CRE), we prove that the breaking soliton equation is solvable. Based on the consistent tan-function expansion, we explicitly derive the interaction solutions between solitary waves and cnoidal periodic waves.
Dirac and Klein-Gordon-Fock equations in Grumiller’s spacetime

NASA Astrophysics Data System (ADS)

Al-Badawi, A.; Sakalli, I.

We study the Dirac and the chargeless Klein-Gordon-Fock equations in the geometry of Grumiller’s spacetime that describes a model for gravity of a central object at large distances. The Dirac equation is separated into radial and angular equations by adopting the Newman-Penrose formalism. The angular part of the both wave equations are analytically solved. For the radial equations, we managed to reduce them to one dimensional Schrödinger-type wave equations with their corresponding effective potentials. Fermions’s potentials are numerically analyzed by serving their some characteristic plots. We also compute the quasinormal frequencies of the chargeless and massive scalar waves. With the aid of those quasinormal frequencies, Bekenstein’s area conjecture is tested for the Grumiller black hole. Thus, the effects of the Rindler acceleration on the waves of fermions and scalars are thoroughly analyzed.
Intermittency in generalized NLS equation with focusing six-wave interactions

NASA Astrophysics Data System (ADS)

Agafontsev, D. S.; Zakharov, V. E.

2015-10-01

We study numerically the statistics of waves for generalized one-dimensional Nonlinear Schrödinger (NLS) equation that takes into account focusing six-wave interactions, dumping and pumping terms. We demonstrate the universal behavior of this system for the region of parameters when six-wave interactions term affects significantly only the largest waves. In particular, in the statistically steady state of this system the probability density function (PDF) of wave amplitudes turns out to be strongly non-Rayleigh one for large waves, with characteristic "fat tail" decaying with amplitude | Ψ | close to ∝ exp ⁡ (- γ | Ψ |), where γ > 0 is constant. The corresponding non-Rayleigh addition to the PDF indicates strong intermittency, vanishes in the absence of six-wave interactions, and increases with six-wave coupling coefficient.
Two-and-one-half-dimensional magnetohydrodynamic simulations of the plasma sheet in the presence of oxygen ions: The plasma sheet oscillation and compressional Pc 5 waves

NASA Astrophysics Data System (ADS)

Lu, Li; Liu, Zhen-Xing; Cao, Jin-Bin

2002-02-01

Two-and-one-half-dimensional magnetohydrodynamic simulations of the multicomponent plasma sheet with the velocity curl term in the magnetic equation are represented. The simulation results can be summarized as follows: (1) There is an oscillation of the plasma sheet with the period on the order of 400 s (Pc 5 range); (2) the magnetic equator is a node of the magnetic field disturbance; (3) the magnetic energy integral varies antiphase with the internal energy integral; (4) disturbed waves have a propagating speed on the order of 10 km/s earthward; (5) the abundance of oxygen ions influences amplitude, period, and dissipation of the plasma sheet oscillation. It is suggested that the compressional Pc 5 waves, which are observed in the plasma sheet close to the magnetic equator, may be caused by the plasma sheet oscillation, or may be generated from the resonance of the plasma sheet oscillation with some Pc 5 perturbation waves coming from the outer magnetosphere.
New Patterns of the Two-Dimensional Rogue Waves: (2+1)-Dimensional Maccari System

NASA Astrophysics Data System (ADS)

Wang, Gai-Hua; Wang, Li-Hong; Rao, Ji-Guang; He, Jing-Song

2017-06-01

The ocean rogue wave is one kind of puzzled destructive phenomenon that has not been understood thoroughly so far. The two-dimensional nature of this wave has inspired the vast endeavors on the recognizing new patterns of the rogue waves based on the dynamical equations with two-spatial variables and one-temporal variable, which is a very crucial step to prevent this disaster event at the earliest stage. Along this issue, we present twelve new patterns of the two-dimensional rogue waves, which are reduced from a rational and explicit formula of the solutions for a (2+1)-dimensional Maccari system. The extreme points (lines) of the first-order lumps (rogue waves) are discussed according to their analytical formulas. For the lower-order rogue waves, we show clearly in formula that parameter b 2 plays a significant role to control these patterns. Supported by the National Natural Science Foundation of China under Grant No. 11671219, the K. C. Wong Magna Fund in Ningbo University, Gai-Hua Wang is also supported by the Scientific Research Foundation of Graduate School of Ningbo University
Strongly coupled stress waves in heterogeneous plates.

NASA Technical Reports Server (NTRS)

Wang, A. S. D.; Chou, P. C.; Rose, J. L.

1972-01-01

Consideration of coupled stress waves generated by an impulsive load applied at one end of a semiinfinite plate. For the field equations governing the one-dimensional coupled waves a hyperbolic system of equations is obtained in which a strong coupling in the second derivatives exists. The method of characteristics described by Chou and Mortimer (1967) is extended to cover the case of strong coupling, and a study is made of the transient stress waves in a semiinfinite plate subjected to an initial step input. Coupled discontinuity fronts are found to propagate at different velocities. The normal plate stress and the bending moment at different time regimes are illustrated by graphs.
Lie symmetry analysis, Bäcklund transformations, and exact solutions of a (2 + 1)-dimensional Boiti-Leon-Pempinelli system

NASA Astrophysics Data System (ADS)

Zhao, Zhonglong; Han, Bo

2017-10-01

In this paper, the Lie symmetry analysis method is employed to investigate the Lie point symmetries and the one-parameter transformation groups of a (2 + 1)-dimensional Boiti-Leon-Pempinelli system. By using Ibragimov's method, the optimal system of one-dimensional subalgebras of this system is constructed. Truncated Painlevé analysis is used for deriving the Bäcklund transformation. The method of constructing lump-type solutions of integrable equations by means of Bäcklund transformation is first presented. Meanwhile, the lump-type solutions of the (2 + 1)-dimensional Boiti-Leon-Pempinelli system are obtained. The lump-type wave is one kind of rogue wave. The fusion-type N-solitary wave solutions are also constructed. In addition, this system is integrable in terms of the consistent Riccati expansion method.
Development of a particle method of characteristics (PMOC) for one-dimensional shock waves

NASA Astrophysics Data System (ADS)

Hwang, Y.-H.

2018-03-01

In the present study, a particle method of characteristics is put forward to simulate the evolution of one-dimensional shock waves in barotropic gaseous, closed-conduit, open-channel, and two-phase flows. All these flow phenomena can be described with the same set of governing equations. The proposed scheme is established based on the characteristic equations and formulated by assigning the computational particles to move along the characteristic curves. Both the right- and left-running characteristics are traced and represented by their associated computational particles. It inherits the computational merits from the conventional method of characteristics (MOC) and moving particle method, but without their individual deficiencies. In addition, special particles with dual states deduced to the enforcement of the Rankine-Hugoniot relation are deliberately imposed to emulate the shock structure. Numerical tests are carried out by solving some benchmark problems, and the computational results are compared with available analytical solutions. From the derivation procedure and obtained computational results, it is concluded that the proposed PMOC will be a useful tool to replicate one-dimensional shock waves.
Analysis of Eigenvalue and Eigenfunction of Klein Gordon Equation Using Asymptotic Iteration Method for Separable Non-central Cylindrical Potential

NASA Astrophysics Data System (ADS)

Suparmi, A.; Cari, C.; Lilis Elviyanti, Isnaini

2018-04-01

Analysis of relativistic energy and wave function for zero spin particles using Klein Gordon equation was influenced by separable noncentral cylindrical potential was solved by asymptotic iteration method (AIM). By using cylindrical coordinates, the Klein Gordon equation for the case of symmetry spin was reduced to three one-dimensional Schrodinger like equations that were solvable using variable separation method. The relativistic energy was calculated numerically with Matlab software, and the general unnormalized wave function was expressed in hypergeometric terms.
Theory and Experiment Analysis of Two-Dimensional Acousto-Optic Interaction.

DTIC Science & Technology

1995-01-03

The universal coupled wave equation of two dimensional acousto optic effect has been deduced and the solution of normal Raman-Hath acousto optic diffraction...was derived from it. The theory was compared with the experimental results of a two dimensional acousto optic device consisting of two one dimensional modulators. The experiment results agree with the theory. (AN)
Travelling wave solutions of the homogeneous one-dimensional FREFLO model

NASA Astrophysics Data System (ADS)

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.

The solution of the dam-break problem in the Porous Shallow water Equations

NASA Astrophysics Data System (ADS)

Cozzolino, Luca; Pepe, Veronica; Cimorelli, Luigi; D'Aniello, Andrea; Della Morte, Renata; Pianese, Domenico

2018-04-01

The Porous Shallow water Equations are commonly used to evaluate the propagation of flooding waves in the urban environment. These equations may exhibit not only classic shocks, rarefactions, and contact discontinuities, as in the ordinary two-dimensional Shallow water Equations, but also special discontinuities at abrupt porosity jumps. In this paper, an appropriate parameterization of the stationary weak solutions of one-dimensional Porous Shallow water Equations supplies the inner structure of the porosity jumps. The exact solution of the corresponding dam-break problem is presented, and six different wave configurations are individuated, proving that the solution exists and it is unique for given initial conditions and geometric characteristics. These results can be used as a benchmark in order to validate one- and two-dimensional numerical models for the solution of the Porous Shallow water Equations. In addition, it is presented a novel Finite Volume scheme where the porosity jumps are taken into account by means of a variables reconstruction approach. The dam-break results supplied by this numerical scheme are compared with the exact dam-break results, showing the promising capabilities of this numerical approach. Finally, the advantages of the novel porosity jump definition are shown by comparison with other definitions available in the literature, demonstrating its advantages, and the issues raising in real world applications are discussed.
Several reverse-time integrable nonlocal nonlinear equations: Rogue-wave solutions

NASA Astrophysics Data System (ADS)

Yang, Bo; Chen, Yong

2018-05-01

A study of rogue-wave solutions in the reverse-time nonlocal nonlinear Schrödinger (NLS) and nonlocal Davey-Stewartson (DS) equations is presented. By using Darboux transformation (DT) method, several types of rogue-wave solutions are constructed. Dynamics of these rogue-wave solutions are further explored. It is shown that the (1 + 1)-dimensional fundamental rogue-wave solutions in the reverse-time NLS equation can be globally bounded or have finite-time blowing-ups. It is also shown that the (2 + 1)-dimensional line rogue waves in the reverse-time nonlocal DS equations can be bounded for all space and time or develop singularities in critical time. In addition, the multi- and higher-order rogue waves exhibit richer structures, most of which have no counterparts in the corresponding local nonlinear equations.
Generation of Rising-tone Chorus in a Two-dimensional Mirror Field by Using the General Curvilinear PIC Code

NASA Astrophysics Data System (ADS)

Ke, Y.; Gao, X.; Lu, Q.; Wang, X.; Wang, S.

2017-12-01

Recently, the generation of rising-tone chorus has been implemented with one-dimensional (1-D) particle-in-cell (PIC) simulations in an inhomogeneous background magnetic field, where both the propagation of waves and motion of electrons are simply forced to be parallel to the background magnetic field. We have developed a two-dimensional(2-D) general curvilinear PIC simulation code, and successfully reproduced rising-tone chorus waves excited from an anisotropic electron distribution in a 2-D mirror field. Our simulation results show that whistler waves are mainly generated around the magnetic equator, and continuously gain growth during their propagation toward higher-latitude regions. The rising-tone chorus waves are formed off the magnetic equator, which propagate quasi-parallel to the background magnetic field with the finite wave normal angle. Due to the propagating effect, the wave normal angle of chorus waves is increasing during their propagation toward higher-latitude regions along an enough curved field line. The chirping rate of chorus waves are found to be larger along a field line more close to the middle field line in the mirror field.
Generation of rising-tone chorus in a two-dimensional mirror field by using the general curvilinear PIC code

NASA Astrophysics Data System (ADS)

Ke, Yangguang; Gao, Xinliang; Lu, Quanming; Wang, Xueyi; Wang, Shui

2017-08-01

Recently, the generation of rising-tone chorus has been implemented with one-dimensional (1-D) particle-in-cell (PIC) simulations in an inhomogeneous background magnetic field, where both the propagation of waves and motion of electrons are simply forced to be parallel to the background magnetic field. In this paper, we have developed a two-dimensional (2-D) general curvilinear PIC simulation code and successfully reproduced rising-tone chorus waves excited from an anisotropic electron distribution in a 2-D mirror field. Our simulation results show that whistler waves are mainly generated around the magnetic equator and continuously gain growth during their propagation toward higher-latitude regions. The rising-tone chorus waves are observed off the magnetic equator, which propagate quasi-parallel to the background magnetic field with the wave normal angle smaller than 25°. Due to the propagating effect, the wave normal angle of chorus waves is increasing during their propagation toward higher-latitude regions along an enough curved field line. The chirping rate of chorus waves is found to be larger along a field line with a smaller curvature.
Nonlinear ion acoustic waves scattered by vortexes

NASA Astrophysics Data System (ADS)

Ohno, Yuji; Yoshida, Zensho

2016-09-01

The Kadomtsev-Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here, we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes 'scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are 'ambient' because they do not receive reciprocal reactions from the waves (i.e., the vortex equation is independent of the wave fields). This model describes a minimal departure from the integrable KP system. By the Painlevé test, we delineate how the vorticity term violates integrability, bringing about an essential three-dimensionality to the solutions. By numerical simulation, we show how the solitons are scattered by vortexes and become chaotic.
Nonlinear Conservation Laws and Finite Volume Methods

NASA Astrophysics Data System (ADS)

Leveque, Randall J.

Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References
a Speculative Study on Negative-Dimensional Potential and Wave Problems by Implicit Calculus Modeling Approach

NASA Astrophysics Data System (ADS)

Chen, Wen; Wang, Fajie

Based on the implicit calculus equation modeling approach, this paper proposes a speculative concept of the potential and wave operators on negative dimensionality. Unlike the standard partial differential equation (PDE) modeling, the implicit calculus modeling approach does not require the explicit expression of the PDE governing equation. Instead the fundamental solution of physical problem is used to implicitly define the differential operator and to implement simulation in conjunction with the appropriate boundary conditions. In this study, we conjecture an extension of the fundamental solution of the standard Laplace and Helmholtz equations to negative dimensionality. And then by using the singular boundary method, a recent boundary discretization technique, we investigate the potential and wave problems using the fundamental solution on negative dimensionality. Numerical experiments reveal that the physics behaviors on negative dimensionality may differ on positive dimensionality. This speculative study might open an unexplored territory in research.
Gaussian variational ansatz in the problem of anomalous sea waves: Comparison with direct numerical simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ruban, V. P., E-mail: ruban@itp.ac.ru

2015-05-15

The nonlinear dynamics of an obliquely oriented wave packet on a sea surface is analyzed analytically and numerically for various initial parameters of the packet in relation to the problem of the so-called rogue waves. Within the Gaussian variational ansatz applied to the corresponding (1+2)-dimensional hyperbolic nonlinear Schrödinger equation (NLSE), a simplified Lagrangian system of differential equations is derived that describes the evolution of the coefficients of the real and imaginary quadratic forms appearing in the Gaussian. This model provides a semi-quantitative description of the process of nonlinear spatiotemporal focusing, which is one of the most probable mechanisms of roguemore » wave formation in random wave fields. The system of equations is integrated in quadratures, which allows one to better understand the qualitative differences between linear and nonlinear focusing regimes of a wave packet. Predictions of the Gaussian model are compared with the results of direct numerical simulation of fully nonlinear long-crested waves.« less
KP Equation in a Three-Dimensional Unmagnetized Warm Dusty Plasma with Variable Dust Charge

NASA Astrophysics Data System (ADS)

El-Shorbagy, Kh. H.; Mahassen, Hania; El-Bendary, Atef Ahmed

2017-12-01

In this work, we investigate the propagation of three-dimensional nonlinear dust-acoustic and dust-Coulomb waves in an unmagnetized warm dusty plasma consisting of electrons, ions, and charged dust particles. The grain charge fluctuation is incorporated through the current balance equation. Using the perturbation method, a Kadomtsev-Petviashvili (KP) equation is obtained. It has been shown that the charge fluctuation would modify the wave structures, and the waves in such systems are unstable due to high-order long wave perturbations.
Nonlinear dynamics of resonant electrons interacting with coherent Langmuir waves

NASA Astrophysics Data System (ADS)

Tobita, Miwa; Omura, Yoshiharu

2018-03-01

We study the nonlinear dynamics of resonant particles interacting with coherent waves in space plasmas. Magnetospheric plasma waves such as whistler-mode chorus, electromagnetic ion cyclotron waves, and hiss emissions contain coherent wave structures with various discrete frequencies. Although these waves are electromagnetic, their interaction with resonant particles can be approximated by equations of motion for a charged particle in a one-dimensional electrostatic wave. The equations are expressed in the form of nonlinear pendulum equations. We perform test particle simulations of electrons in an electrostatic model with Langmuir waves and a non-oscillatory electric field. We solve equations of motion and study the dynamics of particles with different values of inhomogeneity factor S defined as a ratio of the non-oscillatory electric field intensity to the wave amplitude. The simulation results demonstrate deceleration/acceleration, thermalization, and trapping of particles through resonance with a single wave, two waves, and multiple waves. For two-wave and multiple-wave cases, we describe the wave-particle interaction as either coherent or incoherent based on the probability of nonlinear trapping.
Nonlocal Reformulations of Water and Internal Waves and Asymptotic Reductions

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.

2009-09-01

Nonlocal reformulations of the classical equations of water waves and two ideal fluids separated by a free interface, bounded above by either a rigid lid or a free surface, are obtained. The kinematic equations may be written in terms of integral equations with a free parameter. By expressing the pressure, or Bernoulli, equation in terms of the surface/interface variables, a closed system is obtained. An advantage of this formulation, referred to as the nonlocal spectral (NSP) formulation, is that the vertical component is eliminated, thus reducing the dimensionality and fixing the domain in which the equations are posed. The NSP equations and the Dirichlet-Neumann operators associated with the water wave or two-fluid equations can be related to each other and the Dirichlet-Neumann series can be obtained from the NSP equations. Important asymptotic reductions obtained from the two-fluid nonlocal system include the generalizations of the Benney-Luke and Kadomtsev-Petviashvili (KP) equations, referred to as intermediate-long wave (ILW) generalizations. These 2+1 dimensional equations possess lump type solutions. In the water wave problem high-order asymptotic series are obtained for two and three dimensional gravity-capillary solitary waves. In two dimensions, the first term in the asymptotic series is the well-known hyperbolic secant squared solution of the KdV equation; in three dimensions, the first term is the rational lump solution of the KP equation.
Analysis of sound propagation in ducts using the wave envelope concept

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1974-01-01

A finite difference formulation is presented for sound propagation in a rectangular two-dimensional duct without steady flow for plane wave input. Before the difference equations are formulated, the governing Helmholtz equation is first transformed to a form whose solution does not oscillate along the length of the duct. This transformation reduces the required number of grid points by an order of magnitude, and the number of grid points becomes independent of the sound frequency. Physically, the transformed pressure represents the amplitude of the conventional sound wave. Example solutions are presented for sound propagation in a one-dimensional straight hard-wall duct and in a two-dimensional straight soft-wall duct without steady flow. The numerical solutions show evidence of the existence along the duct wall of a developing acoustic pressure diffusion boundary layer which is similar in nature to the conventional viscous flow boundary layer. In order to better illustrate this concept, the wave equation and boundary conditions are written such that the frequency no longer appears explicitly in them. The frequency effects in duct propagation can be visualized solely as an expansion and stretching of the suppressor duct.
A generic efficient adaptive grid scheme for rocket propulsion modeling

NASA Technical Reports Server (NTRS)

Mo, J. D.; Chow, Alan S.

1993-01-01

The objective of this research is to develop an efficient, time-accurate numerical algorithm to discretize the Navier-Stokes equations for the predictions of internal one-, two-dimensional and axisymmetric flows. A generic, efficient, elliptic adaptive grid generator is implicitly coupled with the Lower-Upper factorization scheme in the development of ALUNS computer code. The calculations of one-dimensional shock tube wave propagation and two-dimensional shock wave capture, wave-wave interactions, shock wave-boundary interactions show that the developed scheme is stable, accurate and extremely robust. The adaptive grid generator produced a very favorable grid network by a grid speed technique. This generic adaptive grid generator is also applied in the PARC and FDNS codes and the computational results for solid rocket nozzle flowfield and crystal growth modeling by those codes will be presented in the conference, too. This research work is being supported by NASA/MSFC.
On mass transport in porosity waves

NASA Astrophysics Data System (ADS)

Jordan, Jacob S.; Hesse, Marc A.; Rudge, John F.

2018-03-01

Porosity waves arise naturally from the equations describing fluid migration in ductile rocks. Here, we show that higher-dimensional porosity waves can transport mass and therefore preserve geochemical signatures, at least partially. Fluid focusing into these high porosity waves leads to recirculation in their center. This recirculating fluid is separated from the background flow field by a circular dividing streamline and transported with the phase velocity of the porosity wave. Unlike models for one-dimensional chromatography in geological porous media, tracer transport in higher-dimensional porosity waves does not produce chromatographic separations between relatively incompatible elements due to the circular flow pattern. This may allow melt that originated from the partial melting of fertile heterogeneities or fluid produced during metamorphism to retain distinct geochemical signatures as they rise buoyantly towards the surface.
On nonlinear evolution of low-frequency Alfvén waves in weakly-expanding solar wind plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nariyuki, Y.

A multi-dimensional nonlinear evolution equation for Alfvén waves in weakly-expanding solar wind plasmas is derived by using the reductive perturbation method. The expansion of solar wind plasma parcels is modeled by an expanding box model, which includes the accelerating expansion. It is shown that the resultant equation agrees with the Wentzel-Kramers-Brillouin prediction of the low-frequency Alfvén waves in the linear limit. In the cold and one-dimensional limit, a modified derivative nonlinear Schrodinger equation is obtained. Direct numerical simulations are carried out to discuss the effect of the expansion on the modulational instability of monochromatic Alfvén waves and the propagation ofmore » Alfvén solitons. By using the instantaneous frequency, it is quantitatively shown that as far as the expansion rate is much smaller than wave frequencies, effects of the expansion are almost adiabatic. It is also confirmed that while shapes of Alfvén solitons temporally change due to the expansion, some of them can stably propagate after their collision in weakly-expanding plasmas.« less
Propagation of acoustic waves in a one-dimensional macroscopically inhomogeneous poroelastic material.

PubMed

Gautier, G; Kelders, L; Groby, J P; Dazel, O; De Ryck, L; Leclaire, P

2011-09-01

Wave propagation in macroscopically inhomogeneous porous materials has received much attention in recent years. The wave equation, derived from the alternative formulation of Biot's theory of 1962, was reduced and solved recently in the case of rigid frame inhomogeneous porous materials. This paper focuses on the solution of the full wave equation in which the acoustic and the elastic properties of the poroelastic material vary in one-dimension. The reflection coefficient of a one-dimensional macroscopically inhomogeneous porous material on a rigid backing is obtained numerically using the state vector (or the so-called Stroh) formalism and Peano series. This coefficient can then be used to straightforwardly calculate the scattered field. To validate the method of resolution, results obtained by the present method are compared to those calculated by the classical transfer matrix method at both normal and oblique incidence and to experimental measurements at normal incidence for a known two-layers porous material, considered as a single inhomogeneous layer. Finally, discussion about the absorption coefficient for various inhomogeneity profiles gives further perspectives. © 2011 Acoustical Society of America
Integral method for the calculation of Hawking radiation in dispersive media. I. Symmetric asymptotics.

PubMed

Robertson, Scott; Leonhardt, Ulf

2014-11-01

Hawking radiation has become experimentally testable thanks to the many analog systems which mimic the effects of the event horizon on wave propagation. These systems are typically dominated by dispersion and give rise to a numerically soluble and stable ordinary differential equation only if the rest-frame dispersion relation Ω^{2}(k) is a polynomial of relatively low degree. Here we present a new method for the calculation of wave scattering in a one-dimensional medium of arbitrary dispersion. It views the wave equation as an integral equation in Fourier space, which can be solved using standard and efficient numerical techniques.
Whitham modulation theory for (2 + 1)-dimensional equations of Kadomtsev–Petviashvili type

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Biondini, Gino; Rumanov, Igor

2018-05-01

Whitham modulation theory for certain two-dimensional evolution equations of Kadomtsev–Petviashvili (KP) type is presented. Three specific examples are considered in detail: the KP equation, the two-dimensional Benjamin–Ono (2DBO) equation and a modified KP (m2KP) equation. A unified derivation is also provided. In the case of the m2KP equation, the corresponding Whitham modulation system exhibits features different from the other two. The approach presented here does not require integrability of the original evolution equation. Indeed, while the KP equation is known to be a completely integrable equation, the 2DBO equation and the m2KP equation are not known to be integrable. In each of the cases considered, the Whitham modulation system obtained consists of five first-order quasilinear partial differential equations. The Riemann problem (i.e. the analogue of the Gurevich–Pitaevskii problem) for the one-dimensional reduction of the m2KP equation is studied. For the m2KP equation, the system of modulation equations is used to analyze the linear stability of traveling wave solutions.
Freak oscillation in a dusty plasma.

PubMed

Zhang, Heng; Yang, Yang; Hong, Xue-Ren; Qi, Xin; Duan, Wen-Shan; Yang, Lei

2017-05-01

The freak oscillation in one-dimensional dusty plasma is studied numerically by particle-in-cell method. Using a perturbation method, the basic set of fluid equations is reduced to a nonlinear Schrödinger equation (NLSE). The rational solution of the NLSE is presented, which is proposed as an effective tool for studying the rogue waves in dusty plasma. Additionally, the application scope of the analytical solution of the rogue wave described by the NLSE is given.
A convergent series expansion for hyperbolic systems of conservation laws

NASA Technical Reports Server (NTRS)

Harabetian, E.

1985-01-01

The discontinuities piecewise analytic initial value problem for a wide class of conservation laws is considered which includes the full three-dimensional Euler equations. The initial interaction at an arbitrary curved surface is resolved in time by a convergent series. Among other features the solution exhibits shock, contact, and expansion waves as well as sound waves propagating on characteristic surfaces. The expansion waves correspond to he one-dimensional rarefactions but have a more complicated structure. The sound waves are generated in place of zero strength shocks, and they are caused by mismatches in derivatives.

Restoration of the contact surface in FORCE-type centred schemes I: Homogeneous two-dimensional shallow water equations

NASA Astrophysics Data System (ADS)

Canestrelli, Alberto; Toro, Eleuterio F.

2012-10-01

Recently, the FORCE centred scheme for conservative hyperbolic multi-dimensional systems has been introduced in [34] and has been applied to Euler and relativistic MHD equations, solved on unstructured meshes. In this work we propose a modification of the FORCE scheme, named FORCE-Contact, that provides improved resolution of contact and shear waves. This paper presents the technique in full detail as applied to the two-dimensional homogeneous shallow water equations. The improvements due to the new method are particularly evident when an additional equation is solved for a tracer, since the modified scheme exactly resolves isolated and steady contact discontinuities. The improvement is considerable also for slowly moving contact discontinuities, for shear waves and for steady states in meandering channels. For these types of flow fields, the numerical results provided by the new FORCE-Contact scheme are comparable with, and sometimes better than, the results obtained from upwind schemes, such as Roes scheme for example. In a companion paper, a similar approach to restoring the missing contact wave and preserving well-balanced properties for non-conservative one- and two-layer shallow water equations is introduced. However, the procedure is general and it is in principle applicable to other multidimensional hyperbolic systems in conservative and non-conservative form, such as the Euler equations for compressible gas dynamics.
Control of Combustion-Instabilities Through Various Passive Devices

NASA Technical Reports Server (NTRS)

Frendi, Kader

2005-01-01

It is well known that under some operating conditions, rocket engines (using solid or liquid fuels) exhibit unstable modes of operation that can lead to engine malfunction and shutdown. The sources of these instabilities are diverse and are dependent on fuel, chamber geometry and various upstream sources such as pumps, valves and injection mechanism. It is believed that combustion-acoustic instabilities occur when the acoustic energy increase due to the unsteady heat release of the flame is greater than the losses of acoustic energy from the system [1, 2]. Giammar and Putnam [3] performed a comprehensive study of noise generated by gasfired industrial burners and made several key observations; flow noise was sometimes more intense than combustion roar, which tended to have a characteristic frequency spectrum. Turbulence was amplified by the flame. The noise power varied directly with combustion intensity and also with the product of pressure drop and heat release rate. Karchmer [4] correlated the noise emitted from a turbofan jet engine with that in the combustion chamber. This is important, since it quantified how much of the noise from an engine originates in the combustor. A physical interpretation of the interchange of energy between sound waves and unsteady heat release rates was given by Rayleigh [5] for inviscid, linear perturbations. Bloxidge et al [6] extended Rayleigh s criterion to describe the interaction of unsteady combustion with one-dimensional acoustic waves in a duct. Solutions to the mass, momentum and energy conservation equations in the pre- and post-flame zones were matched by making several assumptions about the combustion process. They concluded that changes in boundary conditions affect the energy balance of acoustic waves in the combustor. Abouseif et al [7] also solved the one-dimensional flow equations, but they used a onestep reaction to evaluate the unsteady heat release rate by relating it to temperature and velocity perturbations. Their analysis showed that oscillations arise from coupling between entropy waves produced at the flame and pressure waves originating from the nozzle. Yang and Culick [8] assumed a thin flame sheet, which is distorted by velocity and pressure oscillations. Conservation equations were expressed in integral form and solutions for the acoustic wave equations and complex frequencies were obtained. The imaginary part of the frequency indicated stability regions of the flame. Activation energy asymptotics together with a one-step reaction were used by McIntosh [9] to study the effects of acoustic forcing and feedback on unsteady, one-dimensional flames. He found that the flame stability was altered by the upstream acoustic feedback. Shyy et al [10] used a high-accuracy TVD scheme to simulate unsteady, one-dimensional longitudinal, combustion instabilities. However, numerical diffusion was not completely eliminated. Recently, Prasad [11] investigated numerically the interactions of pressure perturbations with premixed flames. He used complex chemistry to study responses of pressure perturbations in one-dimensional combustors. His results indicated that reflected and transmitted waves differed significantly from incident waves.
Spatiotemporal chaos and two-dimensional dissipative rogue waves in Lugiato-Lefever model

NASA Astrophysics Data System (ADS)

Panajotov, Krassimir; Clerc, Marcel G.; Tlidi, Mustapha

2017-06-01

Driven nonlinear optical cavities can exhibit complex spatiotemporal dynamics. We consider the paradigmatic Lugiato-Lefever model describing driven nonlinear optical resonator. This model is one of the most-studied nonlinear equations in optics. It describes a large spectrum of nonlinear phenomena from bistability, to periodic patterns, localized structures, self-pulsating localized structures and to a complex spatiotemporal behavior. The model is considered also as prototype model to describe several optical nonlinear devices such as Kerr media, liquid crystals, left handed materials, nonlinear fiber cavity, and frequency comb generation. We focus our analysis on a spatiotemporal chaotic dynamics in one-dimension. We identify a route to spatiotemporal chaos through an extended quasiperiodicity. We have estimated the Kaplan-Yorke dimension that provides a measure of the strange attractor complexity. Likewise, we show that the Lugiato-Leferver equation supports rogues waves in two-dimensional settings. We characterize rogue-wave formation by computing the probability distribution of the pulse height. Contribution to the Topical Issue "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.
Explicit and exact nontraveling wave solutions of the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama equation

NASA Astrophysics Data System (ADS)

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.
New solitary wave solutions of (3 + 1)-dimensional nonlinear extended Zakharov-Kuznetsov and modified KdV-Zakharov-Kuznetsov equations and their applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, A. R.; Arshad, M.; Wang, Jun

In this paper, new exact solitary wave, soliton and elliptic function solutions are constructed in various forms of three dimensional nonlinear partial differential equations (PDEs) in mathematical physics by utilizing modified extended direct algebraic method. Soliton solutions in different forms such as bell and anti-bell periodic, dark soliton, bright soliton, bright and dark solitary wave in periodic form etc are obtained, which have large applications in different branches of physics and other areas of applied sciences. The obtained solutions are also presented graphically. Furthermore, many other nonlinear evolution equations arising in mathematical physics and engineering can also be solved by this powerful, reliable and capable method. The nonlinear three dimensional extended Zakharov-Kuznetsov dynamica equation and (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsov equation are selected to show the reliability and effectiveness of the current method.
A single-sided representation for the homogeneous Green's function of a unified scalar wave equation.

PubMed

Wapenaar, Kees

2017-06-01

A unified scalar wave equation is formulated, which covers three-dimensional (3D) acoustic waves, 2D horizontally-polarised shear waves, 2D transverse-electric EM waves, 2D transverse-magnetic EM waves, 3D quantum-mechanical waves and 2D flexural waves. The homogeneous Green's function of this wave equation is a combination of the causal Green's function and its time-reversal, such that their singularities at the source position cancel each other. A classical representation expresses this homogeneous Green's function as a closed boundary integral. This representation finds applications in holographic imaging, time-reversed wave propagation and Green's function retrieval by cross correlation. The main drawback of the classical representation in those applications is that it requires access to a closed boundary around the medium of interest, whereas in many practical situations the medium can be accessed from one side only. Therefore, a single-sided representation is derived for the homogeneous Green's function of the unified scalar wave equation. Like the classical representation, this single-sided representation fully accounts for multiple scattering. The single-sided representation has the same applications as the classical representation, but unlike the classical representation it is applicable in situations where the medium of interest is accessible from one side only.
A theoretical prediction of the acoustic pressure generated by turbulence-flame front interactions

NASA Technical Reports Server (NTRS)

Huff, R. G.

1984-01-01

The equations of momentum annd continuity are combined and linearized yielding the one dimensional nonhomogeneous acoustic wave equation. Three terms in the non-homogeneous equation act as acoustic sources and are taken to be forcing functions acting on the homogeneous wave equation. The three source terms are: fluctuating entropy, turbulence gradients, and turbulence-flame interactions. Each source term is discussed. The turbulence-flame interaction source is used as the basis for computing the source acoustic pressure from the Fourier transformed wave equation. Pressure fluctuations created in turbopump gas generators and turbines may act as a forcing function for turbine and propellant tube vibrations in Earth to orbit space propulsion systems and could reduce their life expectancy. A preliminary assessment of the acoustic pressure fluctuations in such systems is presented.
A theoretical prediction of the acoustic pressure generated by turbulence-flame front interactions

NASA Technical Reports Server (NTRS)

Huff, R. G.

1984-01-01

The equations of momentum and continuity are combined and linearized yielding the one dimensional nonhomogeneous acoustic wave equation. Three terms in the non-homogeneous equation act as acoustic sources and are taken to be forcing functions acting on the homogeneous wave equation. The three source terms are: fluctuating entropy, turbulence gradients, and turbulence-flame interactions. Each source term is discussed. The turbulence-flame interaction source is used as the basis for computing the source acoustic pressure from the Fourier transformed wave equation. Pressure fluctuations created in turbopump gas generators and turbines may act as a forcing function for turbine and propellant tube vibrations in earth to orbit space propulsion systems and could reduce their life expectancy. A preliminary assessment of the acoustic pressure fluctuations in such systems is presented.
A (2+1)-dimensional Korteweg-de Vries type equation in water waves: Lie symmetry analysis; multiple exp-function method; conservation laws

NASA Astrophysics Data System (ADS)

Adem, Abdullahi Rashid

2016-05-01

We consider a (2+1)-dimensional Korteweg-de Vries type equation which models the shallow-water waves, surface and internal waves. In the analysis, we use the Lie symmetry method and the multiple exp-function method. Furthermore, conservation laws are computed using the multiplier method.
Analytic study of solutions for a (3 + 1) -dimensional generalized KP equation

NASA Astrophysics Data System (ADS)

Gao, Hui; Cheng, Wenguang; Xu, Tianzhou; Wang, Gangwei

2018-03-01

The (3 + 1) -dimensional generalized KP (gKP) equation is an important nonlinear partial differential equation in theoretical and mathematical physics which can be used to describe nonlinear wave motion. Through the Hirota bilinear method, one-solition, two-solition and N-solition solutions are derived via symbolic computation. Two classes of lump solutions, rationally localized in all directions in space, to the dimensionally reduced cases in (2 + 1)-dimensions, are constructed by using a direct method based on the Hirota bilinear form of the equation. It implies that we can derive the lump solutions of the reduced gKP equation from positive quadratic function solutions to the aforementioned bilinear equation. Meanwhile, we get interaction solutions between a lump and a kink of the gKP equation. The lump appears from a kink and is swallowed by it with the change of time. This work offers a possibility which can enrich the variety of the dynamical features of solutions for higher-dimensional nonlinear evolution equations.
Periodic wave, breather wave and travelling wave solutions of a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation in fluids or plasmas

NASA Astrophysics Data System (ADS)

Hu, Wen-Qiang; Gao, Yi-Tian; Jia, Shu-Liang; Huang, Qian-Min; Lan, Zhong-Zhou

2016-11-01

In this paper, a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation is investigated, which has been presented as a model for the shallow water wave in fluids or the electrostatic wave potential in plasmas. By virtue of the binary Bell polynomials, the bilinear form of this equation is obtained. With the aid of the bilinear form, N -soliton solutions are obtained by the Hirota method, periodic wave solutions are constructed via the Riemann theta function, and breather wave solutions are obtained according to the extended homoclinic test approach. Travelling waves are constructed by the polynomial expansion method as well. Then, the relations between soliton solutions and periodic wave solutions are strictly established, which implies the asymptotic behaviors of the periodic waves under a limited procedure. Furthermore, we obtain some new solutions of this equation by the standard extended homoclinic test approach. Finally, we give a generalized form of this equation, and find that similar analytical solutions can be obtained from the generalized equation with arbitrary coefficients.
Sine-Gordon Equation in (1+2) and (1+3) dimensions: Existence and Classification of Traveling-Wave Solutions.

PubMed

Zarmi, Yair

2015-01-01

The (1+1)-dimensional Sine-Gordon equation passes integrability tests commonly applied to nonlinear evolution equations. Its kink solutions (one-dimensional fronts) are obtained by a Hirota algorithm. In higher space-dimensions, the equation does not pass these tests. Although it has been derived over the years for quite a few physical systems that have nothing to do with Special Relativity, the Sine-Gordon equation emerges as a non-linear relativistic wave equation. This opens the way for exploiting the tools of the Theory of Special Relativity. Using no more than the relativistic kinematics of tachyonic momentum vectors, from which the solutions are constructed through the Hirota algorithm, the existence and classification of N-moving-front solutions of the (1+2)- and (1+3)-dimensional equations for all N ≥ 1 are presented. In (1+2) dimensions, each multi-front solution propagates rigidly at one velocity. The solutions are divided into two subsets: Solutions whose velocities are lower than a limiting speed, c = 1, or are greater than or equal to c. To connect with concepts of the Theory of Special Relativity, c will be called "the speed of light." In (1+3)-dimensions, multi-front solutions are characterized by spatial structure and by velocity composition. The spatial structure is either planar (rotated (1+2)-dimensional solutions), or genuinely three-dimensional--branes. Planar solutions, propagate rigidly at one velocity, which is lower than, equal to, or higher than c. Branes must contain clusters of fronts whose speed exceeds c = 1. Some branes are "hybrids": different clusters of fronts propagate at different velocities. Some velocities may be lower than c but some must be equal to, or exceed, c. Finally, the speed of light cannot be approached from within the subset of slower-than-light solutions in both (1+2) and (1+3) dimensions.
Dispersion relations of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with initial stresses.

PubMed

Guo, Xiao; Wei, Peijun

2016-03-01

The dispersion relations of elastic waves in a one-dimensional phononic crystal formed by periodically repeating of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are studied in this paper. The influences of initial stress on the dispersive relation are considered based on the incremental stress theory. First, the incremental stress theory of elastic solid is extended to the magneto-electro-elasto solid. The governing equations, constitutive equations, and boundary conditions of the incremental stresses in a magneto-electro-elasto solid are derived with consideration of the existence of initial stresses. Then, the transfer matrices of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are formulated, respectively. The total transfer matrix of a single cell in the phononic crystal is obtained by the multiplication of two transfer matrixes related with two adjacent slabs. Furthermore, the Bloch theorem is used to obtain the dispersive equations of in-plane and anti-plane Bloch waves. The dispersive equations are solved numerically and the numerical results are shown graphically. The oblique propagation and the normal propagation situations are both considered. In the case of normal propagation of elastic waves, the analytical expressions of the dispersion equation are derived and compared with other literatures. The influences of initial stresses, including the normal initial stresses and shear initial stresses, on the dispersive relations are both discussed based on the numerical results. Copyright © 2015 Elsevier B.V. All rights reserved.
One-dimensional wave bottom boundary layer model comparison: specific eddy viscosity and turbulence closure models

USGS Publications Warehouse

Puleo, J.A.; Mouraenko, O.; Hanes, D.M.

2004-01-01

Six one-dimensional-vertical wave bottom boundary layer models are analyzed based on different methods for estimating the turbulent eddy viscosity: Laminar, linear, parabolic, k—one equation turbulence closure, k−ε—two equation turbulence closure, and k−ω—two equation turbulence closure. Resultant velocity profiles, bed shear stresses, and turbulent kinetic energy are compared to laboratory data of oscillatory flow over smooth and rough beds. Bed shear stress estimates for the smooth bed case were most closely predicted by the k−ω model. Normalized errors between model predictions and measurements of velocity profiles over the entire computational domain collected at 15° intervals for one-half a wave cycle show that overall the linear model was most accurate. The least accurate were the laminar and k−ε models. Normalized errors between model predictions and turbulence kinetic energy profiles showed that the k−ω model was most accurate. Based on these findings, when the smallest overall velocity profile prediction error is required, the processing requirements and error analysis suggest that the linear eddy viscosity model is adequate. However, if accurate estimates of bed shear stress and TKE are required then, of the models tested, the k−ω model should be used.
A numerical study of the 3-periodic wave solutions to KdV-type equations

NASA Astrophysics Data System (ADS)

Zhang, Yingnan; Hu, Xingbiao; Sun, Jianqing

2018-02-01

In this paper, by using the direct method of calculating periodic wave solutions proposed by Akira Nakamura, we present a numerical process to calculate the 3-periodic wave solutions to several KdV-type equations: the Korteweg-de Vries equation, the Sawada-Koterra equation, the Boussinesq equation, the Ito equation, the Hietarinta equation and the (2 + 1)-dimensional Kadomtsev-Petviashvili equation. Some detailed numerical examples are given to show the existence of the three-periodic wave solutions numerically.
Discrete spacetime, quantum walks, and relativistic wave equations

NASA Astrophysics Data System (ADS)

Mlodinow, Leonard; Brun, Todd A.

2018-04-01

It has been observed that quantum walks on regular lattices can give rise to wave equations for relativistic particles in the continuum limit. In this paper, we define the three-dimensional discrete-time walk as a product of three coined one-dimensional walks. The factor corresponding to each one-dimensional walk involves two projection operators that act on an internal coin space; each projector is associated with either the "forward" or "backward" direction in that physical dimension. We show that the simple requirement that there is no preferred axis or direction along an axis—that is, that the walk be symmetric under parity transformations and steps along different axes of the cubic lattice be uncorrelated—leads, in the case of the simplest solution, to the requirement that the continuum limit of the walk is fully Lorentz-invariant. We show further that, in the case of a massive particle, this symmetry requirement necessitates the use of a four-dimensional internal space (as in the Dirac equation). The "coin flip" operation is generated by the parity transformation on the internal coin space, while the differences of the projection operators associated with each dimension must all anticommute. Finally, we discuss the leading correction to the continuum limit, and the possibility of distinguishing through experiment between the discrete random walk and the continuum-based Dirac equation as a description of fermion dynamics.
An ansatz for solving nonlinear partial differential equations in mathematical physics.

PubMed

Akbar, M Ali; Ali, Norhashidah Hj Mohd

2016-01-01

In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems.
Finite-amplitude strain waves in laser-excited plates.

PubMed

Mirzade, F Kh

2008-07-09

The governing equations for two-dimensional finite-amplitude longitudinal strain waves in isotropic laser-excited solid plates are derived. Geometric and weak material nonlinearities are included, and the interaction of longitudinal displacements with the field of concentration of non-equilibrium laser-generated atomic defects is taken into account. An asymptotic approach is used to show that the equations are reducible to the Kadomtsev-Petviashvili-Burgers nonlinear evolution equation for a longitudinal self-consistent strain field. It is shown that two-dimensional shock waves can propagate in plates.
Effective one-dimensional approach to the source reconstruction problem of three-dimensional inverse optoacoustics

NASA Astrophysics Data System (ADS)

Stritzel, J.; Melchert, O.; Wollweber, M.; Roth, B.

2017-09-01

The direct problem of optoacoustic signal generation in biological media consists of solving an inhomogeneous three-dimensional (3D) wave equation for an initial acoustic stress profile. In contrast, the more defiant inverse problem requires the reconstruction of the initial stress profile from a proper set of observed signals. In this article, we consider an effectively 1D approach, based on the assumption of a Gaussian transverse irradiation source profile and plane acoustic waves, in which the effects of acoustic diffraction are described in terms of a linear integral equation. The respective inverse problem along the beam axis can be cast into a Volterra integral equation of the second kind for which we explore here efficient numerical schemes in order to reconstruct initial stress profiles from observed signals, constituting a methodical progress of computational aspects of optoacoustics. In this regard, we explore the validity as well as the limits of the inversion scheme via numerical experiments, with parameters geared toward actual optoacoustic problem instances. The considered inversion input consists of synthetic data, obtained in terms of the effectively 1D approach, and, more generally, a solution of the 3D optoacoustic wave equation. Finally, we also analyze the effect of noise and different detector-to-sample distances on the optoacoustic signal and the reconstructed pressure profiles.
Conservation laws and conserved quantities for (1+1)D linearized Boussinesq equations

NASA Astrophysics Data System (ADS)

Carvalho, Cindy; Harley, Charis

2017-05-01

Conservation laws and physical conserved quantities for the (1+1)D linearized Boussinesq equations at a constant water depth are presented. These equations describe incompressible, inviscid, irrotational fluid flow in the form of a non steady solitary wave. A systematic multiplier approach is used to obtain the conservation laws of the system of third order partial differential equations (PDEs) in dimensional form. Physical conserved quantities are derived by integrating the conservation laws in the direction of wave propagation and imposing decaying boundary conditions in the horizontal direction. One of these is a newly discovered conserved quantity which relates to an energy flux density.

Nonlinear layered lattice model and generalized solitary waves in imperfectly bonded structures.

PubMed

Khusnutdinova, Karima R; Samsonov, Alexander M; Zakharov, Alexey S

2009-05-01

We study nonlinear waves in a two-layered imperfectly bonded structure using a nonlinear lattice model. The key element of the model is an anharmonic chain of oscillating dipoles, which can be viewed as a basic lattice analog of a one-dimensional macroscopic waveguide. Long nonlinear longitudinal waves in a layered lattice with a soft middle (or bonding) layer are governed by a system of coupled Boussinesq-type equations. For this system we find conservation laws and show that pure solitary waves, which exist in a single equation and can exist in the coupled system in the symmetric case, are structurally unstable and are replaced with generalized solitary waves.
Multiexponential models of (1+1)-dimensional dilaton gravity and Toda-Liouville integrable models

NASA Astrophysics Data System (ADS)

de Alfaro, V.; Filippov, A. T.

2010-01-01

We study general properties of a class of two-dimensional dilaton gravity (DG) theories with potentials containing several exponential terms. We isolate and thoroughly study a subclass of such theories in which the equations of motion reduce to Toda and Liouville equations. We show that the equation parameters must satisfy a certain constraint, which we find and solve for the most general multiexponential model. It follows from the constraint that integrable Toda equations in DG theories generally cannot appear without accompanying Liouville equations. The most difficult problem in the two-dimensional Toda-Liouville (TL) DG is to solve the energy and momentum constraints. We discuss this problem using the simplest examples and identify the main obstacles to solving it analytically. We then consider a subclass of integrable two-dimensional theories where scalar matter fields satisfy the Toda equations and the two-dimensional metric is trivial. We consider the simplest case in some detail. In this example, we show how to obtain the general solution. We also show how to simply derive wavelike solutions of general TL systems. In the DG theory, these solutions describe nonlinear waves coupled to gravity and also static states and cosmologies. For static states and cosmologies, we propose and study a more general one-dimensional TL model typically emerging in one-dimensional reductions of higher-dimensional gravity and supergravity theories. We especially attend to making the analytic structure of the solutions of the Toda equations as simple and transparent as possible.
Analysis of band structure, transmission properties, and dispersion behavior of THz wave in one-dimensional parabolic plasma photonic crystal

DOE Office of Scientific and Technical Information (OSTI.GOV)

Askari, Nasim; Eslami, Esmaeil, E-mail: eeslami@iust.ac.ir; Mirzaie, Reza

2015-11-15

The photonic band gap of obliquely incident terahertz electromagnetic waves in a one-dimensional plasma photonic crystal is studied. The periodic structure consists of lossless dielectric and inhomogeneous plasma with a parabolic density profile. The dispersion relation and the THz wave transmittance are analyzed based on the electromagnetic equations and transfer matrix method. The dependence of effective plasma frequency and photonic band gap characteristics on dielectric and plasma thickness, plasma density, and incident angle are discussed in detail. A theoretical calculation for effective plasma frequency is presented and compared with numerical results. Results of these two methods are in good agreement.
Lump Solitons in Surface Tension Dominated Flows

NASA Astrophysics Data System (ADS)

Milewski, Paul; Berger, Kurt

1999-11-01

The Kadomtsev-Petviashvilli I equation (KPI) which models small-amplitude, weakly three-dimensional surface-tension dominated long waves is integrable and allows for algebraically decaying lump solitary waves. It is not known (theoretically or numerically) whether the full free-surface Euler equations support such solutions. We consider an intermediate model, the generalised Benney-Luke equation (gBL) which is isotropic (not weakly three-dimensional) and contains KPI as a limit. We show numerically that: 1. gBL supports lump solitary waves; 2. These waves collide elastically and are stable; 3. They are generated by resonant flow over an obstacle.
Characteristics of the solitary waves and rogue waves with interaction phenomena in a (2 + 1)-dimensional Breaking Soliton equation

NASA Astrophysics Data System (ADS)

Hossen, Md. Belal; Roshid, Harun-Or; Ali, M. Zulfikar

2018-05-01

Under inquisition in this paper is a (2 + 1)-dimensional Breaking Soliton equation, which can describe various nonlinear scenarios in fluid dynamics. Using the Bell polynomials, some proficient auxiliary functions are offered to apparently construct its bilinear form and corresponding soliton solutions which are different from the previous literatures. Moreover, a direct method is used to construct its rogue wave and solitary wave solutions using particular auxiliary function with the assist of bilinear formalism. Finally, the interactions between solitary waves and rogue waves are offered with a complete derivation. These results enhance the variety of the dynamics of higher dimensional nonlinear wave fields related to mathematical physics and engineering.
Capsize of polarization in dilute photonic crystals.

PubMed

Gevorkian, Zhyrair; Hakhoumian, Arsen; Gasparian, Vladimir; Cuevas, Emilio

2017-11-29

We investigate, experimentally and theoretically, polarization rotation effects in dilute photonic crystals with transverse permittivity inhomogeneity perpendicular to the traveling direction of waves. A capsize, namely a drastic change of polarization to the perpendicular direction is observed in a one-dimensional photonic crystal in the frequency range 10 ÷ 140 GHz. To gain more insights into the rotational mechanism, we have developed a theoretical model of dilute photonic crystal, based on Maxwell's equations with a spatially dependent two dimensional inhomogeneous dielectric permittivity. We show that the polarization's rotation can be explained by an optical splitting parameter appearing naturally in Maxwell's equations for magnetic or electric fields components. This parameter is an optical analogous of Rashba like spin-orbit interaction parameter present in quantum waves, introduces a correction to the band structure of the two-dimensional Bloch states, creates the dynamical phase shift between the waves propagating in the orthogonal directions and finally leads to capsizing of the initial polarization. Excellent agreement between theory and experiment is found.
From the paddle to the beach - A Boussinesq shallow water numerical wave tank based on Madsen and Sørensen's equations

NASA Astrophysics Data System (ADS)

Orszaghova, Jana; Borthwick, Alistair G. L.; Taylor, Paul H.

2012-01-01

This article describes a one-dimensional numerical model of a shallow-water flume with an in-built piston paddle moving boundary wavemaker. The model is based on a set of enhanced Boussinesq equations and the nonlinear shallow water equations. Wave breaking is described approximately, by locally switching to the nonlinear shallow water equations when a critical wave steepness is reached. The moving shoreline is calculated as part of the solution. The piston paddle wavemaker operates on a movable grid, which is Lagrangian on the paddle face and Eulerian away from the paddle. The governing equations are, however, evolved on a fixed mapped grid, and the newly calculated solution is transformed back onto the moving grid via a domain mapping technique. Validation test results are compared against analytical solutions, confirming correct discretisation of the governing equations, wave generation via the numerical paddle, and movement of the wet/dry front. Simulations are presented that reproduce laboratory experiments of wave runup on a plane beach and wave overtopping of a laboratory seawall, involving solitary waves and compact wave groups. In practice, the numerical model is suitable for simulating the propagation of weakly dispersive waves and can additionally model any associated inundation, overtopping or inland flooding within the same simulation.
Comparison of the Effect of Horizontal Vibrations on Interfacial Waves in a Two-Layer System of Inviscid Liquids to Effective Gravity Inversion

NASA Astrophysics Data System (ADS)

Pimenova, Anastasiya V.; Goldobin, Denis S.; Lyubimova, Tatyana P.

2018-02-01

We study the waves at the interface between two thin horizontal layers of immiscible liquids subject to high-frequency tangential vibrations. Nonlinear governing equations are derived for the cases of two- and three-dimensional flows and arbitrary ratio of layer thicknesses. The derivation is performed within the framework of the long-wavelength approximation, which is relevant as the linear instability of a thin-layers system is long-wavelength. The dynamics of equations is integrable and the equations themselves can be compared to the Boussinesq equation for the gravity waves in shallow water, which allows one to compare the action of the vibrational field to the action of the gravity and its possible effective inversion.
A Python Program for Solving Schro¨dinger's Equation in Undergraduate Physical Chemistry

ERIC Educational Resources Information Center

Srnec, Matthew N.; Upadhyay, Shiv; Madura, Jeffry D.

2017-01-01

In undergraduate physical chemistry, Schrödinger's equation is solved for a variety of cases. In doing so, the energies and wave functions of the system can be interpreted to provide connections with the physical system being studied. Solving this equation by hand for a one-dimensional system is a manageable task, but it becomes time-consuming…
A relativistic toy model for Unruh black holes

NASA Astrophysics Data System (ADS)

Carbonaro, P.

2014-08-01

We consider the wave propagation in terms of acoustic geometry in a quantum relativistic system. This reduces, in the hydrodynamic limit, to the equations which govern the motion of a relativistic Fermi-degenerate gas in one space dimension. The derivation of an acoustic metric for one-dimensional (1D) systems is in general plagued with the impossibility of defining a conformal factor. Here we show that, although the system is intrinsically one-dimensional, the Unruh procedure continues to work because of the particular structure symmetry of the model. By analyzing the dispersion relation, attention is also paid to the quantum effects on the wave propagation.
The limitation and applicability of Musher-Sturman equation to two dimensional lower hybrid wave collapse

NASA Technical Reports Server (NTRS)

Tam, Sunny W. Y.; Chang, Tom

1995-01-01

The existence of localized regions of intense lower hybrid waves in the auroral ionosphere recently observed by rocket and satellite experiments can be understood by the study of a non-linear two-timescale coupling process. In this Letter, we demonstrate that the leading non-linear term in the standard Musher-Sturman equation vanishes identically in strict two-dimensions (normal to the magnetic field). Instead, the new two-dimensional equation is characterized by a much weaker non-linear term which arises from the ponderomotive force perpendicular to the magnetic field, particularly that due to the ions. The old and new equations are compared by means of time-evolution calculations of wave fields. The results exhibit a remarkable difference in the evolution of the waves as governed by the two equations. Such dissimilar outcomes motivate our investigation of the limitation of Musher-Sturman equation in quasi-two-dimensions. Only within all these limits can Musher-Sturman equation adequately describe the collapse of lower hybrid waves.
One-dimensional high-order compact method for solving Euler's equations

NASA Astrophysics Data System (ADS)

Mohamad, M. A. H.; Basri, S.; Basuno, B.

2012-06-01

In the field of computational fluid dynamics, many numerical algorithms have been developed to simulate inviscid, compressible flows problems. Among those most famous and relevant are based on flux vector splitting and Godunov-type schemes. Previously, this system was developed through computational studies by Mawlood [1]. However the new test cases for compressible flows, the shock tube problems namely the receding flow and shock waves were not investigated before by Mawlood [1]. Thus, the objective of this study is to develop a high-order compact (HOC) finite difference solver for onedimensional Euler equation. Before developing the solver, a detailed investigation was conducted to assess the performance of the basic third-order compact central discretization schemes. Spatial discretization of the Euler equation is based on flux-vector splitting. From this observation, discretization of the convective flux terms of the Euler equation is based on a hybrid flux-vector splitting, known as the advection upstream splitting method (AUSM) scheme which combines the accuracy of flux-difference splitting and the robustness of flux-vector splitting. The AUSM scheme is based on the third-order compact scheme to the approximate finite difference equation was completely analyzed consequently. In one-dimensional problem for the first order schemes, an explicit method is adopted by using time integration method. In addition to that, development and modification of source code for the one-dimensional flow is validated with four test cases namely, unsteady shock tube, quasi-one-dimensional supersonic-subsonic nozzle flow, receding flow and shock waves in shock tubes. From these results, it was also carried out to ensure that the definition of Riemann problem can be identified. Further analysis had also been done in comparing the characteristic of AUSM scheme against experimental results, obtained from previous works and also comparative analysis with computational results generated by van Leer, KFVS and AUSMPW schemes. Furthermore, there is a remarkable improvement with the extension of the AUSM scheme from first-order to third-order accuracy in terms of shocks, contact discontinuities and rarefaction waves.
Exact solutions of a hierarchy of mixing speeds models

NASA Astrophysics Data System (ADS)

Cornille, H.; Platkowski, T.

1992-07-01

This paper presents several new aspects of discrete kinetic theory (DKT). First a hierarchy of d-dimensional (d=1,2,3) models is proposed with (2d+3) velocities and three moduli speeds: 0, 2, and a third one that can be arbitrary. It is assumed that the particles at rest have an internal energy which, for microscopic collisions, supplies for the loss of the kinetic energy. In a more general way than usual, collisions are allowed that mix particles with different speeds. Second, for the (1+1)-dimensional restriction of the systems of PDE for these models which have two independent quadratic collision terms we construct different exact solutions. The usual types of exact solutions are studied: periodic solutions and shock wave solutions obtained from the standard linearization of the scalar Riccati equations called Riccatian shock waves. Then other types of solutions of the coupled Riccati equations are found called non-Riccatian shock waves and they are compared with the previous ones. The main new result is that, between the upstream and downstream states, these new solutions are not necessarily monotonous. Further, for the shock problem, a two-dimensional dynamical system of ODE is solved numerically with limit values corresponding to the upstream and downstream states. As a by-product of this study two new linearizations for the Riccati coupled equations with two functions are proposed.
Computation and visualization of spreading depression based on reaction-diffusion equation with recovery

NASA Astrophysics Data System (ADS)

Ding, Hongxia; Chen, Shangbin; Zeng, Shuai; Zeng, Shaoqun; Liu, Qian; Luo, Qingming

2008-12-01

Spreading depression (SD) shows as propagating suppression of electrical activity, which relates with migraine and focal cerebral ischaemia. The putative mechanism of SD is the reaction-diffusion hypothesis involving potassium ions. In part inspired by optical imaging of two SD waves collision, we aimed to show the merged and large wavefront but not annihilation during collision by experimental and computational study. This paper modified Reggia et al established bistable equation with recovery to compute and visualize SD. Firstly, the media tissue of SD was assumed as one-dimensional continuum. The Crank-Nicholson method was used to solve the modified equations with recovery term. Then, the computation results were extended to two-dimensional space by symmetry. One individual SD was visualized as a concentric wave initiating from the stimulation point. The mergence but not annihilation of two colliding waves of SD was demonstrated. In addition, the dynamics of SD depending on the parameters was studied and presented. The results allied SD with the emerging concepts of volume transmission. This work not only supplied a paradigm to compute and visualize SD but also became a tool to explore the mechanisms of SD.
Thermal Non-Equilibrium Flows in Three Space Dimensions

NASA Astrophysics Data System (ADS)

Zeng, Yanni

2016-01-01

We study the equations describing the motion of a thermal non-equilibrium gas in three space dimensions. It is a hyperbolic system of six equations with a relaxation term. The dissipation mechanism induced by the relaxation is weak in the sense that the Shizuta-Kawashima criterion is violated. This implies that a perturbation of a constant equilibrium state consists of two parts: one decays in time while the other stays. In fact, the entropy wave grows weakly along the particle path as the process is irreversible. We study thermal properties related to the well-posedness of the nonlinear system. We also obtain a detailed pointwise estimate on the Green's function for the Cauchy problem when the system is linearized around an equilibrium constant state. The Green's function provides a complete picture of the wave pattern, with an exact and explicit leading term. Comparing with existing results for one dimensional flows, our results reveal a new feature of three dimensional flows: not only does the entropy wave not decay, but the velocity also contains a non-decaying part, strongly coupled with its decaying one. The new feature is supported by the second order approximation via the Chapman-Enskog expansions, which are the Navier-Stokes equations with vanished shear viscosity and heat conductivity.
Existence and amplitude bounds for irrotational water waves in finite depth

NASA Astrophysics Data System (ADS)

Kogelbauer, Florian

2017-12-01

We prove the existence of solutions to the irrotational water-wave problem in finite depth and derive an explicit upper bound on the amplitude of the nonlinear solutions in terms of the wavenumber, the total hydraulic head, the wave speed and the relative mass flux. Our approach relies upon a reformulation of the water-wave problem as a one-dimensional pseudo-differential equation and the Newton-Kantorovich iteration for Banach spaces. This article is part of the theme issue 'Nonlinear water waves'.
Spatio-temporal dynamics of an active, polar, viscoelastic ring.

PubMed

Marcq, Philippe

2014-04-01

Constitutive equations for a one-dimensional, active, polar, viscoelastic liquid are derived by treating the strain field as a slow hydrodynamic variable. Taking into account the couplings between strain and polarity allowed by symmetry, the hydrodynamics of an active, polar, viscoelastic body include an evolution equation for the polarity field that generalizes the damped Kuramoto-Sivashinsky equation. Beyond thresholds of the active coupling coefficients between the polarity and the stress or the strain rate, bifurcations of the homogeneous state lead first to stationary waves, then to propagating waves of the strain, stress and polarity fields. I argue that these results are relevant to living matter, and may explain rotating actomyosin rings in cells and mechanical waves in epithelial cell monolayers.
Solution of the Wang Chang-Uhlenbeck equation for molecular hydrogen

NASA Astrophysics Data System (ADS)

Anikin, Yu. A.

2017-06-01

Molecular hydrogen is modeled by numerically solving the Wang Chang-Uhlenbeck equation. The differential scattering cross sections of molecules are calculated using the quantum mechanical scattering theory of rigid rotors. The collision integral is computed by applying a fully conservative projection method. Numerical results for relaxation, heat conduction, and a one-dimensional shock wave are presented.
Whitham modulation theory for the two-dimensional Benjamin-Ono equation.

PubMed

Ablowitz, Mark; Biondini, Gino; Wang, Qiao

2017-09-01

Whitham modulation theory for the two-dimensional Benjamin-Ono (2DBO) equation is presented. A system of five quasilinear first-order partial differential equations is derived. The system describes modulations of the traveling wave solutions of the 2DBO equation. These equations are transformed to a singularity-free hydrodynamic-like system referred to here as the 2DBO-Whitham system. Exact reductions of this system are discussed, the formulation of initial value problems is considered, and the system is used to study the transverse stability of traveling wave solutions of the 2DBO equation.
Three-dimensional wave-induced current model equations and radiation stresses

NASA Astrophysics Data System (ADS)

Xia, Hua-yong

2017-08-01

After the approach by Mellor (2003, 2008), the present paper reports on a repeated effort to derive the equations for three-dimensional wave-induced current. Via the vertical momentum equation and a proper coordinate transformation, the phase-averaged wave dynamic pressure is well treated, and a continuous and depth-dependent radiation stress tensor, rather than the controversial delta Dirac function at the surface shown in Mellor (2008), is provided. Besides, a phase-averaged vertical momentum flux over a sloping bottom is introduced. All the inconsistencies in Mellor (2003, 2008), pointed out by Ardhuin et al. (2008) and Bennis and Ardhuin (2011), are overcome in the presently revised equations. In a test case with a sloping sea bed, as shown in Ardhuin et al. (2008), the wave-driving forces derived in the present equations are in good balance, and no spurious vertical circulation occurs outside the surf zone, indicating that Airy's wave theory and the approach of Mellor (2003, 2008) are applicable for the derivation of the wave-induced current model.

Multi-Periodic Waves in Shallow Water

DTIC Science & Technology

1992-09-01

models-the Kadomtsev - Petviashvili (KP) equation . The KP equation describes the evolu- tion of weakly nonlinear, weakly two-dimensional waves on water of...experimentally. The analytical model is a family of periodic solutions of the Kadomtsev -Petviashuili equation . The experiments demonstrate the accuracy... Petviashvili Equation (with Norman Schef- fner & Harvey Segur). Proceedings, Nonlinear Water Waves Workshop, University of Bristol. England, 1991. Resonant
One-dimensional optical wave turbulence: Experiment and theory

NASA Astrophysics Data System (ADS)

Laurie, Jason; Bortolozzo, Umberto; Nazarenko, Sergey; Residori, Stefania

2012-05-01

We present a review of the latest developments in one-dimensional (1D) optical wave turbulence (OWT). Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context. The experimental system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. The long-wave limit corresponds to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit, when wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional (2D) turbulence, which can be described by wave turbulence (WT) theory, and conclude that the cascades are induced by a six-wave resonant interaction process. WT theory predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schrödinger equation (NLSE) (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave numbers becomes strong. Subsequently, due to the focusing nature of the nonlinearity, this leads to modulational instability (MI) of the condensate and the formation of solitons. Finally, with the aid of the probability density function (PDF) description of WT theory, we explain the coexistence and mutual interactions between solitons and the weakly nonlinear random wave background in the form of a wave turbulence life cycle (WTLC).
General high-order breathers and rogue waves in the (3 + 1) -dimensional KP-Boussinesq equation

NASA Astrophysics Data System (ADS)

Sun, Baonan; Wazwaz, Abdul-Majid

2018-11-01

In this work, we investigate the (3 + 1) -dimensional KP-Boussinesq equation, which can be used to describe the nonlinear dynamic behavior in scientific and engineering applications. We derive general high-order soliton solutions by using the Hirota's bilinear method combined with the perturbation expansion technique. We also obtain periodic solutions comprising of high-order breathers, periodic line waves, and mixed solutions consisting of breathers and periodic line waves upon selecting particular parameter constraints of the obtained soliton solutions. Furthermore, smooth rational solutions are generated by taking a long wave limit of the soliton solutions. These smooth rational solutions include high-order rogue waves, high-order lumps, and hybrid solutions consisting of lumps and line rogue waves. To better understand the dynamical behaviors of these solutions, we discuss some illustrative graphical analyses. It is expected that our results can enrich the dynamical behavior of the (3 + 1) -dimensional nonlinear evolution equations of other forms.
Some new traveling wave exact solutions of the (2+1)-dimensional Boiti-Leon-Pempinelli equations.

PubMed

Qi, Jian-ming; Zhang, Fu; Yuan, Wen-jun; Huang, Zi-feng

2014-01-01

We employ the complex method to obtain all meromorphic exact solutions of complex (2+1)-dimensional Boiti-Leon-Pempinelli equations (BLP system of equations). The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic traveling wave exact solutions of the equations (BLP) are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions ur,2 (z) and simply periodic solutions us,2-6(z) which are not only new but also not degenerated successively by the elliptic function solutions. We believe that this method should play an important role for finding exact solutions in the mathematical physics. For these new traveling wave solutions, we give some computer simulations to illustrate our main results.
The Effect of Orifice Eccentricity on Instability of Liquid Jets

NASA Astrophysics Data System (ADS)

Amini, Ghobad; Dolatabadi, Ali

2011-11-01

The hydrodynamic instability of inviscid jets issuing from elliptic orifices is studied. A linear stability analysis is presented for liquid jets that includes the effect of the surrounding gas and an explicit dispersion equation is derived for waves on an infinite uniform jet column. Elliptic configuration has two extreme cases; round jet when ratio of minor to major axis is unity and plane sheet when this ratio approaches zero. Dispersion equation of elliptic jet is approximated for large and small aspect ratios considering asymptotic of the dispersion equation. In case of aspect ratio equal to one, the dispersion equation is analogous to one of the circular jets derived by Yang. In case of aspect ratio approaches zero, the behavior of waves is qualitatively similar to that of long waves on a two dimensional liquid jets and the varicose and sinuous modes are predicted. The growth rate of initial disturbances for various azimuthal modes has been presented in a wide range of disturbances. PhD Candidate.
Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.

2006-01-01

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.
Dynamic of solitary wave solutions in some nonlinear pseudoparabolic models and Dodd-Bullough-Mikhailov equation

NASA Astrophysics Data System (ADS)

Ilhan, O. A.; Bulut, H.; Sulaiman, T. A.; Baskonus, H. M.

2018-02-01

In this study, the modified exp ( - Φ (η )) -expansion function method is used in constructing some solitary wave solutions to the Oskolkov-Benjamin-Bona-Mahony-Burgers, one-dimensional Oskolkov equations and the Dodd-Bullough-Mikhailov equation. We successfully construct some singular solitons and singular periodic waves solutions with the hyperbolic, trigonometric and exponential function structures to these three nonlinear models. Under the choice of some suitable values of the parameters involved, we plot the 2D and 3D graphics to some of the obtained solutions in this study. All the obtained solutions in this study verify their corresponding equation. We perform all the computations in this study with the help of the Wolfram Mathematica software. The obtained solutions in this study may be helpful in explaining some practical physical problems.
Body and Surface Wave Modeling of Observed Seismic Events. Part 2.

DTIC Science & Technology

1987-05-12

is based on expand - ing the complete three dimensional solution of the wave equation expressed in cylindrical S coordinates in an asymptotic form which...using line source (2-D) theory. It is based on expand - ing the complete three dimensional solution of the wave equation expressed in cylindrical...generating synthetic point-source seismograms for shear dislocation sources using line source (2-D) theory. It is based on expanding the complete three
Traveling wave solutions of the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Akbari-Moghanjoughi, M.

2017-10-01

In this paper, we investigate the traveling soliton and the periodic wave solutions of the nonlinear Schrödinger equation (NLSE) with generalized nonlinear functionality. We also explore the underlying close connection between the well-known KdV equation and the NLSE. It is remarked that both one-dimensional KdV and NLSE models share the same pseudoenergy spectrum. We also derive the traveling wave solutions for two cases of weakly nonlinear mathematical models, namely, the Helmholtz and the Duffing oscillators' potentials. It is found that these models only allow gray-type NLSE solitary propagations. It is also found that the pseudofrequency ratio for the Helmholtz potential between the nonlinear periodic carrier and the modulated sinusoidal waves is always in the range 0.5 ≤ Ω/ω ≤ 0.537285 regardless of the potential parameter values. The values of Ω/ω = {0.5, 0.537285} correspond to the cnoidal waves modulus of m = {0, 1} for soliton and sinusoidal limits and m = 0.5, respectively. Moreover, the current NLSE model is extended to fully NLSE (FNLSE) situation for Sagdeev oscillator pseudopotential which can be derived using a closed set of hydrodynamic fluid equations with a fully integrable Hamiltonian system. The generalized quasi-three-dimensional traveling wave solution is also derived. The current simple hydrodynamic plasma model may also be generalized to two dimensions and other complex situations including different charged species and cases with magnetic or gravitational field effects.
Exact solutions for (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation and coupled Klein-Gordon equations.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Islam, S M Rayhanul

2014-01-01

In this work, recently developed modified simple equation (MSE) method is applied to find exact traveling wave solutions of nonlinear evolution equations (NLEEs). To do so, we consider the (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and coupled Klein-Gordon (cKG) equations. Two classes of explicit exact solutions-hyperbolic and trigonometric solutions of the associated equations are characterized with some free parameters. Then these exact solutions correspond to solitary waves for particular values of the parameters. 02.30.Jr; 02.70.Wz; 05.45.Yv; 94.05.Fg.
Riccati parameterized self-similar waves in two-dimensional graded-index waveguide

NASA Astrophysics Data System (ADS)

Kumar De, Kanchan; Goyal, Amit; Raju, Thokala Soloman; Kumar, C. N.; Panigrahi, Prasanta K.

2015-04-01

An analytical method based on gauge-similarity transformation technique has been employed for mapping a (2+1)- dimensional variable coefficient coupled nonlinear Schrödinger equations (vc-CNLSE) with dispersion, nonlinearity and gain to standard NLSE. Under certain functional relations we construct a large family of self-similar waves in the form of bright similaritons, Akhmediev breathers and rogue waves. We report the effect of dispersion on the intensity of the solitary waves. Further, we illustrate the procedure to amplify the intensity of self-similar waves using isospectral Hamiltonian approach. This approach provides an efficient mechanism to generate analytically a wide class of tapering profiles and widths by exploiting the Riccati parameter. Equivalently, it enables one to control efficiently the self-similar wave structures and hence their evolution.
Relativistic nonlinear plasma waves in a magnetic field

NASA Technical Reports Server (NTRS)

Kennel, C. F.; Pellat, R.

1975-01-01

Five relativistic plane nonlinear waves were investigated: circularly polarized waves and electrostatic plasma oscillations propagating parallel to the magnetic field, relativistic Alfven waves, linearly polarized transverse waves propagating in zero magnetic field, and the relativistic analog of the extraordinary mode propagating at an arbitrary angle to the magnetic field. When the ions are driven relativistic, they behave like electrons, and the assumption of an 'electron-positron' plasma leads to equations which have the form of a one-dimensional potential well. The solutions indicate that a large-amplitude superluminous wave determines the average plasma properties.
Strong shock waves and nonequilibrium response in a one-dimensional gas: a Boltzmann equation approach.

PubMed

Hurtado, Pablo I

2005-10-01

We investigate the nonequilibrium behavior of a one-dimensional binary fluid on the basis of Boltzmann equation, using an infinitely strong shock wave as probe. Density, velocity, and temperature profiles are obtained as a function of the mixture mass ratio mu. We show that temperature overshoots near the shock layer, and that heavy particles are denser, slower, and cooler than light particles in the strong nonequilibrium region around the shock. The shock width omega(mu), which characterizes the size of this region, decreases as omega(mu) approximately mu(1/3) for mu-->0. In this limit, two very different length scales control the fluid structure, with heavy particles equilibrating much faster than light ones. Hydrodynamic fields relax exponentially toward equilibrium: phi(chi) approximately exp[-chi/lambda]. The scale separation is also apparent here, with two typical scales, lambda1 and lambda2, such that lambda1 approximately mu(1/2 as mu-->0, while lambda2, which is the slow scale controlling the fluid's asymptotic relaxation, increases to a constant value in this limit. These results are discussed in light of recent numerical studies on the nonequilibrium behavior of similar one-dimensional binary fluids.
An Experiment on Two-Dimensional Interaction of Solitary Waves in Shallow Water System

NASA Astrophysics Data System (ADS)

Tsuji, Hidekazu; Yufu, Kei; Marubayashi, Kenji

2012-11-01

The dynamics of solitary waves in horizontally two-dimensional region is not yet well understood. Recently two-dimensional soliton interaction of Kadmotsetv-Petviashvili (KP) equation which describes the weakly nonlinear long wave in shallow water system has been theoretically studied (e.g. Kodama (2010)). It is clarified that the ``resonant'' interaction which forms Y-shaped triad can be described by exact solution. Li et al. (2011) experimentally studied the reflection of solitary wave at the wall and verified the theory of KP equation. To investigate more general interaction process, an experiment in wave tank using two wave makers which are controlled independently is carried out. The wave tank is 4 m in length and 3.6 m in width. The depth of the water is about 8cm. The wavemakers, which are piston-type and have board about 1.5 m in length, can produce orderly solitary wave which amplitude is 1.0-3.5 cm. We observe newly generated solitary wave due to interaction of original solitary waves which have different amplitude and/or propagation direction. The results are compared with the aforementioned theory of KP equation.
Assessment of numerical techniques for unsteady flow calculations

NASA Technical Reports Server (NTRS)

Hsieh, Kwang-Chung

1989-01-01

The characteristics of unsteady flow motions have long been a serious concern in the study of various fluid dynamic and combustion problems. With the advancement of computer resources, numerical approaches to these problems appear to be feasible. The objective of this paper is to assess the accuracy of several numerical schemes for unsteady flow calculations. In the present study, Fourier error analysis is performed for various numerical schemes based on a two-dimensional wave equation. Four methods sieved from the error analysis are then adopted for further assessment. Model problems include unsteady quasi-one-dimensional inviscid flows, two-dimensional wave propagations, and unsteady two-dimensional inviscid flows. According to the comparison between numerical and exact solutions, although second-order upwind scheme captures the unsteady flow and wave motions quite well, it is relatively more dissipative than sixth-order central difference scheme. Among various numerical approaches tested in this paper, the best performed one is Runge-Kutta method for time integration and six-order central difference for spatial discretization.
Similarity solutions of some two-space-dimensional nonlinear wave evolution equations

NASA Technical Reports Server (NTRS)

Redekopp, L. G.

1980-01-01

Similarity reductions of the two-space-dimensional versions of the Korteweg-de Vries, modified Korteweg-de Vries, Benjamin-Davis-Ono, and nonlinear Schroedinger equations are presented, and some solutions of the reduced equations are discussed. Exact dispersive solutions of the two-dimensional Korteweg-de Vries equation are obtained, and the similarity solution of this equation is shown to be reducible to the second Painleve transcendent.
Fission and fusion interaction phenomena of mixed lump kink solutions for a generalized (3+1)-dimensional B-type Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Liu, Yaqing; Wen, Xiaoyong

2018-05-01

In this paper, a generalized (3+1)-dimensional B-type Kadomtsev-Petviashvili (gBKP) equation is investigated by using the Hirota’s bilinear method. With the aid of symbolic computation, some new lump, mixed lump kink and periodic lump solutions are derived. Based on the derived solutions, some novel interaction phenomena like the fission and fusion interactions between one lump soliton and one kink soliton, the fission and fusion interactions between one lump soliton and a pair of kink solitons and the interactions between two periodic lump solitons are discussed graphically. Results might be helpful for understanding the propagation of the shallow water wave.
Solving the Vlasov equation in two spatial dimensions with the Schrödinger method

NASA Astrophysics Data System (ADS)

Kopp, Michael; Vattis, Kyriakos; Skordis, Constantinos

2017-12-01

We demonstrate that the Vlasov equation describing collisionless self-gravitating matter may be solved with the so-called Schrödinger method (ScM). With the ScM, one solves the Schrödinger-Poisson system of equations for a complex wave function in d dimensions, rather than the Vlasov equation for a 2 d -dimensional phase space density. The ScM also allows calculating the d -dimensional cumulants directly through quasilocal manipulations of the wave function, avoiding the complexity of 2 d -dimensional phase space. We perform for the first time a quantitative comparison of the ScM and a conventional Vlasov solver in d =2 dimensions. Our numerical tests were carried out using two types of cold cosmological initial conditions: the classic collapse of a sine wave and those of a Gaussian random field as commonly used in cosmological cold dark matter N-body simulations. We compare the first three cumulants, that is, the density, velocity and velocity dispersion, to those obtained by solving the Vlasov equation using the publicly available code ColDICE. We find excellent qualitative and quantitative agreement between these codes, demonstrating the feasibility and advantages of the ScM as an alternative to N-body simulations. We discuss, the emergence of effective vorticity in the ScM through the winding number around the points where the wave function vanishes. As an application we evaluate the background pressure induced by the non-linearity of large scale structure formation, thereby estimating the magnitude of cosmological backreaction. We find that it is negligibly small and has time dependence and magnitude compatible with expectations from the effective field theory of large scale structure.
Diffraction of a plane wave on two-dimensional conductive structures and a surface wave

NASA Astrophysics Data System (ADS)

Davidovich, Mikhael V.

2018-04-01

We consider the structures type of two-dimensional electron gas in the form of a thin conductive, in particular, graphene films described by tensor conductivity, which are isolated or located on the dielectric layers. The dispersion equation for hybrid modes, as well as scattering parameters. We show that free wave (eigenwaves) problem follow from the problem of diffraction when linking the amplitude of the current of the linear equations are unsolvable, i.e., the determinant of this system is zero. As a particular case the dispersion equation follow from the conditions of matching (with zero reflection coefficient).
Effective equations for matter-wave gap solitons in higher-order transversal states.

PubMed

Mateo, A Muñoz; Delgado, V

2013-10-01

We demonstrate that an important class of nonlinear stationary solutions of the three-dimensional (3D) Gross-Pitaevskii equation (GPE) exhibiting nontrivial transversal configurations can be found and characterized in terms of an effective one-dimensional (1D) model. Using a variational approach we derive effective equations of lower dimensionality for BECs in (m,n(r)) transversal states (states featuring a central vortex of charge m as well as n(r) concentric zero-density rings at every z plane) which provides us with a good approximate solution of the original 3D problem. Since the specifics of the transversal dynamics can be absorbed in the renormalization of a couple of parameters, the functional form of the equations obtained is universal. The model proposed finds its principal application in the study of the existence and classification of 3D gap solitons supported by 1D optical lattices, where in addition to providing a good estimate for the 3D wave functions it is able to make very good predictions for the μ(N) curves characterizing the different fundamental families. We have corroborated the validity of our model by comparing its predictions with those from the exact numerical solution of the full 3D GPE.

One-dimensional nonlinear elastodynamic models and their local conservation laws with applications to biological membranes.

PubMed

Cheviakov, A F; Ganghoffer, J-F

2016-05-01

The framework of incompressible nonlinear hyperelasticity and viscoelasticity is applied to the derivation of one-dimensional models of nonlinear wave propagation in fiber-reinforced elastic solids. Equivalence transformations are used to simplify the resulting wave equations and to reduce the number of parameters. Local conservation laws and global conserved quantities of the models are systematically computed and discussed, along with other related mathematical properties. Sample numerical solutions are presented. The models considered in the paper are appropriate for the mathematical description of certain aspects of the behavior of biological membranes and similar structures. Copyright © 2015 Elsevier Ltd. All rights reserved.
Exact periodic cross-kink wave solutions for the new (2+1)-dimensional KdV equation in fluid flows and plasma physics.

PubMed

Liu, Jian-Guo; Du, Jian-Qiang; Zeng, Zhi-Fang; Ai, Guo-Ping

2016-10-01

The Korteweg-de Vries (KdV)-type models have been shown to describe many important physical situations such as fluid flows, plasma physics, and solid state physics. In this paper, a new (2 + 1)-dimensional KdV equation is discussed. Based on the Hirota's bilinear form and a generalized three-wave approach, we obtain new exact solutions for the new (2 + 1)-dimensional KdV equation. With the help of symbolic computation, the properties for some new solutions are presented with some figures.
Rayleigh-Bloch waves trapped by a periodic perturbation: exact solutions

NASA Astrophysics Data System (ADS)

Merzon, A.; Zhevandrov, P.; Romero Rodríguez, M. I.; De la Paz Méndez, J. E.

2018-06-01

Exact solutions describing the Rayleigh-Bloch waves for the two-dimensional Helmholtz equation are constructed in the case when the refractive index is a sum of a constant and a small amplitude function which is periodic in one direction and of finite support in the other. These solutions are quasiperiodic along the structure and exponentially decay in the orthogonal direction. A simple formula for the dispersion relation of these waves is obtained.
A new (2+1) dimensional integrable evolution equation for an ion acoustic wave in a magnetized plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mukherjee, Abhik, E-mail: abhik.mukherjee@saha.ac.in; Janaki, M. S., E-mail: ms.janaki@saha.ac.in; Kundu, Anjan, E-mail: anjan.kundu@saha.ac.in

2015-07-15

A new, completely integrable, two dimensional evolution equation is derived for an ion acoustic wave propagating in a magnetized, collisionless plasma. The equation is a multidimensional generalization of a modulated wavepacket with weak transverse propagation, which has resemblance to nonlinear Schrödinger (NLS) equation and has a connection to Kadomtsev-Petviashvili equation through a constraint relation. Higher soliton solutions of the equation are derived through Hirota bilinearization procedure, and an exact lump solution is calculated exhibiting 2D structure. Some mathematical properties demonstrating the completely integrable nature of this equation are described. Modulational instability using nonlinear frequency correction is derived, and the correspondingmore » growth rate is calculated, which shows the directional asymmetry of the system. The discovery of this novel (2+1) dimensional integrable NLS type equation for a magnetized plasma should pave a new direction of research in the field.« less
Electron distribution function in a laser plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kalal, M.; Stoll, I.

1983-01-01

An accurate analytic solution of the Vlasov equation in the one-dimensional case is given for plasma electrons in the potential electric field of a monochromatic high-frequency wave of arbitrary amplitude and spatial modulation allowing for a self-consistent field. The phase velocity of the plasma waves is assumed to be appreciably higher than the electron thermal velocity (the case of nonresonant diffusion).
Numerical modeling of the early interaction of a planar shock with a dense particle field

NASA Astrophysics Data System (ADS)

Regele, Jonathan; Blanquart, Guillaume

2011-11-01

Dense compressible multiphase flows are of interest for multiphase turbomachinary and energetic material detonations. Still, there is little understanding of the detailed interaction mechanisms between shock waves and dense (particle volume fraction αd > 0 . 001) particle fields. A recent experimental study [Wagner et al, AIAA Aero. Sci., Orlando, 2011-188] has focused on the impingement of a planar shock wave on a dense particle curtain. In the present work, numerical solutions of the Euler equations in one and two dimensions are performed for a planar shock wave impinging on a fixed particle curtain and are compared to the experimental data for early times. Comparison of the one- and two-dimensional results demonstrate that the one-dimensional description captures the large scale flow behavior, but is inadequate to capture all the details observed in the experiments. The two-dimensional solutions are shown to reproduce the experimentally observed flow structures and provide insight into how these details originate.
Building 1D resonance broadened quasilinear (RBQ) code for fast ions Alfvénic relaxations

NASA Astrophysics Data System (ADS)

Gorelenkov, Nikolai; Duarte, Vinicius; Berk, Herbert

2016-10-01

The performance of the burning plasma is limited by the confinement of superalfvenic fusion products, e.g. alpha particles, which are capable of resonating with the Alfvénic eigenmodes (AEs). The effect of AEs on fast ions is evaluated using a resonance line broadened diffusion coefficient. The interaction of fast ions and AEs is captured for cases where there are either isolated or overlapping modes. A new code RBQ1D is being built which constructs diffusion coefficients based on realistic eigenfunctions that are determined by the ideal MHD code NOVA. The wave particle interaction can be reduced to one-dimensional dynamics where for the Alfvénic modes typically the particle kinetic energy is nearly constant. Hence to a good approximation the Quasi-Linear (QL) diffusion equation only contains derivatives in the angular momentum. The diffusion equation is then one dimensional that is efficiently solved simultaneously for all particles with the equation for the evolution of the wave angular momentum. The evolution of fast ion constants of motion is governed by the QL diffusion equations which are adapted to find the ion distribution function.
Two-dimensional cylindrical ion-acoustic solitary and rogue waves in ultrarelativistic plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ata-ur-Rahman; National Centre for Physics at QAU Campus, Shahdrah Valley Road, Islamabad 44000; Ali, S.

2013-07-15

The propagation of ion-acoustic (IA) solitary and rogue waves is investigated in a two-dimensional ultrarelativistic degenerate warm dense plasma. By using the reductive perturbation technique, the cylindrical Kadomtsev–Petviashvili (KP) equation is derived, which can be further transformed into a Korteweg–de Vries (KdV) equation. The latter admits a solitary wave solution. However, when the frequency of the carrier wave is much smaller than the ion plasma frequency, the KdV equation can be transferred to a nonlinear Schrödinger equation to study the nonlinear evolution of modulationally unstable modified IA wavepackets. The propagation characteristics of the IA solitary and rogue waves are stronglymore » influenced by the variation of different plasma parameters in an ultrarelativistic degenerate dense plasma. The present results might be helpful to understand the nonlinear electrostatic excitations in astrophysical degenerate dense plasmas.« less
Jordan form, parabolicity and other features of change of type transition for hydrodynamic type systems

NASA Astrophysics Data System (ADS)

Konopelchenko, B. G.; Ortenzi, G.

2017-05-01

Changes of type transitions for two-component hydrodynamic type systems are discussed. It is shown that these systems generically assume the Jordan form (with 2 × 2 Jordan block) on the transition line with hodograph equations becoming parabolic. Conditions which allow or forbid the transition from the hyperbolic domain to elliptic one are discussed. Hamiltonian systems and their special subclasses and equations, such as dispersionless nonlinear Schrödinger, dispersionless Boussinesq, one-dimensional isentropic gas dynamics equations, and nonlinear wave equations are studied. Numerical results concerning the crossing of transition line for the dispersionless Boussinesq equation are also presented.
New extended (G'/G)-expansion method to solve nonlinear evolution equation: the (3 + 1)-dimensional potential-YTSF equation.

PubMed

Roshid, Harun-Or-; Akbar, M Ali; Alam, Md Nur; Hoque, Md Fazlul; Rahman, Nizhum

2014-01-01

In this article, a new extended (G'/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have been achieved of this equation. It has been shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in applied mathematics, engineering and mathematical physics.
Refraction of dispersive shock waves

NASA Astrophysics Data System (ADS)

El, G. A.; Khodorovskii, V. V.; Leszczyszyn, A. M.

2012-09-01

We study a dispersive counterpart of the classical gas dynamics problem of the interaction of a shock wave with a counter-propagating simple rarefaction wave, often referred to as the shock wave refraction. The refraction of a one-dimensional dispersive shock wave (DSW) due to its head-on collision with the centred rarefaction wave (RW) is considered in the framework of the defocusing nonlinear Schrödinger (NLS) equation. For the integrable cubic nonlinearity case we present a full asymptotic description of the DSW refraction by constructing appropriate exact solutions of the Whitham modulation equations in Riemann invariants. For the NLS equation with saturable nonlinearity, whose modulation system does not possess Riemann invariants, we take advantage of the recently developed method for the DSW description in non-integrable dispersive systems to obtain main physical parameters of the DSW refraction. The key features of the DSW-RW interaction predicted by our modulation theory analysis are confirmed by direct numerical solutions of the full dispersive problem.
Linearized compressible-flow theory for sonic flight speeds

NASA Technical Reports Server (NTRS)

Heaslet, Max A; Lomax, Harvard; Spreiter, John R

1950-01-01

The partial differential equation for the perturbation velocity potential is examined for free-stream Mach numbers close to and equal to one. It is found that, under the assumptions of linearized theory, solutions can be found consistent with the theory for lifting-surface problems both in stationary three-dimensional flow and in unsteady two-dimensional flow. Several examples are solved including a three dimensional swept-back wing and two dimensional harmonically-oscillating wing, both for a free stream Mach number equal to one. Momentum relations for the evaluation of wave and vortex drag are also discussed. (author)
Generalized fourier analyses of the advection-diffusion equation - Part II: two-dimensional domains

NASA Astrophysics Data System (ADS)

Voth, Thomas E.; Martinez, Mario J.; Christon, Mark A.

2004-07-01

Part I of this work presents a detailed multi-methods comparison of the spatial errors associated with the one-dimensional finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. In Part II we extend the analysis to two-dimensional domains and also consider the effects of wave propagation direction and grid aspect ratio on the phase speed, and the discrete and artificial diffusivities. The observed dependence of dispersive and diffusive behaviour on propagation direction makes comparison of methods more difficult relative to the one-dimensional results. For this reason, integrated (over propagation direction and wave number) error and anisotropy metrics are introduced to facilitate comparison among the various methods. With respect to these metrics, the consistent mass Galerkin and consistent mass control-volume finite element methods, and their streamline upwind derivatives, exhibit comparable accuracy, and generally out-perform their lumped mass counterparts and finite-difference based schemes. While this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common mathematical framework. Published in 2004 by John Wiley & Sons, Ltd.
Rogue Waves and Lump Solitons of the (3+1)-Dimensional Generalized B-type Kadomtsev-Petviashvili Equation for Water Waves

NASA Astrophysics Data System (ADS)

Sun, Yan; Tian, Bo; Liu, Lei; Chai, Han-Peng; Yuan, Yu-Qiang

2017-12-01

In this paper, the (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation for water waves is investigated. Through the Hirota method and Kadomtsev-Petviashvili hierarchy reduction, we obtain the first-order, higher-order, multiple rogue waves and lump solitons based on the solutions in terms of the Gramian. The first-order rogue waves are the line rogue waves which arise from the constant background and then disappear into the constant background again, while the first-order lump solitons propagate stably. Interactions among several first-order rogue waves which are described by the multiple rogue waves are presented. Elastic interactions of several first-order lump solitons are also presented. We find that the higher-order rogue waves and lump solitons can be treated as the superpositions of several first-order ones, while the interaction between the second-order lump solitons is inelastic. Supported by the National Natural Science Foundation of China under Grant Nos. 11772017, 11272023, and 11471050, by the Open Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05), and by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02
The big bang as a higher-dimensional shock wave

NASA Astrophysics Data System (ADS)

Wesson, P. S.; Liu, H.; Seahra, S. S.

2000-06-01

We give an exact solution of the five-dimensional field equations which describes a shock wave moving in time and the extra (Kaluza-Klein) coordinate. The matter in four-dimensional spacetime is a cosmology with good physical properties. The solution suggests to us that the 4D big bang was a 5D shock wave.
Efficient three-dimensional resist profile-driven source mask optimization optical proximity correction based on Abbe-principal component analysis and Sylvester equation

NASA Astrophysics Data System (ADS)

Lin, Pei-Chun; Yu, Chun-Chang; Chen, Charlie Chung-Ping

2015-01-01

As one of the critical stages of a very large scale integration fabrication process, postexposure bake (PEB) plays a crucial role in determining the final three-dimensional (3-D) profiles and lessening the standing wave effects. However, the full 3-D chemically amplified resist simulation is not widely adopted during the postlayout optimization due to the long run-time and huge memory usage. An efficient simulation method is proposed to simulate the PEB while considering standing wave effects and resolution enhancement techniques, such as source mask optimization and subresolution assist features based on the Sylvester equation and Abbe-principal component analysis method. Simulation results show that our algorithm is 20× faster than the conventional Gaussian convolution method.
Soliton and kink jams in traffic flow with open boundaries.

PubMed

Muramatsu, M; Nagatani, T

1999-07-01

Soliton density wave is investigated numerically and analytically in the optimal velocity model (a car-following model) of a one-dimensional traffic flow with open boundaries. Soliton density wave is distinguished from the kink density wave. It is shown that the soliton density wave appears only at the threshold of occurrence of traffic jams. The Korteweg-de Vries (KdV) equation is derived from the optimal velocity model by the use of the nonlinear analysis. It is found that the traffic soliton appears only near the neutral stability line. The soliton solution is analytically obtained from the perturbed KdV equation. It is shown that the soliton solution obtained from the nonlinear analysis is consistent with that of the numerical simulation.
Three dimensional cylindrical Kadomtsev-Petviashvili equation in a very dense electron-positron-ion plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moslem, W. M.; Sabry, R.; Shukla, P. K.

2010-03-15

By using the hydrodynamic equations of ions, Thomas-Fermi electron/positron density distribution, and Poisson equation, a three-dimensional cylindrical Kadomtsev-Petviashvili (CKP) equation is derived for small but finite amplitude ion-acoustic waves. The generalized expansion method is used to analytically solve the CKP equation. New class of solutions admits a train of well-separated bell-shaped periodic pulses is obtained. At certain condition, the latter degenerates to solitary wave solution. The effects of physical parameters on the solitary pulse structures are examined. Furthermore, the energy integral equation is used to study the existence regions of the localized pulses. The present study might be helpful tomore » understand the excitation of nonlinear ion-acoustic waves in a very dense astrophysical objects such as white dwarfs.« less
The modified alternative (G'/G)-expansion method to nonlinear evolution equation: application to the (1+1)-dimensional Drinfel'd-Sokolov-Wilson equation.

PubMed

Akbar, M Ali; Mohd Ali, Norhashidah Hj; Mohyud-Din, Syed Tauseef

2013-01-01

Over the years, (G'/G)-expansion method is employed to generate traveling wave solutions to various wave equations in mathematical physics. In the present paper, the alternative (G'/G)-expansion method has been further modified by introducing the generalized Riccati equation to construct new exact solutions. In order to illustrate the novelty and advantages of this approach, the (1+1)-dimensional Drinfel'd-Sokolov-Wilson (DSW) equation is considered and abundant new exact traveling wave solutions are obtained in a uniform way. These solutions may be imperative and significant for the explanation of some practical physical phenomena. It is shown that the modified alternative (G'/G)-expansion method an efficient and advance mathematical tool for solving nonlinear partial differential equations in mathematical physics.
A numerical scheme for nonlinear Helmholtz equations with strong nonlinear optical effects.

PubMed

Xu, Zhengfu; Bao, Gang

2010-11-01

A numerical scheme is presented to solve the nonlinear Helmholtz (NLH) equation modeling second-harmonic generation (SHG) in photonic bandgap material doped with a nonlinear χ((2)) effect and the NLH equation modeling wave propagation in Kerr type gratings with a nonlinear χ((3)) effect in the one-dimensional case. Both of these nonlinear phenomena arise as a result of the combination of high electromagnetic mode density and nonlinear reaction from the medium. When the mode intensity of the incident wave is significantly strong, which makes the nonlinear effect non-negligible, numerical methods based on the linearization of the essentially nonlinear problem will become inadequate. In this work, a robust, stable numerical scheme is designed to simulate the NLH equations with strong nonlinearity.

Test of a new heat-flow equation for dense-fluid shock waves.

PubMed

Holian, Brad Lee; Mareschal, Michel; Ravelo, Ramon

2010-09-21

Using a recently proposed equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, we model shockwave propagation in the dense Lennard-Jones fluid. Disequilibrium among the three components of temperature, namely, the difference between the kinetic temperature in the direction of a planar shock wave and those in the transverse directions, particularly in the region near the shock front, gives rise to a new transport (equilibration) mechanism not seen in usual one-dimensional heat-flow situations. The modification of the heat-flow equation was tested earlier for the case of strong shock waves in the ideal gas, which had been studied in the past and compared to Navier-Stokes-Fourier solutions. Now, the Lennard-Jones fluid, whose equation of state and transport properties have been determined from independent calculations, allows us to study the case where potential, as well as kinetic contributions are important. The new heat-flow treatment improves the agreement with nonequilibrium molecular-dynamics simulations under strong shock wave conditions, compared to Navier-Stokes.
Some Interaction Solutions of a Reduced Generalised (3+1)-Dimensional Shallow Water Wave Equation for Lump Solutions and a Pair of Resonance Solitons

NASA Astrophysics Data System (ADS)

Wang, Yao; Chen, Mei-Dan; Li, Xian; Li, Biao

2017-05-01

Through Hirota bilinear transformation and symbolic computation with Maple, a class of lump solutions, rationally localised in all directions in the space, to a reduced generalised (3+1)-dimensional shallow water wave (SWW) equation are prensented. The resulting lump solutions all contain six parameters, two of which are free due to the translation invariance of the SWW equation and the other four of which must satisfy a nonzero determinant condition guaranteeing analyticity and rational localisation of the solutions. Then we derived the interaction solutions for lump solutions and one stripe soliton and the result shows that the particular lump solutions with specific values of the involved parameters will be drowned or swallowed by the stripe soliton. Furthermore, we extend this method to a more general combination of positive quadratic function and hyperbolic functions. Especially, it is interesting that a rogue wave is found to be aroused by the interaction between lump solutions and a pair of resonance stripe solitons. By choosing the values of the parameters, the dynamic properties of lump solutions, interaction solutions for lump solutions and one stripe soliton and interaction solutions for lump solutions and a pair of resonance solitons, are shown by dynamic graphs.
Exact Solutions of Atmospheric (2+1)-Dimensional Nonlinear Incompressible Non-hydrostatic Boussinesq Equations

NASA Astrophysics Data System (ADS)

Liu, Ping; Wang, Ya-Xiong; Ren, Bo; Li, Jin-Hua

2016-12-01

Exact solutions of the atmospheric (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space. Supported by the National Natural Science Foundation of China under Grant Nos. 11305031 and 11305106, and Training Programme Foundation for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province under Grant No. Yq2013205
Three-variable solution in the (2+1)-dimensional null-surface formulation

NASA Astrophysics Data System (ADS)

Harriott, Tina A.; Williams, J. G.

2018-04-01

The null-surface formulation of general relativity (NSF) describes gravity by using families of null surfaces instead of a spacetime metric. Despite the fact that the NSF is (to within a conformal factor) equivalent to general relativity, the equations of the NSF are exceptionally difficult to solve, even in 2+1 dimensions. The present paper gives the first exact (2+1)-dimensional solution that depends nontrivially upon all three of the NSF's intrinsic spacetime variables. The metric derived from this solution is shown to represent a spacetime whose source is a massless scalar field that satisfies the general relativistic wave equation and the Einstein equations with minimal coupling. The spacetime is identified as one of a family of (2+1)-dimensional general relativistic spacetimes discovered by Cavaglià.
Existence and Stability of Spatial Plane Waves for the Incompressible Navier-Stokes in R^3

NASA Astrophysics Data System (ADS)

Correia, Simão; Figueira, Mário

2018-03-01

We consider the three-dimensional incompressible Navier-Stokes equation on the whole space. We observe that this system admits a L^∞ family of global spatial plane wave solutions, which are connected with the two-dimensional equation. We then proceed to prove local well-posedness over a space which includes L^3(R^3) and these solutions. Finally, we prove L^3-stability of spatial plane waves, with no condition on their size.
Dispersive shock waves in Bose-Einstein condensates and nonlinear nano-oscillators in ferromagnetic thin films

NASA Astrophysics Data System (ADS)

Hoefer, Mark A.

This thesis examines nonlinear wave phenomena, in two physical systems: a Bose-Einstein condensate (BEC) and thin film ferromagnets where the magnetization dynamics are excited by the spin momentum transfer (SMT) effect. In the first system, shock waves generated by steep gradients in the BEC wavefunction are shown to be of the disperse type. Asymptotic and averaging methods are used to determine shock speeds and structure in one spatial dimension. These results are compared with multidimensional numerical simulations and experiment showing good, qualitative agreement. In the second system, a model of magnetization dynamics due to SMT is presented. Using this model, nonlinear oscillating modes---nano-oscillators---are found numerically and analytically using perturbative methods. These results compare well with experiment. A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g. traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical 1D dissipative and dispersive shock problem shows significant differences in shock structure and shock front speed. Numerical results associated with laboratory experiments show that three and two-dimensional approximations are in excellent agreement and one dimensional approximations are in qualitative agreement. The interaction of two DSWs is investigated analytically and numerically. Using one dimensional DSW theory it is argued that the experimentally observed blast waves may be viewed as dispersive shock waves. A nonlinear mathematical model of spin-wave excitation using a point contact in a thin ferromagnetic film is introduced. This work incorporates a recently proposed spin-torque contribution to classical magnetodynamic theory with a variable coefficient terra in the magnetic torque equation. Large-amplitude magnetic solitary waves are computed, which help explain recent spin-torque experiments. Numerical simulations of the full nonlinear model predict excitation frequencies in excess of 0.2 THz for contact diameters smaller than 6 nm. Simulations also predict a saturation and red shift of the frequency at currents large enough to invert the magnetization tinder the point contact. In the weak nonlinear limit, the theory is approximated by a cubic complex Ginzburg-Landau type equation. The mode's nonlinear frequency shift is found by use of perturbation techniques, whose results agree with those of direct numerical simulations.
Versatile rogue waves in scalar, vector, and multidimensional nonlinear systems

NASA Astrophysics Data System (ADS)

Chen, Shihua; Baronio, Fabio; Soto-Crespo, Jose M.; Grelu, Philippe; Mihalache, Dumitru

2017-11-01

This review is dedicated to recent progress in the active field of rogue waves, with an emphasis on the analytical prediction of versatile rogue wave structures in scalar, vector, and multidimensional integrable nonlinear systems. We first give a brief outline of the historical background of the rogue wave research, including referring to relevant up-to-date experimental results. Then we present an in-depth discussion of the scalar rogue waves within two different integrable frameworks—the infinite nonlinear Schrödinger (NLS) hierarchy and the general cubic-quintic NLS equation, considering both the self-focusing and self-defocusing Kerr nonlinearities. We highlight the concept of chirped Peregrine solitons, the baseband modulation instability as an origin of rogue waves, and the relation between integrable turbulence and rogue waves, each with illuminating examples confirmed by numerical simulations. Later, we recur to the vector rogue waves in diverse coupled multicomponent systems such as the long-wave short-wave equations, the three-wave resonant interaction equations, and the vector NLS equations (alias Manakov system). In addition to their intriguing bright-dark dynamics, a series of other peculiar structures, such as coexisting rogue waves, watch-hand-like rogue waves, complementary rogue waves, and vector dark three sisters, are reviewed. Finally, for practical considerations, we also remark on higher-dimensional rogue waves occurring in three closely-related (2 + 1)D nonlinear systems, namely, the Davey-Stewartson equation, the composite (2 + 1)D NLS equation, and the Kadomtsev-Petviashvili I equation. As an interesting contrast to the peculiar X-shaped light bullets, a concept of rogue wave bullets intended for high-dimensional systems is particularly put forward by combining contexts in nonlinear optics.
Development of a grid-independent approximate Riemannsolver. Ph.D. Thesis - Michigan Univ.

NASA Technical Reports Server (NTRS)

Rumsey, Christopher Lockwood

1991-01-01

A grid-independent approximate Riemann solver for use with the Euler and Navier-Stokes equations was introduced and explored. The two-dimensional Euler and Navier-Stokes equations are described in Cartesian and generalized coordinates, as well as the traveling wave form of the Euler equations. The spatial and temporal discretization are described for both explicit and implicit time-marching schemes. The grid-aligned flux function of Roe is outlined, while the 5-wave grid-independent flux function is derived. The stability and monotonicity analysis of the 5-wave model are presented. Two-dimensional results are provided and extended to three dimensions. The corresponding results are presented.
Full-Scale Direct Numerical Simulation of Two- and Three-Dimensional Instabilities and Rivulet Formulation in Heated Falling Films

NASA Technical Reports Server (NTRS)

Krishnamoorthy, S.; Ramaswamy, B.; Joo, S. W.

1995-01-01

A thin film draining on an inclined plate has been studied numerically using finite element method. Three-dimensional governing equations of continuity, momentum and energy with a moving boundary are integrated in an arbitrary Lagrangian Eulerian frame of reference. Kinematic equation is solved to precisely update interface location. Rivulet formation based on instability mechanism has been simulated using full-scale computation. Comparisons with long-wave theory are made to validate the numerical scheme. Detailed analysis of two- and three-dimensional nonlinear wave formation and spontaneous rupture forming rivulets under the influence of combined thermocapillary and surface-wave instabilities is performed.
Generalized wave operators, weighted Killing fields, and perturbations of higher dimensional spacetimes

NASA Astrophysics Data System (ADS)

Araneda, Bernardo

2018-04-01

We present weighted covariant derivatives and wave operators for perturbations of certain algebraically special Einstein spacetimes in arbitrary dimensions, under which the Teukolsky and related equations become weighted wave equations. We show that the higher dimensional generalization of the principal null directions are weighted conformal Killing vectors with respect to the modified covariant derivative. We also introduce a modified Laplace–de Rham-like operator acting on tensor-valued differential forms, and show that the wave-like equations are, at the linear level, appropriate projections off shell of this operator acting on the curvature tensor; the projection tensors being made out of weighted conformal Killing–Yano tensors. We give off shell operator identities that map the Einstein and Maxwell equations into weighted scalar equations, and using adjoint operators we construct solutions of the original field equations in a compact form from solutions of the wave-like equations. We study the extreme and zero boost weight cases; extreme boost corresponding to perturbations of Kundt spacetimes (which includes near horizon geometries of extreme black holes), and zero boost to static black holes in arbitrary dimensions. In 4D our results apply to Einstein spacetimes of Petrov type D and make use of weighted Killing spinors.
A Kinetic Approach to Propagation and Stability of Detonation Waves

NASA Astrophysics Data System (ADS)

Monaco, R.; Bianchi, M. Pandolfi; Soares, A. J.

2008-12-01

The problem of the steady propagation and linear stability of a detonation wave is formulated in the kinetic frame for a quaternary gas mixture in which a reversible bimolecular reaction takes place. The reactive Euler equations and related Rankine-Hugoniot conditions are deduced from the mesoscopic description of the process. The steady propagation problem is solved for a Zeldovich, von Neuman and Doering (ZND) wave, providing the detonation profiles and the wave thickness for different overdrive degrees. The one-dimensional stability of such detonation wave is then studied in terms of an initial value problem coupled with an acoustic radiation condition at the equilibrium final state. The stability equations and their initial data are deduced from the linearized reactive Euler equations and related Rankine-Hugoniot conditions through a normal mode analysis referred to the complex disturbances of the steady state variables. Some numerical simulations for an elementary reaction of the hydrogen-oxygen chain are proposed in order to describe the time and space evolution of the instabilities induced by the shock front perturbation.
Analytical study of laser supported combustion waves in hydrogen

NASA Technical Reports Server (NTRS)

Kemp, N. H.; Root, R. G.

1977-01-01

A one-dimensional energy equation, with constant pressure and area, was used to model the LSC wave. This equation balances convection, conduction, laser energy absorption, radiation energy loss and radiation energy transport. Solutions of this energy equation were obtained to give profiles of temperature and other properties, as well as the relation between laser intensity and mass flux through the wave. The flow through the LSC wave was then conducted through a variable pressure, variable area streamtube to accelerate it to high speed, with the propulsion application in mind. A numerical method for coupling the LSC wave model to the streamtube flow was developed, and a sample calculation was performed. The result shows that 42% of the laser power has been radiated away by the time the gas reaches the throat. It was concluded that in the radially confined flows of interest for propulsion applications, transverse velocities would be less important than in the unconfined flows where air experiments have been conducted.
Two-dimensional dispersion of magnetostatic volume spin waves

NASA Astrophysics Data System (ADS)

Buijnsters, Frank J.; van Tilburg, Lennert J. A.; Fasolino, Annalisa; Katsnelson, Mikhail I.

2018-06-01

Owing to the dipolar (magnetostatic) interaction, long-wavelength spin waves in in-plane magnetized films show an unusual dispersion behavior, which can be mathematically described by the model of and and refinements thereof. However, solving the two-dimensional dispersion requires the evaluation of a set of coupled transcendental equations and one has to rely on numerics. In this work, we present a systematic perturbative analysis of the spin wave model. An expansion in the in-plane wavevector allows us to obtain explicit closed-form expressions for the dispersion relation and mode profiles in various asymptotic regimes. Moreover, we derive a very accurate semi-analytical expression for the dispersion relation of the lowest-frequency mode that is straightforward to evaluate.
Method for determining size of inhomogeneity localization region based on analysis of secondary wave field of second harmonic

NASA Astrophysics Data System (ADS)

Chernov, N. N.; Zagray, N. P.; Laguta, M. V.; Varenikova, A. Yu

2018-05-01

The article describes the research of the method of localization and determining the size of heterogeneity in biological tissues. The equation for the acoustic harmonic wave, which propagates in the positive direction, is taken as the main one. A three-dimensional expression that describes the field of secondary sources at the observation point is obtained. The simulation of the change of the amplitude values of the vibrational velocity of the second harmonic of the acoustic wave at different coordinates of the inhomogeneity location in three-dimensional space is carried out. For the convenience of mathematical calculations, the area of heterogeneity is reduced to a point.
An efficient model for coupling structural vibrations with acoustic radiation

NASA Technical Reports Server (NTRS)

Frendi, Abdelkader; Maestrello, Lucio; Ting, LU

1993-01-01

The scattering of an incident wave by a flexible panel is studied. The panel vibration is governed by the nonlinear plate equations while the loading on the panel, which is the pressure difference across the panel, depends on the reflected and transmitted waves. Two models are used to calculate this structural-acoustic interaction problem. One solves the three dimensional nonlinear Euler equations for the flow-field coupled with the plate equations (the fully coupled model). The second uses the linear wave equation for the acoustic field and expresses the load as a double integral involving the panel oscillation (the decoupled model). The panel oscillation governed by a system of integro-differential equations is solved numerically and the acoustic field is then defined by an explicit formula. Numerical results are obtained using the two models for linear and nonlinear panel vibrations. The predictions given by these two models are in good agreement but the computational time needed for the 'fully coupled model' is 60 times longer than that for 'the decoupled model'.
Dark lump excitations in superfluid Fermi gases

NASA Astrophysics Data System (ADS)

Xu, Yan-Xia; Duan, Wen-Shan

2012-11-01

We study the linear and nonlinear properties of two-dimensional matter-wave pulses in disk-shaped superfluid Fermi gases. A Kadomtsev—Petviashvili I (KPI) solitary wave has been realized for superfluid Fermi gases in the limited cases of Bardeen—Cooper—Schrieffer (BCS) regime, Bose—Einstein condensate (BEC) regime, and unitarity regime. One-lump solution as well as one-line soliton solutions for the KPI equation are obtained, and two-line soliton solutions with the same amplitude are also studied in the limited cases. The dependence of the lump propagating velocity and the sound speed of two-dimensional superfluid Fermi gases on the interaction parameter are investigated for the limited cases of BEC and unitarity.
Modulated amplitude waves in collisionally inhomogeneous Bose Einstein condensates

NASA Astrophysics Data System (ADS)

Porter, Mason A.; Kevrekidis, P. G.; Malomed, Boris A.; Frantzeskakis, D. J.

2007-05-01

We investigate the dynamics of an effectively one-dimensional Bose-Einstein condensate (BEC) with scattering length a subjected to a spatially periodic modulation, a=a(x)=a(x+L). This “collisionally inhomogeneous” BEC is described by a Gross-Pitaevskii (GP) equation whose nonlinearity coefficient is a periodic function of x. We transform this equation into a GP equation with a constant coefficient and an additional effective potential and study a class of extended wave solutions of the transformed equation. For weak underlying inhomogeneity, the effective potential takes a form resembling a superlattice, and the amplitude dynamics of the solutions of the constant-coefficient GP equation obey a nonlinear generalization of the Ince equation. In the small-amplitude limit, we use averaging to construct analytical solutions for modulated amplitude waves (MAWs), whose stability we subsequently examine using both numerical simulations of the original GP equation and fixed-point computations with the MAWs as numerically exact solutions. We show that “on-site” solutions, whose maxima correspond to maxima of a(x), are more robust and likely to be observed than their “off-site” counterparts.
A dimensionally split Cartesian cut cell method for hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Gokhale, Nandan; Nikiforakis, Nikos; Klein, Rupert

2018-07-01

We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a full description of its three-dimensional implementation in the dimensionally split framework of Klein et al. [1]. The convergence and stability of the method are proved for the one-dimensional linear advection equation, while its multi-dimensional numerical performance is investigated through the computation of solutions to a number of test problems for the linear advection and Euler equations. When compared to the cut cell flux of Klein et al., it was found that the new flux alleviates the problem of oscillatory boundary solutions produced by the former at higher Courant numbers, and also enables the computation of more accurate solutions near stagnation points. Being dimensionally split, the method is simple to implement and extends readily to multiple dimensions.
Global boundary flattening transforms for acoustic propagation under rough sea surfaces.

PubMed

Oba, Roger M

2010-07-01

This paper introduces a conformal transform of an acoustic domain under a one-dimensional, rough sea surface onto a domain with a flat top. This non-perturbative transform can include many hundreds of wavelengths of the surface variation. The resulting two-dimensional, flat-topped domain allows direct application of any existing, acoustic propagation model of the Helmholtz or wave equation using transformed sound speeds. Such a transform-model combination applies where the surface particle velocity is much slower than sound speed, such that the boundary motion can be neglected. Once the acoustic field is computed, the bijective (one-to-one and onto) mapping permits the field interpolation in terms of the original coordinates. The Bergstrom method for inverse Riemann maps determines the transform by iterated solution of an integral equation for a surface matching term. Rough sea surface forward scatter test cases provide verification of the method using a particular parabolic equation model of the Helmholtz equation.
Detecting Moving Targets by Use of Soliton Resonances

NASA Technical Reports Server (NTRS)

Zak, Michael; Kulikov, Igor

2003-01-01

A proposed method of detecting moving targets in scenes that include cluttered or noisy backgrounds is based on a soliton-resonance mathematical model. The model is derived from asymptotic solutions of the cubic Schroedinger equation for a one-dimensional system excited by a position-and-time-dependent externally applied potential. The cubic Schroedinger equation has general significance for time-dependent dispersive waves. It has been used to approximate several phenomena in classical as well as quantum physics, including modulated beams in nonlinear optics, and superfluids (in particular, Bose-Einstein condensates). In the proposed method, one would take advantage of resonant interactions between (1) a soliton excited by the position-and-time-dependent potential associated with a moving target and (2) eigen-solitons, which represent dispersive waves and are solutions of the cubic Schroedinger equation for a time-independent potential.

3-Dimensional stereo implementation of photoacoustic imaging based on a new image reconstruction algorithm without using discrete Fourier transform

NASA Astrophysics Data System (ADS)

Ham, Woonchul; Song, Chulgyu

2017-05-01

In this paper, we propose a new three-dimensional stereo image reconstruction algorithm for a photoacoustic medical imaging system. We also introduce and discuss a new theoretical algorithm by using the physical concept of Radon transform. The main key concept of proposed theoretical algorithm is to evaluate the existence possibility of the acoustic source within a searching region by using the geometric distance between each sensor element of acoustic detector and the corresponding searching region denoted by grid. We derive the mathematical equation for the magnitude of the existence possibility which can be used for implementing a new proposed algorithm. We handle and derive mathematical equations of proposed algorithm for the one-dimensional sensing array case as well as two dimensional sensing array case too. A mathematical k-wave simulation data are used for comparing the image quality of the proposed algorithm with that of general conventional algorithm in which the FFT should be necessarily used. From the k-wave Matlab simulation results, we can prove the effectiveness of the proposed reconstruction algorithm.
Drift ion acoustic shock waves in an inhomogeneous two-dimensional quantum magnetoplasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Masood, W.; Siddiq, M.; Karim, S.

2009-04-15

Linear and nonlinear propagation characteristics of drift ion acoustic waves are investigated in an inhomogeneous quantum plasma with neutrals in the background employing the quantum hydrodynamics (QHD) model. In this regard, a quantum Kadomtsev-Petviashvili-Burgers (KPB) equation is derived for the first time. It is shown that the ion acoustic wave couples with the drift wave if the parallel motion of ions is taken into account. Discrepancies in the earlier works on drift solitons and shocks in inhomogeneous plasmas are also pointed out and a correct theoretical framework is presented to study the one-dimensional as well as the two-dimensional propagation ofmore » shock waves in an inhomogeneous quantum plasma. Furthermore, the solution of KPB equation is presented using the tangent hyperbolic (tanh) method. The variation of the shock profile with the quantum Bohm potential, collision frequency, and ratio of drift to shock velocity in the comoving frame, v{sub *}/u, are also investigated. It is found that increasing the number density and collision frequency enhances the strength of the shock. It is also shown that the fast drift shock (i.e., v{sub *}/u>0) increases, whereas the slow drift shock (i.e., v{sub *}/u<0) decreases the strength of the shock. The relevance of the present investigation with regard to dense astrophysical environments is also pointed out.« less
Soliton interactions and Bäcklund transformation for a (2+1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili equation in fluid dynamics

NASA Astrophysics Data System (ADS)

Xiao, Zi-Jian; Tian, Bo; Sun, Yan

2018-01-01

In this paper, we investigate a (2+1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili (mKP) equation in fluid dynamics. With the binary Bell-polynomial and an auxiliary function, bilinear forms for the equation are constructed. Based on the bilinear forms, multi-soliton solutions and Bell-polynomial-type Bäcklund transformation for such an equation are obtained through the symbolic computation. Soliton interactions are presented. Based on the graphic analysis, Parametric conditions for the existence of the shock waves, elevation solitons and depression solitons are given, and it is shown that under the condition of keeping the wave vectors invariable, the change of α(t) and β(t) can lead to the change of the solitonic velocities, but the shape of each soliton remains unchanged, where α(t) and β(t) are the variable coefficients in the equation. Oblique elastic interactions can exist between the (i) two shock waves, (ii) two elevation solitons, and (iii) elevation and depression solitons. However, oblique interactions between (i) shock waves and elevation solitons, (ii) shock waves and depression solitons are inelastic.
Characteristics of wind waves in shallow tidal basins and how they affect bed shear stress, bottom erosion, and the morphodynamic evolution of coupled marsh and mudflat landforms

NASA Astrophysics Data System (ADS)

Tommasini, Laura; Carniello, Luca; Goodwin, Guillaume; Mudd, Simon M.; Matticchio, Bruno; D'Alpaos, Andrea

2017-04-01

Wind-wave induced erosion is one of the main processes controlling the morphodynamic evolution of shallow tidal basins, because wind waves promote the erosion of subtidal platforms, tidal flats and salt marshes. Our study considered zero-, one-and two-dimensional wave models. First, we analyzed the relations between wave parameters, depth and bed shear stress with constant and variable wave period considering two zero-dimensional models based on the Young and Verhagen (1996), and Carniello et al. (2005, 2011) approaches. The first one is an empirical method that computes wave height and the variable wave period from wind velocity, fetch and water depth. The second one is based on the solution of wave action conservation equation, we use this second approach for computing the bottom shear stress and wave height, considering variable and constant (t=2s) wave period. Second, we compared the wave spectral model SWAN with a fully coupled Wind-Wave Tidal Model applied to a 1D rectangular domain. These models describe both the growth and propagation of wind waves. Finally, we applied the two-dimensional Wind Wave Tidal Model (WWTM) to six different configurations of the Venice lagoon considering the same boundary conditions and we evaluated the spatial variation of mean wave power density. The analysis with zero-dimensional models show that the effects of the different model assumptions on the wave period and on the wave height computation cannot be neglected. In particular, the relationships between bottom shear stress and water depth have different shapes. Two results emerge: first, the differences are higher for small depths, and then the maximum values reached with the Young and Verhagen (1996) approach are greater than the maximum values obtained with WWTM approach. The results obtained with two-dimensional models suggest that the wave height is different in particular for small fetch, this could be due to the different formulation of the wave period. Finally, the application of WWTM for the entire Lagoon basin underlines an increase of the mean power density in the last four centuries, in particular in the central-southern part of the lagoon between Chioggia and Malamocco inlets.
One-dimensional Coulomb problem in Dirac materials

NASA Astrophysics Data System (ADS)

Downing, C. A.; Portnoi, M. E.

2014-11-01

We investigate the one-dimensional Coulomb potential with application to a class of quasirelativistic systems, so-called Dirac-Weyl materials, described by matrix Hamiltonians. We obtain the exact solution of the shifted and truncated Coulomb problems, with the wave functions expressed in terms of special functions (namely, Whittaker functions), while the energy spectrum must be determined via solutions to transcendental equations. Most notably, there are critical band gaps below which certain low-lying quantum states are missing in a manifestation of atomic collapse.
Multiple periodic-soliton solutions of the (3+1)-dimensional generalised shallow water equation

NASA Astrophysics Data System (ADS)

Li, Ye-Zhou; Liu, Jian-Guo

2018-06-01

Based on the extended variable-coefficient homogeneous balance method and two new ansätz functions, we construct auto-Bäcklund transformation and multiple periodic-soliton solutions of (3 {+} 1)-dimensional generalised shallow water equations. Completely new periodic-soliton solutions including periodic cross-kink wave, periodic two-solitary wave and breather type of two-solitary wave are obtained. In addition, cross-kink three-soliton and cross-kink four-soliton solutions are derived. Furthermore, propagation characteristics and interactions of the obtained solutions are discussed and illustrated in figures.
Optimization of one-way wave equations.

USGS Publications Warehouse

Lee, M.W.; Suh, S.Y.

1985-01-01

The theory of wave extrapolation is based on the square-root equation or one-way equation. The full wave equation represents waves which propagate in both directions. On the contrary, the square-root equation represents waves propagating in one direction only. A new optimization method presented here improves the dispersion relation of the one-way wave equation. -from Authors
Structure and Stability of One-Dimensional Detonations in Ethylene-Air Mixtures

NASA Technical Reports Server (NTRS)

Yungster, S.; Radhakrishnan, K.; Perkins, High D. (Technical Monitor)

2003-01-01

The propagation of one-dimensional detonations in ethylene-air mixtures is investigated numerically by solving the one-dimensional Euler equations with detailed finite-rate chemistry. The numerical method is based on a second-order spatially accurate total-variation-diminishing scheme and a point implicit, first-order-accurate, time marching algorithm. The ethylene-air combustion is modeled with a 20-species, 36-step reaction mechanism. A multi-level, dynamically adaptive grid is utilized, in order to resolve the structure of the detonation. Parametric studies over an equivalence ratio range of 0.5 less than phi less than 3 for different initial pressures and degrees of detonation overdrive demonstrate that the detonation is unstable for low degrees of overdrive, but the dynamics of wave propagation varies with fuel-air equivalence ratio. For equivalence ratios less than approximately 1.2 the detonation exhibits a short-period oscillatory mode, characterized by high-frequency, low-amplitude waves. Richer mixtures (phi greater than 1.2) exhibit a low-frequency mode that includes large fluctuations in the detonation wave speed; that is, a galloping propagation mode is established. At high degrees of overdrive, stable detonation wave propagation is obtained. A modified McVey-Toong short-period wave-interaction theory is in excellent agreement with the numerical simulations.
Error Estimates for Approximate Solutions of the Riccati Equation with Real or Complex Potentials

NASA Astrophysics Data System (ADS)

Finster, Felix; Smoller, Joel

2010-09-01

A method is presented for obtaining rigorous error estimates for approximate solutions of the Riccati equation, with real or complex potentials. Our main tool is to derive invariant region estimates for complex solutions of the Riccati equation. We explain the general strategy for applying these estimates and illustrate the method in typical examples, where the approximate solutions are obtained by gluing together WKB and Airy solutions of corresponding one-dimensional Schrödinger equations. Our method is motivated by, and has applications to, the analysis of linear wave equations in the geometry of a rotating black hole.
Nonstandard Analysis and Shock Wave Jump Conditions in a One-Dimensional Compressible Gas

NASA Technical Reports Server (NTRS)

Baty, Roy S.; Farassat, Fereidoun; Hargreaves, John

2007-01-01

Nonstandard analysis is a relatively new area of mathematics in which infinitesimal numbers can be defined and manipulated rigorously like real numbers. This report presents a fairly comprehensive tutorial on nonstandard analysis for physicists and engineers with many examples applicable to generalized functions. To demonstrate the power of the subject, the problem of shock wave jump conditions is studied for a one-dimensional compressible gas. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions in the thermodynamic and fluid dynamic parameters occur smoothly across this interval. To use conservations laws, smooth pre-distributions of the Dirac delta measure are applied whose supports are contained within the shock thickness. Furthermore, smooth pre-distributions of the Heaviside function are applied which vary from zero to one across the shock wave. It is shown that if the equations of motion are expressed in nonconservative form then the relationships between the jump functions for the flow parameters may be found unambiguously. The analysis yields the classical Rankine-Hugoniot jump conditions for an inviscid shock wave. Moreover, non-monotonic entropy jump conditions are obtained for both inviscid and viscous flows. The report shows that products of generalized functions may be defined consistently using nonstandard analysis; however, physically meaningful products of generalized functions must be determined from the physics of the problem and not the mathematical form of the governing equations.
Time-evolution of quantum systems via a complex nonlinear Riccati equation. I. Conservative systems with time-independent Hamiltonian

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cruz, Hans, E-mail: hans@ciencias.unam.mx; Schuch, Dieter; Castaños, Octavio, E-mail: ocasta@nucleares.unam.mx

2015-09-15

The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems with exact analytic solutions with the form of Gaussian wave packets. In particular, one-dimensional conservative systems with at most quadratic Hamiltonians are studied.
Microscale shock tube

NASA Astrophysics Data System (ADS)

Mirshekari, Gholamreza

This project aims at the simulation, design, fabrication and testing of a microscale shock tube. A step by step procedure has been followed to develop the different components of the microscale shock tube and then combine them together to realize the final device. The document reports on the numerical simulation of flows in a microscale shock tube, the experimental study of gas flow in microchannels, the design, microfabrication, and the test of a microscale shock tube. In the first step, a one-dimensional numerical model for simulation of transport effects at small-scale, appeared in low Reynolds number shock tubes is developed. The conservation equations have been integrated in the lateral directions and three-dimensional effects have been introduced as carefully controlled sources of mass, momentum and energy, into the one-dimensional model. The unsteady flow of gas behind the shock wave is reduced to a quasi-steady laminar flow solution, similar to the Blasius solution. The resulting one-dimensional equations are solved numerically and the simulations are performed for previously reported low Reynolds number shock tube experiments. Good agreement between the shock structure simulation and the attenuation due to the boundary layers has been observed. The simulation for predicting the performance of a microscale shock tube shows the large attenuation of shock wave at low pressure ratios. In the next step the steady flow inside microchannels has been experimentally studied. A set of microchannels with different geometries were fabricated. These microchannels have been used to measure the pressure drop as a function of flow rate in a steady compressible flow. The results of the experiments confirm that the flow inside the microscale shock tube follows the laminar model over the experiment's range of Knudsen number. The microscale shock tube is fabricated by deposition and patterning of different thin layers of selected materials on the silicon substrate. The direct sensing piezoelectric sensors were fabricated and integrated with microchannels patterned on the substrate. The channels were then covered with another substrate. This shock tube is 2000 mum long and it has a 2000 mum wide and 17 mum high rectangular cross section equipped with 5 piezoelectric sensors along the tube. The packaged microscale shock tube was installed in an ordinary shock tube and shock waves with different Mach numbers were directed into the channel. A one-dimensional inviscid calculation as well as viscous simulation using the one-dimensional model have also been performed for the above mentioned geometry. The comparison of results with those of the same geometry for an inviscid flow shows the considerable attenuation of shock strength and deceleration of the shock wave for both incident and reflected shock waves in the channel. The comparison of results with numerically generated results with the one-dimensional model presents good agreement for incident shock waves. Keywords. Shock wave, Shock tube, MEMS, Microfluidic, Piezoelectric sensor, Microchannel, Transport phenomena.
Hybrid soliton solutions in the (2+1)-dimensional nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Chen, Meidan; Li, Biao

2017-11-01

Rational solutions and hybrid solutions from N-solitons are obtained by using the bilinear method and a long wave limit method. Line rogue waves and lumps in the (2+1)-dimensional nonlinear Schrödinger (NLS) equation are derived from two-solitons. Then from three-solitons, hybrid solutions between kink soliton with breathers, periodic line waves and lumps are derived. Interestingly, after the collision, the breathers are kept invariant, but the amplitudes of the periodic line waves and lumps change greatly. For the four-solitons, the solutions describe as breathers with breathers, line rogue waves or lumps. After the collision, breathers and lumps are kept invariant, but the line rogue wave has a great change.
On the solution of the generalized wave and generalized sine-Gordon equations

NASA Technical Reports Server (NTRS)

Ablowitz, M. J.; Beals, R.; Tenenblat, K.

1986-01-01

The generalized wave equation and generalized sine-Gordon equations are known to be natural multidimensional differential geometric generalizations of the classical two-dimensional versions. In this paper, a system of linear differential equations is associated with these equations, and it is shown how the direct and inverse problems can be solved for appropriately decaying data on suitable lines. An initial-boundary value problem is solved for these equations.
Computational methods and traveling wave solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave dynamical equation via two methods and its applications

NASA Astrophysics Data System (ADS)

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

2018-05-01

The aim of this article is to construct some new traveling wave solutions and investigate localized structures for fourth-order nonlinear Ablowitz-Kaup-Newell-Segur (AKNS) water wave dynamical equation. The simple equation method (SEM) and the modified simple equation method (MSEM) are applied in this paper to construct the analytical traveling wave solutions of AKNS equation. The different waves solutions are derived by assigning special values to the parameters. The obtained results have their importance in the field of physics and other areas of applied sciences. All the solutions are also graphically represented. The constructed results are often helpful for studying several new localized structures and the waves interaction in the high-dimensional models.
Computing the Evans function via solving a linear boundary value ODE

NASA Astrophysics Data System (ADS)

Wahl, Colin; Nguyen, Rose; Ventura, Nathaniel; Barker, Blake; Sandstede, Bjorn

2015-11-01

Determining the stability of traveling wave solutions to partial differential equations can oftentimes be computationally intensive but of great importance to understanding the effects of perturbations on the physical systems (chemical reactions, hydrodynamics, etc.) they model. For waves in one spatial dimension, one may linearize around the wave and form an Evans function - an analytic Wronskian-like function which has zeros that correspond in multiplicity to the eigenvalues of the linearized system. If eigenvalues with a positive real part do not exist, the traveling wave will be stable. Two methods exist for calculating the Evans function numerically: the exterior-product method and the method of continuous orthogonalization. The first is numerically expensive, and the second reformulates the originally linear system as a nonlinear system. We develop a new algorithm for computing the Evans function through appropriate linear boundary-value problems. This algorithm is cheaper than the previous methods, and we prove that it preserves analyticity of the Evans function. We also provide error estimates and implement it on some classical one- and two-dimensional systems, one being the Swift-Hohenberg equation in a channel, to show the advantages.
Rogue waves and lump solitons for a ?-dimensional B-type Kadomtsev-Petviashvili equation in fluid dynamics

NASA Astrophysics Data System (ADS)

Sun, Yan; Tian, Bo; Xie, Xi-Yang; Chai, Jun; Yin, Hui-Min

2018-07-01

Under investigation is a ?-dimensional B-type Kadomtsev-Petviashvili equation, which has applications in the propagation of non-linear waves in fluid dynamics. Through the Hirota method and the extended homoclinic test technique, we obtain the breather-type kink soliton solutions and breather rational soliton solutions. Rogue wave solutions are derived, which come from the derivation of breather rational solitons with respect to x. Amplitudes of the breather-type kink solitons and rogue waves decrease with a non-zero parameter in the equation, ?, increasing when ?. In addition, dark rogue waves are derived when ?. Furthermore, with the aid of the Hirota method and symbolic computation, two types of the lump solitons are obtained with the different choices of the parameters. We graphically study the lump solitons related to the parameter ?, and amplitude of the lump soliton is negatively correlated with ? when ?.
A new equation in two dimensional fast magnetoacoustic shock waves in electron-positron-ion plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Masood, W.; Jehan, Nusrat; Mirza, Arshad M.

2010-03-15

Nonlinear properties of the two dimensional fast magnetoacoustic waves are studied in a three-component plasma comprising of electrons, positrons, and ions. In this regard, Kadomtsev-Petviashvili-Burger (KPB) equation is derived using the small amplitude perturbation expansion method. Under the condition that the electron and positron inertia are ignored, Burger-Kadomtsev-Petviashvili (Burger-KP) for a fast magnetoacoustic wave is derived for the first time, to the best of author's knowledge. The solutions of both KPB and Burger-KP equations are obtained using the tangent hyperbolic method. The effects of positron concentration, kinematic viscosity, and plasma beta are explored both for the KPB and the Burger-KPmore » shock waves and the differences between the two are highlighted. The present investigation may have relevance in the study of nonlinear electromagnetic shock waves both in laboratory and astrophysical plasmas.« less
Bifurcations of solitary wave solutions for (two and three)-dimensional nonlinear partial differential equation in quantum and magnetized plasma by using two different methods

NASA Astrophysics Data System (ADS)

Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen

2018-06-01

In this research, we study new two techniques that called the extended simple equation method and the novel (G‧/G) -expansion method. The extended simple equation method depend on the auxiliary equation (dϕ/dξ = α + λϕ + μϕ2) which has three ways for solving depends on the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (α = 0) this auxiliary equation reduces to Bernoulli equation and when (α ≠ 0, λ ≠ 0, μ ≠ 0) we the general solutions of this auxiliary equation while the novel (G‧/G) -expansion method depends also on similar auxiliary equation (G‧/G)‧ = μ + λ(G‧/G) + (v - 1)(G‧/G) 2 which depend also on the value of (λ2 - 4 (v - 1) μ) and the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (μ = 0) this auxiliary equation reduces to Bernoulli equation and when (λ2 ≠ 4 (v - 1) μ) we the general solutions of this auxiliary equation. This show how both of these auxiliary equation are special cases of Riccati equation. We apply these methods on two dimensional nonlinear Kadomtsev-Petviashvili Burgers equation in quantum plasma and three-dimensional nonlinear modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma. We obtain the exact traveling wave solutions of these important models and under special condition on the parameters, we get solitary traveling wave solutions. All calculations in this study have been established and verified back with the aid of the Maple package program. The executed method is powerful, effective and straightforward for solving nonlinear partial differential equations to obtain more and new solutions.
Secondary Bifurcation and Change of Type for Three Dimensional Standing Waves in Shallow Water.

DTIC Science & Technology

1986-02-01

field of standing K-P waves. A set of two non-interacting (to first order) solutions of the K-P equation ( Kadomtsev - Petviashvili 1970). The K-P equation ...P equation was first derived by Kadomtsev & Petviashvili (1970) in their study of the stability of solitary waves to transverse perturbations. A...Scientists, Springer-Verlag 6. B.A. Dubrovin (1981), "Theta Functions and Non-linear Equations ", Russian Mat. Surveys, 36, 11-92 7 B.B. Kadomtsev

Emergence and space-time structure of lump solution to the (2+1)-dimensional generalized KP equation

NASA Astrophysics Data System (ADS)

Tan, Wei; Dai, Houping; Dai, Zhengde; Zhong, Wenyong

2017-11-01

A periodic breather-wave solution is obtained using homoclinic test approach and Hirota's bilinear method with a small perturbation parameter u0 for the (2+1)-dimensional generalized Kadomtsev-Petviashvili equation. Based on the periodic breather-wave, a lump solution is emerged by limit behaviour. Finally, three different forms of the space-time structure of the lump solution are investigated and discussed using the extreme value theory.
Analytic solutions for Long's equation and its generalization

NASA Astrophysics Data System (ADS)

Humi, Mayer

2017-12-01

Two-dimensional, steady-state, stratified, isothermal atmospheric flow over topography is governed by Long's equation. Numerical solutions of this equation were derived and used by several authors. In particular, these solutions were applied extensively to analyze the experimental observations of gravity waves. In the first part of this paper we derive an extension of this equation to non-isothermal flows. Then we devise a transformation that simplifies this equation. We show that this simplified equation admits solitonic-type solutions in addition to regular gravity waves. These new analytical solutions provide new insights into the propagation and amplitude of gravity waves over topography.
Turbulence in the Ott-Antonsen equation for arrays of coupled phase oscillators

NASA Astrophysics Data System (ADS)

Wolfrum, M.; Gurevich, S. V.; Omel'chenko, O. E.

2016-02-01

In this paper we study the transition to synchrony in an one-dimensional array of oscillators with non-local coupling. For its description in the continuum limit of a large number of phase oscillators, we use a corresponding Ott-Antonsen equation, which is an integro-differential equation for the evolution of the macroscopic profiles of the local mean field. Recently, it was reported that in the spatially extended case at the synchronisation threshold there appear partially coherent plane waves with different wave numbers, which are organised in the well-known Eckhaus scenario. In this paper, we show that for Kuramoto-Sakaguchi phase oscillators the phase lag parameter in the interaction function can induce a Benjamin-Feir-type instability of the partially coherent plane waves. The emerging collective macroscopic chaos appears as an intermediate stage between complete incoherence and stable partially coherent plane waves. We give an analytic treatment of the Benjamin-Feir instability and its onset in a codimension-two bifurcation in the Ott-Antonsen equation as well as a numerical study of the transition from phase turbulence to amplitude turbulence inside the Benjamin-Feir unstable region.
Two different kinds of rogue waves in weakly crossing sea states

NASA Astrophysics Data System (ADS)

Ruban, V. P.

2009-06-01

Formation of giant waves in sea states with two spectral maxima centered at close wave vectors k0±Δk/2 in the Fourier plane is numerically simulated using the fully nonlinear model for long-crested water waves [V. P. Ruban, Phys. Rev. E 71, 055303(R) (2005)]. Depending on an angle θ between the vectors k0 and Δk , which determines a typical orientation of interference stripes in the physical plane, rogue waves arise having different spatial structure. If θ≲arctan(1/2) , then typical giant waves are relatively long fragments of essentially two-dimensional (2D) ridges, separated by wide valleys and consisting of alternating oblique crests and troughs. At nearly perpendicular k0 and Δk , the interference minima develop to coherent structures similar to the dark solitons of the nonlinear Schrodinger equation, and a 2D freak wave looks much as a piece of a one-dimensional freak wave bounded in the transversal direction by two such dark solitons.
Rogue waves and lump solutions for a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation in fluid mechanics

NASA Astrophysics Data System (ADS)

Wu, Xiao-Yu; Tian, Bo; Chai, Han-Peng; Sun, Yan

2017-08-01

Under investigation in this letter is a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation, which describes the weakly dispersive waves propagating in a fluid. Employing the Hirota method and symbolic computation, we obtain the lump, breather-wave and rogue-wave solutions under certain constraints. We graphically study the lump waves with the influence of the parameters h1, h3 and h5 which are all the real constants: When h1 increases, amplitude of the lump wave increases, and location of the peak moves; when h3 increases, lump wave’s amplitude decreases, but location of the peak keeps unchanged; when h5 changes, lump wave’s peak location moves, but amplitude keeps unchanged. Breather waves and rogue waves are displayed: Rogue waves emerge when the periods of the breather waves go to the infinity.
The effects of the Asselin time filter on numerical solutions to the linearized shallow-water wave equations

NASA Technical Reports Server (NTRS)

Schlesinger, R. E.; Johnson, D. R.; Uccellini, L. W.

1983-01-01

In the present investigation, a one-dimensional linearized analysis is used to determine the effect of Asselin's (1972) time filter on both the computational stability and phase error of numerical solutions for the shallow water wave equations, in cases with diffusion but without rotation. An attempt has been made to establish the approximate optimal values of the filtering parameter nu for each of the 'lagged', Dufort-Frankel, and Crank-Nicholson diffusion schemes, suppressing the computational wave mode without materially altering the physical wave mode. It is determined that in the presence of diffusion, the optimum filter length depends on whether waves are undergoing significant propagation. When moderate propagation is present, with or without diffusion, the Asselin filter has little effect on the spatial phase lag of the physical mode for the leapfrog advection scheme of the three diffusion schemes considered.
Two dimensional cylindrical fast magnetoacoustic solitary waves in a dust plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu Haifeng; Wang Shiqing; Engineering and Technical College of Chengdu University of Technology, Leshan 614000

2011-04-15

The nonlinear fast magnetoacoustic solitary waves in a dust plasma with the combined effects of bounded cylindrical geometry and transverse perturbation are investigated in a new equation. In this regard, cylindrical Kadomtsev-Petviashvili (CKP) equation is derived using the small amplitude perturbation expansion method. Under a suitable coordinate transformation, the CKP equation can be solved analytically. It is shown that the dust cylindrical fast magnetoacoustic solitary waves can exist in the CKP equation. The present investigation may have relevance in the study of nonlinear electromagnetic soliton waves both in laboratory and astrophysical plasmas.
Amplification of light in one-dimensional vibrating metal photonic crystal

NASA Astrophysics Data System (ADS)

Ueta, Tsuyoshi

2012-04-01

Photon-phonon interaction on the analogy of electron-phonon interaction is considered in one-dimensional metal photonic crystal. When lattice vibration is artificially introduced to the photonic crystal, a governing equation of electromagnetic field is derived. A simple model is numerically analyzed, and the following novel phenomena are found out. The lattice vibration generates the light of frequency which added the integral multiple of the vibration frequency to that of the incident wave and also amplifies the incident wave resonantly. On a resonance, the amplification factor increases very rapidly with the number of layers. Resonance frequencies change with the phases of lattice vibration. The amplification phenomenon is analytically discussed for low frequency of the lattice vibration and is confirmed by numerical works.
Analysis of Three-Dimensional, Nonlinear Development of Wave-Like Structure in a Compressible Round Jet

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Mankbadi, Reda R.

2002-01-01

An analysis of the nonlinear development of the large-scale structures or instability waves in compressible round jets was conducted using the integral energy method. The equations of motion were decomposed into two sets of equations; one set governing the mean flow motion and the other set governing the large-scale structure motion. The equations in each set were then combined to derive kinetic energy equations that were integrated in the radial direction across the jet after the boundary-layer approximations were applied. Following the application of further assumptions regarding the radial shape of the mean flow and the large structures, equations were derived that govern the nonlinear, streamwise development of the large structures. Using numerically generated mean flows, calculations show the energy exchanges and the effects of the initial amplitude on the coherent structure development in the jet.
Nonlinear stability of solar type 3 radio bursts. 1: Theory

NASA Technical Reports Server (NTRS)

Smith, R. A.; Goldstein, M. L.; Papadopoulos, K.

1978-01-01

A theory of the excitation of solar type 3 bursts is presented. Electrons initially unstable to the linear bump-in-tail instability are shown to rapidly amplify Langmuir waves to energy densities characteristic of strong turbulence. The three-dimensional equations which describe the strong coupling (wave-wave) interactions are derived. For parameters characteristic of the interplanetary medium the equations reduce to one dimension. In this case, the oscillating two stream instability (OTSI) is the dominant nonlinear instability, and is stablized through the production of nonlinear ion density fluctuations that efficiently scatter Langmuir waves out of resonance with the electron beam. An analytical model of the electron distribution function is also developed which is used to estimate the total energy losses suffered by the electron beam as it propagates from the solar corona to 1 A.U. and beyond.
Signatures of extra dimensions in gravitational waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Andriot, David; Gómez, Gustavo Lucena, E-mail: andriotphysics@gmail.com, E-mail: glucenag@aei.mpg.de

2017-06-01

Considering gravitational waves propagating on the most general 4+ N -dimensional space-time, we investigate the effects due to the N extra dimensions on the four-dimensional waves. All wave equations are derived in general and discussed. On Minkowski{sub 4} times an arbitrary Ricci-flat compact manifold, we find: a massless wave with an additional polarization, the breathing mode, and extra waves with high frequencies fixed by Kaluza-Klein masses. We discuss whether these two effects could be observed.
Letter: Modeling reactive shock waves in heterogeneous solids at the continuum level with stochastic differential equations

NASA Astrophysics Data System (ADS)

Kittell, D. E.; Yarrington, C. D.; Lechman, J. B.; Baer, M. R.

2018-05-01

A new paradigm is introduced for modeling reactive shock waves in heterogeneous solids at the continuum level. Inspired by the probability density function methods from turbulent reactive flows, it is hypothesized that the unreacted material microstructures lead to a distribution of heat release rates from chemical reaction. Fluctuations in heat release, rather than velocity, are coupled to the reactive Euler equations which are then solved via the Riemann problem. A numerically efficient, one-dimensional hydrocode is used to demonstrate this new approach, and simulation results of a representative impact calculation (inert flyer into explosive target) are discussed.
Propagation of large-amplitude waves on dielectric liquid sheets in a tangential electric field: exact solutions in three-dimensional geometry.

PubMed

Zubarev, Nikolay M; Zubareva, Olga V

2010-10-01

Nonlinear waves on sheets of dielectric liquid in the presence of an external tangential electric field are studied theoretically. It is shown that waves of arbitrary shape in three-dimensional geometry can propagate along (or against) the electric field direction without distortion, i.e., the equations of motion admit a wide class of exact traveling wave solutions. This unusual situation occurs for nonconducting ideal liquids with high dielectric constants in the case of a sufficiently strong field strength. Governing equations for evolution of plane symmetric waves on fluid sheets are derived using conformal variables. A dispersion relation for the evolution of small perturbations of the traveling wave solutions is obtained. It follows from this relation that, regardless of the wave shape, the amplitudes of small-scale perturbations do not increase with time and, hence, the traveling waves are stable. We also study the interaction of counterpropagating symmetric waves with small but finite amplitudes. The corresponding solution of the equations of motion describes the nonlinear superposition of the oppositely directed waves. The results obtained are applicable for the description of long waves on fluid sheets in a horizontal magnetic field.
An analytical solution to the one-dimensional heat conduction-convection equation in soil

USDA-ARS?s Scientific Manuscript database

Heat transfer in soil occurs by conduction and convection. Infiltrating water affects soil temperature distributions, and measuring soil temperature distributions below infiltrating water can provide a signal for the flux of water. In earlier work a sine wave function (hereinafter referred to as the...
Exact traveling-wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional Schrödinger equation with polynomial nonlinearity of arbitrary order.

PubMed

Petrović, Nikola Z; Belić, Milivoj; Zhong, Wei-Ping

2011-02-01

We obtain exact traveling wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation with variable coefficients and polynomial Kerr nonlinearity of an arbitrarily high order. Exact solutions, given in terms of Jacobi elliptic functions, are presented for the special cases of cubic-quintic and septic models. We demonstrate that the widely used method for finding exact solutions in terms of Jacobi elliptic functions is not applicable to the nonlinear Schrödinger equation with saturable nonlinearity. ©2011 American Physical Society
Single-cone finite-difference schemes for the (2+1)-dimensional Dirac equation in general electromagnetic textures

NASA Astrophysics Data System (ADS)

Pötz, Walter

2017-11-01

A single-cone finite-difference lattice scheme is developed for the (2+1)-dimensional Dirac equation in presence of general electromagnetic textures. The latter is represented on a (2+1)-dimensional staggered grid using a second-order-accurate finite difference scheme. A Peierls-Schwinger substitution to the wave function is used to introduce the electromagnetic (vector) potential into the Dirac equation. Thereby, the single-cone energy dispersion and gauge invariance are carried over from the continuum to the lattice formulation. Conservation laws and stability properties of the formal scheme are identified by comparison with the scheme for zero vector potential. The placement of magnetization terms is inferred from consistency with the one for the vector potential. Based on this formal scheme, several numerical schemes are proposed and tested. Elementary examples for single-fermion transport in the presence of in-plane magnetization are given, using material parameters typical for topological insulator surfaces.
On nonlinear Tollmien-Schlichting/vortex interaction in three-dimensional boundary layers

NASA Technical Reports Server (NTRS)

Davis, Dominic A. R.; Smith, Frank T.

1993-01-01

The instability of an incompressible three-dimensional boundary layer (that is, one with cross-flow) is considered theoretically and computationally in the context of vortex/wave interactions. Specifically the work centers on two low amplitude, lower-branch Tollmien-Schlichting waves which mutually interact to induce a weak longitudinal vortex flow; the vortex motion, in turn, gives rise to significant wave-modulation via wall-shear forcing. The characteristic Reynolds number is taken as a large parameter and, as a consequence, the waves' and the vortex motion are governed primarily by triple-deck theory. The nonlinear interaction is captured by a viscous partial-differential system for the vortex coupled with a pair of amplitude equations for each wave pressure. Three distinct possibilities were found to emerge for the nonlinear behavior of the flow solution downstream - an algebraic finite-distance singularity, far downstream saturation or far-downstream wave-decay (leaving pure vortex flow) - depending on the input conditions, the wave angles, and the size of the cross-flow.
A three-dimensional, finite element model for coastal and estuarine circulation

USGS Publications Warehouse

Walters, R.A.

1992-01-01

This paper describes the development and application of a three-dimensional model for coastal and estuarine circulation. The model uses a harmonic expansion in time and a finite element discretization in space. All nonlinear terms are retained, including quadratic bottom stress, advection and wave transport (continuity nonlinearity). The equations are solved as a global and a local problem, where the global problem is the solution of the wave equation formulation of the shallow water equations, and the local problem is the solution of the momentum equation for the vertical velocity profile. These equations are coupled to the advection-diffusion equation for salt so that density gradient forcing is included in the momentum equations. The model is applied to a study of Delaware Bay, U.S.A., where salinity intrusion is the primary focus. ?? 1991.
Solution of D dimensional Dirac equation for hyperbolic tangent potential using NU method and its application in material properties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suparmi, A., E-mail: soeparmi@staff.uns.ac.id; Cari, C., E-mail: cari@staff.uns.ac.id; Pratiwi, B. N., E-mail: namakubetanurpratiwi@gmail.com

2016-02-08

The analytical solution of D-dimensional Dirac equation for hyperbolic tangent potential is investigated using Nikiforov-Uvarov method. In the case of spin symmetry the D dimensional Dirac equation reduces to the D dimensional Schrodinger equation. The D dimensional relativistic energy spectra are obtained from D dimensional relativistic energy eigen value equation by using Mat Lab software. The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi polynomials. The thermodynamically properties of materials are generated from the non-relativistic energy eigen-values in the classical limit. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy.more » The thermal quantities of the system, partition function and specific heat, are expressed in terms of error function and imaginary error function which are numerically calculated using Mat Lab software.« less
Numerical Recovering of a Speed of Sound by the BC-Method in 3D

NASA Astrophysics Data System (ADS)

Pestov, Leonid; Bolgova, Victoria; Danilin, Alexandr

We develop the numerical algorithm for solving the inverse problem for the wave equation by the Boundary Control method. The problem, which we refer to as a forward one, is an initial boundary value problem for the wave equation with zero initial data in the bounded domain. The inverse problem is to find the speed of sound c(x) by the measurements of waves induced by a set of boundary sources. The time of observation is assumed to be greater then two acoustical radius of the domain. The numerical algorithm for sound reconstruction is based on two steps. The first one is to find a (sufficiently large) number of controls {f_j} (the basic control is defined by the position of the source and some time delay), which generates the same number of known harmonic functions, i.e. Δ {u_j}(.,T) = 0 , where {u_j} is the wave generated by the control {f_j} . After that the linear integral equation w.r.t. the speed of sound is obtained. The piecewise constant model of the speed is used. The result of numerical testing of 3-dimensional model is presented.

Dirac Equation in (1 +1 )-Dimensional Curved Spacetime and the Multiphoton Quantum Rabi Model

NASA Astrophysics Data System (ADS)

Pedernales, J. S.; Beau, M.; Pittman, S. M.; Egusquiza, I. L.; Lamata, L.; Solano, E.; del Campo, A.

2018-04-01

We introduce an exact mapping between the Dirac equation in (1 +1 )-dimensional curved spacetime (DCS) and a multiphoton quantum Rabi model (QRM). A background of a (1 +1 )-dimensional black hole requires a QRM with one- and two-photon terms that can be implemented in a trapped ion for the quantum simulation of Dirac particles in curved spacetime. We illustrate our proposal with a numerical analysis of the free fall of a Dirac particle into a (1 +1 )-dimensional black hole, and find that the Zitterbewegung effect, measurable via the oscillatory trajectory of the Dirac particle, persists in the presence of gravity. From the duality between the squeezing term in the multiphoton QRM and the metric coupling in the DCS, we show that gravity generates squeezing of the Dirac particle wave function.
Siegert-state expansion for nonstationary systems. IV. Three-dimensional case

NASA Astrophysics Data System (ADS)

Tolstikhin, Oleg I.

2008-03-01

The Siegert-state expansion approach [O. I. Tolstikhin, Phys. Rev. A 73, 062705 (2006)] is extended to the three-dimensional case. Coupled equations defining the time evolution of coefficients in the expansion of the solution to the time-dependent Schrödinger equation in terms of partial-wave Siegert states are derived, and physical observables (probabilities of transitions to discrete states and the momentum distribution of ejected particles) are expressed in terms of these coefficients. The approach is implemented in terms of Siegert pseudostates and illustrated by calculations of the photodetachment of H- by strong high-frequency laser pulses. The present calculations demonstrate that the interference effect in the laser-atom interaction dynamics found recently in the one-dimensional case [K. Toyota , Phys. Rev. A 76, 043418 (2007)] reveals itself in the three-dimensional case as well.
Chaos for cardiac arrhythmias through a one-dimensional modulation equation for alternans

PubMed Central

Dai, Shu; Schaeffer, David G.

2010-01-01

Instabilities in cardiac dynamics have been widely investigated in recent years. One facet of this work has studied chaotic behavior, especially possible correlations with fatal arrhythmias. Previously chaotic behavior was observed in various models, specifically in the breakup of spiral and scroll waves. In this paper we study cardiac dynamics and find spatiotemporal chaotic behavior through the Echebarria–Karma modulation equation for alternans in one dimension. Although extreme parameter values are required to produce chaos in this model, it seems significant mathematically that chaos may occur by a different mechanism from previous observations. PMID:20590327
Effect of nonthermal electrons on the propagation characteristics and stability of two-dimensional nonlinear electrostatic coherent structures in relativistic electron positron ion plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Masood, W.; National Centre for Physics; Rizvi, H.

2011-06-15

Two-dimensional propagation of nonlinear ion acoustic shock and solitary waves in an unmagnetized plasma consisting of nonthermal electrons, Boltzmannian positrons, and singly charged hot ions streaming with relativistic velocities are investigated. The system of fluid equations is reduced to Kadomtsev-Petviashvili-Burgers and Kadomtsev-Petviashvili (KP) equations in the limit of small amplitude perturbation. The dependence of the ion acoustic shock and solitary waves on various plasma parameters are explored in detail. Interestingly, it is observed that increasing the nonthermal electron population increases the wave dispersion which enervates the strength of the ion acoustic shock wave; however, the same effect leads to anmore » enhancement of the soliton amplitude due to the absence of dissipation in the KP equation. The present investigation may be useful to understand the two-dimensional propagation characteristics of small but finite amplitude localized shock and solitary structures in planetary magnetospheres and auroral plasmas where nonthermal populations of electrons have been observed by several satellite missions.« less
Lump waves and breather waves for a (3+1)-dimensional generalized Kadomtsev-Petviashvili Benjamin-Bona-Mahony equation for an offshore structure

NASA Astrophysics Data System (ADS)

Yin, Ying; Tian, Bo; Wu, Xiao-Yu; Yin, Hui-Min; Zhang, Chen-Rong

2018-04-01

In this paper, we investigate a (3+1)-dimensional generalized Kadomtsev-Petviashvili Benjamin-Bona-Mahony equation, which describes the fluid flow in the case of an offshore structure. By virtue of the Hirota method and symbolic computation, bilinear forms, the lump-wave and breather-wave solutions are derived. Propagation characteristics and interaction of lump waves and breather waves are graphically discussed. Amplitudes and locations of the lump waves, amplitudes and periods of the breather waves all vary with the wavelengths in the three spatial directions, ratio of the wave amplitude to the depth of water, or product of the depth of water and the relative wavelength along the main direction of propagation. Of the interactions between the lump waves and solitons, there exist two different cases: (i) the energy is transferred from the lump wave to the soliton; (ii) the energy is transferred from the soliton to the lump wave.
An analytical model of a curved beam with a T shaped cross section

NASA Astrophysics Data System (ADS)

Hull, Andrew J.; Perez, Daniel; Cox, Donald L.

2018-03-01

This paper derives a comprehensive analytical dynamic model of a closed circular beam that has a T shaped cross section. The new model includes in-plane and out-of-plane vibrations derived using continuous media expressions which produces results that have a valid frequency range above those available from traditional lumped parameter models. The web is modeled using two-dimensional elasticity equations for in-plane motion and the classical flexural plate equation for out-of-plane motion. The flange is modeled using two sets of Donnell shell equations: one for the left side of the flange and one for the right side of the flange. The governing differential equations are solved with unknown wave propagation coefficients multiplied by spatial domain and time domain functions which are inserted into equilibrium and continuity equations at the intersection of the web and flange and into boundary conditions at the edges of the system resulting in 24 algebraic equations. These equations are solved to yield the wave propagation coefficients and this produces a solution to the displacement field in all three dimensions. An example problem is formulated and compared to results from finite element analysis.
Observationally constrained modeling of sound in curved ocean internal waves: examination of deep ducting and surface ducting at short range.

PubMed

Duda, Timothy F; Lin, Ying-Tsong; Reeder, D Benjamin

2011-09-01

A study of 400 Hz sound focusing and ducting effects in a packet of curved nonlinear internal waves in shallow water is presented. Sound propagation roughly along the crests of the waves is simulated with a three-dimensional parabolic equation computational code, and the results are compared to measured propagation along fixed 3 and 6 km source/receiver paths. The measurements were made on the shelf of the South China Sea northeast of Tung-Sha Island. Construction of the time-varying three-dimensional sound-speed fields used in the modeling simulations was guided by environmental data collected concurrently with the acoustic data. Computed three-dimensional propagation results compare well with field observations. The simulations allow identification of time-dependent sound forward scattering and ducting processes within the curved internal gravity waves. Strong acoustic intensity enhancement was observed during passage of high-amplitude nonlinear waves over the source/receiver paths, and is replicated in the model. The waves were typical of the region (35 m vertical displacement). Two types of ducting are found in the model, which occur asynchronously. One type is three-dimensional modal trapping in deep ducts within the wave crests (shallow thermocline zones). The second type is surface ducting within the wave troughs (deep thermocline zones). © 2011 Acoustical Society of America
Geometrically induced nonlinear dynamics in one-dimensional lattices

NASA Astrophysics Data System (ADS)

Hamilton, Merle D.; de Alcantara Bonfim, O. F.

2006-03-01

We present a lattice model consisting of a single one-dimensional chain, where the masses are interconnected by linear springs and allowed to move in a horizontal direction only, as in a monorail. In the transverse direction each mass is also attached to two other linear springs, one on each side of the mass. The ends of these springs are kept at fixed positions. The nonlinearity in the model arises from the geometric constraints imposed on the motion of the masses, as well as from the configuration of the springs, where in the transverse direction the springs are either in the extended or compressed state depending on the position of the masses. Under these conditions we show that solitary waves are present in the system. In the long wavelength limit an analytic solution for these nonlinear waves is found. Numerical integrations of the equations of motion in the full system are also performed to analyze the conditions for the existence and stability of the nonlinear waves.
Evaluation of a wave-vector-frequency-domain method for nonlinear wave propagation

PubMed Central

Jing, Yun; Tao, Molei; Clement, Greg T.

2011-01-01

A wave-vector-frequency-domain method is presented to describe one-directional forward or backward acoustic wave propagation in a nonlinear homogeneous medium. Starting from a frequency-domain representation of the second-order nonlinear acoustic wave equation, an implicit solution for the nonlinear term is proposed by employing the Green’s function. Its approximation, which is more suitable for numerical implementation, is used. An error study is carried out to test the efficiency of the model by comparing the results with the Fubini solution. It is shown that the error grows as the propagation distance and step-size increase. However, for the specific case tested, even at a step size as large as one wavelength, sufficient accuracy for plane-wave propagation is observed. A two-dimensional steered transducer problem is explored to verify the nonlinear acoustic field directional independence of the model. A three-dimensional single-element transducer problem is solved to verify the forward model by comparing it with an existing nonlinear wave propagation code. Finally, backward-projection behavior is examined. The sound field over a plane in an absorptive medium is backward projected to the source and compared with the initial field, where good agreement is observed. PMID:21302985
Analysis of wave motion in one-dimensional structures through fast-Fourier-transform-based wavelet finite element method

NASA Astrophysics Data System (ADS)

Shen, Wei; Li, Dongsheng; Zhang, Shuaifang; Ou, Jinping

2017-07-01

This paper presents a hybrid method that combines the B-spline wavelet on the interval (BSWI) finite element method and spectral analysis based on fast Fourier transform (FFT) to study wave propagation in One-Dimensional (1D) structures. BSWI scaling functions are utilized to approximate the theoretical wave solution in the spatial domain and construct a high-accuracy dynamic stiffness matrix. Dynamic reduction on element level is applied to eliminate the interior degrees of freedom of BSWI elements and substantially reduce the size of the system matrix. The dynamic equations of the system are then transformed and solved in the frequency domain through FFT-based spectral analysis which is especially suitable for parallel computation. A comparative analysis of four different finite element methods is conducted to demonstrate the validity and efficiency of the proposed method when utilized in high-frequency wave problems. Other numerical examples are utilized to simulate the influence of crack and delamination on wave propagation in 1D rods and beams. Finally, the errors caused by FFT and their corresponding solutions are presented.
A one-dimensional model of the semiannual oscillation driven by convectively forced gravity waves

NASA Technical Reports Server (NTRS)

Sassi, Fabrizio; Garcia, Rolando R.

1994-01-01

A one-dimensional model that solves the time-dependent equations for the zonal mean wind and a wave of specified zonal wavenumber has been used to illustrate the ability of gravity waves forced by time-dependent tropospheric heating to produce a semiannual oscillation (SAO) in the middle atmosphere. When the heating has a strong diurnal cycle, as observed over tropical landmasses, gravity waves with zonal wavelengths of a few thousand kilometers and phase velocities in the range +/- 40-50 m/sec are excited efficiently by the maximum vertical projection criterion (vertical wavelength approximately equals 2 x forcing depth). Calculations show that these waves can account for large zonal mean wind accelerations in the middle atmosphere, resulting in realistic stratopause and mesopause oscillations. Calculations of the temporal evolution of a quasi-conserved tracer indicate strong down-welling in the upper stratosphere near the equinoxes, which is associated with the descent of the SAO westerlies. In the upper mesosphere, there is a semiannual oscillation in tracer mixing ratio driven by seasonal variability in eddy mixing, which increases at the solstices and decreases at the equinoxes.
Rogue waves: from nonlinear Schrödinger breather solutions to sea-keeping test.

PubMed

Onorato, Miguel; Proment, Davide; Clauss, Günther; Klein, Marco

2013-01-01

Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship.
Rogue Waves: From Nonlinear Schrödinger Breather Solutions to Sea-Keeping Test

PubMed Central

Onorato, Miguel; Proment, Davide; Clauss, Günther; Klein, Marco

2013-01-01

Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship. PMID:23405086
Exact traveling wave solutions for system of nonlinear evolution equations.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H

2016-01-01

In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.
MCDU-8-A Computer Code for One-Dimensional Blast Wave Problems

DTIC Science & Technology

1975-07-01

medium surrounding the explosion is assuned to be air obeying an ideal gas equation of state with a constant specific heat ratio, y2, of 1.4. The...characteristics Explosive blast Pentolite spheres ■ 20.\\ASSTRACT (Continue on reverie eld* II neceeemry end Identify by block number) he method...INVOLVING THE. SUDDEN RELEASE OF A HIGHLY COMPRESSED AIR SPHERE 11 V. A SAMPLE PROBLEM INVOLVING A BLAST WAVE RESULTING FROM THE DETONATION OF A
High-Resolution Genuinely Multidimensional Solution of Conservation Laws by the Space-Time Conservation Element and Solution Element Method

NASA Technical Reports Server (NTRS)

Himansu, Ananda; Chang, Sin-Chung; Yu, Sheng-Tao; Wang, Xiao-Yen; Loh, Ching-Yuen; Jorgenson, Philip C. E.

1999-01-01

In this overview paper, we review the basic principles of the method of space-time conservation element and solution element for solving the conservation laws in one and two spatial dimensions. The present method is developed on the basis of local and global flux conservation in a space-time domain, in which space and time are treated in a unified manner. In contrast to the modern upwind schemes, the approach here does not use the Riemann solver and the reconstruction procedure as the building blocks. The drawbacks of the upwind approach, such as the difficulty of rationally extending the 1D scalar approach to systems of equations and particularly to multiple dimensions is here contrasted with the uniformity and ease of generalization of the Conservation Element and Solution Element (CE/SE) 1D scalar schemes to systems of equations and to multiple spatial dimensions. The assured compatibility with the simplest type of unstructured meshes, and the uniquely simple nonreflecting boundary conditions of the present method are also discussed. The present approach has yielded high-resolution shocks, rarefaction waves, acoustic waves, vortices, ZND detonation waves, and shock/acoustic waves/vortices interactions. Moreover, since no directional splitting is employed, numerical resolution of two-dimensional calculations is comparable to that of the one-dimensional calculations. Some sample applications displaying the strengths and broad applicability of the CE/SE method are reviewed.
Higher-order rational solitons and rogue-like wave solutions of the (2 + 1)-dimensional nonlinear fluid mechanics equations

NASA Astrophysics Data System (ADS)

Wen, Xiao-Yong; Yan, Zhenya

2017-02-01

The novel generalized perturbation (n, M)-fold Darboux transformations (DTs) are reported for the (2 + 1)-dimensional Kadomtsev-Petviashvili (KP) equation and its extension by using the Taylor expansion of the Darboux matrix. The generalized perturbation (1 , N - 1) -fold DTs are used to find their higher-order rational solitons and rogue wave solutions in terms of determinants. The dynamics behaviors of these rogue waves are discussed in detail for different parameters and time, which display the interesting RW and soliton structures including the triangle, pentagon, heptagon profiles, etc. Moreover, we find that a new phenomenon that the parameter (a) can control the wave structures of the KP equation from the higher-order rogue waves (a ≠ 0) into higher-order rational solitons (a = 0) in (x, t)-space with y = const . These results may predict the corresponding dynamical phenomena in the models of fluid mechanics and other physically relevant systems.
Evaluation of Full Reynolds Stress Turbulence Models in FUN3D

NASA Technical Reports Server (NTRS)

Dudek, Julianne C.; Carlson, Jan-Renee

2017-01-01

Full seven-equation Reynolds stress turbulence models are promising tools for today’s aerospace technology challenges. This paper examines two such models for computing challenging turbulent flows including shock-wave boundary layer interactions, separation and mixing layers. The Wilcox and the SSG/LRR full second-moment Reynolds stress models have been implemented into the FUN3D (Fully Unstructured Navier-Stokes Three Dimensional) unstructured Navier-Stokes code and were evaluated for four problems: a transonic two-dimensional diffuser, a supersonic axisymmetric compression corner, a compressible planar shear layer, and a subsonic axisymmetric jet. Simulation results are compared with experimental data and results computed using the more commonly used Spalart-Allmaras (SA) one-equation and the Menter Shear Stress Transport (SST-V) two-equation turbulence models.
Evaluation of Full Reynolds Stress Turbulence Models in FUN3D

NASA Technical Reports Server (NTRS)

Dudek, Julianne C.; Carlson, Jan-Renee

2017-01-01

Full seven-equation Reynolds stress turbulence models are a relatively new and promising tool for todays aerospace technology challenges. This paper uses two stress-omega full Reynolds stress models to evaluate challenging flows including shock-wave boundary layer interactions, separation and mixing layers. The Wilcox and the SSG/LRR full second-moment Reynolds stress models have been implemented into the FUN3D (Fully Unstructured Navier-Stokes Three Dimensional) unstructured Navier-Stokes code and are evaluated for four problems: a transonic two-dimensional diffuser, a supersonic axisymmetric compression corner, a compressible planar shear layer, and a subsonic axisymmetric jet. Simulation results are compared with experimental data and results using the more commonly used Spalart-Allmaras (SA) one-equation and the Menter Shear Stress Transport (SST-V) two-equation turbulence models.
Two-dimensional solitary waves and periodic waves on coupled nonlinear electrical transmission lines

NASA Astrophysics Data System (ADS)

Wang, Heng; Zheng, Shuhua

2017-06-01

By using the dynamical system approach, the exact travelling wave solutions for a system of coupled nonlinear electrical transmission lines are studied. Based on this method, the bifurcations of phase portraits of a dynamical system are given. The two-dimensional solitary wave solutions and periodic wave solutions on coupled nonlinear transmission lines are obtained. With the aid of Maple, the numerical simulations are conducted for solitary wave solutions and periodic wave solutions to the model equation. The results presented in this paper improve upon previous studies.

Analytical Approach to (2+1)-Dimensional Boussinesq Equation and (3+1)-Dimensional Kadomtsev-Petviashvili Equation

NASA Astrophysics Data System (ADS)

Sarıaydın, Selin; Yıldırım, Ahmet

2010-05-01

In this paper, we studied the solitary wave solutions of the (2+1)-dimensional Boussinesq equation utt -uxx-uyy-(u2)xx-uxxxx = 0 and the (3+1)-dimensional Kadomtsev-Petviashvili (KP) equation uxt -6ux 2 +6uuxx -uxxxx -uyy -uzz = 0. By using this method, an explicit numerical solution is calculated in the form of a convergent power series with easily computable components. To illustrate the application of this method numerical results are derived by using the calculated components of the homotopy perturbation series. The numerical solutions are compared with the known analytical solutions. Results derived from our method are shown graphically.
Self-Consistent Model of Magnetospheric Ring Current and Electromagnetic Ion Cyclotron Waves: The 2-7 May 1998 Storm

NASA Technical Reports Server (NTRS)

Khazanov, G. V.; Gamayunov, K. V.; Jordanova, V. K.

2003-01-01

A complete description of a self-consistent model of magnetospheric ring current interacting with electromagnetic ion cyclotron waves is presented. The model is based on the system of two kinetic equations; one equation describes the ring current ion dynamics, and another equation describes the wave evolution. The effects on ring current ions interacting with electromagnetic ion cyclotron waves and back on waves are considered self-consistently by solving both equations on a global magnetospheric scale under nonsteady state conditions. The developed model is employed to simulate the entire 2-7 May 1998 storm period. First, the trapped number fluxes of the ring current protons are calculated and presented along with comparison with the data measured by the three- dimensional hot plasma instrument Polar/HYDRA. Incorporating in the model the wave-particle interaction leads to much better agreement between the experimental data and the model results. Second, examining of the wave (MLT, L shell) distributions produced by the model during the storm progress reveals an essential intensification of the wave emission about 2 days after the main phase of the storm. This result is well consistent with the earlier ground-based observations. Finally, the theoretical shapes and the occurrence rates of the wave power spectral densities are studied. It is found that about 2 days after the storm s main phase on 4 May, mainly non-Gaussian shapes of power spectral densities are produced.
Transverse instability of periodic and generalized solitary waves for a fifth-order KP model

NASA Astrophysics Data System (ADS)

Haragus, Mariana; Wahlén, Erik

2017-02-01

We consider a fifth-order Kadomtsev-Petviashvili equation which arises as a two-dimensional model in the classical water-wave problem. This equation possesses a family of generalized line solitary waves which decay exponentially to periodic waves at infinity. We prove that these solitary waves are transversely spectrally unstable and that this instability is induced by the transverse instability of the periodic tails. We rely upon a detailed spectral analysis of some suitably chosen linear operators.
In-plane time-harmonic elastic wave motion and resonance phenomena in a layered phononic crystal with periodic cracks.

PubMed

Golub, Mikhail V; Zhang, Chuanzeng

2015-01-01

This paper presents an elastodynamic analysis of two-dimensional time-harmonic elastic wave propagation in periodically multilayered elastic composites, which are also frequently referred to as one-dimensional phononic crystals, with a periodic array of strip-like interior or interface cracks. The transfer matrix method and the boundary integral equation method in conjunction with the Bloch-Floquet theorem are applied to compute the elastic wave fields in the layered periodic composites. The effects of the crack size, spacing, and location, as well as the incidence angle and the type of incident elastic waves on the wave propagation characteristics in the composite structure are investigated in details. In particular, the band-gaps, the localization and the resonances of elastic waves are revealed by numerical examples. In order to understand better the wave propagation phenomena in layered phononic crystals with distributed cracks, the energy flow vector of Umov and the corresponding energy streamlines are visualized and analyzed. The numerical results demonstrate that large energy vortices obstruct elastic wave propagation in layered phononic crystals at resonance frequencies. They occur before the cracks reflecting most of the energy transmitted by the incoming wave and disappear when the problem parameters are shifted from the resonant ones.
Time dependent wave envelope finite difference analysis of sound propagation

NASA Technical Reports Server (NTRS)

Baumeister, K. J.

1984-01-01

A transient finite difference wave envelope formulation is presented for sound propagation, without steady flow. Before the finite difference equations are formulated, the governing wave equation is first transformed to a form whose solution tends not to oscillate along the propagation direction. This transformation reduces the required number of grid points by an order of magnitude. Physically, the transformed pressure represents the amplitude of the conventional sound wave. The derivation for the wave envelope transient wave equation and appropriate boundary conditions are presented as well as the difference equations and stability requirements. To illustrate the method, example solutions are presented for sound propagation in a straight hard wall duct and in a two dimensional straight soft wall duct. The numerical results are in good agreement with exact analytical results.
Interaction Solutions for Lump-line Solitons and Lump-kink Waves of the Dimensionally Reduced Generalised KP Equation

NASA Astrophysics Data System (ADS)

Ahmed, Iftikhar

2017-09-01

In this work, we investigate dimensionally reduced generalised Kadomtsev-Petviashvili equation, which can describe many nonlinear phenomena in fluid dynamics. Based on the bilinear formalism, direct Maple symbolic computations are used with an ansätz function to construct three classes of interaction solutions between lump and line solitons. Furthermore, the dynamics of interaction phenomena is explained with 3D plots and 2D contour plots. For the first class of interaction solutions, lump appeared at t=0, and there was a normal interaction between lump and line solitons at t=1, 2, 5, and 10. For the second class of interaction solutions, lump appeared from one side of line soliton at t=0, but it started moving downward at t=1, 2, and 5. Finally, at t=10, this lump was completely swallowed by other side. By contrast, for the third class of interaction solutions, lump appeared from one side of line soliton at t=0, but it started moving upward at t=1, 2, and 5. Finally, at t=10, this lump was completely swallowed by other side. Furthermore, interaction solutions between lump solutions and kink wave are also investigated. These results might be helpful to understand the propagation processes for nonlinear waves in fluid mechanics.
Traveling wave solutions and conservation laws for nonlinear evolution equation

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa

2018-02-01

In this work, the Riccati-Bernoulli sub-ordinary differential equation and modified tanh-coth methods are used to reach soliton solutions of the nonlinear evolution equation. We acquire new types of traveling wave solutions for the governing equation. We show that the equation is nonlinear self-adjoint by obtaining suitable substitution. Therefore, we construct conservation laws for the equation using new conservation theorem. The obtained solutions in this work may be used to explain and understand the physical nature of the wave spreads in the most dispersive medium. The constraint condition for the existence of solitons is stated. Some three dimensional figures for some of the acquired results are illustrated.
On the Mathematical Modeling of Single and Multiple Scattering of Ultrasonic Guided Waves by Small Scatterers: A Structural Health Monitoring Measurement Model

NASA Astrophysics Data System (ADS)

Strom, Brandon William

In an effort to assist in the paradigm shift from schedule based maintenance to conditioned based maintenance, we derive measurement models to be used within structural health monitoring algorithms. Our models are physics based, and use scattered Lamb waves to detect and quantify pitting corrosion. After covering the basics of Lamb waves and the reciprocity theorem, we develop a technique for the scattered wave solution. The first application is two-dimensional, and is employed in two different ways. The first approach integrates a traction distribution and replaces it by an equivalent force. The second approach is higher order and uses the actual traction distribution. We find that the equivalent force version of the solution technique holds well for small pits at low frequencies. The second application is three-dimensional. The equivalent force caused by the scattered wave of an arbitrary equivalent force is calculated. We obtain functions for the scattered wave displacements as a function of equivalent forces, equivalent forces as a function of incident wave, and scattered wave amplitudes as a function of incident amplitude. The third application uses self-consistency to derive governing equations for the scattered waves due to multiple corrosion pits. We decouple the implicit set of equations and solve explicitly by using a recursive series solution. Alternatively, we solve via an undetermined coefficient method which results in an interaction operator and solution via matrix inversion. The general solution is given for N pits including mode conversion. We show that the two approaches are equivalent, and give a solution for three pits. Various approximations are advanced to simplify the problem while retaining the leading order physics. As a final application, we use the multiple scattering model to investigate resonance of Lamb waves. We begin with a one-dimensional problem and progress to a three-dimensional problem. A directed graph enables interpretation of the interaction operator, and we show that a series solution converges due to loss of energy in the system. We see that there are four causes of resonance and plot the modulation depth as a function of spacing between the pits.
Upstream-advancing waves generated by three-dimensional moving disturbances

NASA Astrophysics Data System (ADS)

Lee, Seung-Joon; Grimshaw, Roger H. J.

1990-02-01

The wave field resulting from a surface pressure or a bottom topography in a horizontally unbounded domain is studied. Upstream-advancing waves successively generated by various forcing disturbances moving with near-resonant speeds are found by numerically solving a forced Kadomtsev-Petviashvili (fKP) equation, which shows in its simplest form the interplay of a basic linear wave operator, longitudinal and transverse dispersion, nonlinearity, and forcing. Curved solitary waves are found as a slowly varying similarity solution of the Kadomtsev-Petviashvili (KP) equation, and are favorably compared with the upstream-advancing waves numerically obtained.
On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Masood Khalique, Chaudry

2018-05-01

In this paper, we study a (2+1) dimensional KdV-mKdV equation, which models many physical phenomena of mathematical physics. This equation has two integral terms in it. By an appropriate substitution, we convert this equation into two partial differential equations, which do not have integral terms and are equivalent to the original equation. We then work with the system of two equations and obtain its exact travelling wave solutions in form of Jacobi elliptic functions. Furthermore, we employ the multiplier method to construct conservation laws for the system. Finally, we revert the results obtained into the original variables of the (2+1) dimensional KdV-mKdV equation.
Modified Chapman-Enskog moment approach to diffusive phonon heat transport.

PubMed

Banach, Zbigniew; Larecki, Wieslaw

2008-12-01

A detailed treatment of the Chapman-Enskog method for a phonon gas is given within the framework of an infinite system of moment equations obtained from Callaway's model of the Boltzmann-Peierls equation. Introducing no limitations on the magnitudes of the individual components of the drift velocity or the heat flux, this method is used to derive various systems of hydrodynamic equations for the energy density and the drift velocity. For one-dimensional flow problems, assuming that normal processes dominate over resistive ones, it is found that the first three levels of the expansion (i.e., the zeroth-, first-, and second-order approximations) yield the equations of hydrodynamics which are linearly stable at all wavelengths. This result can be achieved either by examining the dispersion relations for linear plane waves or by constructing the explicit quadratic Lyapunov entropy functionals for the linear perturbation equations. The next order in the Chapman-Enskog expansion leads to equations which are unstable to some perturbations. Precisely speaking, the linearized equations of motion that describe the propagation of small disturbances in the flow have unstable plane-wave solutions in the short-wavelength limit of the dispersion relations. This poses no problem if the equations are used in their proper range of validity.
Hybrid method (JM-ECS) combining the J-matrix and exterior complex scaling methods for scattering calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vanroose, W.; Broeckhove, J.; Arickx, F.

The paper proposes a hybrid method for calculating scattering processes. It combines the J-matrix method with exterior complex scaling and an absorbing boundary condition. The wave function is represented as a finite sum of oscillator eigenstates in the inner region, and it is discretized on a grid in the outer region. The method is validated for a one- and a two-dimensional model with partial wave equations and a calculation of p-shell nuclear scattering with semirealistic interactions.
Two dimensional numerical prediction of deflagration-to-detonation transition in porous energetic materials.

PubMed

Narin, B; Ozyörük, Y; Ulas, A

2014-05-30

This paper describes a two-dimensional code developed for analyzing two-phase deflagration-to-detonation transition (DDT) phenomenon in granular, energetic, solid, explosive ingredients. The two-dimensional model is constructed in full two-phase, and based on a highly coupled system of partial differential equations involving basic flow conservation equations and some constitutive relations borrowed from some one-dimensional studies that appeared in open literature. The whole system is solved using an optimized high-order accurate, explicit, central-difference scheme with selective-filtering/shock capturing (SF-SC) technique, to augment central-diffencing and prevent excessive dispersion. The sources of the equations describing particle-gas interactions in terms of momentum and energy transfers make the equation system quite stiff, and hence its explicit integration difficult. To ease the difficulties, a time-split approach is used allowing higher time steps. In the paper, the physical model for the sources of the equation system is given for a typical explosive, and several numerical calculations are carried out to assess the developed code. Microscale intergranular and/or intragranular effects including pore collapse, sublimation, pyrolysis, etc. are not taken into account for ignition and growth, and a basic temperature switch is applied in calculations to control ignition in the explosive domain. Results for one-dimensional DDT phenomenon are in good agreement with experimental and computational results available in literature. A typical shaped-charge wave-shaper case study is also performed to test the two-dimensional features of the code and it is observed that results are in good agreement with those of commercial software. Copyright © 2014 Elsevier B.V. All rights reserved.
Exact solution for a non-Markovian dissipative quantum dynamics.

PubMed

Ferialdi, Luca; Bassi, Angelo

2012-04-27

We provide the exact analytic solution of the stochastic Schrödinger equation describing a harmonic oscillator interacting with a non-Markovian and dissipative environment. This result represents an arrival point in the study of non-Markovian dynamics via stochastic differential equations. It is also one of the few exactly solvable models for infinite-dimensional systems. We compute the Green's function; in the case of a free particle and with an exponentially correlated noise, we discuss the evolution of Gaussian wave functions.
Personal computer study of finite-difference methods for the transonic small disturbance equation

NASA Technical Reports Server (NTRS)

Bland, Samuel R.

1989-01-01

Calculation of unsteady flow phenomena requires careful attention to the numerical treatment of the governing partial differential equations. The personal computer provides a convenient and useful tool for the development of meshes, algorithms, and boundary conditions needed to provide time accurate solution of these equations. The one-dimensional equation considered provides a suitable model for the study of wave propagation in the equations of transonic small disturbance potential flow. Numerical results for effects of mesh size, extent, and stretching, time step size, and choice of far-field boundary conditions are presented. Analysis of the discretized model problem supports these numerical results. Guidelines for suitable mesh and time step choices are given.
Modeling of matter-wave solitons in a nonlinear inductor-capacitor network through a Gross-Pitaevskii equation with time-dependent linear potential

NASA Astrophysics Data System (ADS)

Kengne, E.; Lakhssassi, A.; Liu, W. M.

2017-08-01

A lossless nonlinear L C transmission network is considered. With the use of the reductive perturbation method in the semidiscrete limit, we show that the dynamics of matter-wave solitons in the network can be modeled by a one-dimensional Gross-Pitaevskii (GP) equation with a time-dependent linear potential in the presence of a chemical potential. An explicit expression for the growth rate of a purely growing modulational instability (MI) is presented and analyzed. We find that the potential parameter of the GP equation of the system does not affect the different regions of the MI. Neglecting the chemical potential in the GP equation, we derive exact analytical solutions which describe the propagation of both bright and dark solitary waves on continuous-wave (cw) backgrounds. Using the found exact analytical solutions of the GP equation, we investigate numerically the transmission of both bright and dark solitary voltage signals in the network. Our numerical studies show that the amplitude of a bright solitary voltage signal and the depth of a dark solitary voltage signal as well as their width, their motion, and their behavior depend on (i) the propagation frequencies, (ii) the potential parameter, and (iii) the amplitude of the cw background. The GP equation derived in this paper with a time-dependent linear potential opens up different ideas that may be of considerable theoretical interest for the management of matter-wave solitons in nonlinear L C transmission networks.
A Variational Reduction and the Existence of a Fully Localised Solitary Wave for the Three-Dimensional Water-Wave Problem with Weak Surface Tension

NASA Astrophysics Data System (ADS)

Buffoni, Boris; Groves, Mark D.; Wahlén, Erik

2017-12-01

Fully localised solitary waves are travelling-wave solutions of the three- dimensional gravity-capillary water wave problem which decay to zero in every horizontal spatial direction. Their existence has been predicted on the basis of numerical simulations and model equations (in which context they are usually referred to as `lumps'), and a mathematically rigorous existence theory for strong surface tension (Bond number {β} greater than {1/3} ) has recently been given. In this article we present an existence theory for the physically more realistic case {0 < β < 1/3} . A classical variational principle for fully localised solitary waves is reduced to a locally equivalent variational principle featuring a perturbation of the functional associated with the Davey-Stewartson equation. A nontrivial critical point of the reduced functional is found by minimising it over its natural constraint set.
A Variational Reduction and the Existence of a Fully Localised Solitary Wave for the Three-Dimensional Water-Wave Problem with Weak Surface Tension

NASA Astrophysics Data System (ADS)

Buffoni, Boris; Groves, Mark D.; Wahlén, Erik

2018-06-01

Fully localised solitary waves are travelling-wave solutions of the three- dimensional gravity-capillary water wave problem which decay to zero in every horizontal spatial direction. Their existence has been predicted on the basis of numerical simulations and model equations (in which context they are usually referred to as `lumps'), and a mathematically rigorous existence theory for strong surface tension (Bond number {β} greater than {1/3}) has recently been given. In this article we present an existence theory for the physically more realistic case {0 < β < 1/3}. A classical variational principle for fully localised solitary waves is reduced to a locally equivalent variational principle featuring a perturbation of the functional associated with the Davey-Stewartson equation. A nontrivial critical point of the reduced functional is found by minimising it over its natural constraint set.
Eckhaus-Benjamin-Feir Instability in Rotating Convection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Y.; Ecke, R.E.

1997-06-01

We report experimental measurements of a traveling-wave state in rotating Rayleigh-B{acute e}nard convection. The fluid was water with a Prandtl number of 6.3 and a dimensionless rotation rate of 274. The marginal and Eckhaus-Benjamin-Feir stability boundaries were determined and the local amplitude and wave number were obtained from demodulation of shadowgraph images. The phase-diffusion coefficient and group velocity were measured in the stable wave number band. This system was found to be well described by the one-dimensional complex Ginzburg-Landau equation. {copyright} {ital 1997} {ital The American Physical Society}
The method of impedance transformation for electromagnetic waves propagating in one-dimension plasma photonic crystal

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yao, Jingfeng; Yuan, Chengxun, E-mail: yuancx@hit.edu.cn, E-mail: zhouzx@hit.edu.cn; Gao, Ruilin

2016-08-15

This study focuses on the transmission of normal-incidence electromagnetic waves in one-dimensional plasma photonic crystals. Using the Maxwell's equations in a medium, a method that is based on the concept of impendence is employed to perform the simulation. The accuracy of the method was evaluated by simulating a one-layer plasma and conventional photonic crystal. In frequency-domain, the transmission and reflection coefficients in the unmagnetized plasma photonic crystal were calculated, and the influence factors on plasma photonic crystals including dielectric constants of dielectric, spatial period, filling factor, plasma frequency, and collision frequency were studied.

Analysis of the generalized (2+1)-dimensional Nizhnik-Novikov-Veselov equations with variable coefficients in an inhomogeneous medium

NASA Astrophysics Data System (ADS)

Chai, Han-Peng; Tian, Bo; Zhen, Hui-Ling; Chai, Jun; Guan, Yue-Yang

2017-08-01

Korteweg-de Vries (KdV)-type equations are seen to describe the shallow-water waves, lattice structures and ion-acoustic waves in plasmas. Hereby, we consider an extension of the KdV-type equations called the generalized (2+1)-dimensional Nizhnik-Novikov-Veselov equations with variable coefficients in an inhomogeneous medium. Via the Hirota bilinear method and symbolic computation, we derive the bilinear forms, N-soliton solutions and Bäcklund transformation. Effects of the first- and higher-order dispersion terms are investigated. Soliton evolution and interaction are graphically presented and analyzed: Both the propagation velocity and direction of the soliton change when the dispersion terms are time-dependent; The interactions between/among the solitons are elastic, independent of the forms of the coefficients in the equations.
Multi-soliton solutions and Bäcklund transformation for a two-mode KdV equation in a fluid

NASA Astrophysics Data System (ADS)

Xiao, Zi-Jian; Tian, Bo; Zhen, Hui-Ling; Chai, Jun; Wu, Xiao-Yu

2017-01-01

In this paper, we investigate a two-mode Korteweg-de Vries equation, which describes the one-dimensional propagation of shallow water waves with two modes in a weakly nonlinear and dispersive fluid system. With the binary Bell polynomial and an auxiliary variable, bilinear forms, multi-soliton solutions in the two-wave modes and Bell polynomial-type Bäcklund transformation for such an equation are obtained through the symbolic computation. Soliton propagation and collisions between the two solitons are presented. Based on the graphic analysis, it is shown that the increase in s can lead to the increase in the soliton velocities under the condition of ?, but the soliton amplitudes remain unchanged when s changes, where s means the difference between the phase velocities of two-mode waves, ? and ? are the nonlinearity parameter and dispersion parameter respectively. Elastic collisions between the two solitons in both two modes are analyzed with the help of graphic analysis.
A one-dimensional nonlinear problem of thermoelasticity in extended thermodynamics

NASA Astrophysics Data System (ADS)

Rawy, E. K.

2018-06-01

We solve a nonlinear, one-dimensional initial boundary-value problem of thermoelasticity in generalized thermodynamics. A Cattaneo-type evolution equation for the heat flux is used, which differs from the one used extensively in the literature. The hyperbolic nature of the associated linear system is clarified through a study of the characteristic curves. Progressive wave solutions with two finite speeds are noted. A numerical treatment is presented for the nonlinear system using a three-step, quasi-linearization, iterative finite-difference scheme for which the linear system of equations is the initial step in the iteration. The obtained results are discussed in detail. They clearly show the hyperbolic nature of the system, and may be of interest in investigating thermoelastic materials, not only at low temperatures, but also during high temperature processes involving rapid changes in temperature as in laser treatment of surfaces.
Modeling of thin-walled structures interacting with acoustic media as constrained two-dimensional continua

NASA Astrophysics Data System (ADS)

Rabinskiy, L. N.; Zhavoronok, S. I.

2018-04-01

The transient interaction of acoustic media and elastic shells is considered on the basis of the transition function approach. The three-dimensional hyperbolic initial boundary-value problem is reduced to a two-dimensional problem of shell theory with integral operators approximating the acoustic medium effect on the shell dynamics. The kernels of these integral operators are determined by the elementary solution of the problem of acoustic waves diffraction at a rigid obstacle with the same boundary shape as the wetted shell surface. The closed-form elementary solution for arbitrary convex obstacles can be obtained at the initial interaction stages on the background of the so-called “thin layer hypothesis”. Thus, the shell–wave interaction model defined by integro-differential dynamic equations with analytically determined kernels of integral operators becomes hence two-dimensional but nonlocal in time. On the other hand, the initial interaction stage results in localized dynamic loadings and consequently in complex strain and stress states that require higher-order shell theories. Here the modified theory of I.N.Vekua–A.A.Amosov-type is formulated in terms of analytical continuum dynamics. The shell model is constructed on a two-dimensional manifold within a set of field variables, Lagrangian density, and constraint equations following from the boundary conditions “shifted” from the shell faces to its base surface. Such an approach allows one to construct consistent low-order shell models within a unified formal hierarchy. The equations of the N th-order shell theory are singularly perturbed and contain second-order partial derivatives with respect to time and surface coordinates whereas the numerical integration of systems of first-order equations is more efficient. Such systems can be obtained as Hamilton–de Donder–Weyl-type equations for the Lagrangian dynamical system. The Hamiltonian formulation of the elementary N th-order shell theory is here briefly described.
Hydrodynamic optical soliton tunneling

NASA Astrophysics Data System (ADS)

Sprenger, P.; Hoefer, M. A.; El, G. A.

2018-03-01

A notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers considered include smooth rarefaction waves and highly oscillatory dispersive shock waves. Both the soliton and the barrier satisfy the same one-dimensional defocusing nonlinear Schrödinger (NLS) equation, which admits a convenient dispersive hydrodynamic interpretation. Under the scale separation assumption of nonlinear wave (Whitham) modulation theory, the highly nontrivial nonlinear interaction between the soliton and the evolving hydrodynamic barrier is described in terms of self-similar, simple wave solutions to an asymptotic reduction of the Whitham-NLS partial differential equations. One of the Riemann invariants of the reduced modulation system determines the characteristics of a soliton interacting with a mean flow that results in soliton tunneling or trapping. Another Riemann invariant yields the tunneled soliton's phase shift due to hydrodynamic interaction. Soliton interaction with hydrodynamic barriers gives rise to effects that include reversal of the soliton propagation direction and spontaneous soliton cavitation, which further suggest possible methods of dark soliton control in optical fibers.
Hydrodynamic optical soliton tunneling.

PubMed

Sprenger, P; Hoefer, M A; El, G A

2018-03-01

A notion of hydrodynamic optical soliton tunneling is introduced in which a dark soliton is incident upon an evolving, broad potential barrier that arises from an appropriate variation of the input signal. The barriers considered include smooth rarefaction waves and highly oscillatory dispersive shock waves. Both the soliton and the barrier satisfy the same one-dimensional defocusing nonlinear Schrödinger (NLS) equation, which admits a convenient dispersive hydrodynamic interpretation. Under the scale separation assumption of nonlinear wave (Whitham) modulation theory, the highly nontrivial nonlinear interaction between the soliton and the evolving hydrodynamic barrier is described in terms of self-similar, simple wave solutions to an asymptotic reduction of the Whitham-NLS partial differential equations. One of the Riemann invariants of the reduced modulation system determines the characteristics of a soliton interacting with a mean flow that results in soliton tunneling or trapping. Another Riemann invariant yields the tunneled soliton's phase shift due to hydrodynamic interaction. Soliton interaction with hydrodynamic barriers gives rise to effects that include reversal of the soliton propagation direction and spontaneous soliton cavitation, which further suggest possible methods of dark soliton control in optical fibers.
Self-action of Bessel wave packets in a system of coupled light guides and formation of light bullets

NASA Astrophysics Data System (ADS)

Balakin, A. A.; Mironov, V. A.; Skobelev, S. A.

2017-01-01

The self-action of two-dimensional and three-dimensional Bessel wave packets in a system of coupled light guides is considered using the discrete nonlinear Schrödinger equation. The features of the self-action of such wave fields are related to their initial strong spatial inhomogeneity. The numerical simulation shows that for the field amplitude exceeding a critical value, the development of an instability typical of a medium with the cubic nonlinearity is observed. Various regimes are studied: the self-channeling of a wave beam in one light guide at powers not strongly exceeding a critical value, the formation of the "kaleidoscopic" picture of a wave packet during the propagation of higher-power radiation along a stratified medium, the formation of light bullets during competition between self-focusing and modulation instabilities in the case of three-dimensional wave packets, etc. In the problem of laser pulse shortening, the situation is considered when the wave-field stratification in the transverse direction dominates. This process is accompanied by the self-compression of laser pulses in well enough separated light guides. The efficiency of conversion of the initial Bessel field distribution to two flying parallel light bullets is about 50%.
Inverse scattering transform analysis of rogue waves using local periodization procedure

NASA Astrophysics Data System (ADS)

Randoux, Stéphane; Suret, Pierre; El, Gennady

2016-07-01

The nonlinear Schrödinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable turbulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra.
Inverse scattering transform analysis of rogue waves using local periodization procedure

PubMed Central

Randoux, Stéphane; Suret, Pierre; El, Gennady

2016-01-01

The nonlinear Schrödinger equation (NLSE) stands out as the dispersive nonlinear partial differential equation that plays a prominent role in the modeling and understanding of the wave phenomena relevant to many fields of nonlinear physics. The question of random input problems in the one-dimensional and integrable NLSE enters within the framework of integrable turbulence, and the specific question of the formation of rogue waves (RWs) has been recently extensively studied in this context. The determination of exact analytic solutions of the focusing 1D-NLSE prototyping RW events of statistical relevance is now considered as the problem of central importance. Here we address this question from the perspective of the inverse scattering transform (IST) method that relies on the integrable nature of the wave equation. We develop a conceptually new approach to the RW classification in which appropriate, locally coherent structures are specifically isolated from a globally incoherent wave train to be subsequently analyzed by implementing a numerical IST procedure relying on a spatial periodization of the object under consideration. Using this approach we extend the existing classifications of the prototypes of RWs from standard breathers and their collisions to more general nonlinear modes characterized by their nonlinear spectra. PMID:27385164
Incident wave run-up into narrow sloping bays and estuaries

NASA Astrophysics Data System (ADS)

Sinan Özeren, M.; Postacioglu, Nazmi; Canlı, Umut

2015-04-01

The problem is investigated using Carrier Greenspan hodograph transformations.We perform a quasi-one-dimensional solution well into the bay, far enough of the mouth of the bay. The linearized boundary conditions at the mouth of the bay lead to an integral equation for 2-D geometry. A semi analytical optimization method has been developed to solve this integral equation. When the wavelength of the incident wave is much larger than the width of the bay, the conformalmapping of the bay and the semi infinite sea onto upper complex plane provides a solution of the integral equation in closed form. Particular emphasis is placed on the case where the frequency of the incident waves matches the real-part of the natural frequency of the oscillation of the bay. These natural frequencies are complex because of the radiation conditions imposed at the mouth of the bay. It is found that the complex part of these natural frequencies decreases with decreasing width of the bay. Thus the trapping of the waves in narrower bays leads to a strong resonance phenomenon when the frequency of the incident wave is equal to the real part of the natural frequency.
An Investigation of Wave Propagations in Discontinuous Galerkin Method

NASA Technical Reports Server (NTRS)

Hu, Fang Q.

2004-01-01

Analysis of the discontinuous Galerkin method has been carried out for one- and two-dimensional system of hyperbolic equations. Analytical, as well as numerical, properties of wave propagation in a DGM scheme are derived and verified with direct numerical simulations. In addition to a systematic examination of the dissipation and dispersion errors, behaviours of a DG scheme at an interface of two different grid topologies are also studied. Under the same framework, a quantitative discrete analysis of various artificial boundary conditions is also conducted. Progress has been made in numerical boundary condition treatment that is closely related to the application of DGM in aeroacoustics problems. Finally, Fourier analysis of DGM for the Convective diffusion equation has also be studied in connection with the application of DG schemes for the Navier-Stokes equations. This research has resulted in five(5) publications, plus one additional manuscript in preparation, four(4) conference presentations, and three(3) departmental seminars, as summarized in part II. Abstracts of papers are given in part 111 of this report.
CMS-Wave

DTIC Science & Technology

2015-10-30

Coastal Inlets Research Program CMS -Wave CMS -Wave is a two-dimensional spectral wind-wave generation and transformation model that employs a forward...marching, finite-difference method to solve the wave action conservation equation. Capabilities of CMS -Wave include wave shoaling, refraction... CMS -Wave can be used in either on a half- or full-plane mode, with primary waves propagating from the seaward boundary toward shore. It can
A hybrid model of laser energy deposition for multi-dimensional simulations of plasmas and metals

NASA Astrophysics Data System (ADS)

Basko, Mikhail M.; Tsygvintsev, Ilia P.

2017-05-01

The hybrid model of laser energy deposition is a combination of the geometrical-optics ray-tracing method with the one-dimensional (1D) solution of the Helmholtz wave equation in regions where the geometrical optics becomes inapplicable. We propose an improved version of this model, where a new physically consistent criterion for transition to the 1D wave optics is derived, and a special rescaling procedure of the wave-optics deposition profile is introduced. The model is intended for applications in large-scale two- and three-dimensional hydrodynamic codes. Comparison with exact 1D solutions demonstrates that it can fairly accurately reproduce the absorption fraction in both the s- and p-polarizations on arbitrarily steep density gradients, provided that a sufficiently accurate algorithm for gradient evaluation is used. The accuracy of the model becomes questionable for long laser pulses simulated on too fine grids, where the hydrodynamic self-focusing instability strongly manifests itself.
The Shannon entropy information for mixed Manning Rosen potential in D-dimensional Schrodinger equation

NASA Astrophysics Data System (ADS)

Suparmi, A.; Cari, C.; Nur Pratiwi, Beta; Arya Nugraha, Dewanta

2017-01-01

D dimensional Schrodinger equation for the mixed Manning Rosen potential was investigated using supersymmetric quantum mechanics. We obtained the energy eigenvalues from radial part solution and wavefunctions in radial and angular parts solution. From the lowest radial wavefunctions, we evaluated the Shannon entropy information using Matlab software. Based on the entropy densities demonstrated graphically, we obtained that the wave of position information entropy density moves right when the value of potential parameter q increases, while its wave moves left with the increase of parameter α. The wave of momentum information entropy densities were expressed in graphs. We observe that its amplitude increase with increasing parameter q and α
Investigation of Solitary wave solutions for Vakhnenko-Parkes equation via exp-function and Exp(-ϕ(ξ))-expansion method.

PubMed

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.
Extremely Fast Numerical Integration of Ocean Surface Wave Dynamics

DTIC Science & Technology

2007-09-30

sub-processor must be added as shown in the blue box of Fig. 1. We first consider the Kadomtsev - Petviashvili (KP) equation ηt + coηx +αηηx + βη ...analytic integration of the so-called “soliton equations ,” I have discovered how the GFT can be used to solved higher order equations for which study...analytical study and extremely fast numerical integration of the extended nonlinear Schroedinger equation for fully three dimensional wave motion
Exact soliton of (2 + 1)-dimensional fractional Schrödinger equation

NASA Astrophysics Data System (ADS)

Rizvi, S. T. R.; Ali, K.; Bashir, S.; Younis, M.; Ashraf, R.; Ahmad, M. O.

2017-07-01

The nonlinear fractional Schrödinger equation is the basic equation of fractional quantum mechanics introduced by Nick Laskin in 2002. We apply three tools to solve this mathematical-physical model. First, we find the solitary wave solutions including the trigonometric traveling wave solutions, bell and kink shape solitons using the F-expansion and Improve F-expansion method. We also obtain the soliton solution, singular soliton solutions, rational function solution and elliptic integral function solutions, with the help of the extended trial equation method.
Observation of Two-Dimensional Localized Jones-Roberts Solitons in Bose-Einstein Condensates

NASA Astrophysics Data System (ADS)

Meyer, Nadine; Proud, Harry; Perea-Ortiz, Marisa; O'Neale, Charlotte; Baumert, Mathis; Holynski, Michael; Kronjäger, Jochen; Barontini, Giovanni; Bongs, Kai

2017-10-01

Jones-Roberts solitons are the only known class of stable dark solitonic solutions of the nonlinear Schrödinger equation in two and three dimensions. They feature a distinctive elongated elliptical shape that allows them to travel without change of form. By imprinting a triangular phase pattern, we experimentally generate two-dimensional Jones-Roberts solitons in a three-dimensional atomic Bose-Einstein condensate. We monitor their dynamics, observing that this kind of soliton is indeed not affected by dynamic (snaking) or thermodynamic instabilities, that instead make other classes of dark solitons unstable in dimensions higher than one. Our results confirm the prediction that Jones-Roberts solitons are stable solutions of the nonlinear Schrödinger equation and promote them for applications beyond matter wave physics, like energy and information transport in noisy and inhomogeneous environments.
Equation for wave processes in inhomogeneous moving media and functional solution of the acoustic tomography problem based on it

NASA Astrophysics Data System (ADS)

Rumyantseva, O. D.; Shurup, A. S.

2017-01-01

The paper considers the derivation of the wave equation and Helmholtz equation for solving the tomographic problem of reconstruction combined scalar-vector inhomogeneities describing perturbations of the sound velocity and absorption, the vector field of flows, and perturbations of the density of the medium. Restrictive conditions under which the obtained equations are meaningful are analyzed. Results of numerical simulation of the two-dimensional functional-analytical Novikov-Agaltsov algorithm for reconstructing the flow velocity using the the obtained Helmholtz equation are presented.
Solution of two-body relativistic bound state equations with confining plus Coulomb interactions

NASA Technical Reports Server (NTRS)

Maung, Khin Maung; Kahana, David E.; Norbury, John W.

1992-01-01

Studies of meson spectroscopy have often employed a nonrelativistic Coulomb plus Linear Confining potential in position space. However, because the quarks in mesons move at an appreciable fraction of the speed of light, it is necessary to use a relativistic treatment of the bound state problem. Such a treatment is most easily carried out in momentum space. However, the position space Linear and Coulomb potentials lead to singular kernels in momentum space. Using a subtraction procedure we show how to remove these singularities exactly and thereby solve the Schroedinger equation in momentum space for all partial waves. Furthermore, we generalize the Linear and Coulomb potentials to relativistic kernels in four dimensional momentum space. Again we use a subtraction procedure to remove the relativistic singularities exactly for all partial waves. This enables us to solve three dimensional reductions of the Bethe-Salpeter equation. We solve six such equations for Coulomb plus Confining interactions for all partial waves.

Simulations of viscous and compressible gas-gas flows using high-order finite difference schemes

NASA Astrophysics Data System (ADS)

Capuano, M.; Bogey, C.; Spelt, P. D. M.

2018-05-01

A computational method for the simulation of viscous and compressible gas-gas flows is presented. It consists in solving the Navier-Stokes equations associated with a convection equation governing the motion of the interface between two gases using high-order finite-difference schemes. A discontinuity-capturing methodology based on sensors and a spatial filter enables capturing shock waves and deformable interfaces. One-dimensional test cases are performed as validation and to justify choices in the numerical method. The results compare well with analytical solutions. Shock waves and interfaces are accurately propagated, and remain sharp. Subsequently, two-dimensional flows are considered including viscosity and thermal conductivity. In Richtmyer-Meshkov instability, generated on an air-SF6 interface, the influence of the mesh refinement on the instability shape is studied, and the temporal variations of the instability amplitude is compared with experimental data. Finally, for a plane shock wave propagating in air and impacting a cylindrical bubble filled with helium or R22, numerical Schlieren pictures obtained using different grid refinements are found to compare well with experimental shadow-photographs. The mass conservation is verified from the temporal variations of the mass of the bubble. The mean velocities of pressure waves and bubble interface are similar to those obtained experimentally.
An implicit time-marching method for the three-dimensional Navier-Stokes equations of contravariant velocity components

NASA Astrophysics Data System (ADS)

Daiguji, Hisaaki; Yamamoto, Satoru

1988-12-01

The implicit time-marching finite-difference method for solving the three-dimensional compressible Euler equations developed by the authors is extended to the Navier-Stokes equations. The distinctive features of this method are to make use of momentum equations of contravariant velocities instead of physical boundaries, and to be able to treat the periodic boundary condition for the three-dimensional impeller flow easily. These equations can be solved by using the same techniques as the Euler equations, such as the delta-form approximate factorization, diagonalization and upstreaming. In addition to them, a simplified total variation diminishing scheme by the authors is applied to the present method in order to capture strong shock waves clearly. Finally, the computed results of the three-dimensional flow through a transonic compressor rotor with tip clearance are shown.
Controlling rogue waves in inhomogeneous Bose-Einstein condensates.

PubMed

Loomba, Shally; Kaur, Harleen; Gupta, Rama; Kumar, C N; Raju, Thokala Soloman

2014-05-01

We present the exact rogue wave solutions of the quasi-one-dimensional inhomogeneous Gross-Pitaevskii equation by using similarity transformation. Then, by employing the exact analytical solutions we have studied the controllable behavior of rogue waves in the Bose-Einstein condensates context for the experimentally relevant systems. Additionally, we have also investigated the nonlinear tunneling of rogue waves through a conventional hyperbolic barrier and periodic barrier. We have found that, for the conventional nonlinearity barrier case, rogue waves are localized in space and time and get amplified near the barrier, while for the dispersion barrier case rogue waves are localized in space and propagating in time and their amplitude is reduced at the barrier location. In the case of the periodic barrier, the interesting dynamical features of rogue waves are obtained and analyzed analytically.
Nonplanar KdV and KP equations for quantum electron-positron-ion plasma

NASA Astrophysics Data System (ADS)

Dutta, Debjit

2015-12-01

Nonlinear quantum ion-acoustic waves with the effects of nonplanar cylindrical geometry, quantum corrections, and transverse perturbations are studied. By using the standard reductive perturbation technique, a cylindrical Kadomtsev-Petviashvili equation for ion-acoustic waves is derived by incorporating quantum-mechanical effects. The quantum-mechanical effects via quantum diffraction and quantum statistics and the role of transverse perturbations in cylindrical geometry on the dynamics of this wave are studied analytically. It is found that the dynamics of ion-acoustic solitary waves (IASWs) is governed by a three-dimensional cylindrical Kadomtsev-Petviashvili equation (CKPE). The results could help in a theoretical analysis of astrophysical and laser produced plasmas.
Some special solutions to the Hyperbolic NLS equation

NASA Astrophysics Data System (ADS)

Vuillon, Laurent; Dutykh, Denys; Fedele, Francesco

2018-04-01

The Hyperbolic Nonlinear SCHRöDINGER equation (HypNLS) arises as a model for the dynamics of three-dimensional narrow-band deep water gravity waves. In this study, the symmetries and conservation laws of this equation are computed. The PETVIASHVILI method is then exploited to numerically compute bi-periodic time-harmonic solutions of the HypNLS equation. In physical space they represent non-localized standing waves. Non-trivial spatial patterns are revealed and an attempt is made to describe them using symbolic dynamics and the language of substitutions. Finally, the dynamics of a slightly perturbed standing wave is numerically investigated by means a highly accurate FOURIER solver.
Two-Dimensional Computational Model for Wave Rotor Flow Dynamics

NASA Technical Reports Server (NTRS)

Welch, Gerard E.

1996-01-01

A two-dimensional (theta,z) Navier-Stokes solver for multi-port wave rotor flow simulation is described. The finite-volume form of the unsteady thin-layer Navier-Stokes equations are integrated in time on multi-block grids that represent the stationary inlet and outlet ports and the moving rotor passages of the wave rotor. Computed results are compared with three-port wave rotor experimental data. The model is applied to predict the performance of a planned four-port wave rotor experiment. Two-dimensional flow features that reduce machine performance and influence rotor blade and duct wall thermal loads are identified. The performance impact of rounding the inlet port wall, to inhibit separation during passage gradual opening, is assessed.
Nonlinear energy transport in one-dimensional lattices

NASA Astrophysics Data System (ADS)

Vuppuluri, P.; Hamilton, M.; de Alcantara Bonfim, O. F.

2007-03-01

We present a simple lattice model consisting of a one-dimensional chain, where the masses are interconnected by linear springs and allowed to move in the horizontal direction only, as in a monorail. In the transverse direction each mass is also attached to two other springs, one on each side of the mass. The ends of these springs are kept at fixed positions. The nonlinearity in the model arises from the geometric constraints imposed on the motion of the masses, as well as from the configuration of the springs. In the transverse directions the springs are either in the extended or compressed state depending on the position of the mass. Under these conditions we show that solitary waves are present in the system. In the long wavelength limit an analytical solution for these nonlinear waves is found. Numeric integrations of the equations of motion in the full system are also performed to analyze the conditions for the existence and stability of the nonlinear waves. Nonlinear supratransmission is examined and shown to exist in the model and an explanation of its mechanism is presented.
Development and Application of a Three-dimensional Seismo-acoustic Coupled-mode Model

DTIC Science & Technology

2014-09-30

of coral reef fish need to locate a reef , and sound emanating from reefs may act as a cue to guide them. Using acoustic data collected from Bahia...approximate the solution to the wave equation. RELATED PROJECTS Geoacoustic inversion in three-dimensional environments The goal of this project is...shear wave speed Under this project an laboratory measurements the compressional and shear wave speeds and attenuations in coarse and fine grained
Research on radiation characteristic of plasma antenna through FDTD method.

PubMed

Zhou, Jianming; Fang, Jingjing; Lu, Qiuyuan; Liu, Fan

2014-01-01

The radiation characteristic of plasma antenna is investigated by using the finite-difference time-domain (FDTD) approach in this paper. Through using FDTD method, we study the propagation of electromagnetic wave in free space in stretched coordinate. And the iterative equations of Maxwell equation are derived. In order to validate the correctness of this method, we simulate the process of electromagnetic wave propagating in free space. Results show that electromagnetic wave spreads out around the signal source and can be absorbed by the perfectly matched layer (PML). Otherwise, we study the propagation of electromagnetic wave in plasma by using the Boltzmann-Maxwell theory. In order to verify this theory, the whole process of electromagnetic wave propagating in plasma under one-dimension case is simulated. Results show that Boltzmann-Maxwell theory can be used to explain the phenomenon of electromagnetic wave propagating in plasma. Finally, the two-dimensional simulation model of plasma antenna is established under the cylindrical coordinate. And the near-field and far-field radiation pattern of plasma antenna are obtained. The experiments show that the variation of electron density can introduce the change of radiation characteristic.
The aerodynamics of propellers and rotors using an acoustic formulation in the time domain

NASA Technical Reports Server (NTRS)

Long, L. N.

1983-01-01

The aerodynamics of propellers and rotors is especially complicated because of the highly three-dimensional and compressible nature of the flow field. However, in linearized theory the problem is governed by the wave equation, and a numerically-efficient integral formulation can be derived. This reduces the problem from one in space to one over a surface. Many such formulations exist in the aeroacoustics literature, but these become singular integral equations if one naively tries to use them to predict surface pressures, i.e., for aerodynamics. The present paper illustrates how one must interpret these equations in order to obtain nonambiguous results. After the regularized form of the integral equation is derived, a method for solving it numerically is described. This preliminary computer code uses Legendre-Gaussian quadrature to solve the equation. Numerical results are compared to experimental results for ellipsoids, wings, and rotors, including effects due to lift. Compressibility and the farfield boundary conditions are satisfied automatically using this method.
Solution of D dimensional Dirac equation for coulombic potential using NU method and its thermodynamics properties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cari, C., E-mail: cari@staff.uns.ac.id; Suparmi, A., E-mail: soeparmi@staff.uns.ac.id; Yunianto, M., E-mail: muhtaryunianto@staff.uns.ac.id

2016-02-08

The analytical solution of Ddimensional Dirac equation for Coulombic potential is investigated using Nikiforov-Uvarov method. The D dimensional relativistic energy spectra are obtained from relativistic energy eigenvalue equation by using Mat Lab software.The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi and Laguerre Polynomials. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy which will be applied to determine some thermodynamical properties of the system. The thermodynamical properties of the system are expressed in terms of error function and imaginary error function.
The exact solutions and approximate analytic solutions of the (2 + 1)-dimensional KP equation based on symmetry method.

PubMed

Gai, Litao; Bilige, Sudao; Jie, Yingmo

2016-01-01

In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on the Wu-differential characteristic set algorithm and reduced it. In the second part, we constructed the abundant exact travelling wave solutions by using the extended tanh method. These solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions respectively. It should be noted that when the parameters are taken as special values, some solitary wave solutions are derived from the hyperbolic function solutions. Finally, we apply the homotopy perturbation method to obtain the approximate analytic solutions based on four kinds of initial conditions.
Photoacoustic Effect Generated from an Expanding Spherical Source

NASA Astrophysics Data System (ADS)

Bai, Wenyu; Diebold, Gerald J.

2018-02-01

Although the photoacoustic effect is typically generated by amplitude-modulated continuous or pulsed radiation, the form of the wave equation for pressure that governs the generation of sound indicates that optical sources moving in an absorbing fluid can produce sound as well. Here, the characteristics of the acoustic wave produced by a radially symmetric Gaussian source expanding outwardly from the origin are found. The unique feature of the photoacoustic effect from the spherical source is a trailing compressive wave that arises from reflection of an inwardly propagating component of the wave. Similar to the one-dimensional geometry, an unbounded amplification effect is found for the Gaussian source expanding at the sound speed.
A hybrid approach for nonlinear computational aeroacoustics predictions

NASA Astrophysics Data System (ADS)

Sassanis, Vasileios; Sescu, Adrian; Collins, Eric M.; Harris, Robert E.; Luke, Edward A.

2017-01-01

In many aeroacoustics applications involving nonlinear waves and obstructions in the far-field, approaches based on the classical acoustic analogy theory or the linearised Euler equations are unable to fully characterise the acoustic field. Therefore, computational aeroacoustics hybrid methods that incorporate nonlinear wave propagation have to be constructed. In this study, a hybrid approach coupling Navier-Stokes equations in the acoustic source region with nonlinear Euler equations in the acoustic propagation region is introduced and tested. The full Navier-Stokes equations are solved in the source region to identify the acoustic sources. The flow variables of interest are then transferred from the source region to the acoustic propagation region, where the full nonlinear Euler equations with source terms are solved. The transition between the two regions is made through a buffer zone where the flow variables are penalised via a source term added to the Euler equations. Tests were conducted on simple acoustic and vorticity disturbances, two-dimensional jets (Mach 0.9 and 2), and a three-dimensional jet (Mach 1.5), impinging on a wall. The method is proven to be effective and accurate in predicting sound pressure levels associated with the propagation of linear and nonlinear waves in the near- and far-field regions.
Studies of the phase gradient at the boundary of the phase diffusion equation, motivated by peculiar wave patterns of rhythmic contraction in the amoeboid movement of Physarum polycephalum

NASA Astrophysics Data System (ADS)

Iima, Makoto; Kori, Hiroshi; Nakagaki, Toshiyuki

2017-04-01

The boundary of a cell is the interface with its surroundings and plays a key role in controlling the cell movement adaptations to different environments. We propose a study of the boundary effects on the patterns and waves of the rhythmic contractions in plasmodia of Physarum polycephalum, a tractable model organism of the amoeboid type. Boundary effects are defined as the effects of both the boundary conditions and the boundary shape. The rhythmicity of contraction can be modulated by local stimulation of temperature, light and chemicals, and by local deformation of cell shape via mechanosensitive ion channels as well. First, we examined the effects of boundary cell shapes in the case of a special shape resembling a tadpole, while requiring that the natural frequency in the proximity of the boundary is slightly higher and uniform. The simulation model reproduced the approximate propagated wave, from the tail to the head, while the inward waves were observed only near the periphery of the head section of the tadpole-shape. A key finding was that the frequency of the rhythmic contractions depended on the local shape of cell boundary. This implies that the boundary conditions of the phase were not always homogeneous. To understand the dependency, we reduced the two-dimensional model into a one-dimensional continuum model with Neumann boundary conditions. Here, the boundary conditions reflect the frequency distribution at the boundary. We described the analytic solutions and calculated the relationship between the boundary conditions and the wave propagation for a one-dimensional model of the continuous oscillatory field and a discrete coupled oscillator system. The results obtained may not be limited to cell movement of Physarum, but may be applicable to the other physical systems since the analysis used a generic phase diffusion equation.
Tension waves in tethered satellite cables

NASA Technical Reports Server (NTRS)

Lallman, F. J.

1984-01-01

A one-degree-of-freedom simulation of the Tethered Satellite System (TSS) was programmed using a distributed system model of the tether based on the one-dimensional wave equation. This model represents the time varying tension profile along the tether as the sum of two traveling waves of tension moving in opposite directions. A control loop was devised which combines a deployment rate command with the measured tension at the deployer to produce a smooth, stable rate of deployment of the subsatellite. Simulation results show a buildup of periodic bursts of high frequency oscillation in tension. This report covers the mathematical modelling and simulation results and explains the reason for the observed oscillations. The design of a possible vibration damping device is discussed.
Self-action of Bessel wave packets in a system of coupled light guides and formation of light bullets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balakin, A. A., E-mail: balakin.alexey@yandex.ru; Mironov, V. A.; Skobelev, S. A., E-mail: sk.sa1981@gmail.com

The self-action of two-dimensional and three-dimensional Bessel wave packets in a system of coupled light guides is considered using the discrete nonlinear Schrödinger equation. The features of the self-action of such wave fields are related to their initial strong spatial inhomogeneity. The numerical simulation shows that for the field amplitude exceeding a critical value, the development of an instability typical of a medium with the cubic nonlinearity is observed. Various regimes are studied: the self-channeling of a wave beam in one light guide at powers not strongly exceeding a critical value, the formation of the “kaleidoscopic” picture of a wavemore » packet during the propagation of higher-power radiation along a stratified medium, the formation of light bullets during competition between self-focusing and modulation instabilities in the case of three-dimensional wave packets, etc. In the problem of laser pulse shortening, the situation is considered when the wave-field stratification in the transverse direction dominates. This process is accompanied by the self-compression of laser pulses in well enough separated light guides. The efficiency of conversion of the initial Bessel field distribution to two flying parallel light bullets is about 50%.« less
Stability of dust ion acoustic solitary waves in a collisionless unmagnetized nonthermal plasma in presence of isothermal positrons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sardar, Sankirtan; Bandyopadhyay, Anup, E-mail: abandyopadhyay1965@gmail.com; Das, K. P.

A three-dimensional KP (Kadomtsev Petviashvili) equation is derived here describing the propagation of weakly nonlinear and weakly dispersive dust ion acoustic wave in a collisionless unmagnetized plasma consisting of warm adiabatic ions, static negatively charged dust grains, nonthermal electrons, and isothermal positrons. When the coefficient of the nonlinear term of the KP-equation vanishes an appropriate modified KP (MKP) equation describing the propagation of dust ion acoustic wave is derived. Again when the coefficient of the nonlinear term of this MKP equation vanishes, a further modified KP equation is derived. Finally, the stability of the solitary wave solutions of the KPmore » and the different modified KP equations are investigated by the small-k perturbation expansion method of Rowlands and Infeld [J. Plasma Phys. 3, 567 (1969); 8, 105 (1972); 10, 293 (1973); 33, 171 (1985); 41, 139 (1989); Sov. Phys. - JETP 38, 494 (1974)] at the lowest order of k, where k is the wave number of a long-wavelength plane-wave perturbation. The solitary wave solutions of the different evolution equations are found to be stable at this order.« less
Perturbation method for the second-order nonlinear effect of focused acoustic field around a scatterer in an ideal fluid.

PubMed

Liu, Gang; Jayathilake, Pahala Gedara; Khoo, Boo Cheong

2014-02-01

Two nonlinear models are proposed to investigate the focused acoustic waves that the nonlinear effects will be important inside the liquid around the scatterer. Firstly, the one dimensional solutions for the widely used Westervelt equation with different coordinates are obtained based on the perturbation method with the second order nonlinear terms. Then, by introducing the small parameter (Mach number), a dimensionless formulation and asymptotic perturbation expansion via the compressible potential flow theory is applied. This model permits the decoupling between the velocity potential and enthalpy to second order, with the first potential solutions satisfying the linear wave equation (Helmholtz equation), whereas the second order solutions are associated with the linear non-homogeneous equation. Based on the model, the local nonlinear effects of focused acoustic waves on certain volume are studied in which the findings may have important implications for bubble cavitation/initiation via focused ultrasound called HIFU (High Intensity Focused Ultrasound). The calculated results show that for the domain encompassing less than ten times the radius away from the center of the scatterer, the non-linear effect exerts a significant influence on the focused high intensity acoustic wave. Moreover, at the comparatively higher frequencies, for the model of spherical wave, a lower Mach number may result in stronger nonlinear effects. Copyright © 2013 Elsevier B.V. All rights reserved.
RELATIVISTIC MAGNETOHYDRODYNAMICS: RENORMALIZED EIGENVECTORS AND FULL WAVE DECOMPOSITION RIEMANN SOLVER

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anton, Luis; MartI, Jose M; Ibanez, Jose M

2010-05-01

We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, andmore » can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.« less

Numerical Study of Hydrothermal Wave Suppression in Thermocapillary Flow Using a Predictive Control Method

NASA Astrophysics Data System (ADS)

Muldoon, F. H.

2018-04-01

Hydrothermal waves in flows driven by thermocapillary and buoyancy effects are suppressed by applying a predictive control method. Hydrothermal waves arise in the manufacturing of crystals, including the "open boat" crystal growth process, and lead to undesirable impurities in crystals. The open boat process is modeled using the two-dimensional unsteady incompressible Navier-Stokes equations under the Boussinesq approximation and the linear approximation of the surface thermocapillary force. The flow is controlled by a spatially and temporally varying heat flux density through the free surface. The heat flux density is determined by a conjugate gradient optimization algorithm. The gradient of the objective function with respect to the heat flux density is found by solving adjoint equations derived from the Navier-Stokes ones in the Boussinesq approximation. Special attention is given to heat flux density distributions over small free-surface areas and to the maximum admissible heat flux density.
One-dimensional GIS-based model compared with a two-dimensional model in urban floods simulation.

PubMed

Lhomme, J; Bouvier, C; Mignot, E; Paquier, A

2006-01-01

A GIS-based one-dimensional flood simulation model is presented and applied to the centre of the city of Nîmes (Gard, France), for mapping flow depths or velocities in the streets network. The geometry of the one-dimensional elements is derived from the Digital Elevation Model (DEM). The flow is routed from one element to the next using the kinematic wave approximation. At the crossroads, the flows in the downstream branches are computed using a conceptual scheme. This scheme was previously designed to fit Y-shaped pipes junctions, and has been modified here to fit X-shaped crossroads. The results were compared with the results of a two-dimensional hydrodynamic model based on the full shallow water equations. The comparison shows that good agreements can be found in the steepest streets of the study zone, but differences may be important in the other streets. Some reasons that can explain the differences between the two models are given and some research possibilities are proposed.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, K.; Petersson, N. A.; Rodgers, A.

Acoustic waveform modeling is a computationally intensive task and full three-dimensional simulations are often impractical for some geophysical applications such as long-range wave propagation and high-frequency sound simulation. In this study, we develop a two-dimensional high-order accurate finite-difference code for acoustic wave modeling. We solve the linearized Euler equations by discretizing them with the sixth order accurate finite difference stencils away from the boundary and the third order summation-by-parts (SBP) closure near the boundary. Non-planar topographic boundary is resolved by formulating the governing equation in curvilinear coordinates following the interface. We verify the implementation of the algorithm by numerical examplesmore » and demonstrate the capability of the proposed method for practical acoustic wave propagation problems in the atmosphere.« less
Two-dimensional interaction of a shear flow with a free surface in a stratified fluid and its solitary-wave solutions via mathematical methods

NASA Astrophysics Data System (ADS)

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.
On the generation of cnoidal waves in ion beam-dusty plasma containing superthermal electrons and ions

NASA Astrophysics Data System (ADS)

El-Bedwehy, N. A.

2016-07-01

The reductive perturbation technique is used for investigating an ion beam-dusty plasma system consisting of two opposite polarity dusty grains, and superthermal electrons and ions in addition to ion beam. A two-dimensional Kadomtsev-Petviashvili equation is derived. The solution of this equation, employing Painlevé analysis, leads to cnoidal waves. The dependence of the structural features of these waves on the physical plasma parameters is investigated.
On the generation of cnoidal waves in ion beam-dusty plasma containing superthermal electrons and ions

DOE Office of Scientific and Technical Information (OSTI.GOV)

El-Bedwehy, N. A., E-mail: nab-elbedwehy@yahoo.com

2016-07-15

The reductive perturbation technique is used for investigating an ion beam-dusty plasma system consisting of two opposite polarity dusty grains, and superthermal electrons and ions in addition to ion beam. A two-dimensional Kadomtsev–Petviashvili equation is derived. The solution of this equation, employing Painlevé analysis, leads to cnoidal waves. The dependence of the structural features of these waves on the physical plasma parameters is investigated.
Nonlinear Schrödinger equations for Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Galati, Luigi; Zheng, Shijun

2013-10-01

The Gross-Pitaevskii equation, or more generally the nonlinear Schrödinger equation, models the Bose-Einstein condensates in a macroscopic gaseous superfluid wave-matter state in ultra-cold temperature. We provide analytical study of the NLS with L2 initial data in order to understand propagation of the defocusing and focusing waves for the BEC mechanism in the presence of electromagnetic fields. Numerical simulations are performed for the two-dimensional GPE with anisotropic quadratic potentials.
1D Resonance line Broadened Quasilinear (RBQ1D) code for fast ion Alfvenic relaxations and its validations

NASA Astrophysics Data System (ADS)

Gorelenkov, Nikolai; Duarte, Vinicius; Podesta, Mario

2017-10-01

The performance of the burning plasma can be limited by the requirements to confine the superalfvenic fusion products which are capable of resonating with the Alfvénic eigenmodes (AEs). The effect of AEs on fast ions is evaluated using the quasi-linear approach [Berk et al., Ph.Plasmas'96] generalized for this problem recently [Duarte et al., Ph.D.'17]. The generalization involves the resonance line broadened interaction regions with the diffusion coefficient prescribed to find the evolution of the velocity distribution function. The baseline eigenmode structures are found using the NOVA-K code perturbatively [Gorelenkov et al., Ph.Plasmas'99]. A RBQ1D code allowing the diffusion in radial direction is presented here. The wave particle interaction can be reduced to one-dimensional dynamics where for the Alfvénic modes typically the particle kinetic energy is nearly constant. Hence to a good approximation the Quasi-Linear (QL) diffusion equation only contains derivatives in the angular momentum. The diffusion equation is then one dimensional that is efficiently solved simultaneously for all particles with the equation for the evolution of the wave angular momentum. The RBQ1D is validated against recent DIIID results [Collins et al., PRL'16]. Supported by the US Department of Energy under DE-AC02-09CH11466.
An explicit dissipation-preserving method for Riesz space-fractional nonlinear wave equations in multiple dimensions

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.

2018-06-01

In this work, we investigate numerically a model governed by a multidimensional nonlinear wave equation with damping and fractional diffusion. The governing partial differential equation considers the presence of Riesz space-fractional derivatives of orders in (1, 2], and homogeneous Dirichlet boundary data are imposed on a closed and bounded spatial domain. The model under investigation possesses an energy function which is preserved in the undamped regime. In the damped case, we establish the property of energy dissipation of the model using arguments from functional analysis. Motivated by these results, we propose an explicit finite-difference discretization of our fractional model based on the use of fractional centered differences. Associated to our discrete model, we also propose discretizations of the energy quantities. We establish that the discrete energy is conserved in the undamped regime, and that it dissipates in the damped scenario. Among the most important numerical features of our scheme, we show that the method has a consistency of second order, that it is stable and that it has a quadratic order of convergence. Some one- and two-dimensional simulations are shown in this work to illustrate the fact that the technique is capable of preserving the discrete energy in the undamped regime. For the sake of convenience, we provide a Matlab implementation of our method for the one-dimensional scenario.
Simple Numerical Modelling for Gasdynamic Design of Wave Rotors

NASA Astrophysics Data System (ADS)

Okamoto, Koji; Nagashima, Toshio

The precise estimation of pressure waves generated in the passages is a crucial factor in wave rotor design. However, it is difficult to estimate the pressure wave analytically, e.g. by the method of characteristics, because the mechanism of pressure-wave generation and propagation in the passages is extremely complicated as compared to that in a shock tube. In this study, a simple numerical modelling scheme was developed to facilitate the design procedure. This scheme considers the three dominant factors in the loss mechanism —gradual passage opening, wall friction and leakage— for simulating the pressure waves precisely. The numerical scheme itself is based on the one-dimensional Euler equations with appropriate source terms to reduce the calculation time. The modelling of these factors was verified by comparing the results with those of a two-dimensional numerical simulation, which were previously validated by the experimental data in our previous study. Regarding wave rotor miniaturization, the leakage flow effect, which involves the interaction between adjacent cells, was investigated extensively. A port configuration principle was also examined and analyzed in detail to verify the applicability of the present numerical modelling scheme to the wave rotor design.
Two dimensional nonplanar evolution of electrostatic shock waves in pair-ion plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Masood, W.; Rizvi, H.

2012-01-15

Electrostatic waves in a two dimensional nonplanar geometry are studied in an unmagnetized, dissipative pair-ion plasma in the presence of weak transverse perturbations. The dissipation in the system is taken into account by incorporating the kinematic viscosity of both positive and negative ions in plasmas. The nonplanar Kadomtsev-Petviashvili-Burgers (KPB) as well as the Burgers Kadomtsev-Petviashvili (Burgers KP) equations are derived using the small amplitude expansion method and the range of applicability of both the equations are discussed. The system under consideration is observed to admit compressive rarefactive shocks. The present study may have relevance to understand the formation of twomore » dimensional nonplanar electrostatic shocks in laboratory plasmas.« less
Wave scattering from a periodic dielectric surface for a general angle of incidence

NASA Technical Reports Server (NTRS)

Chuang, S. L.; Kong, J. A.

1982-01-01

Electromagnetic waves scattered from a periodic dielectric and perfectly conducting surface are studied for a general angle of incidence. It is shown that the one-dimensional corrugated surface can be solved by using two scalar functions: the components of the electric and magnetic fields along the row direction of the surface, and appropriate boundary conditions to obtain simple matrix equations. Results are compared to the case where the incident angle wave vector is perpendicular to the row direction. Numerical results demonstrate that energy conservation and reciprocity are obeyed for scattering by sinusoidal surfaces for the general case, which checks the consistency of the formalism.
The Kadomtsev-Petviashvili equation under rapid forcing

NASA Astrophysics Data System (ADS)

Moroz, Irene M.

1997-06-01

We consider the initial value problem for the forced Kadomtsev-Petviashvili equation (KP) when the forcing is assumed to be fast compared to the evolution of the unforced equation. This suggests the introduction of two time scales. Solutions to the forced KP are sought by expanding the dependent variable in powers of a small parameter, which is inversely related to the forcing time scale. The unforced system describes weakly nonlinear, weakly dispersive, weakly two-dimensional wave propagation and is studied in two forms, depending upon whether gravity dominates surface tension or vice versa. We focus on the effect that the forcing has on the one-lump solution to the KPI equation (where surface tension dominates) and on the one- and two-line soliton solutions to the KPII equation (when gravity dominates). Solutions to second order in the expansion are computed analytically for some specific choices of the forcing function, which are related to the choice of initial data.
The stability of freak waves with regard to external impact and perturbation of initial data

NASA Astrophysics Data System (ADS)

Smirnova, Anna; Shamin, Roman

2014-05-01

We investigate solutions of the equations, describing freak waves, in perspective of stability with regard to external impact and perturbation of initial data. The modeling of freak waves is based on numerical solution of equations describing a non-stationary potential flow of the ideal fluid with a free surface. We consider the two-dimensional infinitely deep flow. For waves modeling we use the equations in conformal variables. The variant of these equations is offered in [1]. Mathematical correctness of these equations was discussed in [2]. These works establish the uniqueness of solutions, offer the effective numerical solution calculation methods, prove the numerical convergence of these methods. The important aspect of numerical modeling of freak waves is the stability of solutions, describing these waves. In this work we study the questions of stability with regards to external impact and perturbation of initial data. We showed the stability of freak waves numerical model, corresponding to the external impact. We performed series of computational experiments with various freak wave initial data and random external impact. This impact means the power density on free surface. In each experiment examine two waves: the wave that was formed by external impact and without one. In all the experiments we see the stability of equation`s solutions. The random external impact practically does not change the time of freak wave formation and its form. Later our work progresses to the investigation of solution's stability under perturbations of initial data. We take the initial data that provide a freak wave and get the numerical solution. In common we take the numerical solution of equation with perturbation of initial data. The computing experiments showed that the freak waves equations solutions are stable under perturbations of initial data.So we can make a conclusion that freak waves are stable relatively external perturbation and perturbation of initial data both. 1. Zakharov V.E., Dyachenko A.I., Vasilyev O.A. New method for numerical simulation of a nonstationary potential flow of incompressible fluid with a free surface// Eur. J.~Mech. B Fluids. 2002. V. 21. P. 283-291. 2. R.V. Shamin. Dynamics of an Ideal Liquid with a Free Surface in Conformal Variables // Journal of Mathematical Sciences, Vol. 160, No. 5, 2009. P. 537-678. 3. R.V. Shamin, V.E. Zakharov, A.I. Dyachenko. How probability for freak wave formation can be found // THE EUROPEAN PHYSICAL JOURNAL - SPECIAL TOPICS Volume 185, Number 1, 113-124, DOI: 10.1140/epjst/e2010-01242-y
Evaluation of Full Reynolds Stress Turbulence Models in FUN3D

NASA Technical Reports Server (NTRS)

Dudek, Julianne C.; Carlson, Jan-Renee

2017-01-01

Full seven-equation Reynolds stress turbulence models are a relatively new and promising tool for todays aerospace technology challenges. This paper uses two stress-omega full Reynolds stress models to evaluate challenging flows including shock-wave boundary layer interactions, separation and mixing layers. The Wilcox and the SSGLRR full second-moment Reynolds stress models are evaluated for four problems: a transonic two-dimensional diffuser, a supersonic axisymmetric compression corner, a compressible planar shear layer, and a subsonic axisymmetric jet. Simulation results are compared with experimental data and results using the more commonly used Spalart-Allmaras (SA) one-equation and the Menter Shear Stress Transport (SST) two-equation models.
Three dimensional dust-acoustic solitary waves in an electron depleted dusty plasma with two-superthermal ion-temperature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Borhanian, J.; Shahmansouri, M.

2013-01-15

A theoretical investigation is carried out to study the existence and characteristics of propagation of dust-acoustic (DA) waves in an electron-depleted dusty plasma with two-temperature ions, which are modeled by kappa distribution functions. A three-dimensional cylindrical Kadomtsev-Petviashvili equation governing evolution of small but finite amplitude DA waves is derived by means of a reductive perturbation method. The influence of physical parameters on solitary wave structure is examined. Furthermore, the energy integral equation is used to study the existence domains of the localized structures. It is found that the present model can be employed to describe the existence of positive asmore » well as negative polarity DA solitary waves by selecting special values for parameters of the system, e.g., superthermal index of cold and/or hot ions, cold to hot ion density ratio, and hot to cold ion temperature ratio. This model may be useful to understand the excitation of nonlinear DA waves in astrophysical objects.« less
A Study of Alfven Wave Propagation and Heating the Chromosphere

NASA Astrophysics Data System (ADS)

Tu, J.; Song, P.

2013-12-01

Alfven wave propagation, reflection and heating of the solar atmosphere are studied for a one-dimensional solar atmosphere by self-consistently solving plasma and neutral fluid equations and Maxwell's equations with incorporation of the Hall effect, strong electron-neutral, electron-ion, and ion-neutral collisions. The governing equations are very stiff because of the strong coupling between the charged and neutral fluids. We have developed a numerical model based on an implicit backward difference formula (BDF2) of second order accuracy both in time and space to overcome the stiffness. A non-reflecting boundary condition is applied to the top boundary of the simulation domain so that the wave reflection within the domain due to the density gradient can be unambiguously determined. It is shown that the Alfven waves are partially reflected throughout the chromosphere. The reflection is increasingly stronger at higher altitudes and the strongest reflection occurs at the transition region. The waves are damped in the lower chromosphere dominantly through Joule dissipation due to electron collisions with neutrals and ions. The heating resulting from the wave damping is strong enough to balance the radiation energy loss for the quiet chromosphere. The collisional dissipation of the Alfven waves in the weakly collisional corona is negligible. The heating rates are larger for weaker background magnetic fields. In addition, higher frequency waves are subject to heavier damping. There is an upper cutoff frequency, depending on the background magnetic field, above which the waves are completely damped. At the frequencies below which the waves are not strongly damped, the waves may be strongly reflected at the transition region. The reflected waves interacting with the upward propagating waves may produce power at their double frequencies, which leads to more damping. Due to the reflection and damping, the energy flux of the waves transmitted to the corona is one order of magnitude smaller than that of the driving source.
Phase transition of traveling waves in bacterial colony pattern

NASA Astrophysics Data System (ADS)

Wakano, Joe Yuichiro; Komoto, Atsushi; Yamaguchi, Yukio

2004-05-01

Depending on the growth condition, bacterial colonies can exhibit different morphologies. Many previous studies have used reaction diffusion equations to reproduce spatial patterns. They have revealed that nonlinear reaction term can produce diverse patterns as well as nonlinear diffusion coefficient. Typical reaction term consists of nutrient consumption, bacterial reproduction, and sporulation. Among them, the functional form of sporulation rate has not been biologically investigated. Here we report experimentally measured sporulation rate. Then, based on the result, a reaction diffusion model is proposed. One-dimensional simulation showed the existence of traveling wave solution. We study the wave form as a function of the initial nutrient concentration and find two distinct types of solution. Moreover, transition between them is very sharp, which is analogous to phase transition. The velocity of traveling wave also shows sharp transition in nonlinear diffusion model, which is consistent with the previous experimental result. The phenomenon can be explained by separatrix in reaction term dynamics. Results of two-dimensional simulation are also shown and discussed.
Two-dimensional modulated ion-acoustic excitations in electronegative plasmas

NASA Astrophysics Data System (ADS)

Panguetna, Chérif S.; Tabi, Conrad B.; Kofané, Timoléon C.

2017-09-01

Two-dimensional modulated ion-acoustic waves are investigated in an electronegative plasma. Through the reductive perturbation expansion, the governing hydrodynamic equations are reduced to a Davey-Stewartson system with two-space variables. The latter is used to study the modulational instability of ion-acoustic waves along with the effect of plasma parameters, namely, the negative ion concentration ratio (α) and the electron-to-negative ion temperature ratio (σn). A parametric analysis of modulational instability is carried out, where regions of plasma parameters responsible for the emergence of modulated ion-acoustic waves are discussed, with emphasis on the behavior of the instability growth rate. Numerically, using perturbed plane waves as initial conditions, parameters from the instability regions give rise to series of dromion solitons under the activation of modulational instability. The sensitivity of the numerical solutions to plasma parameters is discussed. Some exact solutions in the form one- and two-dromion solutions are derived and their response to the effect of varying α and σn is discussed as well.
Modelling in vivo action potential propagation along a giant axon.

PubMed

George, Stuart; Foster, Jamie M; Richardson, Giles

2015-01-01

A partial differential equation model for the three-dimensional current flow in an excitable, unmyelinated axon is considered. Where the axon radius is significantly below a critical value R(crit) (that depends upon intra- and extra-cellular conductivity and ion channel conductance) the resistance of the intracellular space is significantly higher than that of the extracellular space, such that the potential outside the axon is uniformly small whilst the intracellular potential is approximated by the transmembrane potential. In turn, since the current flow is predominantly axial, it can be shown that the transmembrane potential is approximated by a solution to the one-dimensional cable equation. It is noted that the radius of the squid giant axon, investigated by (Hodgkin and Huxley 1952e), lies close to R(crit). This motivates us to apply the three-dimensional model to the squid giant axon and compare the results thus found to those obtained using the cable equation. In the context of the in vitro experiments conducted in (Hodgkin and Huxley 1952e) we find only a small difference between the wave profiles determined using these two different approaches and little difference between the speeds of action potential propagation predicted. This suggests that the cable equation approximation is accurate in this scenario. However when applied to the it in vivo setting, in which the conductivity of the surrounding tissue is considerably lower than that of the axoplasm, there are marked differences in both wave profile and speed of action potential propagation calculated using the two approaches. In particular, the cable equation significantly over predicts the increase in the velocity of propagation as axon radius increases. The consequences of these results are discussed in terms of the evolutionary costs associated with increasing the speed of action potential propagation by increasing axon radius.

Three-dimensional compact explicit-finite difference time domain scheme with density variation

NASA Astrophysics Data System (ADS)

Tsuchiya, Takao; Maruta, Naoki

2018-07-01

In this paper, the density variation is implemented in the three-dimensional compact-explicit finite-difference time-domain (CE-FDTD) method. The formulation is first developed based on the continuity equation and the equation of motion, which include the density. Some numerical demonstrations are performed for the three-dimensional sound wave propagation in a two density layered medium. The numerical results are compared with the theoretical results to verify the proposed formulation.
Large-displacement statistics of the rightmost particle of the one-dimensional branching Brownian motion.

PubMed

Derrida, Bernard; Meerson, Baruch; Sasorov, Pavel V

2016-04-01

Consider a one-dimensional branching Brownian motion and rescale the coordinate and time so that the rates of branching and diffusion are both equal to 1. If X_{1}(t) is the position of the rightmost particle of the branching Brownian motion at time t, the empirical velocity c of this rightmost particle is defined as c=X_{1}(t)/t. Using the Fisher-Kolmogorov-Petrovsky-Piscounov equation, we evaluate the probability distribution P(c,t) of this empirical velocity c in the long-time t limit for c>2. It is already known that, for a single seed particle, P(c,t)∼exp[-(c^{2}/4-1)t] up to a prefactor that can depend on c and t. Here we show how to determine this prefactor. The result can be easily generalized to the case of multiple seed particles and to branching random walks associated with other traveling-wave equations.
Exact solitary wave solution for higher order nonlinear Schrodinger equation using He's variational iteration method

NASA Astrophysics Data System (ADS)

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.
Type IIB Colliding Plane Waves

NASA Astrophysics Data System (ADS)

Gutperle, M.; Pioline, B.

2003-09-01

Four-dimensional colliding plane wave (CPW) solutions have played an important role in understanding the classical non-linearities of Einstein's equations. In this note, we investigate CPW solutions in 2n+2-dimensional Einstein gravity with a n+1-form flux. By using an isomorphism with the four-dimensional problem, we construct exact solutions analogous to the Szekeres vacuum solution in four dimensions. The higher-dimensional versions of the Khan-Penrose and Bell-Szekeres CPW solutions are studied perturbatively in the vicinity of the light-cone. We find that under small perturbations, a curvature singularity is generically produced, leading to both space-like and time-like singularities. For n = 4, our results pertain to the collision of two ten-dimensional type-IIB Blau-Figueroa o'Farrill-Hull-Papadopoulos plane waves.
A Unique Finite Element Modeling of the Periodic Wave Transformation over Sloping and Barred Beaches by Beji and Nadaoka's Extended Boussinesq Equations

PubMed Central

Jabbari, Mohammad Hadi; Sayehbani, Mesbah; Reisinezhad, Arsham

2013-01-01

This paper presents a numerical model based on one-dimensional Beji and Nadaoka's Extended Boussinesq equations for simulation of periodic wave shoaling and its decomposition over morphological beaches. A unique Galerkin finite element and Adams-Bashforth-Moulton predictor-corrector methods are employed for spatial and temporal discretization, respectively. For direct application of linear finite element method in spatial discretization, an auxiliary variable is hereby introduced, and a particular numerical scheme is offered to rewrite the equations in lower-order form. Stability of the suggested numerical method is also analyzed. Subsequently, in order to display the ability of the presented model, four different test cases are considered. In these test cases, dispersive and nonlinearity effects of the periodic waves over sloping beaches and barred beaches, which are the common coastal profiles, are investigated. Outputs are compared with other existing numerical and experimental data. Finally, it is concluded that the current model can be further developed to model any morphological development of coastal profiles. PMID:23853534
Truncated Painlevé expansion: Tanh-traveling wave solutions and reduction of sine-Poisson equation to a quadrature for stationary and nonstationary three-dimensional collisionless cold plasma

NASA Astrophysics Data System (ADS)

Ibrahim, R. S.; El-Kalaawy, O. H.

2006-10-01

The relativistic nonlinear self-consistent equations for a collisionless cold plasma with stationary ions [R. S. Ibrahim, IMA J. Appl. Math. 68, 523 (2003)] are extended to 3 and 3+1 dimensions. The resulting system of equations is reduced to the sine-Poisson equation. The truncated Painlevé expansion and reduction of the partial differential equation to a quadrature problem (RQ method) are described and applied to obtain the traveling wave solutions of the sine-Poisson equation for stationary and nonstationary equations in 3 and 3+1 dimensions describing the charge-density equilibrium configuration model.
Exact analytic solution of position-dependent mass Schrödinger equation

NASA Astrophysics Data System (ADS)

Rajbongshi, Hangshadhar

2018-03-01

Exact analytic solution of position-dependent mass Schrödinger equation is generated by using extended transformation, a method of mapping a known system into a new system equipped with energy eigenvalues and corresponding wave functions. First order transformation is performed on D-dimensional radial Schrödinger equation with constant mass by taking trigonometric Pöschl-Teller potential as known system. The exactly solvable potentials with position-dependent mass generated for different choices of mass functions through first order transformation are also taken as known systems in the second order transformation performed on D-dimensional radial position-dependent mass Schrödinger equation. The solutions are fitted for "Zhu and Kroemer" ordering of ambiguity. All the wave functions corresponding to nonzero energy eigenvalues are normalizable. The new findings are that the normalizability condition of the wave functions remains independent of mass functions, and some of the generated potentials show a family relationship among themselves where power law potentials also get related to non-power law potentials and vice versa through the transformation.
Light scattering from an atomic gas under conditions of quantum degeneracy

NASA Astrophysics Data System (ADS)

Porozova, V. M.; Gerasimov, L. V.; Havey, M. D.; Kupriyanov, D. V.

2018-05-01

Elastic light scattering from a macroscopic atomic sample existing in the Bose-Einstein condensate phase reveals a unique physical configuration of interacting light and matter waves. However, the joint coherent dynamics of the optical excitation induced by an incident photon is influenced by the presence of incoherent scattering channels. For a sample of sufficient length the excitation transports as a polariton wave and the propagation Green's function obeys the scattering equation which we derive. The polariton dynamics could be tracked in the outgoing channel of the scattered photon as we show via numerical solution of the scattering equation for one-dimensional geometry. The results are analyzed and compared with predictions of the conventional macroscopic Maxwell theory for light scattering from a nondegenerate atomic sample of the same density and size.
Progressive wave expansions and open boundary problems

NASA Technical Reports Server (NTRS)

Hagstrom, T.; Hariharan, S. I.

1995-01-01

In this paper we construct progressive wave expansions and asymptotic boundary conditions for wave-like equations in exterior domains, including applications to electromagnetics, compressible flows and aero-acoustics. The development of the conditions will be discussed in two parts. The first part will include derivations of asymptotic conditions based on the well-known progressive wave expansions for the two-dimensional wave equations. A key feature in the derivations is that the resulting family of boundary conditions involves a single derivative in the direction normal to the open boundary. These conditions are easy to implement and an application in electromagnetics will be presented. The second part of the paper will discuss the theory for hyperbolic systems in two dimensions. Here, the focus will be to obtain the expansions in a general way and to use them to derive a class of boundary conditions that involve only time derivatives or time and tangential derivatives. Maxwell's equations and the compressible Euler equations are used as examples. Simulations with the linearized Euler equations are presented to validate the theory.
Forcing a three-dimensional, hydrostatic, primitive-equation model for application in the surf zone: 2. Application to DUCK94

NASA Astrophysics Data System (ADS)

Newberger, P. A.; Allen, J. S.

2007-08-01

A three-dimensional primitive-equation model for application to the nearshore surf zone has been developed. This model, an extension of the Princeton Ocean Model (POM), predicts the wave-averaged circulation forced by breaking waves. All of the features of the original POM are retained in the extended model so that applications can be made to regions where breaking waves, stratification, rotation, and wind stress make significant contributions to the flow behavior. In this study we examine the effects of breaking waves and wind stress. The nearshore POM circulation model is embedded within the NearCom community model and is coupled with a wave model. This combined modeling system is applied to the nearshore surf zone off Duck, North Carolina, during the DUCK94 field experiment of October 1994. Model results are compared to observations from this experiment, and the effects of parameter choices are examined. A process study examining the effects of tidal depth variation on depth-dependent wave-averaged currents is carried out. With identical offshore wave conditions and model parameters, the strength and spatial structure of the undertow and of the alongshore current vary systematically with water depth. Some three-dimensional solutions show the development of shear instabilities of the alongshore current. Inclusion of wave-current interactions makes an appreciable difference in the characteristics of the instability.
Accuracy & Computational Considerations for Wide--Angle One--way Seismic Propagators and Multiple Scattering by Invariant Embedding

NASA Astrophysics Data System (ADS)

Thomson, C. J.

2004-12-01

Pseudodifferential operators (PSDOs) yield in principle exact one--way seismic wave equations, which are attractive both conceptually and for their promise of computational efficiency. The one--way operators can be extended to include multiple--scattering effects, again in principle exactly. In practice approximations must be made and, as an example, the variable--wavespeed Helmholtz equation for scalar waves in two space dimensions is here factorized to give the one--way wave equation. This simple case permits clear identification of a sequence of physically reasonable approximations to be used when the mathematically exact PSDO one--way equation is implemented on a computer. As intuition suggests, these approximations hinge on the medium gradients in the direction transverse to the main propagation direction. A key point is that narrow--angle approximations are to be avoided in the interests of accuracy. Another key consideration stems from the fact that the so--called ``standard--ordering'' PSDO indicates how lateral interpolation of the velocity structure can significantly reduce computational costs associated with the Fourier or plane--wave synthesis lying at the heart of the calculations. The decision on whether a slow or a fast Fourier transform code should be used rests upon how many lateral model parameters are truly distinct. A third important point is that the PSDO theory shows what approximations are necessary in order to generate an exponential one--way propagator for the laterally varying case, representing the intuitive extension of classical integral--transform solutions for a laterally homogeneous medium. This exponential propagator suggests the use of larger discrete step sizes, and it can also be used to approach phase--screen like approximations (though the latter are not the main interest here). Numerical comparisons with finite--difference solutions will be presented in order to assess the approximations being made and to gain an understanding of computation time differences. The ideas described extend to the three--dimensional, generally anisotropic case and to multiple scattering by invariant embedding.
Information transport in classical statistical systems

NASA Astrophysics Data System (ADS)

Wetterich, C.

2018-02-01

For "static memory materials" the bulk properties depend on boundary conditions. Such materials can be realized by classical statistical systems which admit no unique equilibrium state. We describe the propagation of information from the boundary to the bulk by classical wave functions. The dependence of wave functions on the location of hypersurfaces in the bulk is governed by a linear evolution equation that can be viewed as a generalized Schrödinger equation. Classical wave functions obey the superposition principle, with local probabilities realized as bilinears of wave functions. For static memory materials the evolution within a subsector is unitary, as characteristic for the time evolution in quantum mechanics. The space-dependence in static memory materials can be used as an analogue representation of the time evolution in quantum mechanics - such materials are "quantum simulators". For example, an asymmetric Ising model on a Euclidean two-dimensional lattice represents the time evolution of free relativistic fermions in two-dimensional Minkowski space.
Rogue wave variational modelling through the interaction of two solitary waves

NASA Astrophysics Data System (ADS)

Gidel, Floriane; Bokhove, Onno

2016-04-01

The extreme and unexpected characteristics of Rogue waves have made them legendary for centuries. It is only on the 1st of January 1995 that these mariners' tales started to raise scientist's curiosity, when such a wave was recorded in the North Sea; a sudden wall of water hit the Draupner offshore platform, more than twice higher than the other waves, providing evidence of the existence of rogue or freak waves. Since then, studies have shown that these surface gravity waves of high amplitude (at least twice the height of the other sea waves [Dyste et al., 2008]) appear in non-linear dispersive water motion [Drazin and Johnson, 1989], at any depth, and have caused a lot of damage in recent years [Nikolkina and Didenkulova, 2011 ]. So far, most of the studies have tried to determine their probability of occurrence, but no conclusion has been achieved yet, which means that we are currently unenable to predict or avoid these monster waves. An accurate mathematical and numerical water-wave model would enable simulation and observation of this external forcing on boats and offshore structures and hence reduce their threat. In this work, we aim to model rogue waves through a soliton splash generated by the interaction of two solitons coming from different channels at a specific angle. Kodama indeed showed that one way to produce extreme waves is through the intersection of two solitary waves, or one solitary wave and its oblique reflection on a vertical wall [Yeh, Li and Kodama, 2010 ]. While he modelled Mach reflection from Kadomtsev-Petviashvili (KP) theory, we aim to model rogue waves from the three-dimensional potential flow equations and/or their asymptotic equivalent described by Benney and Luke [Benney and Luke, 1964]. These theories have the advantage to allow wave propagation in several directions, which is not the case with KP equations. The initial solitary waves are generated by removing a sluice gate in each channel. The equations are derived through a variational approach, based on Luke's variational principle [Luke, 1967], and its dynamical equivalent from Miles [Miles, 1977], that describe incompressible and inviscid potential flows with free surface, through the variations of the Lagrangian. This Lagrangian, obtained from Bernouilli's equations, can be expressed in a Hamiltonian form, for which robust time integrators have been derived [Gagarina et al., 2015]. A Galerkin finite element method is then used to solve the system numerically, and we aim to compare our simulations to exact solutions of the KP-equation.
Strong anti-gravity Life in the shock wave

NASA Astrophysics Data System (ADS)

Fabbrichesi, Marco; Roland, Kaj

1992-12-01

Strong anti-gravity is the vanishing of the net force between two massive particles at rest, to all orders in Newton's constant. We study this phenomenon and show that it occurs in any effective theory of gravity which is obtained from a higher-dimensional model by compactification on a manifold with flat directions. We find the exact solution of the Einstein equations in the presence of a point-like source of strong anti-gravity by dimensional reduction of a shock-wave solution in the higher-dimensional model.
Manipulating matter rogue waves and breathers in Bose-Einstein condensates.

PubMed

Manikandan, K; Muruganandam, P; Senthilvelan, M; Lakshmanan, M

2014-12-01

We construct higher-order rogue wave solutions and breather profiles for the quasi-one-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap through the similarity transformation technique. We consider three different forms of traps: (i) the time-independent expulsive trap, (ii) time-dependent monotonous trap, and (iii) time-dependent periodic trap. Our results show that when we change a parameter appearing in the time-independent or time-dependent trap the second- and third-order rogue waves transform into the first-order-like rogue waves. We also analyze the density profiles of breather solutions. Here we also show that the shapes of the breathers change when we tune the strength of the trap parameter. Our results may help to manage rogue waves experimentally in a BEC system.
Spin eigen-states of Dirac equation for quasi-two-dimensional electrons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Eremko, Alexander, E-mail: eremko@bitp.kiev.ua; Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua; Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua

Dirac equation for electrons in a potential created by quantum well is solved and the three sets of the eigen-functions are obtained. In each set the wavefunction is at the same time the eigen-function of one of the three spin operators, which do not commute with each other, but do commute with the Dirac Hamiltonian. This means that the eigen-functions of Dirac equation describe three independent spin eigen-states. The energy spectrum of electrons confined by the rectangular quantum well is calculated for each of these spin states at the values of energies relevant for solid state physics. It is shownmore » that the standard Rashba spin splitting takes place in one of such states only. In another one, 2D electron subbands remain spin degenerate, and for the third one the spin splitting is anisotropic for different directions of 2D wave vector.« less
Static axisymmetric Einstein equations in vacuum: Symmetry, new solutions, and Ricci solitons

NASA Astrophysics Data System (ADS)

Akbar, M. M.; MacCallum, M. A. H.

2015-09-01

An explicit one-parameter Lie point symmetry of the four-dimensional vacuum Einstein equations with two commuting hypersurface-orthogonal Killing vector fields is presented. The parameter takes values over all of the real line and the action of the group can be effected algebraically on any solution of the system. This enables one to construct particular one-parameter extended families of axisymmetric static solutions and cylindrical gravitational wave solutions from old ones, in a simpler way than most solution-generation techniques, including the prescription given by Ernst for this system. As examples, we obtain the families that generalize the Schwarzschild solution and the C -metric. These in effect superpose a Levi-Civita cylindrical solution on the seeds. Exploiting a correspondence between static solutions of Einstein's equations and Ricci solitons (self-similar solutions of the Ricci flow), this also enables us to construct new steady Ricci solitons.
Effect of Prestresses on the Dispersion of Quasi-Lamb Waves in the System Consisting of an Ideal Liquid Layer and a Compressible Elastic Layer

NASA Astrophysics Data System (ADS)

Bagno, A. M.

2017-03-01

The propagation of quasi-Lamb waves in a prestrained compressible elastic layer interacting with a layer of an ideal compressible fluid is studied. The three-dimensional equations of linearized elasticity and the assumption of finite strains for the elastic layer and the three-dimensional linearized Euler equations for the fluid are used. The dispersion curves for the quasi-Lamb modes are plotted over a wide frequency range. The effect of prestresses and the thickness of the elastic and liquid layers on the frequency spectrum of normal quasi-Lamb waves is analyzed. The localization properties of the lower quasi-Lamb modes in the elastic-fluid waveguides are studied. The numerical results are presented in the form of graphs and analyzed
K-P-Burgers equation in negative ion-rich relativistic dusty plasma including the effect of kinematic viscosity

NASA Astrophysics Data System (ADS)

Dev, A. N.; Deka, M. K.; Sarma, J.; Saikia, D.; Adhikary, N. C.

2016-10-01

The stationary solution is obtained for the K-P-Burgers equation that describes the nonlinear propagations of dust ion acoustic waves in a multi-component, collisionless, un-magnetized relativistic dusty plasma consisting of electrons, positive and negative ions in the presence of charged massive dust grains. Here, the Kadomtsev-Petviashvili (K-P) equation, three-dimensional (3D) Burgers equation, and K-P-Burgers equations are derived by using the reductive perturbation method including the effects of viscosity of plasma fluid, thermal energy, ion density, and ion temperature on the structure of a dust ion acoustic shock wave (DIASW). The K-P equation predictes the existences of stationary small amplitude solitary wave, whereas the K-P-Burgers equation in the weakly relativistic regime describes the evolution of shock-like structures in such a multi-ion dusty plasma.
Thermodynamics properties study of diatomic molecules with q-deformed modified Poschl-Teller plus Manning Rosen non-central potential in D dimensions using SUSYQM approach

NASA Astrophysics Data System (ADS)

Suparmi, A.; Cari, C.; Pratiwi, B. N.

2016-04-01

D-dimensional Dirac equation of q-deformed modified Poschl-Teller plus Manning Rosen non-central potential was solved using supersymmetric quantum mechanics (SUSY QM). The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial part of D dimensional Dirac equation and the angular quantum numbers were obtained from angular part of D dimensional Dirac equation. The SUSY operators was used to generate the D dimensional relativistic wave functions both for radial and angular parts. In the non-relativistic limit, the relativistic energy equation was reduced to the non-relativistic energy. In the classical limit, the partition function of vibrational, the specific heat of vibrational, and the mean energy of vibrational of some diatomic molecules were calculated from the equation of non-relativistic energy with the help of error function and Mat-lab 2011.

Quantum supersymmetric Bianchi IX cosmology

NASA Astrophysics Data System (ADS)

Damour, Thibault; Spindel, Philippe

2014-11-01

We study the quantum dynamics of a supersymmetric squashed three-sphere by dimensionally reducing (to one timelike dimension) the action of D =4 simple supergravity for a S U (2 ) -homogeneous (Bianchi IX) cosmological model. The quantization of the homogeneous gravitino field leads to a 64-dimensional fermionic Hilbert space. After imposition of the diffeomorphism constraints, the wave function of the Universe becomes a 64-component spinor of spin(8,4) depending on the three squashing parameters, which satisfies Dirac-like, and Klein-Gordon-like, wave equations describing the propagation of a "quantum spinning particle" reflecting off spin-dependent potential walls. The algebra of the supersymmetry constraints and of the Hamiltonian one is found to close. One finds that the quantum Hamiltonian is built from operators that generate a 64-dimensional representation of the (infinite-dimensional) maximally compact subalgebra of the rank-3 hyperbolic Kac-Moody algebra A E3 . The (quartic-in-fermions) squared-mass term μ^ 2 entering the Klein-Gordon-like equation has several remarkable properties: (i) it commutes with all the other (Kac-Moody-related) building blocks of the Hamiltonian; (ii) it is a quadratic function of the fermion number NF; and (iii) it is negative in most of the Hilbert space. The latter property leads to a possible quantum avoidance of the singularity ("cosmological bounce"), and suggests imposing the boundary condition that the wave function of the Universe vanish when the volume of space tends to zero (a type of boundary condition which looks like a final-state condition when considering the big crunch inside a black hole). The space of solutions is a mixture of "discrete-spectrum states" (parametrized by a few constant parameters, and known in explicit form) and of continuous-spectrum states (parametrized by arbitrary functions entering some initial-value problem). The predominantly negative values of the squared-mass term lead to a "bottle effect" between small-volume universes and large-volume ones, and to a possible reduction of the continuous spectrum to a discrete spectrum of quantum states looking like excited versions of the Planckian-size universes described by the discrete states at fermionic levels NF=0 and 1.
Unsteady three-dimensional marginal separation caused by surface-mounted obstacles and/or local suction

NASA Astrophysics Data System (ADS)

Braun, Stefan; Kluwick, Alfred

2004-09-01

Earlier investigations of steady two-dimensional marginally separated laminar boundary layers have shown that the non-dimensional wall shear (or equivalently the negative non-dimensional perturbation displacement thickness) is governed by a nonlinear integro-differential equation. This equation contains a single controlling parameter Gamma characterizing, for example, the angle of attack of a slender airfoil and has the important property that (real) solutions exist up to a critical value Gamma_c of Gamma only. Here we investigate three-dimensional unsteady perturbations of an incompressible steady two-dimensional marginally separated laminar boundary layer with special emphasis on the flow behaviour near Gamma_c. Specifically, it is shown that the integro differential equation which governs these disturbances if Gamma_c {-} Gamma {=} O(1) reduces to a nonlinear partial differential equation known as the Fisher equation as Gamma approaches the critical value Gamma_c. This in turn leads to a significant simplification of the problem allowing, among other things, a systematic study of devices used in boundary-layer control and an analytical investigation of the conditions leading to the formation of finite-time singularities which have been observed in earlier numerical studies of unsteady two-dimensional and three-dimensional flows in the vicinity of a line of symmetry. Also, it is found that it is possible to construct exact solutions which describe waves of constant form travelling in the spanwise direction. These waves may contain singularities which can be interpreted as vortex sheets. The existence of these solutions strongly suggests that solutions of the Fisher equation which lead to finite-time blow-up may be extended beyond the blow-up time, thereby generating moving singularities which can be interpreted as vortical structures qualitatively similar to those emerging in direct numerical simulations of near critical (i.e. transitional) laminar separation bubbles. This is supported by asymptotic analysis.
A k-Space Method for Moderately Nonlinear Wave Propagation

PubMed Central

Jing, Yun; Wang, Tianren; Clement, Greg T.

2013-01-01

A k-space method for moderately nonlinear wave propagation in absorptive media is presented. The Westervelt equation is first transferred into k-space via Fourier transformation, and is solved by a modified wave-vector time-domain scheme. The present approach is not limited to forward propagation or parabolic approximation. One- and two-dimensional problems are investigated to verify the method by comparing results to analytic solutions and finite-difference time-domain (FDTD) method. It is found that to obtain accurate results in homogeneous media, the grid size can be as little as two points per wavelength, and for a moderately nonlinear problem, the Courant–Friedrichs–Lewy number can be as large as 0.4. Through comparisons with the conventional FDTD method, the k-space method for nonlinear wave propagation is shown here to be computationally more efficient and accurate. The k-space method is then employed to study three-dimensional nonlinear wave propagation through the skull, which shows that a relatively accurate focusing can be achieved in the brain at a high frequency by sending a low frequency from the transducer. Finally, implementations of the k-space method using a single graphics processing unit shows that it required about one-seventh the computation time of a single-core CPU calculation. PMID:22899114
Signatures of extra dimensions in gravitational waves from black hole quasinormal modes

NASA Astrophysics Data System (ADS)

Chakraborty, Sumanta; Chakravarti, Kabir; Bose, Sukanta; SenGupta, Soumitra

2018-05-01

In this work, we have derived the evolution equation for gravitational perturbation in four-dimensional spacetime in the presence of a spatial extra dimension. The evolution equation is derived by perturbing the effective gravitational field equations on the four-dimensional spacetime, which inherits nontrivial higher-dimensional effects. Note that this is different from the perturbation of the five-dimensional gravitational field equations that exist in the literature and possess quantitatively new features. The gravitational perturbation has further been decomposed into a purely four-dimensional part and another piece that depends on extra dimensions. The four-dimensional gravitational perturbation now admits massive propagating degrees of freedom, owing to the existence of higher dimensions. We have also studied the influence of these massive propagating modes on the quasinormal mode frequencies, signaling the higher-dimensional nature of the spacetime, and have contrasted these massive modes with the massless modes in general relativity. Surprisingly, it turns out that the massive modes experience damping much smaller than that of the massless modes in general relativity and may even dominate over and above the general relativity contribution if one observes the ringdown phase of a black hole merger event at sufficiently late times. Furthermore, the whole analytical framework has been supplemented by the fully numerical Cauchy evolution problem, as well. In this context, we have shown that, except for minute details, the overall features of the gravitational perturbations are captured both in the Cauchy evolution as well as in the analysis of quasinormal modes. The implications on observations of black holes with LIGO and proposed space missions such as LISA are also discussed.
Modeling underwater noise propagation from marine hydrokinetic power devices through a time-domain, velocity-pressure solution

DOE PAGES

Hafla, Erin; Johnson, Erick; Johnson, C. Nathan; ...

2018-06-01

Marine hydrokinetic (MHK) devices generate electricity from the motion of tidal and ocean currents, as well as ocean waves, to provide an additional source of renewable energy available to the United States. These devices are a source of anthropogenic noise in the marine ecosystem and must meet regulatory guidelines that mandate a maximum amount of noise that may be generated. In the absence of measured levels from in situ deployments, a model for predicting the propagation of sound from an array of MHK sources in a real environment is essential. A set of coupled, linearized velocity-pressure equations in the time-domainmore » are derived and presented in this paper, which are an alternative solution to the Helmholtz and wave equation methods traditionally employed. Discretizing these equations on a three-dimensional (3D), finite-difference grid ultimately permits a finite number of complex sources and spatially varying sound speeds, bathymetry, and bed composition. The solution to this system of equations has been parallelized in an acoustic-wave propagation package developed at Sandia National Labs, called Paracousti. This work presents the broadband sound pressure levels from a single source in two-dimensional (2D) ideal and Pekeris wave-guides and in a 3D domain with a sloping boundary. Furthermore, the paper concludes with demonstration of Paracousti for an array of MHK sources in a simple wave-guide.« less
Modeling underwater noise propagation from marine hydrokinetic power devices through a time-domain, velocity-pressure solution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hafla, Erin; Johnson, Erick; Johnson, C. Nathan

Marine hydrokinetic (MHK) devices generate electricity from the motion of tidal and ocean currents, as well as ocean waves, to provide an additional source of renewable energy available to the United States. These devices are a source of anthropogenic noise in the marine ecosystem and must meet regulatory guidelines that mandate a maximum amount of noise that may be generated. In the absence of measured levels from in situ deployments, a model for predicting the propagation of sound from an array of MHK sources in a real environment is essential. A set of coupled, linearized velocity-pressure equations in the time-domainmore » are derived and presented in this paper, which are an alternative solution to the Helmholtz and wave equation methods traditionally employed. Discretizing these equations on a three-dimensional (3D), finite-difference grid ultimately permits a finite number of complex sources and spatially varying sound speeds, bathymetry, and bed composition. The solution to this system of equations has been parallelized in an acoustic-wave propagation package developed at Sandia National Labs, called Paracousti. This work presents the broadband sound pressure levels from a single source in two-dimensional (2D) ideal and Pekeris wave-guides and in a 3D domain with a sloping boundary. Furthermore, the paper concludes with demonstration of Paracousti for an array of MHK sources in a simple wave-guide.« less
An Efficient Approximation of the Coronal Heating Rate for use in Global Sun-Heliosphere Simulations

NASA Astrophysics Data System (ADS)

Cranmer, Steven R.

2010-02-01

The origins of the hot solar corona and the supersonically expanding solar wind are still the subject of debate. A key obstacle in the way of producing realistic simulations of the Sun-heliosphere system is the lack of a physically motivated way of specifying the coronal heating rate. Recent one-dimensional models have been found to reproduce many observed features of the solar wind by assuming the energy comes from Alfvén waves that are partially reflected, then dissipated by magnetohydrodynamic turbulence. However, the nonlocal physics of wave reflection has made it difficult to apply these processes to more sophisticated (three-dimensional) models. This paper presents a set of robust approximations to the solutions of the linear Alfvén wave reflection equations. A key ingredient of the turbulent heating rate is the ratio of inward-to-outward wave power, and the approximations developed here allow this to be written explicitly in terms of local plasma properties at any given location. The coronal heating also depends on the frequency spectrum of Alfvén waves in the open-field corona, which has not yet been measured directly. A model-based assumption is used here for the spectrum, but the results of future measurements can be incorporated easily. The resulting expression for the coronal heating rate is self-contained, computationally efficient, and applicable directly to global models of the corona and heliosphere. This paper tests and validates the approximations by comparing the results to exact solutions of the wave transport equations in several cases relevant to the fast and slow solar wind.
Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

DOE PAGES

Ruiz, D. E.; Dodin, I. Y.

2015-07-29

Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the "wave spin". Here, both phenomena are governed by an effective gauge Hamiltonian vanishing in leading-order geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the Stern-Gerlach Hamiltonian that is commonly known for spin-1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometrical-optics rays are derived from the fundamental wave Lagrangian. The resulting Euler-Lagrange equations can describe simultaneous interactions of N resonant modes, where N is arbitrary, and leadmore » to equations for the wave spin, which happens to be an (N 2 - 1)-dimensional spin vector. As a special case, classical equations for a Dirac particle (N = 2) are deduced formally, without introducing additional postulates or interpretations, from the Dirac quantum Lagrangian with the Pauli term. The model reproduces the Bargmann-Michel-Telegdi equations with added Stern-Gerlach force.« less
Behavior of a spin-1/2 massive charged particle in Schwarzschild immersed in an electromagnetic universe

NASA Astrophysics Data System (ADS)

Al-Badawi, A.

2018-02-01

The Dirac equation is considered in a spacetime that represents a Schwarzschild metric coupled to a uniform external electromagnetic field. Due to the presence of electromagnetic field from the surroundings, the interaction with the spin-1/2 massive charged particle is considered. The equations of the spin-1/2 massive charged particle are separated into radial and angular equations by adopting the Newman-Penrose formalism. The angular equations obtained are similar to the Schwarzschild geometry. For the radial equations we manage to obtain the one dimensional Schrödinger-type wave equations with effective potentials. Finally, we study the behavior of the potentials by plotting them as a function of radial distance and expose the effect of the external parameter, charge and the frequency of the particle on them.
The role of nonlinear critical layers in boundary layer transition

NASA Technical Reports Server (NTRS)

Goldstein, M.E.

1995-01-01

Asymptotic methods are used to describe the nonlinear self-interaction between pairs of oblique instability modes that eventually develops when initially linear spatially growing instability waves evolve downstream in nominally two-dimensional laminar boundary layers. The first nonlinear reaction takes place locally within a so-called 'critical layer', with the flow outside this layer consisting of a locally parallel mean flow plus a pair of oblique instability waves - which may or may not be accompanied by an associated plane wave. The amplitudes of these waves, which are completely determined by nonlinear effects within the critical layer, satisfy either a single integro-differential equation or a pair of integro-differential equations with quadratic to quartic-type nonlinearities. The physical implications of these equations are discussed.
Reflection and interference of electromagnetic waves in inhomogeneous media

NASA Technical Reports Server (NTRS)

Geiger, F. E.; Kyle, H. L.

1973-01-01

Solutions were obtained of the wave equation for a plane horizontally polarized electro-magnetic wave incident on a semi infinite two dimensional inhomogeneous medium. Two problems were considered: An inhomogeneous half space, and an inhomogeneous layer of arbitrary thickness. Solutions of the wave equation were obtained in terms of Hankel functions with complex arguments. Numerical calculations were made of the reflection coefficient R at the interface of the homogeneous medium. The startling results show that the reflection coefficient for a complex dielectric constant with gradient, can be less than that of the same medium with zero gradient.
Numerical simulation of boundary layers. Part 2: Ribbon-induced transition in Blasius flow

NASA Technical Reports Server (NTRS)

Spalart, P.; Yang, K. S.

1986-01-01

The early three-dimensional stages of transition in Blasius boundary layers are studied by numerical solution of the Navier-Stokes equations. A finite-amplitude two-dimensional wave and random low-amplitude three-dimensional disturbances are introduced. Rapid amplification of the three-dimensional components is observed and leads to transition. For intermediate amplitudes of the two-dimensional wave the breakdown is of subharmonic type, and the dominant spanwise wave number increases with the amplitude. For high amplitudes the energy of the fundamental mode is comparable to the energy of the subharmonic mode, but never dominates it; the breakdown is of mixed type. Visualizations, energy histories, and spectra are presented. The sensitivity of the results to various physical and numerical parameters is studied. Agreement with experimental and theoretical results is discussed.
Three-dimensional seismic depth migration

NASA Astrophysics Data System (ADS)

Zhou, Hongbo

1998-12-01

One-pass 3-D modeling and migration for poststack seismic data may be implemented by replacing the traditional 45sp° one-way wave equation (a third-order partial differential equation) with a pair of second and first order partial differential equations. Except for an extra correction term, the resulting second order equation has a form similar to Claerbout's 15sp° one-way wave equation, which is known to have a nearly circular horizontal impulse response. In this approach, there is no need to compensate for splitting errors. Numerical tests on synthetic data show that this algorithm has the desirable attributes of being second-order in accuracy and economical to solve. A modification of the Crank-Nicholson implementation maintains stability. Absorbing boundary conditions play an important role in one-way wave extrapolations by reducing reflections at grid edges. Clayton and Engquist's 2-D absorbing boundary conditions for one-way wave extrapolation by depth-stepping in the frequency domain are extended to 3-D using paraxial approximations of the scalar wave equation. Internal consistency is retained by incorporating the interior extrapolation equation with the absorbing boundary conditions. Numerical schemes are designed to make the proposed absorbing boundary conditions both mathematically correct and efficient with negligible extra cost. Synthetic examples illustrate the effectiveness of the algorithm for extrapolation with the 3-D 45sp° one-way wave equation. Frequency-space domain Butterworth and Chebyshev dip filters are implemented. By regrouping the product terms in the filter transfer function into summations, a cascaded (serial) Butterworth dip filter can be made parallel. A parallel Chebyshev dip filter can be similarly obtained, and has the same form as the Butterworth filter; but has different coeffcients. One of the advantages of the Chebyshev filter is that it has a sharper transition zone than that of Butterworth filter of the same order. Both filters are incorporated into 3-D one-way frequency-space depth migration for evanescent energy removal and for phase compensation of splitting errors; a single filter achieves both goals. Synthetic examples illustrate the behavior of the parallel filters. For a given order of filter, the cost of the Butterworth and Chebyshev filters is the same. A Chebyshev filter is more effective for phase compensation than the Butterworth filter of the same order, at the expense of some wavenumber-dependent amplitude ripples. An analytical formula for geometrical spreading is derived for a horizontally layered transversely isotropic medium with a vertical symmetry axis. Under this expression, geometrical spreading can be determined only by the anisotropic parameters in the first layer, the traveltime derivatives, and source-receiver offset. An explicit, numerically feasible expression for geometrical spreading can be further obtained by considering some of the special cases of transverse isotropy, such as weak anisotropy or elliptic anisotropy. Therefore, with the techniques of non-hyerbolic moveout for transverse isotropic media, geometrical spreading can be calculated by using picked traveltimes of primary P-wave reflections without having to know the actual parameters in the deeper subsurface; no ray tracing is needed. Synthetic examples verify the algorithm and show that it is numerically feasible for calculation of geometrical spreading.
Addendum to foundations of multidimensional wave field signal theory: Gaussian source function

NASA Astrophysics Data System (ADS)

Baddour, Natalie

2018-02-01

Many important physical phenomena are described by wave or diffusion-wave type equations. Recent work has shown that a transform domain signal description from linear system theory can give meaningful insight to multi-dimensional wave fields. In N. Baddour [AIP Adv. 1, 022120 (2011)], certain results were derived that are mathematically useful for the inversion of multi-dimensional Fourier transforms, but more importantly provide useful insight into how source functions are related to the resulting wave field. In this short addendum to that work, it is shown that these results can be applied with a Gaussian source function, which is often useful for modelling various physical phenomena.
Hydrodynamic Characteristics and Strength Analysis of a Novel Dot-matrix Oscillating Wave Energy Converter

NASA Astrophysics Data System (ADS)

Shao, Meng; Xiao, Chengsi; Sun, Jinwei; Shao, Zhuxiao; Zheng, Qiuhong

2017-12-01

The paper analyzes hydrodynamic characteristics and the strength of a novel dot-matrix oscillating wave energy converter, which is in accordance with nowadays’ research tendency: high power, high efficiency, high reliability and low cost. Based on three-dimensional potential flow theory, the paper establishes motion control equations of the wave energy converter unit and calculates wave loads and motions. On this basis, a three-dimensional finite element model of the device is built to check its strength. Through the analysis, it can be confirmed that the WEC is feasible and the research results could be a reference for wave energy’s exploration and utilization.
Evolution of large amplitude Alfven waves in solar wind plasmas: Kinetic-fluid models

NASA Astrophysics Data System (ADS)

Nariyuki, Y.

2014-12-01

Large amplitude Alfven waves are ubiquitously observed in solar wind plasmas. Mjolhus(JPP, 1976) and Mio et al(JPSJ, 1976) found that nonlinear evolution of the uni-directional, parallel propagating Alfven waves can be described by the derivative nonlinear Schrodinger equation (DNLS). Later, the multi-dimensional extension (Mjolhus and Wyller, JPP, 1988; Passot and Sulem, POP, 1993; Gazol et al, POP, 1999) and ion kinetic modification (Mjolhus and Wyller, JPP, 1988; Spangler, POP, 1989; Medvedev and Diamond, POP, 1996; Nariyuki et al, POP, 2013) of DNLS have been reported. Recently, Nariyuki derived multi-dimensional DNLS from an expanding box model of the Hall-MHD system (Nariyuki, submitted). The set of equations including the nonlinear evolution of compressional wave modes (TDNLS) was derived by Hada(GRL, 1993). DNLS can be derived from TDNLS by rescaling of the variables (Mjolhus, Phys. Scr., 2006). Nariyuki and Hada(JPSJ, 2007) derived a kinetically modified TDNLS by using a simple Landau closure (Hammet and Perkins, PRL, 1990; Medvedev and Diamond, POP, 1996). In the present study, we revisit the ion kinetic modification of multi-dimensional TDNLS through more rigorous derivations, which is consistent with the past kinetic modification of DNLS. Although the original TDNLS was derived in the multi-dimensional form, the evolution of waves with finite propagation angles in TDNLS has not been paid much attention. Applicability of the resultant models to solar wind turbulence is discussed.
Research on Radiation Characteristic of Plasma Antenna through FDTD Method

PubMed Central

Zhou, Jianming; Fang, Jingjing; Lu, Qiuyuan; Liu, Fan

2014-01-01

The radiation characteristic of plasma antenna is investigated by using the finite-difference time-domain (FDTD) approach in this paper. Through using FDTD method, we study the propagation of electromagnetic wave in free space in stretched coordinate. And the iterative equations of Maxwell equation are derived. In order to validate the correctness of this method, we simulate the process of electromagnetic wave propagating in free space. Results show that electromagnetic wave spreads out around the signal source and can be absorbed by the perfectly matched layer (PML). Otherwise, we study the propagation of electromagnetic wave in plasma by using the Boltzmann-Maxwell theory. In order to verify this theory, the whole process of electromagnetic wave propagating in plasma under one-dimension case is simulated. Results show that Boltzmann-Maxwell theory can be used to explain the phenomenon of electromagnetic wave propagating in plasma. Finally, the two-dimensional simulation model of plasma antenna is established under the cylindrical coordinate. And the near-field and far-field radiation pattern of plasma antenna are obtained. The experiments show that the variation of electron density can introduce the change of radiation characteristic. PMID:25114961
Three New (2+1)-dimensional Integrable Systems and Some Related Darboux Transformations

NASA Astrophysics Data System (ADS)

Guo, Xiu-Rong

2016-06-01

We introduce two operator commutators by using different-degree loop algebras of the Lie algebra A1, then under the framework of zero curvature equations we generate two (2+1)-dimensional integrable hierarchies, including the (2+1)-dimensional shallow water wave (SWW) hierarchy and the (2+1)-dimensional Kaup-Newell (KN) hierarchy. Through reduction of the (2+1)-dimensional hierarchies, we get a (2+1)-dimensional SWW equation and a (2+1)-dimensional KN equation. Furthermore, we obtain two Darboux transformations of the (2+1)-dimensional SWW equation. Similarly, the Darboux transformations of the (2+1)-dimensional KN equation could be deduced. Finally, with the help of the spatial spectral matrix of SWW hierarchy, we generate a (2+1) heat equation and a (2+1) nonlinear generalized SWW system containing inverse operators with respect to the variables x and y by using a reduction spectral problem from the self-dual Yang-Mills equations. Supported by the National Natural Science Foundation of China under Grant No. 11371361, the Shandong Provincial Natural Science Foundation of China under Grant Nos. ZR2012AQ011, ZR2013AL016, ZR2015EM042, National Social Science Foundation of China under Grant No. 13BJY026, the Development of Science and Technology Project under Grant No. 2015NS1048 and A Project of Shandong Province Higher Educational Science and Technology Program under Grant No. J14LI58
The effect of compliant walls on three-dimensional primary and secondary instabilities in boundary layer transition

NASA Astrophysics Data System (ADS)

Joslin, R. D.

1991-04-01

The use of passive devices to obtain drag and noise reduction or transition delays in boundary layers is highly desirable. One such device that shows promise for hydrodynamic applications is the compliant coating. The present study extends the mechanical model to allow for three-dimensional waves. This study also looks at the effect of compliant walls on three-dimensional secondary instabilities. For the primary and secondary instability analysis, spectral and shooting approximations are used to obtain solutions of the governing equations and boundary conditions. The spectral approximation consists of local and global methods of solution while the shooting approach is local. The global method is used to determine the discrete spectrum of eigenvalue without any initial guess. The local method requires a sufficiently accurate initial guess to converge to the eigenvalue. Eigenvectors may be obtained with either local approach. For the initial stage of this analysis, two and three dimensional primary instabilities propagate over compliant coatings. Results over the compliant walls are compared with the rigid wall case. Three-dimensional instabilities are found to dominate transition over the compliant walls considered. However, transition delays are still obtained and compared with transition delay predictions for rigid walls. The angles of wave propagation are plotted with Reynolds number and frequency. Low frequency waves are found to be highly three-dimensional.
A numerical investigation of premixed combustion in wave rotors

NASA Technical Reports Server (NTRS)

Nalim, M. Razi; Paxson, Daniel E.

1996-01-01

Wave rotor cycles which utilize premixed combustion processes within the passages are examined numerically using a one-dimensional CFD-based simulation. Internal-combustion wave rotors are envisioned for use as pressure-gain combustors in gas turbine engines. The simulation methodology is described, including a presentation of the assumed governing equations for the flow and reaction in the channels, the numerical integration method used, and the modeling of external components such as recirculation ducts. A number of cycle simulations are then presented which illustrate both turbulent-deflagration and detonation modes of combustion. Estimates of performance and rotor wall temperatures for the various cycles are made, and the advantages and disadvantages of each are discussed.

Nonstandard Analysis and Jump Conditions for Converging Shock Waves

NASA Technical Reports Server (NTRS)

Baty, Roy S.; Farassat, Fereidoun; Tucker, Don H.

2008-01-01

Nonstandard analysis is an area of modern mathematics which studies abstract number systems containing both infinitesimal and infinite numbers. This article applies nonstandard analysis to derive jump conditions for one-dimensional, converging shock waves in a compressible, inviscid, perfect gas. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions in the thermodynamic and fluid dynamic parameters occur smoothly across this interval. Predistributions of the Heaviside function and the Dirac delta measure are introduced to model the flow parameters across a shock wave. The equations of motion expressed in nonconservative form are then applied to derive unambiguous relationships between the jump functions for the flow parameters.
Bilinear identities for an extended B-type Kadomtsev-Petviashvili hierarchy

NASA Astrophysics Data System (ADS)

Lin, Runliang; Cao, Tiancheng; Liu, Xiaojun; Zeng, Yunbo

2016-03-01

We construct bilinear identities for wave functions of an extended B-type Kadomtsev-Petviashvili (BKP) hierarchy containing two types of (2+1)-dimensional Sawada-Kotera equations with a self-consistent source. Introducing an auxiliary variable corresponding to the extended flow for the BKP hierarchy, we find the τ -function and bilinear identities for this extended BKP hierarchy. The bilinear identities generate all the Hirota bilinear equations for the zero-curvature forms of this extended BKP hierarchy. As examples, we obtain the Hirota bilinear equations for the two types of (2+1)-dimensional Sawada-Kotera equations in explicit form.
Solution of the equations for one-dimensional, two-phase, immiscible flow by geometric methods

NASA Astrophysics Data System (ADS)

Boronin, Ivan; Shevlyakov, Andrey

2018-03-01

Buckley-Leverett equations describe non viscous, immiscible, two-phase filtration, which is often of interest in modelling of oil production. For many parameters and initial conditions, the solutions of these equations exhibit non-smooth behaviour, namely discontinuities in form of shock waves. In this paper we obtain a novel method for the solution of Buckley-Leverett equations, which is based on geometry of differential equations. This method is fast, accurate, stable, and describes non-smooth phenomena. The main idea of the method is that classic discontinuous solutions correspond to the continuous surfaces in the space of jets - the so-called multi-valued solutions (Bocharov et al., Symmetries and conservation laws for differential equations of mathematical physics. American Mathematical Society, Providence, 1998). A mapping of multi-valued solutions from the jet space onto the plane of the independent variables is constructed. This mapping is not one-to-one, and its singular points form a curve on the plane of the independent variables, which is called the caustic. The real shock occurs at the points close to the caustic and is determined by the Rankine-Hugoniot conditions.
Stable two-dimensional solitary pulses in linearly coupled dissipative Kadomtsev-Petviashvili equations.

PubMed

Feng, Bao-Feng; Malomed, Boris A; Kawahara, Takuji

2002-11-01

We present a two-dimensional (2D) generalization of the stabilized Kuramoto-Sivashinsky system, based on the Kadomtsev-Petviashvili (KP) equation including dissipation of the generic [Newell-Whitehead-Segel (NWS)] type and gain. The system directly applies to the description of gravity-capillary waves on the surface of a liquid layer flowing down an inclined plane, with a surfactant diffusing along the layer's surface. Actually, the model is quite general, offering a simple way to stabilize nonlinear media, combining the weakly 2D dispersion of the KP type with gain and NWS dissipation. Other applications are internal waves in multilayer fluids flowing down an inclined plane, double-front flames in gaseous mixtures, etc. Parallel to this weakly 2D model, we also introduce and study a semiphenomenological one, whose dissipative terms are isotropic, rather than of the NWS type, in order to check if qualitative results are sensitive to the exact form of the lossy terms. The models include an additional linear equation of the advection-diffusion type, linearly coupled to the main KP-NWS equation. The extra equation provides for stability of the zero background in the system, thus opening a way for the existence of stable localized pulses. We focus on the most interesting case, when the dispersive part of the system is of the KP-I type, which corresponds, e.g., to capillary waves, and makes the existence of completely localized 2D pulses possible. Treating the losses and gain as small perturbations and making use of the balance equation for the field momentum, we find that the equilibrium between the gain and losses may select two steady-state solitons from their continuous family existing in the absence of the dissipative terms (the latter family is found in an exact analytical form, and is numerically demonstrated to be stable). The selected soliton with the larger amplitude is expected to be stable. Direct simulations completely corroborate the analytical predictions, for both the physical and phenomenological models.
New thermal wave aspects on burn evaluation of skin subjected to instantaneous heating.

PubMed

Liu, J; Chen, X; Xu, L X

1999-04-01

Comparative studies on the well-known Pennes' equation and the newly developed thermal wave model of bioheat transfer (TWMBT) were performed to investigate the wave like behaviors of bioheat transfer occurred in thermal injury of biological bodies. The one-dimensional TWMBT in a finite medium was solved using separation of variables and the analytical solution showed distinctive wave behaviors of bioheat transfer in skin subjected to instantaneous heating. The finite difference method was used to simulate and study practical problems involved in burn injuries in which skin was stratified as three layers with various thermal physical properties. Deviations between the TWMBT and the traditional Pennes' equation imply that, for high flux heating with extremely short duration (i.e., flash fire), the TWMBT which accounts for finite thermal wave propagation may provide realistic predictions on burn evaluation. A general heat flux criterion has been established to determine when the thermal wave propagation dominates the principal heat transfer process and the TWMBT can be used for tissue temperature prediction and burn evaluation. A preliminary interpretation on the mechanisms of the wave like behaviors of heat transfer in living tissues was conducted. The application of thermal wave theory can also be possibly extended to other medical problems which involve instantaneous heating or cooling.
Modifiying shallow-water equations as a model for wave-vortex turbulence

NASA Astrophysics Data System (ADS)

Mohanan, A. V.; Augier, P.; Lindborg, E.

2017-12-01

The one-layer shallow-water equations is a simple two-dimensional model to study the complex dynamics of the oceans and the atmosphere. We carry out forced-dissipative numerical simulations, either by forcing medium-scale wave modes, or by injecting available potential energy (APE). With pure wave forcing in non-rotating cases, a statistically stationary regime is obtained for a range of forcing Froude numbers Ff = ɛ /(kf c), where ɛ is the energy dissipation rate, kf the forcing wavenumber and c the wave speed. Interestingly, the spectra scale as k-2 and third and higher order structure functions scale as r. Such statistics is a manifestation of shock turbulence or Burgulence, which dominate the flow. Rotating cases exhibit some inverse energy cascade, along with a stronger forward energy cascade, dominated by wave-wave interactions. We also propose two modifications to the classical shallow-water equations to construct a toy model. The properties of the model are explored by forcing in APE at a small and a medium wavenumber. The toy model simulations are then compared with results from shallow-water equations and a full General Circulation Model (GCM) simulation. The most distinctive feature of this model is that, unlike shallow-water equations, it avoids shocks and conserves quadratic energy. In Fig. 1, for the shallow-water equations, shocks appear as thin dark lines in the divergence (∇ .{u}) field, and as discontinuities in potential temperature (θ ) field; whereas only waves appear in the corresponding fields from toy model simulation. Forward energy cascade results in a wave field with k-5/3 spectrum, along with equipartition of KE and APE at small scales. The vortical field develops into a k-3 spectrum. With medium forcing wavenumber, at large scales, energy converted from APE to KE undergoes inverse cascade as a result of nonlinear fluxes composed of vortical modes alone. Gradually, coherent vortices emerge with a strong preference for anticyclonic motion. The model can serve as a closer representation of real geophysical turbulence than the classical shallow-water equations. Fig 1. Divergence and potential temperature fields of shallow-water (top row) and toy model (bottom row) simulations.
The staircase method: integrals for periodic reductions of integrable lattice equations

NASA Astrophysics Data System (ADS)

van der Kamp, Peter H.; Quispel, G. R. W.

2010-11-01

We show, in full generality, that the staircase method (Papageorgiou et al 1990 Phys. Lett. A 147 106-14, Quispel et al 1991 Physica A 173 243-66) provides integrals for mappings, and correspondences, obtained as traveling wave reductions of (systems of) integrable partial difference equations. We apply the staircase method to a variety of equations, including the Korteweg-De Vries equation, the five-point Bruschi-Calogero-Droghei equation, the quotient-difference (QD)-algorithm and the Boussinesq system. We show that, in all these cases, if the staircase method provides r integrals for an n-dimensional mapping, with 2r, then one can introduce q <= 2r variables, which reduce the dimension of the mapping from n to q. These dimension-reducing variables are obtained as joint invariants of k-symmetries of the mappings. Our results support the idea that often the staircase method provides sufficiently many integrals for the periodic reductions of integrable lattice equations to be completely integrable. We also study reductions on other quad-graphs than the regular {\\ Z}^2 lattice, and we prove linear growth of the multi-valuedness of iterates of high-dimensional correspondences obtained as reductions of the QD-algorithm.
Sediment transport under wave groups: Relative importance between nonlinear waveshape and nonlinear boundary layer streaming

USGS Publications Warehouse

Yu, X.; Hsu, T.-J.; Hanes, D.M.

2010-01-01

Sediment transport under nonlinear waves in a predominately sheet flow condition is investigated using a two-phase model. Specifically, we study the relative importance between the nonlinear waveshape and nonlinear boundary layer streaming on cross-shore sand transport. Terms in the governing equations because of the nonlinear boundary layer process are included in this one-dimensional vertical (1DV) model by simplifying the two-dimensional vertical (2DV) ensemble-averaged two-phase equations with the assumption that waves propagate without changing their form. The model is first driven by measured time series of near-bed flow velocity because of a wave group during the SISTEX99 large wave flume experiment and validated with the measured sand concentration in the sheet flow layer. Additional studies are then carried out by including and excluding the nonlinear boundary layer terms. It is found that for the grain diameter (0.24 mm) and high-velocity skewness wave condition considered here, nonlinear waveshape (e.g., skewness) is the dominant mechanism causing net onshore transport and nonlinear boundary layer streaming effect only causes an additional 36% onshore transport. However, for conditions of relatively low-wave skewness and a stronger offshore directed current, nonlinear boundary layer streaming plays a more critical role in determining the net transport. Numerical experiments further suggest that the nonlinear boundary layer streaming effect becomes increasingly important for finer grain. When the numerical model is driven by measured near-bed flow velocity in a more realistic surf zone setting, model results suggest nonlinear boundary layer processes may nearly double the onshore transport purely because of nonlinear waveshape. Copyright 2010 by the American Geophysical Union.
Global Solutions to Repulsive Hookean Elastodynamics

NASA Astrophysics Data System (ADS)

Hu, Xianpeng; Masmoudi, Nader

2017-01-01

The global existence of classical solutions to the three dimensional repulsive Hookean elastodynamics around an equilibrium is considered. By linearization and Hodge's decomposition, the compressible part of the velocity, the density, and the compressible part of the transpose of the deformation gradient satisfy Klein-Gordon equations with speed {√{2}}, while the incompressible parts of the velocity and of the transpose of the deformation gradient satisfy wave equations with speed one. The space-time resonance method combined with the vector field method is used in a novel way to obtain the decay of the solution and hence global existence.
On the hyperbolic nature of the equations of alluvial river hydraulics and the equivalence of stable and energy dissipating shocks

NASA Astrophysics Data System (ADS)

Zanraea, D. D. L.; Needham, D. J.

The depth-averaged hydraulic equations augmented with a suitable bed-load sediment transport function form a closed system which governs the one-dimensional flow in an alluvial river or channel. In this paper, it is shown that this system is hyperbolic and yields three families of shock-wave solutions. These are determined to be temporally stable in restricted regions of the (H, F0)-plane, via the Lax shock inequalities. Further, it is demonstrated that this criterion is equivalent to the energy dissipation criterion developed by Needham and Hey (1991).
Full Field Deformation Measurements in Tensile Kolsky Bar Experiments: Studies and Detailed Analysis of the Early Time History

NASA Astrophysics Data System (ADS)

Sutton, M. A.; Gilat, A.; Seidt, J.; Rajan, S.; Kidane, A.

2018-01-01

The very early stages of high rate tensile loading are important when attempting to characterize the response of materials during the transient loading time. To improve understanding of the conditions imposed on the specimen during the transient stage, a series of high rate loading experiments are performed using a Kolsky tensile bar system. Specimen forces and velocities during the high rate loading experiment are obtained by performing a thorough method of characteristics analysis of the system employed in the experiments. The in-situ full-field specimen displacements, velocities and accelerations during the loading process are quantified using modern ultra-high-speed imaging systems to provide detailed measurements of specimen response, with emphasis on the earliest stages of loading. Detailed analysis of the image-based measurements confirms that conditions are nominally consistent with those necessary for use of the one-dimensional wave equation within the relatively thin, dog-bone shaped tensile specimen. Specifically, measurements and use of the one-dimensional wave equation show clearly that the specimen has low inertial stresses in comparison to the applied transmitted force. Though the accelerations of the specimen continue for up to 50 μs, measurements show that the specimen is essentially in force equilibrium beginning a few microseconds after initial loading. These local measurements contrast with predictions based on comparison of the wave-based incident force measurements, which suggest that equilibrium occurs much later, on the order of 40-50 μs .
Geometric calculus-based postulates for the derivation and extension of the Maxwell equations

NASA Astrophysics Data System (ADS)

McClellan, Gene E.

2012-09-01

Clifford analysis, particularly application of the geometric algebra of three-dimensional physical space and its associated geometric calculus, enables a compact formulation of Maxwell's electromagnetic (EM) equations from a set of physically relevant and mathematically pleasing postulates. This formulation results in a natural extension of the Maxwell equations yielding wave solutions in addition to the usual EM waves. These additional solutions do not contradict experiment and have three properties in common with the apparent properties of dark energy. These three properties are that the wave solutions 1) propagate at the speed of light, 2) do not interact with ordinary electric charges or currents, and 3) possess retrograde momentum. By retrograde momentum, we mean that the momentum carried by such a wave is directed oppositely to the direction of energy transport. A "gas" of such waves generates negative pressure.
Solitons in Bose-Einstein Condensates

NASA Astrophysics Data System (ADS)

Carr, Lincoln D.

2003-05-01

The stationary form, dynamical properties, and experimental criteria for creation of matter-wave bright and dark solitons, both singly and in trains, are studied numerically and analytically in the context of Bose-Einstein condensates [1]. The full set of stationary solutions in closed analytic form to the mean field model in the quasi-one-dimensional regime, which is a nonlinear Schrodinger equation equally relevant in nonlinear optics, is developed under periodic and box boundary conditions [2]. These solutions are extended numerically into the two and three dimensional regimes, where it is shown that dark solitons can be used to create vortex-anti-vortex pairs under realistic conditions. Specific experimental prescriptions for creating viable dark and bright solitons in the quasi-one-dimensional regime are provided. These analytic methods are then extended to treat the nonlinear Schrodinger equation with a generalized lattice potential, which models a Bose-Einstein condensate trapped in the potential generated by a standing light wave. A novel solution family is developed and stability criterion are presented. Experiments which successfully carried out these ideas are briefly discussed [3]. [1] Dissertation research completed at the University of Washington Physics Department under the advisorship of Prof. William P. Reinhardt. [2] L. D. Carr, C. W. Clark, and W. P. Reinhardt, Phys. Rev. A v. 62 p. 063610-1--10 and Phys. Rev. A v.62, p.063611-1--10 (2000). [3] L. Khaykovich, F. Schreck, T. Bourdel, J. Cubizolles, G. Ferrari, L. D. Carr, Y. Castin, and C. Salomon, Science v. 296, p.1290--1293 (2002).
The North Atlantic Oscillation Influence on the Wave Regime in Portugal: An Extreme Wave Event Analysis

DTIC Science & Technology

2005-03-01

picture at 22/00Z.............50 x Figure 24. Case 5 – wave parameters........................51 Figure 25. Evolution of energy density (arrow...equation or energy balance equation: . in nl ds F v F S S S S t ∂ + ∇ = ≡ + + ∂ r (1) where ( , ; , )F f x tθ r is the two dimensional...collected from an offshore directional Seawatch buoy, in the vicinity of Cape Silleiro, Rayo Silleiro 19 (“E1”), (Figure 3), was provided by the
Modulation analysis of nonlinear beam refraction at an interface in liquid crystals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Assanto, Gaetano; Smyth, Noel F.; Xia Wenjun

2011-09-15

A theoretical investigation of solitary wave refraction in nematic liquid crystals is undertaken. A modulation theory based on a Lagrangian formulation of the governing optical solitary wave equations is developed. The resulting low-dimensional equations are found to give solutions in excellent agreement with full numerical solutions of the governing equations, as well as with previous experimental studies. The analysis deals with a number of types of refraction from a more to a less optically dense medium, the most famous being the Goos-Haenchen shift upon total internal reflection.
Symmetry-breaking instability of quadratic soliton bound states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Delque, Michaeel; Departement d'Optique P.M. Duffieux, Institut FEMTO-ST, Universite de Franche-Comte, CNRS UMR 6174, F-25030 Besancon; Fanjoux, Gil

We study both numerically and experimentally two-dimensional soliton bound states in quadratic media and demonstrate their symmetry-breaking instability. The experiment is performed in a potassium titanyl phosphate crystal in a type-II configuration. The bound state is generated by the copropagation of the antisymmetric fundamental beam locked in phase with the symmetrical second harmonic one. Experimental results are in good agreement with numerical simulations of the nonlinear wave equations.
Solitons, Bäcklund transformation and Lax pair for a (2+1)-dimensional B-type Kadomtsev-Petviashvili equation in the fluid/plasma mechanics

NASA Astrophysics Data System (ADS)

Lan, Zhong-Zhou; Gao, Yi-Tian; Yang, Jin-Wei; Su, Chuan-Qi; Wang, Qi-Min

2016-09-01

Under investigation in this paper is a (2+1)-dimensional B-type Kadomtsev-Petviashvili equation for the shallow water wave in a fluid or electrostatic wave potential in a plasma. Bilinear form, Bäcklund transformation and Lax pair are derived based on the binary Bell polynomials. Multi-soliton solutions are constructed via the Hirota’s method. Propagation and interaction of the solitons are illustrated graphically: (i) Through the asymptotic analysis, elastic and inelastic interactions between the two solitons are discussed analytically and graphically, respectively. The elastic interaction, amplitudes, velocities and shapes of the two solitons remain unchanged except for a phase shift. However, in the area of the inelastic interaction, amplitudes of the two solitons have a linear superposition. (ii) Elastic interactions among the three solitons indicate that the properties of the elastic interactions among the three solitons are similar to those between the two solitons. Moreover, oblique and overtaking interactions between the two solitons are displayed. Oblique interactions among the three solitons and interactions among the two parallel solitons and a single one are presented as well. (iii) Inelastic-elastic interactions imply that the interaction between the inelastic region and another one is elastic.
A topological study of gravity free-surface waves generated by bluff bodies using the method of steepest descents

PubMed Central

2016-01-01

The standard analytical approach for studying steady gravity free-surface waves generated by a moving body often relies upon a linearization of the physical geometry, where the body is considered asymptotically small in one or several of its dimensions. In this paper, a methodology that avoids any such geometrical simplification is presented for the case of steady-state flows at low speeds. The approach is made possible through a reduction of the water-wave equations to a complex-valued integral equation that can be studied using the method of steepest descents. The main result is a theory that establishes a correspondence between different bluff-bodied free-surface flow configurations, with the topology of the Riemann surface formed by the steepest descent paths. Then, when a geometrical feature of the body is modified, a corresponding change to the Riemann surface is observed, and the resultant effects to the water waves can be derived. This visual procedure is demonstrated for the case of two-dimensional free-surface flow past a surface-piercing ship and over an angled step in a channel. PMID:27493559
One-Dimensional Forward–Forward Mean-Field Games

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gomes, Diogo A., E-mail: diogo.gomes@kaust.edu.sa; Nurbekyan, Levon; Sedjro, Marc

While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward–forward problem is still poorly understood—even in the one-dimensional setting. Here, we consider one-dimensional forward–forward MFGs, study the existence of solutions and their long-time convergence. First, we discuss the relation between these models and systems of conservation laws. In particular, we identify new conserved quantities and study some qualitative properties of these systems. Next, we introduce a class of wave-like equations that are equivalent to forward–forward MFGs, and we derive a novel formulation as a system of conservation laws. Formore » first-order logarithmic forward–forward MFG, we establish the existence of a global solution. Then, we consider a class of explicit solutions and show the existence of shocks. Finally, we examine parabolic forward–forward MFGs and establish the long-time convergence of the solutions.« less
Proceedings, Nonlinear Water Waves Workshop Held at the University of Bristol on October 22-25, 1991

DTIC Science & Technology

1991-01-01

far as I understand, you have studied the case of one -dimensional spectrum of waves. I think that taking into account non- one -dimensional triplets...2b Evolving shoi waves (T- 1.0s). 13 components even became larger than that of the primary wave itself. The short waves (ff= 1.0 Hz), on the...breaking waves. This allows one to study statistics of breaking waves as rare events of high level excursion by a (three-dimensional) field of the wave

Interaction phenomenon to dimensionally reduced p-gBKP equation

NASA Astrophysics Data System (ADS)

Zhang, Runfa; Bilige, Sudao; Bai, Yuexing; Lü, Jianqing; Gao, Xiaoqing

2018-02-01

Based on searching the combining of quadratic function and exponential (or hyperbolic cosine) function from the Hirota bilinear form of the dimensionally reduced p-gBKP equation, eight class of interaction solutions are derived via symbolic computation with Mathematica. The submergence phenomenon, presented to illustrate the dynamical features concerning these obtained solutions, is observed by three-dimensional plots and density plots with particular choices of the involved parameters between the exponential (or hyperbolic cosine) function and the quadratic function. It is proved that the interference between the two solitary waves is inelastic.
Traveling wave solution of driven nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Akbari-Moghanjoughi, M.

2017-09-01

The traveling solitary and cnoidal wave solutions of the one dimensional driven nonlinear Schrödinger equation with a generalized form of nonlinearity are presented in this paper. We examine the modulation of nonlinear solitary excitations in two known weakly nonlinear models of classic oscillators, namely, the Helmholtz and Duffing oscillators and envelope structure formations for different oscillator and driver parameters. It is shown that two distinct regimes of subcritical and supercritical modulations may occur for nonlinear excitations with propagation speeds v <√{4 F0 } and v >√{4 F0 } , respectively, in which F0 is the driver force strength. The envelope soliton and cnoidal waves in these regimes are observed to be fundamentally different. The effect of pseudoenergy on the structure of the modulated envelope excitations is studied in detail for both sub- and supercritical modulation types. The current model for traveling envelope excitations may be easily extended to pseudopotentials with full nonlinearity relevant to more realistic gases, fluids, and plasmas.
Two dimensional electrostatic shock waves in relativistic electron positron ion plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Masood, W.; Rizvi, H.

2010-05-15

Ion-acoustic shock waves (IASWs) are studied in an unmagnetized plasma consisting of electrons, positrons and hot ions. In this regard, Kadomtsev-Petviashvili-Burgers (KPB) equation is derived using the small amplitude perturbation expansion method. The dependence of the IASWs on various plasma parameters is numerically investigated. It is observed that ratio of ion to electron temperature, kinematic viscosity, positron concentration, and the relativistic ion streaming velocity affect the structure of the IASW. Limiting case of the KPB equation is also discussed. Stability of KPB equation is also presented. The present investigation may have relevance in the study of electrostatic shock waves inmore » relativistic electron-positron-ion plasmas.« less
Coprimeness-preserving non-integrable extension to the two-dimensional discrete Toda lattice equation

NASA Astrophysics Data System (ADS)

Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji

2017-01-01

We introduce a so-called coprimeness-preserving non-integrable extension to the two-dimensional Toda lattice equation. We believe that this equation is the first example of such discrete equations defined over a three-dimensional lattice. We prove that all the iterates of the equation are irreducible Laurent polynomials of the initial data and that every pair of two iterates is co-prime, which indicate confined singularities of the equation. By reducing the equation to two- or one-dimensional lattices, we obtain coprimeness-preserving non-integrable extensions to the one-dimensional Toda lattice equation and the Somos-4 recurrence.
Statistical properties of nonlinear one-dimensional wave fields

NASA Astrophysics Data System (ADS)

Chalikov, D.

2005-06-01

A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.
Time-periodic solutions of the Benjamin-Ono equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ambrose , D.M.; Wilkening, Jon

2008-04-01

We present a spectrally accurate numerical method for finding non-trivial time-periodic solutions of non-linear partial differential equations. The method is based on minimizing a functional (of the initial condition and the period) that is positive unless the solution is periodic, in which case it is zero. We solve an adjoint PDE to compute the gradient of this functional with respect to the initial condition. We include additional terms in the functional to specify the free parameters, which, in the case of the Benjamin-Ono equation, are the mean, a spatial phase, a temporal phase and the real part of one ofmore » the Fourier modes at t = 0. We use our method to study global paths of non-trivial time-periodic solutions connecting stationary and traveling waves of the Benjamin-Ono equation. As a starting guess for each path, we compute periodic solutions of the linearized problem by solving an infinite dimensional eigenvalue problem in closed form. We then use our numerical method to continue these solutions beyond the realm of linear theory until another traveling wave is reached (or until the solution blows up). By experimentation with data fitting, we identify the analytical form of the solutions on the path connecting the one-hump stationary solution to the two-hump traveling wave. We then derive exact formulas for these solutions by explicitly solving the system of ODE's governing the evolution of solitons using the ansatz suggested by the numerical simulations.« less
Shock formation in the dispersionless Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Grava, T.; Klein, C.; Eggers, J.

2016-04-01

The dispersionless Kadomtsev-Petviashvili (dKP) equation {{≤ft({{u}t}+u{{u}x}\\right)}x}={{u}yy} is one of the simplest nonlinear wave equations describing two-dimensional shocks. To solve the dKP equation numerically we use a coordinate transformation inspired by the method of characteristics for the one-dimensional Hopf equation {{u}t}+u{{u}x}=0 . We show numerically that the solutions to the transformed equation stays regular for longer times than the solution of the dKP equation. This permits us to extend the dKP solution as the graph of a multivalued function beyond the critical time when the gradients blow up. This overturned solution is multivalued in a lip shape region in the (x, y) plane, where the solution of the dKP equation exists in a weak sense only, and a shock front develops. A local expansion reveals the universal scaling structure of the shock, which after a suitable change of coordinates corresponds to a generic cusp catastrophe. We provide a heuristic derivation of the shock front position near the critical point for the solution of the dKP equation, and study the solution of the dKP equation when a small amount of dissipation is added. Using multiple-scale analysis, we show that in the limit of small dissipation and near the critical point of the dKP solution, the solution of the dissipative dKP equation converges to a Pearcey integral. We test and illustrate our results by detailed comparisons with numerical simulations of both the regularized equation, the dKP equation, and the asymptotic description given in terms of the Pearcey integral.
Mode instability in one-dimensional anharmonic lattices: Variational equation approach

NASA Astrophysics Data System (ADS)

Yoshimura, K.

1999-03-01

The stability of normal mode oscillations has been studied in detail under the single-mode excitation condition for the Fermi-Pasta-Ulam-β lattice. Numerical experiments indicate that the mode stability depends strongly on k/N, where k is the wave number of the initially excited mode and N is the number of degrees of freedom in the system. It has been found that this feature does not change when N increases. We propose an average variational equation - approximate version of the variational equation - as a theoretical tool to facilitate a linear stability analysis. It is shown that this strong k/N dependence of the mode stability can be explained from the view point of the linear stability of the relevant orbits. We introduce a low-dimensional approximation of the average variational equation, which approximately describes the time evolution of variations in four normal mode amplitudes. The linear stability analysis based on this four-mode approximation demonstrates that the parametric instability mechanism plays a crucial role in the strong k/N dependence of the mode stability.
Geometric interpretation of four-wave mixing

NASA Astrophysics Data System (ADS)

Ott, J. R.; Steffensen, H.; Rottwitt, K.; McKinstrie, C. J.

2013-10-01

The nonlinear phenomenon of four-wave mixing (FWM) is investigated using a method, where, without the need of calculus, both phase and amplitudes of the mixing fields are visualized simultaneously, giving a complete overview of the FWM dynamics. This is done by introducing a set of Stokes-like coordinates of the electric fields, which reduce the FWM dynamics to a closed two-dimensional surface, similar to the Bloch sphere of quantum electrodynamics or the Pointcaré sphere in polarization dynamics. The coordinates are chosen so as to use the gauge invariance symmetries of the FWM equations which also give the conservation of action flux known as the Manley-Rowe relations. This reduces the dynamics of FWM to the one-dimensional intersection between the closed two-dimensional surface and the phase-plane given by the conserved Hamiltonian. The analysis is advantageous for visualizing phase-dependent FWM phenomena which are found in a large variety of nonlinear systems and even in various optical communication schemes.
On the transition towards slow manifold in shallow-water and 3D Euler equations in a rotating frame

NASA Technical Reports Server (NTRS)

Mahalov, A.

1994-01-01

The long-time, asymptotic state of rotating homogeneous shallow-water equations is investigated. Our analysis is based on long-time averaged rotating shallow-water equations describing interactions of large-scale, horizontal, two-dimensional motions with surface inertial-gravity waves field for a shallow, uniformly rotating fluid layer. These equations are obtained in two steps: first by introducing a Poincare/Kelvin linear propagator directly into classical shallow-water equations, then by averaging. The averaged equations describe interaction of wave fields with large-scale motions on time scales long compared to the time scale 1/f(sub o) introduced by rotation (f(sub o)/2-angular velocity of background rotation). The present analysis is similar to the one presented by Waleffe (1991) for 3D Euler equations in a rotating frame. However, since three-wave interactions in rotating shallow-water equations are forbidden, the final equations describing the asymptotic state are simplified considerably. Special emphasis is given to a new conservation law found in the asymptotic state and decoupling of the dynamics of the divergence free part of the velocity field. The possible rising of a decoupled dynamics in the asymptotic state is also investigated for homogeneous turbulence subjected to a background rotation. In our analysis we use long-time expansion, where the velocity field is decomposed into the 'slow manifold' part (the manifold which is unaffected by the linear 'rapid' effects of rotation or the inertial waves) and a formal 3D disturbance. We derive the physical space version of the long-time averaged equations and consider an invariant, basis-free derivation. This formulation can be used to generalize Waleffe's (1991) helical decomposition to viscous inhomogeneous flows (e.g. problems in cylindrical geometry with no-slip boundary conditions on the cylinder surface and homogeneous in the vertical direction).
Consistent nonlinear deterministic and stochastic evolution equations for deep to shallow water wave shoaling

NASA Astrophysics Data System (ADS)

Vrecica, Teodor; Toledo, Yaron

2015-04-01

One-dimensional deterministic and stochastic evolution equations are derived for the dispersive nonlinear waves while taking dissipation of energy into account. The deterministic nonlinear evolution equations are formulated using operational calculus by following the approach of Bredmose et al. (2005). Their formulation is extended to include the linear and nonlinear effects of wave dissipation due to friction and breaking. The resulting equation set describes the linear evolution of the velocity potential for each wave harmonic coupled by quadratic nonlinear terms. These terms describe the nonlinear interactions between triads of waves, which represent the leading-order nonlinear effects in the near-shore region. The equations are translated to the amplitudes of the surface elevation by using the approach of Agnon and Sheremet (1997) with the correction of Eldeberky and Madsen (1999). The only current possibility for calculating the surface gravity wave field over large domains is by using stochastic wave evolution models. Hence, the above deterministic model is formulated as a stochastic one using the method of Agnon and Sheremet (1997) with two types of stochastic closure relations (Benney and Saffman's, 1966, and Hollway's, 1980). These formulations cannot be applied to the common wave forecasting models without further manipulation, as they include a non-local wave shoaling coefficients (i.e., ones that require integration along the wave rays). Therefore, a localization method was applied (see Stiassnie and Drimer, 2006, and Toledo and Agnon, 2012). This process essentially extracts the local terms that constitute the mean nonlinear energy transfer while discarding the remaining oscillatory terms, which transfer energy back and forth. One of the main findings of this work is the understanding that the approximated non-local coefficients behave in two essentially different manners. In intermediate water depths these coefficients indeed consist of rapidly oscillating terms, but as the water depth becomes shallow they change to an exponential growth (or decay) behavior. Hence, the formerly used localization technique cannot be justified for the shallow water region. A new formulation is devised for the localization in shallow water, it approximates the nonlinear non-local shoaling coefficient in shallow water and matches it to the one fitting to the intermediate water region. This allows the model behavior to be consistent from deep water to intermediate depths and up to the shallow water regime. Various simulations of the model were performed for the cases of intermediate, and shallow water, overall the model was found to give good results in both shallow and intermediate water depths. The essential difference between the shallow and intermediate nonlinear shoaling physics is explained via the dominating class III Bragg resonances phenomenon. By inspecting the resonance conditions and the nature of the dispersion relation, it is shown that unlike in the intermediate water regime, in shallow water depths the formation of resonant interactions is possible without taking into account bottom components. References Agnon, Y. & Sheremet, A. 1997 Stochastic nonlinear shoaling of directional spectra. J. Fluid Mech. 345, 79-99. Benney, D. J. & Saffman, P. G. 1966 Nonlinear interactions of random waves. Proc. R. Soc. Lond. A 289, 301-321. Bredmose, H., Agnon, Y., Madsen, P.A. & Schaffer, H.A. 2005 Wave transformation models with exact second-order transfer. European J. of Mech. - B/Fluids 24 (6), 659-682. Eldeberky, Y. & Madsen, P. A. 1999 Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves. Coastal Engineering 38, 1-24. Kaihatu, J. M. & Kirby, J. T. 1995 Nonlinear transformation of waves in infinite water depth. Phys. Fluids 8, 175-188. Holloway, G. 1980 Oceanic internal waves are not weak waves. J. Phys. Oceanogr. 10, 906-914. Stiassnie, M. & Drimer, N. 2006 Prediction of long forcing waves for harbor agitation studies. J. of waterways, port, coastal and ocean engineering 132(3), 166-171. Toledo, Y. & Agnon, Y. 2012 Stochastic evolution equations with localized nonlinear shoaling coefficients. European J. of Mech. - B/Fluids 34, 13-18.
A pseudoenergy wave-activity relation for ageostrophic and non-hydrostatic moist atmosphere

NASA Astrophysics Data System (ADS)

Ran, Ling-Kun; Ping, Fan

2015-05-01

By employing the energy-Casimir method, a three-dimensional virtual pseudoenergy wave-activity relation for a moist atmosphere is derived from a complete system of nonhydrostatic equations in Cartesian coordinates. Since this system of equations includes the effects of water substance, mass forcing, diabatic heating, and dissipations, the derived wave-activity relation generalizes the previous result for a dry atmosphere. The Casimir function used in the derivation is a monotonous function of virtual potential vorticity and virtual potential temperature. A virtual energy equation is employed (in place of the previous zonal momentum equation) in the derivation, and the basic state is stationary but can be three-dimensional or, at least, not necessarily zonally symmetric. The derived wave-activity relation is further used for the diagnosis of the evolution and propagation of meso-scale weather systems leading to heavy rainfall. Our diagnosis of two real cases of heavy precipitation shows that positive anomalies of the virtual pseudoenergy wave-activity density correspond well with the strong precipitation and are capable of indicating the movement of the precipitation region. This is largely due to the cyclonic vorticity perturbation and the vertically increasing virtual potential temperature over the precipitation region. Project supported by the National Basic Research Program of China (Grant No. 2013CB430105), the Key Program of the Chinese Academy of Sciences (Grant No. KZZD-EW-05), the National Natural Science Foundation of China (Grant No. 41175060), and the Project of CAMS, China (Grant No. 2011LASW-B15).
Fully pseudospectral solution of the conformally invariant wave equation near the cylinder at spacelike infinity. III: nonspherical Schwarzschild waves and singularities at null infinity

NASA Astrophysics Data System (ADS)

Frauendiener, Jörg; Hennig, Jörg

2018-03-01

We extend earlier numerical and analytical considerations of the conformally invariant wave equation on a Schwarzschild background from the case of spherically symmetric solutions, discussed in Frauendiener and Hennig (2017 Class. Quantum Grav. 34 045005), to the case of general, nonsymmetric solutions. A key element of our approach is the modern standard representation of spacelike infinity as a cylinder. With a decomposition into spherical harmonics, we reduce the four-dimensional wave equation to a family of two-dimensional equations. These equations can be used to study the behaviour at the cylinder, where the solutions turn out to have, in general, logarithmic singularities at infinitely many orders. We derive regularity conditions that may be imposed on the initial data, in order to avoid the first singular terms. We then demonstrate that the fully pseudospectral time evolution scheme can be applied to this problem leading to a highly accurate numerical reconstruction of the nonsymmetric solutions. We are particularly interested in the behaviour of the solutions at future null infinity, and we numerically show that the singularities spread to null infinity from the critical set, where the cylinder approaches null infinity. The observed numerical behaviour is consistent with similar logarithmic singularities found analytically on the critical set. Finally, we demonstrate that even solutions with singularities at low orders can be obtained with high accuracy by virtue of a coordinate transformation that converts solutions with logarithmic singularities into smooth solutions.
Fully vectorial accelerating diffraction-free Helmholtz beams.

PubMed

Aleahmad, Parinaz; Miri, Mohammad-Ali; Mills, Matthew S; Kaminer, Ido; Segev, Mordechai; Christodoulides, Demetrios N

2012-11-16

We show that new families of diffraction-free nonparaxial accelerating optical beams can be generated by considering the symmetries of the underlying vectorial Helmholtz equation. Both two-dimensional transverse electric and magnetic accelerating wave fronts are possible, capable of moving along elliptic trajectories. Experimental results corroborate these predictions when these waves are launched from either the major or minor axis of the ellipse. In addition, three-dimensional spherical nondiffracting field configurations are presented along with their evolution dynamics. Finally, fully vectorial self-similar accelerating optical wave solutions are obtained via oblate-prolate spheroidal wave functions. In all occasions, these effects are illustrated via pertinent examples.
A dynamic model of the piezoelectric traveling wave rotary ultrasonic motor stator with the finite volume method.

PubMed

Renteria Marquez, I A; Bolborici, V

2017-05-01

This manuscript presents a method to model in detail the piezoelectric traveling wave rotary ultrasonic motor (PTRUSM) stator response under the action of DC and AC voltages. The stator is modeled with a discrete two dimensional system of equations using the finite volume method (FVM). In order to obtain accurate results, a model of the stator bridge is included into the stator model. The model of the stator under the action of DC voltage is presented first, and the results of the model are compared versus a similar model using the commercial finite element software COMSOL Multiphysics. One can observe that there is a difference of less than 5% between the displacements of the stator using the proposed model and the one with COMSOL Multiphysics. After that, the model of the stator under the action of AC voltages is presented. The time domain analysis shows the generation of the traveling wave in the stator surface. One can use this model to accurately calculate the stator surface velocities, elliptical motion of the stator surface and the amplitude and shape of the stator traveling wave. A system of equations discretized with the finite volume method can easily be transformed into electrical circuits, because of that, FVM may be a better choice to develop a model-based control strategy for the PTRUSM. Copyright © 2017 Elsevier B.V. All rights reserved.
New solitary wave solutions to the (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff and the Kadomtsev-Petviashvili hierarchy equations

NASA Astrophysics Data System (ADS)

Baskonus, Haci Mehmet; Sulaiman, Tukur Abdulkadir; Bulut, Hasan

2017-10-01

In this paper, with the help of Wolfram Mathematica 9 we employ the powerful sine-Gordon expansion method in investigating the solution structures of the two well known nonlinear evolution equations, namely; Calogero-Bogoyavlenskii-Schiff and Kadomtsev-Petviashvili hierarchy equations. We obtain new solutions with complex, hyperbolic and trigonometric function structures. All the obtained solutions in this paper verified their corresponding equations. We also plot the three- and two-dimensional graphics of all the obtained solutions in this paper by using the same program in Wolfram Mathematica 9. We finally submit a comprehensive conclusion.
The simulation of shock- and impact-driven flows with Mie-Gruneisen equations of state

NASA Astrophysics Data System (ADS)

Ward, Geoffrey M.

An investigation of shock- and impact-driven flows with Mie-Gruneisen equation of state derived from a linear shock-particle speed Hugoniot relationship is presented. Cartesian mesh methods using structured adaptive refinement are applied to simulate several flows of interest in an Eulerian frame of reference. The flows central to the investigation include planar Richtmyer-Meshkov instability, the impact of a sphere with a plate, and an impact-driven Mach stem. First, for multicomponent shock-driven flows, a dimensionally unsplit, spatially high-order, hybrid, center-difference, limiter methodology is developed. Effective switching between center-difference and upwinding schemes is achieved by a set of robust tolerance and Lax-entropy-based criteria [49]. Oscillations that result from such a mixed stencil scheme are minimized by requiring that the upwinding method approaches the center-difference method in smooth regions. The solver is then applied to investigate planar Richtmyer-Meshkov instability in the context of an equation of state comparison. Comparisons of simulations with materials modeled by isotropic stress Mie-Gruneisen equations of state derived from a linear shock-particle speed Hugoniot relationship [36,52] to those of perfect gases are made with the intention of exposing the role of the equation of state. First, results for single- and triple-mode planar Richtmyer-Meshkov instability between mid-ocean ridge basalt (MORB) and molybdenum modeled by Mie-Gruneisen equations of state are presented for the case of a reflected shock. The single-mode case is explored for incident shock Mach numbers of 1.5 and 2.5. Additionally, examined is single-mode Richtmyer-Meshkov instability when a reflected expansion wave is present for incident Mach numbers of 1.5 and 2.5. Comparison to perfect gas solutions in such cases yields a higher degree of similarity in start-up time and growth rate oscillations. Vorticity distribution and corrugation centerline shortly after shock interaction is also examined. The formation of incipient weak shock waves in the heavy fluid driven by waves emanating from the perturbed transmitted shock is observed when an expansion wave is reflected. Next, the ghost fluid method [83] is explored for application to impact-driven flows with Mie-Gruneisen equations of state in a vacuum. Free surfaces are defined utilizing a level-set approach. The level-set is reinitialized to the signed distance function periodically by solution to a Hamilton-Jacobi differential equation in artificial time. Flux reconstruction along each Cartesian direction of the domain is performed by subdividing in a way that allows for robust treatment of grid-scale sized voids. Ghost cells in voided regions near the material-vacuum interface are determined from surface-normal Riemann problem solution. The method is then applied to several impact problems of interest. First, a one-dimensional impact problem is examined in Mie-Gruneisen aluminum with simple point erosion used to model separation by spallation under high tension. A similar three-dimensional axisymmetric simulation of two rods impacting is then performed without a model for spallation. Further results for three-dimensional axisymmetric simulation of a sphere hitting a plate are then presented. Finally, a brief investigation of the assumptions utilized in modeling solids as isotropic fluids is undertaken. An Eulerian solver approach to handling elastic and elastic-plastic solids is utilized for comparison to the simple fluid model assumption. First, in one dimension an impact problem is examined for elastic, elastic-plastic, and fluid equations of state for aluminum. The results demonstrate that in one dimension the fluid models the plastic shock structure of the flow well. Further investigation is made using a three-dimensional axisymmetric simulation of an impact problem involving a copper cylinder surrounded by aluminum. An aluminum slab impact drives a faster shock in the outer aluminum region yielding a Mach reflection in the copper. The results demonstrate similar plastic shock structures. Several differences are also notable that include a lack of roll-up instability at the material interface and slip-line emanating from the Mach stem's triple point. (Abstract shortened by UMI.)
Parameter variation effects on temperature elevation in a steady-state, one-dimensional thermal model for millimeter wave exposure of one- and three-layer human tissue.

PubMed

Kanezaki, Akio; Hirata, Akimasa; Watanabe, Soichi; Shirai, Hiroshi

2010-08-21

The present study describes theoretical parametric analysis of the steady-state temperature elevation in one-dimensional three-layer (skin, fat and muscle) and one-layer (skin only) models due to millimeter-wave exposure. The motivation of this fundamental investigation is that some variability of warmth sensation in the human skin has been reported. An analytical solution for a bioheat equation was derived by using the Laplace transform for the one-dimensional human models. Approximate expressions were obtained to investigate the dependence of temperature elevation on different thermal and tissue thickness parameters. It was shown that the temperature elevation on the body surface decreases monotonically with the blood perfusion rate, heat conductivity and heat transfer from the body to air. Also revealed were the conditions where maximum and minimum surface temperature elevations were observed for different thermal and tissue thickness parameters. The surface temperature elevation in the three-layer model is 1.3-2.8 times greater than that in the one-layer model. The main reason for this difference is attributed to the adiabatic nature of the fat layer. By considering the variation range of thermal and tissue thickness parameters which causes the maximum and minimum temperature elevations, the dominant parameter influencing the surface temperature elevation was found to be the heat transfer coefficient between the body surface and air.
Optical Random Riemann Waves in Integrable Turbulence

NASA Astrophysics Data System (ADS)

Randoux, Stéphane; Gustave, François; Suret, Pierre; El, Gennady

2017-06-01

We examine integrable turbulence (IT) in the framework of the defocusing cubic one-dimensional nonlinear Schrödinger equation. This is done theoretically and experimentally, by realizing an optical fiber experiment in which the defocusing Kerr nonlinearity strongly dominates linear dispersive effects. Using a dispersive-hydrodynamic approach, we show that the development of IT can be divided into two distinct stages, the initial, prebreaking stage being described by a system of interacting random Riemann waves. We explain the low-tailed statistics of the wave intensity in IT and show that the Riemann invariants of the asymptotic nonlinear geometric optics system represent the observable quantities that provide new insight into statistical features of the initial stage of the IT development by exhibiting stationary probability density functions.
Discretized energy minimization in a wave guide with point sources

NASA Technical Reports Server (NTRS)

Propst, G.

1994-01-01

An anti-noise problem on a finite time interval is solved by minimization of a quadratic functional on the Hilbert space of square integrable controls. To this end, the one-dimensional wave equation with point sources and pointwise reflecting boundary conditions is decomposed into a system for the two propagating components of waves. Wellposedness of this system is proved for a class of data that includes piecewise linear initial conditions and piecewise constant forcing functions. It is shown that for such data the optimal piecewise constant control is the solution of a sparse linear system. Methods for its computational treatment are presented as well as examples of their applicability. The convergence of discrete approximations to the general optimization problem is demonstrated by finite element methods.

Relativistic Eulerian Vlasov simulations of the amplification of seed pulses by Brillouin backscattering in plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shoucri, M., E-mail: Shoucri.Magdi@ireq.ca; Matte, J.-P.; Vidal, F.

We apply an Eulerian Vlasov code to study the amplification by Brillouin scattering of a short seed laser pulse by a long pump laser pulse in an underdense plasma. The stimulated Brillouin backscattering interaction is the coupling of the pump and seed electromagnetic waves propagating in opposite directions, and the ion plasma wave. The code solves the one-dimensional relativistic Vlasov-Maxwell set of equations. Large amplitude ion waves are generated. In the simulations we present, the density plateau of the plasma is n{sub e}=0.3 n{sub c} (n{sub c} is the critical density), which excludes spurious stimulated Raman scattering amplification (which can occurmore » only if n{sub e}« less
Investigation of Convection and Pressure Treatment with Splitting Techniques

NASA Technical Reports Server (NTRS)

Thakur, Siddharth; Shyy, Wei; Liou, Meng-Sing

1995-01-01

Treatment of convective and pressure fluxes in the Euler and Navier-Stokes equations using splitting formulas for convective velocity and pressure is investigated. Two schemes - controlled variation scheme (CVS) and advection upstream splitting method (AUSM) - are explored for their accuracy in resolving sharp gradients in flows involving moving or reflecting shock waves as well as a one-dimensional combusting flow with a strong heat release source term. For two-dimensional compressible flow computations, these two schemes are implemented in one of the pressure-based algorithms, whose very basis is the separate treatment of convective and pressure fluxes. For the convective fluxes in the momentum equations as well as the estimation of mass fluxes in the pressure correction equation (which is derived from the momentum and continuity equations) of the present algorithm, both first- and second-order (with minmod limiter) flux estimations are employed. Some issues resulting from the conventional use in pressure-based methods of a staggered grid, for the location of velocity components and pressure, are also addressed. Using the second-order fluxes, both CVS and AUSM type schemes exhibit sharp resolution. Overall, the combination of upwinding and splitting for the convective and pressure fluxes separately exhibits robust performance for a variety of flows and is particularly amenable for adoption in pressure-based methods.
Lee wave breaking region: the map of instability development scenarios

NASA Astrophysics Data System (ADS)

Yakovenko, S. N.

2017-10-01

Numerical study of a stably stratified flow above the two-dimensional cosine-shaped obstacle has been performed by DNS and LES. These methods were implemented to solve the three-dimensional Navier-Stokes equations in the Boussinesq approximation, together with by the scalar diffusion equation. The results of scanning in the wide ranges of physical parameters (Reynolds and Prandtl/Schmidt numbers relating to laboratory experiment cases and atmospheric or oceanic situations) are presented for instability and turbulence development scenarios in the overturning internal lee waves. The latter is generated by the obstacle in a flow with the constant inflow values of velocity and stable density gradient. Evolution of lee-wave breaking is explored by visualization of velocity and scalar (density) fields, and the analysis of spectra. Based on the numerical simulation results, the power-law dependence on Reynolds number is demonstrated for the wavelength of the most unstable perturbation.
Improved computational treatment of transonic flow about swept wings

NASA Technical Reports Server (NTRS)

Ballhaus, W. F.; Bailey, F. R.; Frick, J.

1976-01-01

Relaxation solutions to classical three-dimensional small-disturbance (CSD) theory for transonic flow about lifting swept wings are reported. For such wings, the CSD theory was found to be a poor approximation to the full potential equation in regions of the flow field that are essentially two-dimensional in a plane normal to the sweep direction. The effect of this deficiency on the capture of embedded shock waves in terms of (1) the conditions under which shock waves can exist and (2) the relations they must satisfy when they do exist is emphasized. A modified small-disturbance (MSD) equation, derived by retaining two previously neglected terms, was proposed and shown to be a consistent approximation to the full potential equation over a wider range of sweep angles. The effect of these extra terms is demonstrated by comparing CSD, MSD, and experimental wing surface pressures.
A new method for solving the quantum hydrodynamic equations of motion: application to two-dimensional reactive scattering.

PubMed

Pauler, Denise K; Kendrick, Brian K

2004-01-08

The de Broglie-Bohm hydrodynamic equations of motion are solved using a meshless method based on a moving least squares approach and an arbitrary Lagrangian-Eulerian frame of reference. A regridding algorithm adds and deletes computational points as needed in order to maintain a uniform interparticle spacing, and unitary time evolution is obtained by propagating the wave packet using averaged fields. The numerical instabilities associated with the formation of nodes in the reflected portion of the wave packet are avoided by adding artificial viscosity to the equations of motion. The methodology is applied to a two-dimensional model collinear reaction with an activation barrier. Reaction probabilities are computed as a function of both time and energy, and are in excellent agreement with those based on the quantum trajectory method. (c) 2004 American Institute of Physics
Observation of Quasi-Two-Dimensional Nonlinear Interactions in a Drift-Wave Streamer

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yamada, T.; Nagashima, Y.; Itoh, S.-I.

2010-11-26

A streamer, which is a bunching of drift-wave fluctuations, and its mediator, which generates the streamer by coupling with other fluctuations, have been observed in a cylindrical magnetized plasma. Their radial structures were investigated in detail by using the biphase analysis. Their quasi-two-dimensional structures were revealed to be equivalent with a pair of fast and slow modes predicted by a nonlinear Schroedinger equation based on the Hasegawa-Mima model.
Investigation of unsteadiness in Shock-particle cloud interaction: Fully resolved two-dimensional simulation and one-dimensional modeling

NASA Astrophysics Data System (ADS)

Hosseinzadeh-Nik, Zahra; Regele, Jonathan D.

2015-11-01

Dense compressible particle-laden flow, which has a complex nature, exists in various engineering applications. Shock waves impacting a particle cloud is a canonical problem to investigate this type of flow. It has been demonstrated that large flow unsteadiness is generated inside the particle cloud from the flow induced by the shock passage. It is desirable to develop models for the Reynolds stress to capture the energy contained in vortical structures so that volume-averaged models with point particles can be simulated accurately. However, the previous work used Euler equations, which makes the prediction of vorticity generation and propagation innacurate. In this work, a fully resolved two dimensional (2D) simulation using the compressible Navier-Stokes equations with a volume penalization method to model the particles has been performed with the parallel adaptive wavelet-collocation method. The results still show large unsteadiness inside and downstream of the particle cloud. A 1D model is created for the unclosed terms based upon these 2D results. The 1D model uses a two-phase simple low dissipation AUSM scheme (TSLAU) developed by coupled with the compressible two phase kinetic energy equation.
Pseudo-One-Dimensional Magnonic Crystals for High-Frequency Nanoscale Devices

NASA Astrophysics Data System (ADS)

Banerjee, Chandrima; Choudhury, Samiran; Sinha, Jaivardhan; Barman, Anjan

2017-07-01

The synthetic magnonic crystals (i.e., periodic composites consisting of different magnetic materials) form one fascinating class of emerging research field, which aims to command the process and flow of information by means of spin waves, such as in magnonic waveguides. One of the intriguing features of magnonic crystals is the presence and tunability of band gaps in the spin-wave spectrum, where the high attenuation of the frequency bands can be utilized for frequency-dependent control on the spin waves. However, to find a feasible way of band tuning in terms of a realistic integrated device is still a challenge. Here, we introduce an array of asymmetric saw-tooth-shaped width-modulated nanoscale ferromagnetic waveguides forming a pseudo-one-dimensional magnonic crystal. The frequency dispersion of collective modes measured by the Brillouin light-scattering technique is compared with the band diagram obtained by numerically solving the eigenvalue problem derived from the linearized Landau-Lifshitz magnetic torque equation. We find that the magnonic band-gap width, position, and the slope of dispersion curves are controllable by changing the angle between the spin-wave propagation channel and the magnetic field. The calculated profiles of the dynamic magnetization reveal that the corrugation at the lateral boundary of the waveguide effectively engineers the edge modes, which forms the basis of the interactive control in magnonic circuits. The results represent a prospective direction towards managing the internal field distribution as well as the dispersion properties, which find potential applications in dynamic spin-wave filters and magnonic waveguides in the gigahertz frequency range.
Numerical study on the instabilities in H2-air rotating detonation engines

NASA Astrophysics Data System (ADS)

Liu, Yan; Zhou, Weijiang; Yang, Yunjun; Liu, Zhou; Wang, Jianping

2018-04-01

Numerical simulations of rotating detonation engines (RDEs) are performed using two-dimensional Euler equations and a detailed chemistry model of H2-air. Two propagation modes, the one-wave mode and the two-wave mode, are observed in the RDEs. The instabilities of the RDEs are studied and analyzed specifically. A low frequency instability and a high frequency instability are found from the pressure-time trace measured at a fixed location and the average density-time trace of the RDEs. For the low frequency instability, the pressure peak of the pressure-time trace oscillates with a low frequency while the average density is stable. The deviation between the measurement location and the location of the detonation wave results in the low frequency instability. For the high frequency instability, the average density of the RDEs oscillates regularly with a single frequency while the pressure oscillates irregularly with several frequencies. The oscillation of the detonation wave height results in the high frequency instability. Furthermore, the low frequency instability and the high frequency instability both occur in the one-wave and two-wave mode RDEs.
An Advanced One-Dimensional Finite Element Model for Incompressible Thermally Expandable Flow

DOE PAGES

Hu, Rui

2017-03-27

Here, this paper provides an overview of a new one-dimensional finite element flow model for incompressible but thermally expandable flow. The flow model was developed for use in system analysis tools for whole-plant safety analysis of sodium fast reactors. Although the pressure-based formulation was implemented, the use of integral equations in the conservative form ensured the conservation laws of the fluid. A stabilization scheme based on streamline-upwind/Petrov-Galerkin and pressure-stabilizing/Petrov-Galerkin formulations is also introduced. The flow model and its implementation have been verified by many test problems, including density wave propagation, steep gradient problems, discharging between tanks, and the conjugate heatmore » transfer in a heat exchanger.« less
An Advanced One-Dimensional Finite Element Model for Incompressible Thermally Expandable Flow

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Rui

Here, this paper provides an overview of a new one-dimensional finite element flow model for incompressible but thermally expandable flow. The flow model was developed for use in system analysis tools for whole-plant safety analysis of sodium fast reactors. Although the pressure-based formulation was implemented, the use of integral equations in the conservative form ensured the conservation laws of the fluid. A stabilization scheme based on streamline-upwind/Petrov-Galerkin and pressure-stabilizing/Petrov-Galerkin formulations is also introduced. The flow model and its implementation have been verified by many test problems, including density wave propagation, steep gradient problems, discharging between tanks, and the conjugate heatmore » transfer in a heat exchanger.« less
Self-consistent approach to many-body localization and subdiffusion

NASA Astrophysics Data System (ADS)

Prelovšek, P.; Herbrych, J.

2017-07-01

An analytical theory, based on the perturbative treatment of the disorder and extended into a self-consistent set of equations for the dynamical density correlations, is developed and applied to the prototype one-dimensional model of many-body localization. Results show a qualitative agreement with the numerically obtained dynamical structure factor in the whole range of frequencies and wave vectors, as well as across the transition to nonergodic behavior. The theory reveals the singular nature of the one-dimensional problem, whereby on the ergodic side the dynamics is subdiffusive with dynamical conductivity σ (ω ) ∝|ω| α , i.e., with vanishing dc limit σ0=0 and α <1 varying with disorder, while we get α >1 in the localized phase.
Wave-vortex interactions in the nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Guo, Yuan; Bühler, Oliver

2014-02-01

This is a theoretical study of wave-vortex interaction effects in the two-dimensional nonlinear Schrödinger equation, which is a useful conceptual model for the limiting dynamics of superfluid quantum condensates at zero temperature. The particular wave-vortex interaction effects are associated with the scattering and refraction of small-scale linear waves by the straining flows induced by quantized point vortices and, crucially, with the concomitant nonlinear back-reaction, the remote recoil, that these scattered waves exert on the vortices. Our detailed model is a narrow, slowly varying wavetrain of small-amplitude waves refracted by one or two vortices. Weak interactions are studied using a suitable perturbation method in which the nonlinear recoil force on the vortex then arises at second order in wave amplitude, and is computed in terms of a Magnus-type force expression for both finite and infinite wavetrains. In the case of an infinite wavetrain, an explicit asymptotic formula for the scattering angle is also derived and cross-checked against numerical ray tracing. Finally, under suitable conditions a wavetrain can be so strongly refracted that it collapses all the way onto a zero-size point vortex. This is a strong wave-vortex interaction by definition. The conditions for such a collapse are derived and the validity of ray tracing theory during the singular collapse is investigated.
On the v-representabilty problem in density functional theory: Application to non-interacting systems

DOE PAGES

Dane, Markus; Gonis, Antonios

2016-07-05

Based on a computational procedure for determining the functional derivative with respect to the density of any antisymmetric N-particle wave function for a non-interacting system that leads to the density, we devise a test as to whether or not a wave function known to lead to a given density corresponds to a solution of a Schrödinger equation for some potential. We examine explicitly the case of non-interacting systems described by Slater determinants. Here, numerical examples for the cases of a one-dimensional square-well potential with infinite walls and the harmonic oscillator potential illustrate the formalism.
A higher-order conservation element solution element method for solving hyperbolic differential equations on unstructured meshes

NASA Astrophysics Data System (ADS)

Bilyeu, David

This dissertation presents an extension of the Conservation Element Solution Element (CESE) method from second- to higher-order accuracy. The new method retains the favorable characteristics of the original second-order CESE scheme, including (i) the use of the space-time integral equation for conservation laws, (ii) a compact mesh stencil, (iii) the scheme will remain stable up to a CFL number of unity, (iv) a fully explicit, time-marching integration scheme, (v) true multidimensionality without using directional splitting, and (vi) the ability to handle two- and three-dimensional geometries by using unstructured meshes. This algorithm has been thoroughly tested in one, two and three spatial dimensions and has been shown to obtain the desired order of accuracy for solving both linear and non-linear hyperbolic partial differential equations. The scheme has also shown its ability to accurately resolve discontinuities in the solutions. Higher order unstructured methods such as the Discontinuous Galerkin (DG) method and the Spectral Volume (SV) methods have been developed for one-, two- and three-dimensional application. Although these schemes have seen extensive development and use, certain drawbacks of these methods have been well documented. For example, the explicit versions of these two methods have very stringent stability criteria. This stability criteria requires that the time step be reduced as the order of the solver increases, for a given simulation on a given mesh. The research presented in this dissertation builds upon the work of Chang, who developed a fourth-order CESE scheme to solve a scalar one-dimensional hyperbolic partial differential equation. The completed research has resulted in two key deliverables. The first is a detailed derivation of a high-order CESE methods on unstructured meshes for solving the conservation laws in two- and three-dimensional spaces. The second is the code implementation of these numerical methods in a computer code. For code development, a one-dimensional solver for the Euler equations was developed. This work is an extension of Chang's work on the fourth-order CESE method for solving a one-dimensional scalar convection equation. A generic formulation for the nth-order CESE method, where n ≥ 4, was derived. Indeed, numerical implementation of the scheme confirmed that the order of convergence was consistent with the order of the scheme. For the two- and three-dimensional solvers, SOLVCON was used as the basic framework for code implementation. A new solver kernel for the fourth-order CESE method has been developed and integrated into the framework provided by SOLVCON. The main part of SOLVCON, which deals with unstructured meshes and parallel computing, remains intact. The SOLVCON code for data transmission between computer nodes for High Performance Computing (HPC). To validate and verify the newly developed high-order CESE algorithms, several one-, two- and three-dimensional simulations where conducted. For the arbitrary order, one-dimensional, CESE solver, three sets of governing equations were selected for simulation: (i) the linear convection equation, (ii) the linear acoustic equations, (iii) the nonlinear Euler equations. All three systems of equations were used to verify the order of convergence through mesh refinement. In addition the Euler equations were used to solve the Shu-Osher and Blastwave problems. These two simulations demonstrated that the new high-order CESE methods can accurately resolve discontinuities in the flow field.For the two-dimensional, fourth-order CESE solver, the Euler equation was employed in four different test cases. The first case was used to verify the order of convergence through mesh refinement. The next three cases demonstrated the ability of the new solver to accurately resolve discontinuities in the flows. This was demonstrated through: (i) the interaction between acoustic waves and an entropy pulse, (ii) supersonic flow over a circular blunt body, (iii) supersonic flow over a guttered wedge. To validate and verify the three-dimensional, fourth-order CESE solver, two different simulations where selected. The first used the linear convection equations to demonstrate fourth-order convergence. The second used the Euler equations to simulate supersonic flow over a spherical body to demonstrate the scheme's ability to accurately resolve shocks. All test cases used are well known benchmark problems and as such, there are multiple sources available to validate the numerical results. Furthermore, the simulations showed that the high-order CESE solver was stable at a CFL number near unity.
Analytical study of laser-supported combustion waves in hydrogen

NASA Technical Reports Server (NTRS)

Kemp, N. H.; Root, R. G.

1978-01-01

Laser supported combustion (LSC) waves are an important ingredient in the fluid mechanics of CW laser propulsion using a hydrogen propellant and 10.6 micron lasers. Therefore, a computer model has been constructed to solve the one-dimensional energy equation with constant pressure and area. Physical processes considered include convection, conduction, absorption of laser energy, radiation energy loss, and accurate properties of equilibrium hydrogen. Calculations for 1, 3, 10 and 30 atm were made for intensities of 10 to the 4th to 10 to the 6th W/sq cm, which gave temperature profiles, wave speed, etc. To pursue the propulsion application, a second computer model was developed to describe the acceleration of the gas emerging from the LSC wave into a variable-pressure, converging streamtube, still including all the above-mentioned physical processes. The results show very high temperatures in LSC waves which absorb all the laser energy, and high radiative losses.
Rigorous results for the minimal speed of Kolmogorov-Petrovskii-Piscounov monotonic fronts with a cutoffa)

NASA Astrophysics Data System (ADS)

Benguria, Rafael D.; Depassier, M. Cristina; Loss, Michael

2012-12-01

We study the effect of a cutoff on the speed of pulled fronts of the one-dimensional reaction diffusion equation. To accomplish this, we first use variational techniques to prove the existence of a heteroclinic orbit in phase space for traveling wave solutions of the corresponding reaction diffusion equation under conditions that include discontinuous reaction profiles. This existence result allows us to prove rigorous upper and lower bounds on the minimal speed of monotonic fronts in terms of the cut-off parameter ɛ. From these bounds we estimate the range of validity of the Brunet-Derrida formula for a general class of reaction terms.
An Euler-Lagrange method considering bubble radial dynamics for modeling sonochemical reactors.

PubMed

Jamshidi, Rashid; Brenner, Gunther

2014-01-01

Unsteady numerical computations are performed to investigate the flow field, wave propagation and the structure of bubbles in sonochemical reactors. The turbulent flow field is simulated using a two-equation Reynolds-Averaged Navier-Stokes (RANS) model. The distribution of the acoustic pressure is solved based on the Helmholtz equation using a finite volume method (FVM). The radial dynamics of a single bubble are considered by applying the Keller-Miksis equation to consider the compressibility of the liquid to the first order of acoustical Mach number. To investigate the structure of bubbles, a one-way coupling Euler-Lagrange approach is used to simulate the bulk medium and the bubbles as the dispersed phase. Drag, gravity, buoyancy, added mass, volume change and first Bjerknes forces are considered and their orders of magnitude are compared. To verify the implemented numerical algorithms, results for one- and two-dimensional simplified test cases are compared with analytical solutions. The results show good agreement with experimental results for the relationship between the acoustic pressure amplitude and the volume fraction of the bubbles. The two-dimensional axi-symmetric results are in good agreement with experimentally observed structure of bubbles close to sonotrode. Copyright © 2013 Elsevier B.V. All rights reserved.
Three-dimensional modelling of thin liquid films over spinning disks

NASA Astrophysics Data System (ADS)

Zhao, Kun; Wray, Alex; Yang, Junfeng; Matar, Omar

2016-11-01

In this research the dynamics of a thin film flowing over a rapidly spinning, horizontal disk is considered. A set of non-axisymmetric evolution equations for the film thickness, radial and azimuthal flow rates are derived using a boundary-layer approximation in conjunction with the Karman-Polhausen approximation for the velocity distribution in the film. These highly nonlinear partial differential equations are then solved numerically in order to reveal the formation of two and three-dimensional large-amplitude waves that travel from the disk inlet to its periphery. The spatio-temporal profile of film thickness provides us with visualization of flow structures over the entire disk and by varying system parameters(volumetric flow rate of fluid and rotational speed of disk) different wave patterns can be observed, including spiral, concentric, smooth waves and wave break-up in exceptional conditions. Similar types of waves can be found by experimentalists in literature and CFD simulation and our results show good agreement with both experimental and CFD results. Furthermore, the semi-parabolic velocity profile assumed in our model under the waves is directly compared with CFD data in various flow regimes in order to validate our model. EPSRC UK Programme Grant EP/K003976/1.
Conceptual Foundations of Soliton Versus Particle Dualities Toward a Topological Model for Matter

NASA Astrophysics Data System (ADS)

Kouneiher, Joseph

2016-06-01

The idea that fermions could be solitons was actually confirmed in theoretical models in 1975 in the case when the space-time is two-dimensional and with the sine-Gordon model. More precisely S. Coleman showed that two different classical models end up describing the same fermions particle, when the quantum theory is constructed. But in one model the fermion is a quantum excitation of the field and in the other model the particle is a soliton. Hence both points of view can be reconciliated.The principal aim in this paper is to exhibit a solutions of topological type for the fermions in the wave zone, where the equations of motion are non-linear field equations, i.e. using a model generalizing sine- Gordon model to four dimensions, and describe the solutions for linear and circular polarized waves. In other words, the paper treat fermions as topological excitations of a bosonic field.

Effects of bleed-hole geometry and plenum pressure on three-dimensional shock-wave/boundary-layer/bleed interactions

NASA Technical Reports Server (NTRS)

Chyu, Wei J.; Rimlinger, Mark J.; Shih, Tom I.-P.

1993-01-01

A numerical study was performed to investigate 3D shock-wave/boundary-layer interactions on a flat plate with bleed through one or more circular holes that vent into a plenum. This study was focused on how bleed-hole geometry and pressure ratio across bleed holes affect the bleed rate and the physics of the flow in the vicinity of the holes. The aspects of the bleed-hole geometry investigated include angle of bleed hole and the number of bleed holes. The plenum/freestream pressure ratios investigated range from 0.3 to 1.7. This study is based on the ensemble-averaged, 'full compressible' Navier-Stokes (N-S) equations closed by the Baldwin-Lomax algebraic turbulence model. Solutions to the ensemble-averaged N-S equations were obtained by an implicit finite-volume method using the partially-split, two-factored algorithm of Steger on an overlapping Chimera grid.
One-dimensional nonlinear theory for rectangular helix traveling-wave tube

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fu, Chengfang, E-mail: fchffchf@126.com; Zhao, Bo; Yang, Yudong

A 1-D nonlinear theory of a rectangular helix traveling-wave tube (TWT) interacting with a ribbon beam is presented in this paper. The RF field is modeled by a transmission line equivalent circuit, the ribbon beam is divided into a sequence of thin rectangular electron discs with the same cross section as the beam, and the charges are assumed to be uniformly distributed over these discs. Then a method of computing the space-charge field by solving Green's Function in the Cartesian Coordinate-system is fully described. Nonlinear partial differential equations for field amplitudes and Lorentz force equations for particles are solved numericallymore » using the fourth-order Runge-Kutta technique. The tube's gain, output power, and efficiency of the above TWT are computed. The results show that increasing the cross section of the ribbon beam will improve a rectangular helix TWT's efficiency and reduce the saturated length.« less
Nonlinear Wave Propagation.

DTIC Science & Technology

1981-11-25

dimensional KdV ( Kadomtsev - Petviashvili ) equation [56). Furthermore it has been found that these newly found decaying mode solutions and usual soliton...Ablowitz and R. Haberman, Phys. Rev. Lett. 35, 1185, 1975. 26. S.V. !anakov, "On the Solutions of the Kadomtsev - Petviashvili equation ; Proc. of Symposium...accomplished relates to fluid mechanics, nonlinear optics, multidimensional solitons, Painlev e equations , long time asymptotic solu- tions, new
On the dynamics of exotic matter: Towards creation of Perpetuum Mobile of third kind

NASA Astrophysics Data System (ADS)

Ivanov, Pavel

2009-09-01

The one-dimensional dynamics of a classical ideal ‘exotic’ fluid with equation of state p=p(γ)<0 violating the weak energy condition is discussed. Under certain assumptions it is shown that the well-known Hwa-Bjorken exact solution of one-dimensional relativistic hydrodynamics is confined within the future/past light cone. It is also demonstrated that the total energy of such a solution is equal to zero and that there are regions within the light cone with negative (-) and positive (+) total energies. For certain equations of state there is a continuous energy transfer from the (-)-regions to the (+)-regions resulting in indefinite growth of energy in the (+)-regions with time, which may be interpreted as action of a specific ‘Perpetuum Mobile’ (Perpetuum Motion). It is speculated that if it is possible to construct a three-dimensional non-stationary flow of an exotic fluid having a finite negative value of energy such a situation would also occur. Such a flow may continuously transfer positive energy to gravitational waves, resulting in a runaway. It is conjectured that theories plagued by such solutions should be discarded as inherently unstable.
Control of extreme events in the bubbling onset of wave turbulence.

PubMed

Galuzio, P P; Viana, R L; Lopes, S R

2014-04-01

We show the existence of an intermittent transition from temporal chaos to turbulence in a spatially extended dynamical system, namely, the forced and damped one-dimensional nonlinear Schrödinger equation. For some values of the forcing parameter, the system dynamics intermittently switches between ordered states and turbulent states, which may be seen as extreme events in some contexts. In a Fourier phase space, the intermittency takes place due to the loss of transversal stability of unstable periodic orbits embedded in a low-dimensional subspace. We mapped these transversely unstable regions and perturbed the system in order to significantly reduce the occurrence of extreme events of turbulence.
Wave-induced response of a floating two-dimensional body with a moonpool

PubMed Central

Fredriksen, Arnt G.; Kristiansen, Trygve; Faltinsen, Odd M.

2015-01-01

Regular wave-induced behaviour of a floating stationary two-dimensional body with a moonpool is studied. The focus is on resonant piston-mode motion in the moonpool and rigid-body motions. Dedicated two-dimensional experiments have been performed. Two numerical hybrid methods, which have previously been applied to related problems, are further developed. Both numerical methods couple potential and viscous flow. The semi-nonlinear hybrid method uses linear free-surface and body-boundary conditions. The other one uses fully nonlinear free-surface and body-boundary conditions. The harmonic polynomial cell method solves the Laplace equation in the potential flow domain, while the finite volume method solves the Navier–Stokes equations in the viscous flow domain near the body. Results from the two codes are compared with the experimental data. The nonlinear hybrid method compares well with the data, while certain discrepancies are observed for the semi-nonlinear method. In particular, the roll motion is over-predicted by the semi-nonlinear hybrid method. Error sources in the semi-nonlinear hybrid method are discussed. The moonpool strongly affects heave motions in a frequency range around the piston-mode resonance frequency of the moonpool. No resonant water motions occur in the moonpool at the piston-mode resonance frequency. Instead large moonpool motions occur at a heave natural frequency associated with small damping near the piston-mode resonance frequency. PMID:25512594
Variational modelling of extreme waves through oblique interaction of solitary waves: application to Mach reflection

NASA Astrophysics Data System (ADS)

Gidel, Floriane; Bokhove, Onno; Kalogirou, Anna

2017-01-01

In this work, we model extreme waves that occur due to Mach reflection through the intersection of two obliquely incident solitary waves. For a given range of incident angles and amplitudes, the Mach stem wave grows linearly in length and amplitude, reaching up to 4 times the amplitude of the incident waves. A variational approach is used to derive the bidirectional Benney-Luke equations, an asymptotic equivalent of the three-dimensional potential-flow equations modelling water waves. This nonlinear and weakly dispersive model has the advantage of allowing wave propagation in two horizontal directions, which is not the case with the unidirectional Kadomtsev-Petviashvili (KP) equation used in most previous studies. A variational Galerkin finite-element method is applied to solve the system numerically in Firedrake with a second-order Störmer-Verlet temporal integration scheme, in order to obtain stable simulations that conserve the overall mass and energy of the system. Using this approach, we are able to get close to the 4-fold amplitude amplification predicted by Miles.
Kinetic theory of turbulence for parallel propagation revisited: Formal results

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yoon, Peter H., E-mail: yoonp@umd.edu

2015-08-15

In a recent paper, Gaelzer et al. [Phys. Plasmas 22, 032310 (2015)] revisited the second-order nonlinear kinetic theory for turbulence propagating in directions parallel/anti-parallel to the ambient magnetic field. The original work was according to Yoon and Fang [Phys. Plasmas 15, 122312 (2008)], but Gaelzer et al. noted that the terms pertaining to discrete-particle effects in Yoon and Fang's theory did not enjoy proper dimensionality. The purpose of Gaelzer et al. was to restore the dimensional consistency associated with such terms. However, Gaelzer et al. was concerned only with linear wave-particle interaction terms. The present paper completes the analysis bymore » considering the dimensional correction to nonlinear wave-particle interaction terms in the wave kinetic equation.« less
Existence regimes for shocks in inhomogeneous magneto-plasmas having entropy

NASA Astrophysics Data System (ADS)

Iqbal, Javed; Yaqub Khan, M.

2018-04-01

The finding of connection of plasma density and temperature with entropy gives an incitement to study different plasma models with respect to entropy. Nonlinear dissipative one- and two-dimensional structures (shocks) are investigated in nonuniform magnetized plasma with respect to entropy. The dissipation comes in the medium through ion-neutral collisions. The linear dispersion relation is derived. The Korteweg-deVries-Burgers and Kadomtsev-Petviashvili-Burgers equations are derived for nonlinear drift waves in 1-D and 2-D by employing the drift approximation. It is found that vd/u ( vd is the diamagnetic drift velocity and u is the velocity of nonlinear structure) plays a significant role in the shock formation. It is also found that entropy has a significant effect on the strength of shocks. It is noticed that v d/u determines the rarefactive and compressive nature of the shocks. It is observed that upper and lower bounds exist for the shock velocity. It is also observed that the existing regimes for both one- and two-dimensional shocks for kappa distributed electrons are different from shocks with Cairns distributed electrons. Both rarefactive and compressive shocks are found for the 1-D drift waves with kappa distributed electrons. Interestingly, it is noticed that entropy enhances the strength of one- and two-dimensional shocks.
Nonlinear Fourier algorithm applied to solving equations of gravitational gas dynamics

NASA Technical Reports Server (NTRS)

Kolosov, B. I.

1979-01-01

Two dimensional gas flow problems were reduced to an approximating system of common differential equations, which were solved by a standard procedure of the Runge-Kutta type. A theorem of the existence of stationary conical shock waves with the cone vertex in the gravitating center was proved.
Determination of Shear Wave Velocity in Offshore Terengganu for Ground Response Analysis

NASA Astrophysics Data System (ADS)

Mazlina, M.; Liew, M. S.; Adnan, A.; Harahap, I. S. H.; Hamid, N. A.

2018-04-01

Amount of vibration received in any location can be analysed by conducting ground response analysis. Even though there are three different methods available in this analysis, One Dimensional ground response analysis method has been widely used. Shear wave velocity is one of the key parameters in this analysis. A lot of correlations have been formulated to determine shear wave velocity with cone penetration test. In this study, correlations developed for Quaternary geological age have been selected. Six equations have been adopted comprise of all soil and soil type dependent correlations. Two platforms sites consist of clay and combination of clay and sand have been analysed. Shear velocity to be used in ground response analysis has been obtained. Results have been illustrated in graphs where shear velocity for each case has been plotted. In avoiding under or over predicting of shear wave velocity, the average of all soil and soil type dependent results will be used as final Vs value.
Spectral Indices in Simulations of Imbalanced Magnetohydrodynamic Turbulence

NASA Astrophysics Data System (ADS)

Ng, C. S.; Dennis, T. J.

2017-12-01

Three-dimensional (3D) simulations of imbalanced magnetohydrodynamic (MHD) turbulence based on reduced MHD equations have been performed. Alfven waves are launched from both ends of a long tube along the background uniform magnetic field so that turbulence develops due to collision between counter propagating Alfven waves in the interior region. Waves are launched randomly with specified correlation time Tc such that the length of the tube, L, is greater than (but of the same order of) VA Tc such that turbulence can fill most of the tube. While waves at both ends are launched with equal power, turbulence generated is imbalanced in general, with normalized cross-helicity gets close to -1 at one end and 1 at the other end. One fundamental unresolved problem in the theory of imbalanced turbulence is how turbulence spectral indices depend on the normalized cross-helicity. We will present turbulence spectral indices found in our latest simulations and discuss theoretical implications. This work is supported by a NASA grant NNX15AU61G.
On Gravitational Effects in the Schrödinger Equation

NASA Astrophysics Data System (ADS)

Pollock, M. D.

2014-04-01

The Schrödinger equation for a particle of rest mass and electrical charge interacting with a four-vector potential can be derived as the non-relativistic limit of the Klein-Gordon equation for the wave function , where and , or equivalently from the one-dimensional action for the corresponding point particle in the semi-classical approximation , both methods yielding the equation in Minkowski space-time , where and . We show that these two methods generally yield equations that differ in a curved background space-time , although they coincide when if is replaced by the effective mass in both the Klein-Gordon action and , allowing for non-minimal coupling to the gravitational field, where is the Ricci scalar and is a constant. In this case , where and , the correctness of the gravitational contribution to the potential having been verified to linear order in the thermal-neutron beam interferometry experiment due to Colella et al. Setting and regarding as the quasi-particle wave function, or order parameter, we obtain the generalization of the fundamental macroscopic Ginzburg-Landau equation of superconductivity to curved space-time. Conservation of probability and electrical current requires both electromagnetic gauge and space-time coordinate conditions to be imposed, which exemplifies the gravito-electromagnetic analogy, particularly in the stationary case, when div, where and . The quantum-cosmological Schrödinger (Wheeler-DeWitt) equation is also discussed in the -dimensional mini-superspace idealization, with particular regard to the vacuum potential and the characteristics of the ground state, assuming a gravitational Lagrangian which contains higher-derivative terms up to order . For the heterotic superstring theory , consists of an infinite series in , where is the Regge slope parameter, and in the perturbative approximation , is positive semi-definite for . The maximally symmetric ground state satisfying the field equations is Minkowski space for and anti-de Sitter space for.
DOE Office of Scientific and Technical Information (OSTI.GOV)

Lue Xing; Sun Kun; Wang Pan

In the framework of Bell-polynomial manipulations, under investigation hereby are three single-field bilinearizable equations: the (1+1)-dimensional shallow water wave model, Boiti-Leon-Manna-Pempinelli model, and (2+1)-dimensional Sawada-Kotera model. Based on the concept of scale invariance, a direct and unifying Bell-polynomial scheme is employed to achieve the Baecklund transformations and Lax pairs associated with those three soliton equations. Note that the Bell-polynomial expressions and Bell-polynomial-typed Baecklund transformations for those three soliton equations can be, respectively, cast into the bilinear equations and bilinear Baecklund transformations with symbolic computation. Consequently, it is also shown that the Bell-polynomial-typed Baecklund transformations can be linearized into the correspondingmore » Lax pairs.« less
Mechanical balance laws for fully nonlinear and weakly dispersive water waves

NASA Astrophysics Data System (ADS)

Kalisch, Henrik; Khorsand, Zahra; Mitsotakis, Dimitrios

2016-10-01

The Serre-Green-Naghdi system is a coupled, fully nonlinear system of dispersive evolution equations which approximates the full water wave problem. The system is known to describe accurately the wave motion at the surface of an incompressible inviscid fluid in the case when the fluid flow is irrotational and two-dimensional. The system is an extension of the well known shallow-water system to the situation where the waves are long, but not so long that dispersive effects can be neglected. In the current work, the focus is on deriving mass, momentum and energy densities and fluxes associated with the Serre-Green-Naghdi system. These quantities arise from imposing balance equations of the same asymptotic order as the evolution equations. In the case of an even bed, the conservation equations are satisfied exactly by the solutions of the Serre-Green-Naghdi system. The case of variable bathymetry is more complicated, with mass and momentum conservation satisfied exactly, and energy conservation satisfied only in a global sense. In all cases, the quantities found here reduce correctly to the corresponding counterparts in both the Boussinesq and the shallow-water scaling. One consequence of the present analysis is that the energy loss appearing in the shallow-water theory of undular bores is fully compensated by the emergence of oscillations behind the bore front. The situation is analyzed numerically by approximating solutions of the Serre-Green-Naghdi equations using a finite-element discretization coupled with an adaptive Runge-Kutta time integration scheme, and it is found that the energy is indeed conserved nearly to machine precision. As a second application, the shoaling of solitary waves on a plane beach is analyzed. It appears that the Serre-Green-Naghdi equations are capable of predicting both the shape of the free surface and the evolution of kinetic and potential energy with good accuracy in the early stages of shoaling.
Nonlinear modes of the tensor Dirac equation and CPT violation

NASA Technical Reports Server (NTRS)

Reifler, Frank J.; Morris, Randall D.

1993-01-01

Recently, it has been shown that Dirac's bispinor equation can be expressed, in an equivalent tensor form, as a constrained Yang-Mills equation in the limit of an infinitely large coupling constant. It was also shown that the free tensor Dirac equation is a completely integrable Hamiltonian system with Lie algebra type Poisson brackets, from which Fermi quantization can be derived directly without using bispinors. The Yang-Mills equation for a finite coupling constant is investigated. It is shown that the nonlinear Yang-Mills equation has exact plane wave solutions in one-to-one correspondence with the plane wave solutions of Dirac's bispinor equation. The theory of nonlinear dispersive waves is applied to establish the existence of wave packets. The CPT violation of these nonlinear wave packets, which could lead to new observable effects consistent with current experimental bounds, is investigated.
General multicomponent Yajima-Oikawa system: Painlevé analysis, soliton solutions, and energy-sharing collisions.

PubMed

Kanna, T; Sakkaravarthi, K; Tamilselvan, K

2013-12-01

We consider the multicomponent Yajima-Oikawa (YO) system and show that the two-component YO system can be derived in a physical setting of a three-coupled nonlinear Schrödinger (3-CNLS) type system by the asymptotic reduction method. The derivation is further generalized to the multicomponent case. This set of equations describes the dynamics of nonlinear resonant interaction between a one-dimensional long wave and multiple short waves. The Painlevé analysis of the general multicomponent YO system shows that the underlying set of evolution equations is integrable for arbitrary nonlinearity coefficients which will result in three different sets of equations corresponding to positive, negative, and mixed nonlinearity coefficients. We obtain the general bright N-soliton solution of the multicomponent YO system in the Gram determinant form by using Hirota's bilinearization method and explicitly analyze the one- and two-soliton solutions of the multicomponent YO system for the above mentioned three choices of nonlinearity coefficients. We also point out that the 3-CNLS system admits special asymptotic solitons of bright, dark, anti-dark, and gray types, when the long-wave-short-wave resonance takes place. The short-wave component solitons undergo two types of energy-sharing collisions. Specifically, in the two-component YO system, we demonstrate that two types of energy-sharing collisions-(i) energy switching with opposite nature for a particular soliton in two components and (ii) similar kind of energy switching for a given soliton in both components-result for two different choices of nonlinearity coefficients. The solitons appearing in the long-wave component always exhibit elastic collision whereas those of short-wave components exhibit standard elastic collisions only for a specific choice of parameters. We have also investigated the collision dynamics of asymptotic solitons in the original 3-CNLS system. For completeness, we explore the three-soliton interaction and demonstrate the pairwise nature of collisions and unravel the fascinating state restoration property.
Acoustic impact on the laminated plates placed between barriers

NASA Astrophysics Data System (ADS)

Paimushin, V. N.; Gazizullin, R. K.; Fedotenkov, G. V.

2016-11-01

On the basis of previously derived equations, analytical solutions are established on the forced vibrations of two-layer and three-layers rectangular plates hinged in an opening of absolutely rigid walls during the transmission of monoharmonic sound waves. It is assumed that the partition wall is situated between two absolutely rigid barriers, one of them by harmonic oscillation with a given displacements amplitude on the plate forms the incident sound wave, and the other is stationary and has a coating of deformable energy absorbing material with high damping properties. The behavior of acoustic environments in the spaces between the deformable plate and the barriers described by classical wave equation based on the ideal compressible fluid model. To describe the process of dynamic deformation of the energy absorbing coating of fixed barrier, two-dimensional equations of motion based on the use of models transversely soft layer are derived with a linear approximation of the displacement field in the thickness direction of the coating and taking into account the damping properties of the material and the hysteresis model for it. The influence of the physical and mechanical properties of the concerned mechanical system and the frequency of the incident sound wave on the parameters of its insulation properties of the plate, as well as on the parameters of the stress-strain state of the plate has been analyzed.
Direct Calculation of the Scattering Amplitude Without Partial Wave Decomposition. III; Inclusion of Correlation Effects

NASA Technical Reports Server (NTRS)

Shertzer, Janine; Temkin, Aaron

2007-01-01

In the first two papers in this series, we developed a method for studying electron-hydrogen scattering that does not use partial wave analysis. We constructed an ansatz for the wave function in both the static and static exchange approximations and calculated the full scattering amplitude. Here we go beyond the static exchange approximation, and include correlation in the wave function via a modified polarized orbital. This correlation function provides a significant improvement over the static exchange approximation: the resultant elastic scattering amplitudes are in very good agreement with fully converged partial wave calculations for electron-hydrogen scattering. A fully variational modification of this approach is discussed in the conclusion of the article Popular summary of Direct calculation of the scattering amplitude without partial wave expansion. III ....." by J. Shertzer and A. Temkin. In this paper we continue the development of In this paper we continue the development of a new approach to the way in which researchers have traditionally used to calculate the scattering cross section of (low-energy) electrons from atoms. The basic mathematical problem is to solve the Schroedinger Equation (SE) corresponding the above physical process. Traditionally it was always the case that the SE was reduced to a sequence of one-dimensional (ordinary) differential equations - called partial waves which were solved and from the solutions "phase shifts" were extracted, from which the scattering cross section was calculated.
Perturbed soliton excitations of Rao-dust Alfvén waves in magnetized dusty plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kavitha, L., E-mail: louiskavitha@yahoo.co.in; The Abdus Salam International Centre for Theoretical Physics, Trieste; Lavanya, C.

We investigate the propagation dynamics of the perturbed soliton excitations in a three component fully ionized dusty magnetoplasma consisting of electrons, ions, and heavy charged dust particulates. We derive the governing equation of motion for the two dimensional Rao-dust magnetohydrodynamic (R-D-MHD) wave by employing the inertialess electron equation of motion, inertial ion equation of motion, the continuity equations in a plasma with immobile charged dust grains, together with the Maxwell's equations, by assuming quasi neutrality and neglecting the displacement current in Ampere's law. Furthermore, we assume the massive dust particles are practically immobile since we are interested in timescales muchmore » shorter than the dusty plasma period, thereby neglecting any damping of the modes due to the grain charge fluctuations. We invoke the reductive perturbation method to represent the governing dynamics by a perturbed cubic nonlinear Schrödinger (pCNLS) equation. We solve the pCNLS, along the lines of Kodama-Ablowitz multiple scale nonlinear perturbation technique and explored the R-D-MHD waves as solitary wave excitations in a magnetized dusty plasma. Since Alfvén waves play an important role in energy transport in driving field-aligned currents, particle acceleration and heating, solar flares, and the solar wind, this representation of R-D-MHD waves as soliton excitations may have extensive applications to study the lower part of the earth's ionosphere.« less

A first-order statistical smoothing approximation for the coherent wave field in random porous random media

NASA Astrophysics Data System (ADS)

Müller, Tobias M.; Gurevich, Boris

2005-04-01

An important dissipation mechanism for waves in randomly inhomogeneous poroelastic media is the effect of wave-induced fluid flow. In the framework of Biot's theory of poroelasticity, this mechanism can be understood as scattering from fast into slow compressional waves. To describe this conversion scattering effect in poroelastic random media, the dynamic characteristics of the coherent wavefield using the theory of statistical wave propagation are analyzed. In particular, the method of statistical smoothing is applied to Biot's equations of poroelasticity. Within the accuracy of the first-order statistical smoothing an effective wave number of the coherent field, which accounts for the effect of wave-induced flow, is derived. This wave number is complex and involves an integral over the correlation function of the medium's fluctuations. It is shown that the known one-dimensional (1-D) result can be obtained as a special case of the present 3-D theory. The expression for the effective wave number allows to derive a model for elastic attenuation and dispersion due to wave-induced fluid flow. These wavefield attributes are analyzed in a companion paper. .
Solvability of the Initial Value Problem to the Isobe-Kakinuma Model for Water Waves

NASA Astrophysics Data System (ADS)

Nemoto, Ryo; Iguchi, Tatsuo

2017-09-01

We consider the initial value problem to the Isobe-Kakinuma model for water waves and the structure of the model. The Isobe-Kakinuma model is the Euler-Lagrange equations for an approximate Lagrangian which is derived from Luke's Lagrangian for water waves by approximating the velocity potential in the Lagrangian. The Isobe-Kakinuma model is a system of second order partial differential equations and is classified into a system of nonlinear dispersive equations. Since the hypersurface t=0 is characteristic for the Isobe-Kakinuma model, the initial data have to be restricted in an infinite dimensional manifold for the existence of the solution. Under this necessary condition and a sign condition, which corresponds to a generalized Rayleigh-Taylor sign condition for water waves, on the initial data, we show that the initial value problem is solvable locally in time in Sobolev spaces. We also discuss the linear dispersion relation to the model.
Assessment of the further improved (G'/G)-expansion method and the extended tanh-method in probing exact solutions of nonlinear PDEs.

PubMed

Akbar, M Ali; Ali, Norhashidah Hj Mohd; Mohyud-Din, Syed Tauseef

2013-01-01

The (G'/G)-expansion method is one of the most direct and effective method for obtaining exact solutions of nonlinear partial differential equations (PDEs). In the present article, we construct the exact traveling wave solutions of nonlinear evolution equations in mathematical physics via the (2 + 1)-dimensional breaking soliton equation by using two methods: namely, a further improved (G'/G)-expansion method, where G(ξ) satisfies the auxiliary ordinary differential equation (ODE) [G'(ξ)](2) = p G (2)(ξ) + q G (4)(ξ) + r G (6)(ξ); p, q and r are constants and the well known extended tanh-function method. We demonstrate, nevertheless some of the exact solutions bring out by these two methods are analogous, but they are not one and the same. It is worth mentioning that the first method has not been exercised anybody previously which gives further exact solutions than the second one. PACS numbers 02.30.Jr, 05.45.Yv, 02.30.Ik.
Numerical modelling of nonlinear full-wave acoustic propagation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Velasco-Segura, Roberto, E-mail: roberto.velasco@ccadet.unam.mx; Rendón, Pablo L., E-mail: pablo.rendon@ccadet.unam.mx

2015-10-28

The various model equations of nonlinear acoustics are arrived at by making assumptions which permit the observation of the interaction with propagation of either single or joint effects. We present here a form of the conservation equations of fluid dynamics which are deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A two-dimensional, finite-volume method using Roe’s linearisation has been implemented to obtain numerically the solution of the proposed equations. This code, which has been written for parallel execution on amore » GPU, can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from models of diagnostic and therapeutic HIFU, to parametric acoustic arrays and nonlinear propagation in acoustic waveguides. Examples related to these applications are shown and discussed.« less
DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Wenlong; Kevrekidis, P. G.

We have performed a systematic study quantifying the variation of solitary wave behavior from that of an ordered cloud resembling a “crystalline” configuration to that of a disordered state that can be characterized as a soliton “gas.” As our illustrative examples, we use both one-component, as well as two-component, one-dimensional atomic gases very close to zero temperature, where in the presence of repulsive interatomic interactions and of a parabolic trap, a cloud of dark (dark-bright) solitons can form in the one- (two-) component system. We corroborate our findings through three distinct types of approaches, namely a Gross-Pitaevskii type of partialmore » differential equation, particle-based ordinary differential equations describing the soliton dynamical system, and Monte Carlo simulations for the particle system. In addition, we define an “empirical” order parameter to characterize the order of the soliton lattices and study how this changes as a function of the strength of the “thermally” (i.e., kinetically) induced perturbations. As may be anticipated by the one-dimensional nature of our system, the transition from order to disorder is gradual without, apparently, a genuine phase transition ensuing in the intermediate regime.« less
Transitions from order to disorder in multiple dark and multiple dark-bright soliton atomic clouds.

PubMed

Wang, Wenlong; Kevrekidis, P G

2015-03-01

We have performed a systematic study quantifying the variation of solitary wave behavior from that of an ordered cloud resembling a "crystalline" configuration to that of a disordered state that can be characterized as a soliton "gas." As our illustrative examples, we use both one-component, as well as two-component, one-dimensional atomic gases very close to zero temperature, where in the presence of repulsive interatomic interactions and of a parabolic trap, a cloud of dark (dark-bright) solitons can form in the one- (two-) component system. We corroborate our findings through three distinct types of approaches, namely a Gross-Pitaevskii type of partial differential equation, particle-based ordinary differential equations describing the soliton dynamical system, and Monte Carlo simulations for the particle system. We define an "empirical" order parameter to characterize the order of the soliton lattices and study how this changes as a function of the strength of the "thermally" (i.e., kinetically) induced perturbations. As may be anticipated by the one-dimensional nature of our system, the transition from order to disorder is gradual without, apparently, a genuine phase transition ensuing in the intermediate regime.
Parabolic equation for nonlinear acoustic wave propagation in inhomogeneous moving media

NASA Astrophysics Data System (ADS)

Aver'yanov, M. V.; Khokhlova, V. A.; Sapozhnikov, O. A.; Blanc-Benon, Ph.; Cleveland, R. O.

2006-12-01

A new parabolic equation is derived to describe the propagation of nonlinear sound waves in inhomogeneous moving media. The equation accounts for diffraction, nonlinearity, absorption, scalar inhomogeneities (density and sound speed), and vectorial inhomogeneities (flow). A numerical algorithm employed earlier to solve the KZK equation is adapted to this more general case. A two-dimensional version of the algorithm is used to investigate the propagation of nonlinear periodic waves in media with random inhomogeneities. For the case of scalar inhomogeneities, including the case of a flow parallel to the wave propagation direction, a complex acoustic field structure with multiple caustics is obtained. Inclusion of the transverse component of vectorial random inhomogeneities has little effect on the acoustic field. However, when a uniform transverse flow is present, the field structure is shifted without changing its morphology. The impact of nonlinearity is twofold: it produces strong shock waves in focal regions, while, outside the caustics, it produces higher harmonics without any shocks. When the intensity is averaged across the beam propagating through a random medium, it evolves similarly to the intensity of a plane nonlinear wave, indicating that the transverse redistribution of acoustic energy gives no considerable contribution to nonlinear absorption.
Static and Monoharmonic Acoustic Impact on a Laminated Plate

NASA Astrophysics Data System (ADS)

Paimushin, V. N.; Gazizullin, R. K.

2017-07-01

A discrete layered damping model of a multilayer plate at small displacements and deformations, with account of the internal damping of layers according to the Thompson-Kelvin-Voight model, is presented. Based on the equations derived, an analytical solution to the static deformation problem for single-layer rectangular plate hinge-supported along its contour and subjected of a uniformly distributed pressure applied to one of its boundary planes is obtained. Its convergence to the three-dimensional solution is analyzed in relation to the dimension of mesh in the thickness direction of the plate. It is found that, for thin plates, the dimension of the problem formulated can be reduced on the basis of simplified hypotheses applied to each layer. An analytical solutions is also constructed for the forced vibrations of two- and three-layer rectangular plates hinged in the opening of an absolutely stiff dividing wall upon transmission of a monoharmonic sound wave through them. It was assumed that the dividing wall is situated between two absolutely stiff barriers; one of them, owing to the harmonic vibration with a given displacement amplitude of the plate, forms an incident sound wave, and the other is stationary and is coated by a energy-absorbing material with high damping properties. Behavior of the acoustic media in spaces between the deformable plate and the barriers is described by the classical wave equations based on the model of an ideal compressible fluid. To describe the process of dynamic deformation of the energy-absorbing coating of the fixed barrier, two-dimensional equations of motion are derived based on the model of a transversely soft layer, a linear approximation of displacement fields in the thickness direction of the coating, and the account of damping properties of its material by using the hysteresis model. The effect of physical and mechanical parameters of the mechanical system considered and of frequency of the incident sound wave on the parameter of its sound insulation, and the characteristics of stress-strain state of the plate is investigated
Numerical study of chemically reacting viscous flow relevant to pulsed detonation engines

NASA Astrophysics Data System (ADS)

Yi, Tae-Hyeong

2005-11-01

A computational fluid dynamics code for two-dimensional, multi-species, laminar Navier-Stokes equations is developed to simulate a recently proposed engine concept for a pulsed detonation based propulsion system and to investigate the feasibility of the engine of the concept. The governing equations that include transport phenomena such as viscosity, thermal conduction and diffusion are coupled with chemical reactions. The gas is assumed to be thermally perfect and in chemically non-equilibrium. The stiffness due to coupling the fluid dynamics and the chemical kinetics is properly taken care of by using a time-operator splitting method and a variable coefficient ordinary differential equation solver. A second-order Roe scheme with a minmod limiter is explicitly used for space descretization, while a second-order, two-step Runge-Kutta method is used for time descretization. In space integration, a finite volume method and a cell-centered scheme are employed. The first-order derivatives in the equations of transport properties are discretized by a central differencing with Green's theorem. Detailed chemistry is involved in this study. Two chemical reaction mechanisms are extracted from GRI-Mech, which are forty elementary reactions with thirteen species for a hydrogen-air mixture and twenty-seven reactions with eight species for a hydrogen-oxygen mixture. The code is ported to a high-performance parallel machine with Message-Passing Interface. Code validation is performed with chemical kinetic modeling for a stoichiometric hydrogen-air mixture, an one-dimensional detonation tube, a two-dimensional, inviscid flow over a wedge and a viscous flow over a flat plate. Detonation is initiated using a numerically simulated arc-ignition or shock-induced ignition system. Various freestream conditions are utilized to study the propagation of the detonation in the proposed concept of the engine. Investigation of the detonation propagation is performed for a pulsed detonation rocket and a supersonic combustion chamber. For a pulsed detonation rocket case, the detonation tube is embedded in a mixing chamber where an initiator is added to the main detonation chamber. Propagating detonation waves in a supersonic combustion chamber is investigated for one- and two-dimensional cases. The detonation initiated by an arc and a shock wave is studied in the inviscid and viscous flow, respectively. Various features including a detonation-shock interaction, a detonation diffraction, a base flow and a vortex are observed.
Octonacci photonic crystals with negative refraction index materials

NASA Astrophysics Data System (ADS)

Brandão, E. R.; Vasconcelos, M. S.; Anselmo, D. H. A. L.

2016-12-01

We investigate the optical transmission spectra for s-polarized (TE) and p-polarized (TM) waves in one-dimensional photonic quasicrystals on a quasiperiodic multilayer structure made up by alternate layers of SiO2 and metamaterials, organized by following the Octonacci sequence. Maxwell's equations and the transfer-matrix technique are used to derive the transmission spectra for the propagation of normally and obliquely incident optical fields. We assume Drude-Lorentz-type dispersive response for the dielectric permittivity and magnetic permeability of the metamaterials. For normally incident waves, we observe that the spectra does not have self-similar behavior or mirror symmetry and it also features the absence of optical band gap. Also for normally incident waves, we show regions of full transmittance when the incident angle θC = 0° in a particular frequency range.
Simulation of Wave-Current Interaction Using a Three-Dimensional Hydrodynamic Model Coupled With a Phase Averaged Wave Model

NASA Astrophysics Data System (ADS)

Marsooli, R.; Orton, P. M.; Georgas, N.; Blumberg, A. F.

2016-02-01

The Stevens Institute of Technology Estuarine and Coastal Ocean Model (sECOM) has been coupled with a more advanced surface wave model to simulate wave‒current interaction, and results have been validated in estuarine and nearshore waters. sECOM is a three‒dimensional, hydrostatic, free surface, primitive equation model. It solves the Navier‒Stokes equations and the conservation equations for temperature and salinity using a finite‒difference method on an Arakawa C‒grid with a terrain‒following (sigma) vertical coordinate and orthogonal curvilinear horizontal coordinate system. The model is coupled with the surface wave model developed by Mellor et al. (2008), which solves the spectral equation and takes into account depth and current refraction, and deep and shallow water. The wave model parameterizes the energy distribution in frequency space and the wave‒wave interaction process by using a specified spectrum shape. The coupled wave‒hydrodynamic model considers the wave‒current interaction through wave‒induced bottom stress, depth‒dependent radiation stress, and wave effects on wind‒induced surface stress. The model is validated using the data collected at a natural sandy beach at Duck, North Carolina, during the DUCK94 experiment. This test case reveals the capability of the model to simulate the wave‒current interaction in nearshore coastal systems. The model is further validated using the data collected in Jamaica Bay, a semi‒enclosed body of water located in New York City region. This test reveals the applicability of the model to estuarine systems. These validations of the model and comparisons to its prior wave model, the Great Lakes Environmental Research Laboratory (GLERL) wave model (Donelan 1977), are presented and discussed. ReferencesG.L. Mellor, M.A. Donelan, and L‒Y. Oey, 2008, A Surface Wave Model for Coupling with Numerical Ocean Circulation Models. J. Atmos. Oceanic Technol., 25, 1785‒1807.Donelan, M. A 1977. A simple numerical model for wave and wind stress application. Report, National Water Research Institute, Burlington, Ontario, Canada, 28 pp.
Simulation of propagation of the HPM in the low-pressure argon plasma

NASA Astrophysics Data System (ADS)

Zhigang, LI; Zhongcai, YUAN; Jiachun, WANG; Jiaming, SHI

2018-02-01

The propagation of the high-power microwave (HPM) with a frequency of 6 GHz in the low-pressure argon plasma was studied by the method of fluid approximation. The two-dimensional transmission model was built based on the wave equation, the electron drift-diffusion equations and the heavy species transport equations, which were solved by means of COMSOL Multiphysics software. The simulation results showed that the propagation characteristic of the HPM was closely related to the average electron density of the plasma. The attenuation of the transmitted wave increased nonlinearly with the electron density. Specifically, the growth of the attenuation slowed down as the electron density increased uniformly. In addition, the concrete transmission process of the HPM wave in the low-pressure argon plasma was given.
Group-kinetic theory and modeling of atmospheric turbulence

NASA Technical Reports Server (NTRS)

Tchen, C. M.

1989-01-01

A group kinetic method is developed for analyzing eddy transport properties and relaxation to equilibrium. The purpose is to derive the spectral structure of turbulence in incompressible and compressible media. Of particular interest are: direct and inverse cascade, boundary layer turbulence, Rossby wave turbulence, two phase turbulence; compressible turbulence, and soliton turbulence. Soliton turbulence can be found in large scale turbulence, turbulence connected with surface gravity waves and nonlinear propagation of acoustical and optical waves. By letting the pressure gradient represent the elementary interaction among fluid elements and by raising the Navier-Stokes equation to higher dimensionality, the master equation was obtained for the description of the microdynamical state of turbulence.
Time Reversal Mirrors and Cross Correlation Functions in Acoustic Wave Propagation

NASA Astrophysics Data System (ADS)

Fishman, Louis; Jonsson, B. Lars G.; de Hoop, Maarten V.

2009-03-01

In time reversal acoustics (TRA), a signal is recorded by an array of transducers, time reversed, and then retransmitted into the configuration. The retransmitted signal propagates back through the same medium and retrofocuses on the source that generated the signal. If the transducer array is a single, planar (flat) surface, then this configuration is referred to as a planar, one-sided, time reversal mirror (TRM). In signal processing, for example, in active-source seismic interferometry, the measurement of the wave field at two distinct receivers, generated by a common source, is considered. Cross correlating these two observations and integrating the result over the sources yield the cross correlation function (CCF). Adopting the TRM experiments as the basic starting point and identifying the kinematically correct correspondences, it is established that the associated CCF signal processing constructions follow in a specific, infinite recording time limit. This perspective also provides for a natural rationale for selecting the Green's function components in the TRM and CCF expressions. For a planar, one-sided, TRM experiment and the corresponding CCF signal processing construction, in a three-dimensional homogeneous medium, the exact expressions are explicitly calculated, and the connecting limiting relationship verified. Finally, the TRM and CCF results are understood in terms of the underlying, governing, two-way wave equation, its corresponding time reversal invariance (TRI) symmetry, and the absence of TRI symmetry in the associated one-way wave equations, highlighting the role played by the evanescent modal contributions.
Designing scattering-free isotropic index profiles using phase-amplitude equations

NASA Astrophysics Data System (ADS)

King, C. G.; Horsley, S. A. R.; Philbin, T. G.

2018-05-01

The Helmholtz equation can be written as coupled equations for the amplitude and phase. By considering spatial phase distributions corresponding to reflectionless wave propagation in the plane and solving for the amplitude in terms of this phase, we designed two-dimensional graded-index media which do not scatter light. We give two illustrative examples, the first of which is a periodic grating for which diffraction is completely suppressed at a single frequency at normal incidence to the periodicity. The second example is a medium which behaves as a "beam shifter" at a single frequency; acting to laterally shift a plane wave, or sufficiently wide beam, without reflection.
Spacetime representation of topological phononics

NASA Astrophysics Data System (ADS)

Deymier, Pierre A.; Runge, Keith; Lucas, Pierre; Vasseur, Jérôme O.

2018-05-01

Non-conventional topology of elastic waves arises from breaking symmetry of phononic structures either intrinsically through internal resonances or extrinsically via application of external stimuli. We develop a spacetime representation based on twistor theory of an intrinsic topological elastic structure composed of a harmonic chain attached to a rigid substrate. Elastic waves in this structure obey the Klein–Gordon and Dirac equations and possesses spinorial character. We demonstrate the mapping between straight line trajectories of these elastic waves in spacetime and the twistor complex space. The twistor representation of these Dirac phonons is related to their topological and fermion-like properties. The second topological phononic structure is an extrinsic structure composed of a one-dimensional elastic medium subjected to a moving superlattice. We report an analogy between the elastic behavior of this time-dependent superlattice, the scalar quantum field theory and general relativity of two types of exotic particle excitations, namely temporal Dirac phonons and temporal ghost (tachyonic) phonons. These phonons live on separate sides of a two-dimensional frequency space and are delimited by ghost lines reminiscent of the conventional light cone. Both phonon types exhibit spinorial amplitudes that can be measured by mapping the particle behavior to the band structure of elastic waves.
Dispersion of capillary waves in elliptical cylindrical jets

NASA Astrophysics Data System (ADS)

Amini, Ghobad; Dolatabadi, Ali

2011-11-01

In this work motion of a low speed liquid jet issuing from an elliptic orifice through the air is studied. Mathematical solution of viscous free-surface flow for this asymmetric geometry is simplified by using one-dimensional Cosserat (directed curve) equations which can be assumed as a low order form of Navier-Stokes equations for slender jets. Linear solution is performed and temporal and spatial dispersion equations are derived. Growth rate and phase speed of unstable and stable modes under various conditions are presented. The possibility of instability of asymmetric disturbances is studied too. With distance down the jet, major and minor axes are altered and finally jet breaks up due to capillary instability. The effect of jet velocity and viscosity and also orifice ellipticity on axis-switching and breakup is investigated.
Schrödinger–Langevin equation with quantum trajectories for photodissociation dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw

The Schrödinger–Langevin equation is integrated to study the wave packet dynamics of quantum systems subject to frictional effects by propagating an ensemble of quantum trajectories. The equations of motion for the complex action and quantum trajectories are derived from the Schrödinger–Langevin equation. The moving least squares approach is used to evaluate the spatial derivatives of the complex action required for the integration of the equations of motion. Computational results are presented and analyzed for the evolution of a free Gaussian wave packet, a two-dimensional barrier model, and the photodissociation dynamics of NOCl. The absorption spectrum of NOCl obtained from themore » Schrödinger–Langevin equation displays a redshift when frictional effects increase. This computational result agrees qualitatively with the experimental results in the solution-phase photochemistry of NOCl.« less
A method for the computational modeling of the physics of heart murmurs

NASA Astrophysics Data System (ADS)

Seo, Jung Hee; Bakhshaee, Hani; Garreau, Guillaume; Zhu, Chi; Andreou, Andreas; Thompson, William R.; Mittal, Rajat

2017-05-01

A computational method for direct simulation of the generation and propagation of blood flow induced sounds is proposed. This computational hemoacoustic method is based on the immersed boundary approach and employs high-order finite difference methods to resolve wave propagation and scattering accurately. The current method employs a two-step, one-way coupled approach for the sound generation and its propagation through the tissue. The blood flow is simulated by solving the incompressible Navier-Stokes equations using the sharp-interface immersed boundary method, and the equations corresponding to the generation and propagation of the three-dimensional elastic wave corresponding to the murmur are resolved with a high-order, immersed boundary based, finite-difference methods in the time-domain. The proposed method is applied to a model problem of aortic stenosis murmur and the simulation results are verified and validated by comparing with known solutions as well as experimental measurements. The murmur propagation in a realistic model of a human thorax is also simulated by using the computational method. The roles of hemodynamics and elastic wave propagation on the murmur are discussed based on the simulation results.
A diagnostic model to estimate winds and small-scale drag from Mars Observer PMIRR data

NASA Technical Reports Server (NTRS)

Barnes, J. R.

1993-01-01

Theoretical and modeling studies indicate that small-scale drag due to breaking gravity waves is likely to be of considerable importance for the circulation in the middle atmospheric region (approximately 40-100 km altitude) on Mars. Recent earth-based spectroscopic observations have provided evidence for the existence of circulation features, in particular, a warm winter polar region, associated with gravity wave drag. Since the Mars Observer PMIRR experiment will obtain temperature profiles extending from the surface up to about 80 km altitude, it will be extensively sampling middle atmospheric regions in which gravity wave drag may play a dominant role. Estimating the drag then becomes crucial to the estimation of the atmospheric winds from the PMIRR-observed temperatures. An interative diagnostic model based upon one previously developed and tested with earth satellite temperature data will be applied to the PMIRR measurements to produce estimates of the small-scale zonal drag and three-dimensional wind fields in the Mars middle atmosphere. This model is based on the primitive equations, and can allow for time dependence (the time tendencies used may be based upon those computed in a Fast Fourier Mapping procedure). The small-scale zonal drag is estimated as the residual in the zonal momentum equation; the horizontal winds having first been estimated from the meridional momentum equation and the continuity equation. The scheme estimates the vertical motions from the thermodynamic equation, and thus needs estimates of the diabatic heating based upon the observed temperatures. The latter will be generated using a radiative model. It is hoped that the diagnostic scheme will be able to produce good estimates of the zonal gravity wave drag in the Mars middle atmosphere, estimates that can then be used in other diagnostic or assimilation efforts, as well as more theoretical studies.

Analysis of vegetation effect on waves using a vertical 2-D RANS model

USDA-ARS?s Scientific Manuscript database

A vertical two-dimensional (2-D) model has been applied in the simulation of wave propagation through vegetated water bodies. The model is based on an existing model SOLA-VOF which solves the Reynolds-Averaged Navier-Stokes (RANS) equations with the finite difference method on a staggered rectangula...
A two-dimensional, time-dependent model of suspended sediment transport and bed reworking for continental shelves

USGS Publications Warehouse

Harris, C.K.; Wiberg, P.L.

2001-01-01

A two-dimensional, time-dependent solution to the transport equation is formulated to account for advection and diffusion of sediment suspended in the bottom boundary layer of continental shelves. This model utilizes a semi-implicit, upwind-differencing scheme to solve the advection-diffusion equation across a two-dimensional transect that is configured so that one dimension is the vertical, and the other is a horizontal dimension usually aligned perpendicular to shelf bathymetry. The model calculates suspended sediment concentration and flux; and requires as input wave properties, current velocities, sediment size distributions, and hydrodynamic sediment properties. From the calculated two-dimensional suspended sediment fluxes, we quantify the redistribution of shelf sediment, bed erosion, and deposition for several sediment sizes during resuspension events. The two-dimensional, time-dependent approach directly accounts for cross-shelf gradients in bed shear stress and sediment properties, as well as transport that occurs before steady-state suspended sediment concentrations have been attained. By including the vertical dimension in the calculations, we avoid depth-averaging suspended sediment concentrations and fluxes, and directly account for differences in transport rates and directions for fine and coarse sediment in the bottom boundary layer. A flux condition is used as the bottom boundary condition for the transport equation in order to capture time-dependence of the suspended sediment field. Model calculations demonstrate the significance of both time-dependent and spatial terms on transport and depositional patterns on continental shelves. ?? 2001 Elsevier Science Ltd. All rights reserved.
Bessel-Gauss resonator with spherical output mirror: geometrical- and wave-optics analysis.

PubMed

Gutiérrez-Vega, Julio C; Rodríguez-Masegosa, Rodolfo; Chávez-Cerda, Sabino

2003-11-01

A detailed study of the axicon-based Bessel-Gauss resonator with concave output coupler is presented. We employ a technique to convert the Huygens-Fresnel integral self-consistency equation into a matrix equation and then find the eigenvalues and the eigenfields of the resonator at one time. A paraxial ray analysis is performed to find the self-consistency condition to have stable periodic ray trajectories after one or two round trips. The fast-Fourier-transform-based Fox and Li algorithm is applied to describe the three-dimensional intracavity field distribution. Special attention was directed to the dependence of the output transverse profiles, the losses, and the modal-frequency changes on the curvature of the output coupler and the cavity length. The propagation of the output beam is discussed.
Spatially Extended Relativistic Particles Out of Traveling Front Solutions of Sine-Gordon Equation in (1+2) Dimensions

PubMed Central

Zarmi, Yair

2016-01-01

Slower-than-light multi-front solutions of the Sine-Gordon in (1+2) dimensions, constructed through the Hirota algorithm, are mapped onto spatially localized structures, which emulate free, spatially extended, massive relativistic particles. A localized structure is an image of the junctions at which the fronts intersect. It propagates together with the multi-front solution at the velocity of the latter. The profile of the localized structure obeys the linear wave equation in (1+2) dimensions, to which a term that represents interaction with a slower-than-light, Sine-Gordon-multi-front solution has been added. This result can be also formulated in terms of a (1+2)-dimensional Lagrangian system, in which the Sine-Gordon and wave equations are coupled. Expanding the Euler-Lagrange equations in powers of the coupling constant, the zero-order part of the solution reproduces the (1+2)-dimensional Sine-Gordon fronts. The first-order part is the spatially localized structure. PACS: 02.30.Ik, 03.65.Pm, 05.45.Yv, 02.30.Ik. PMID:26930077
Advances in Quantum Trajectory Approaches to Dynamics

NASA Astrophysics Data System (ADS)

Askar, Attila

2001-03-01

The quantum fluid dynamics (QFD) formulation is based on the separation of the amplitude and phase of the complex wave function in Schrodinger's equation. The approach leads to conservation laws for an equivalent "gas continuum". The Lagrangian [1] representation corresponds to following the particles of the fluid continuum, i. e. calculating "quantum trajectories". The Eulerian [2] representation on the other hand, amounts to observing the dynamics of the gas continuum at the points of a fixed coordinate frame. The combination of several factors leads to a most encouraging computational efficiency. QFD enables the numerical analysis to deal with near monotonic amplitude and phase functions. The Lagrangian description concentrates the computation effort to regions of highest probability as an optimal adaptive grid. The Eulerian representation allows the study of multi-coordinate problems as a set of one-dimensional problems within an alternating direction methodology. An explicit time integrator limits the increase in computational effort with the number of discrete points to linear. Discretization of the space via local finite elements [1,2] and global radial functions [3] will be discussed. Applications include wave packets in four-dimensional quadratic potentials and two coordinate photo-dissociation problems for NOCl and NO2. [1] "Quantum fluid dynamics (QFD) in the Lagrangian representation with applications to photo-dissociation problems", F. Sales, A. Askar and H. A. Rabitz, J. Chem. Phys. 11, 2423 (1999) [2] "Multidimensional wave-packet dynamics within the fluid dynamical formulation of the Schrodinger equation", B. Dey, A. Askar and H. A. Rabitz, J. Chem. Phys. 109, 8770 (1998) [3] "Solution of the quantum fluid dynamics equations with radial basis function interpolation", Xu-Guang Hu, Tak-San Ho, H. A. Rabitz and A. Askar, Phys. Rev. E. 61, 5967 (2000)
Application of fast Fourier transforms to the direct solution of a class of two-dimensional separable elliptic equations on the sphere

NASA Technical Reports Server (NTRS)

Moorthi, Shrinivas; Higgins, R. W.

1993-01-01

An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.
On the metal-insulator-transition in vanadium dioxide

NASA Astrophysics Data System (ADS)

Jovaini, Azita; Fujita, Shigeji; Godoy, Salvador; Suzuki, Akira

2012-02-01

Vanadium dioxide (VO2) undergoes a metal-insulator transition (MIT) at 340 K with the structural change from tetragonal to monoclinic crystal. The conductivity σ drops at MIT by four orders of magnitude. The low temperature monoclinic phase is known to have a lower ground-state energy. The existence of the k-vector k is prerequisite for the conduction since the k appears in the semiclassical equation of motion for the conduction electron (wave packet). The tetragonal (VO2)3 unit is periodic along the crystal's x-, y-, and z-axes, and hence there is a three-dimensional k-vector. There is a one-dimensional k for a monoclinic crystal. We believe this difference in the dimensionality of the k-vector is the cause of the conductivity drop.
The existence of minimum speed of traveling wave solutions to a non-KPP isothermal diffusion system

NASA Astrophysics Data System (ADS)

Chen, Xinfu; Liu, Guirong; Qi, Yuanwei

2017-08-01

The reaction-diffusion system at =axx - abn ,bt = Dbxx + abn, where n ≥ 1 and D > 0, arises from many real-world chemical reactions. Whereas n = 1 is the KPP type nonlinearity, which is much studied and very important results obtained in literature not only in one dimensional spatial domains, but also multi-dimensional spaces, but n > 1 proves to be much harder. One of the interesting features of the system is the existence of traveling wave solutions. In particular, for the traveling wave solution a (x , t) = a (x - vt), b (x , t) = b (x - vt), where v > 0, if we fix lim x → - ∞ ⁡ (a , b) = (0 , 1) it was proved by many authors with different bounds v* (n , D) > 0 such that a traveling wave solution exists for any v ≥v* when n > 1. For the latest progress, see [7]. That is, the traveling wave problem exhibits the mono-stable phenomenon for traveling wave of scalar equation ut =uxx + f (u) with f (0) = f (1) = 0, f (u) > 0 in (0 , 1) and, u = 0 is unstable and u = 1 is stable. A natural and significant question is whether, like the scalar case, there exists a minimum speed. That is, whether there exists a minimum speed vmin > 0 such that traveling wave solution of speed v exists iff v ≥vmin? This is an open question, in spite of many works on traveling wave of the system in last thirty years. This is duo to the reason, unlike the KPP case, the minimum speed cannot be obtained through linear analysis at equilibrium points (a , b) = (0 , 1) and (a , b) = (1 , 0). In this work, we give an affirmative answer to this question.
Time-dependent calculations of transfer ionization by fast proton-helium collision in one-dimensional kinematics

NASA Astrophysics Data System (ADS)

Serov, Vladislav V.; Kheifets, A. S.

2014-12-01

We analyze a transfer ionization (TI) reaction in the fast proton-helium collision H++He →H0+He2 ++ e- by solving a time-dependent Schrödinger equation (TDSE) under the classical projectile motion approximation in one-dimensional kinematics. In addition, we construct various time-independent analogs of our model using lowest-order perturbation theory in the form of the Born series. By comparing various aspects of the TDSE and the Born series calculations, we conclude that the recent discrepancies of experimental and theoretical data may be attributed to deficiency of the Born models used by other authors. We demonstrate that the correct Born series for TI should include the momentum-space overlap between the double-ionization amplitude and the wave function of the transferred electron.
Numerical studies of identification in nonlinear distributed parameter systems

NASA Technical Reports Server (NTRS)

Banks, H. T.; Lo, C. K.; Reich, Simeon; Rosen, I. G.

1989-01-01

An abstract approximation framework and convergence theory for the identification of first and second order nonlinear distributed parameter systems developed previously by the authors and reported on in detail elsewhere are summarized and discussed. The theory is based upon results for systems whose dynamics can be described by monotone operators in Hilbert space and an abstract approximation theorem for the resulting nonlinear evolution system. The application of the theory together with numerical evidence demonstrating the feasibility of the general approach are discussed in the context of the identification of a first order quasi-linear parabolic model for one dimensional heat conduction/mass transport and the identification of a nonlinear dissipation mechanism (i.e., damping) in a second order one dimensional wave equation. Computational and implementational considerations, in particular, with regard to supercomputing, are addressed.
Alfvén Turbulence Driven by High-Dimensional Interior Crisis in the Solar Wind

NASA Astrophysics Data System (ADS)

Chian, A. C.-L.; Rempel, E. L.; Macau, E. E. N.; Rosa, R. R.; Christiansen, F.

2003-09-01

Alfvén intermittent turbulence has been observed in the solar wind. It has been previously shown that the interplanetary Alfvén intermittent turbulence can appear due to a low-dimensional temporal chaos [1]. In this paper, we study the nonlinear spatiotemporal dynamics of Alfvén waves governed by the Kuramoto-Sivashinsky equation which describes the phase evolution of a large-amplitude Alfvén wave. We investigate the Alfvén turbulence driven by a high-dimensional interior crisis, which is a global bifurcation caused by the collision of a chaotic attractor with an unstable periodic orbit. This nonlinear phenomenon is analyzed using the numerical solutions of the model equation. The identification of the unstable periodic orbits and their invariant manifolds is fundamental for understanding the instability, chaos and turbulence in complex systems such as the solar wind plasma. The high-dimensional dynamical system approach to space environment turbulence developed in this paper can improve our interpretation of the origin and the nature of Alfvén turbulence observed in the solar wind.
Lie symmetry analysis, conservation laws, solitary and periodic waves for a coupled Burger equation

NASA Astrophysics Data System (ADS)

Xu, Mei-Juan; Tian, Shou-Fu; Tu, Jian-Min; Zhang, Tian-Tian

2017-01-01

Under investigation in this paper is a generalized (2 + 1)-dimensional coupled Burger equation with variable coefficients, which describes lots of nonlinear physical phenomena in geophysical fluid dynamics, condense matter physics and lattice dynamics. By employing the Lie group method, the symmetry reductions and exact explicit solutions are obtained, respectively. Based on a direct method, the conservations laws of the equation are also derived. Furthermore, by virtue of the Painlevé analysis, we successfully obtain the integrable condition on the variable coefficients, which plays an important role in further studying the integrability of the equation. Finally, its auto-Bäcklund transformation as well as some new analytic solutions including solitary and periodic waves are also presented via algebraic and differential manipulation.
Numerical applications of the advective-diffusive codes for the inner magnetosphere

NASA Astrophysics Data System (ADS)

Aseev, N. A.; Shprits, Y. Y.; Drozdov, A. Y.; Kellerman, A. C.

2016-11-01

In this study we present analytical solutions for convection and diffusion equations. We gather here the analytical solutions for the one-dimensional convection equation, the two-dimensional convection problem, and the one- and two-dimensional diffusion equations. Using obtained analytical solutions, we test the four-dimensional Versatile Electron Radiation Belt code (the VERB-4D code), which solves the modified Fokker-Planck equation with additional convection terms. The ninth-order upwind numerical scheme for the one-dimensional convection equation shows much more accurate results than the results obtained with the third-order scheme. The universal limiter eliminates unphysical oscillations generated by high-order linear upwind schemes. Decrease in the space step leads to convergence of a numerical solution of the two-dimensional diffusion equation with mixed terms to the analytical solution. We compare the results of the third- and ninth-order schemes applied to magnetospheric convection modeling. The results show significant differences in electron fluxes near geostationary orbit when different numerical schemes are used.
Solving the Helmholtz equation in conformal mapped ARROW structures using homotopy perturbation method.

PubMed

Reck, Kasper; Thomsen, Erik V; Hansen, Ole

2011-01-31

The scalar wave equation, or Helmholtz equation, describes within a certain approximation the electromagnetic field distribution in a given system. In this paper we show how to solve the Helmholtz equation in complex geometries using conformal mapping and the homotopy perturbation method. The solution of the mapped Helmholtz equation is found by solving an infinite series of Poisson equations using two dimensional Fourier series. The solution is entirely based on analytical expressions and is not mesh dependent. The analytical results are compared to a numerical (finite element method) solution.
Conjugate Compressible Fluid Flow and Heat Transfer in Ducts

NASA Technical Reports Server (NTRS)

Cross, M. F.

2011-01-01

A computational approach to modeling transient, compressible fluid flow with heat transfer in long, narrow ducts is presented. The primary application of the model is for analyzing fluid flow and heat transfer in solid propellant rocket motor nozzle joints during motor start-up, but the approach is relevant to a wide range of analyses involving rapid pressurization and filling of ducts. Fluid flow is modeled through solution of the spatially one-dimensional, transient Euler equations. Source terms are included in the governing equations to account for the effects of wall friction and heat transfer. The equation solver is fully-implicit, thus providing greater flexibility than an explicit solver. This approach allows for resolution of pressure wave effects on the flow as well as for fast calculation of the steady-state solution when a quasi-steady approach is sufficient. Solution of the one-dimensional Euler equations with source terms significantly reduces computational run times compared to general purpose computational fluid dynamics packages solving the Navier-Stokes equations with resolved boundary layers. In addition, conjugate heat transfer is more readily implemented using the approach described in this paper than with most general purpose computational fluid dynamics packages. The compressible flow code has been integrated with a transient heat transfer solver to analyze heat transfer between the fluid and surrounding structure. Conjugate fluid flow and heat transfer solutions are presented. The author is unaware of any previous work available in the open literature which uses the same approach described in this paper.
First and second sound in a two-dimensional harmonically trapped Bose gas across the Berezinskii–Kosterlitz–Thouless transition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Xia-Ji, E-mail: xiajiliu@swin.edu.au; Hu, Hui, E-mail: hhu@swin.edu.au

2014-12-15

We theoretically investigate first and second sound of a two-dimensional (2D) atomic Bose gas in harmonic traps by solving Landau’s two-fluid hydrodynamic equations. For an isotropic trap, we find that first and second sound modes become degenerate at certain temperatures and exhibit typical avoided crossings in mode frequencies. At these temperatures, second sound has significant density fluctuation due to its hybridization with first sound and has a divergent mode frequency towards the Berezinskii–Kosterlitz–Thouless (BKT) transition. For a highly anisotropic trap, we derive the simplified one-dimensional hydrodynamic equations and discuss the sound-wave propagation along the weakly confined direction. Due to themore » universal jump of the superfluid density inherent to the BKT transition, we show that the first sound velocity exhibits a kink across the transition. These predictions might be readily examined in current experimental setups for 2D dilute Bose gases with a sufficiently large number of atoms, where the finite-size effect due to harmonic traps is relatively weak.« less
Dispersion relations with crossing symmetry for {pi}{pi}D- and F1-wave amplitudes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kaminski, R.

Results of implementation of dispersion relations with imposed crossing symmetry condition to description of {pi}{pi}D and F1 wave amplitudes are presented. We use relations with only one subtraction what leads to small uncertainties of results and to strong constraints for tested {pi}{pi} amplitudes. Presented equations are similar to those with one subtraction (so called GKPY equations) and to those with two subtractions (the Roy's equations) for the S and P waves. Numerical calculations are done with the S and P wave input amplitudes tested already with use of the Roy's and GKPY equations.
Super-stable Poissonian structures

NASA Astrophysics Data System (ADS)

Eliazar, Iddo

2012-10-01

In this paper we characterize classes of Poisson processes whose statistical structures are super-stable. We consider a flow generated by a one-dimensional ordinary differential equation, and an ensemble of particles ‘surfing’ the flow. The particles start from random initial positions, and are propagated along the flow by stochastic ‘wave processes’ with general statistics and general cross correlations. Setting the initial positions to be Poisson processes, we characterize the classes of Poisson processes that render the particles’ positions—at all times, and invariantly with respect to the wave processes—statistically identical to their initial positions. These Poisson processes are termed ‘super-stable’ and facilitate the generalization of the notion of stationary distributions far beyond the realm of Markov dynamics.
Electronic transport in disordered chains with saturable nonlinearity

NASA Astrophysics Data System (ADS)

dos Santos, J. L. L.; Nguyen, Ba Phi; de Moura, F. A. B. F.

2015-10-01

In this work we study numerically the dynamics of an initially localized wave packet in one-dimensional disordered chains with saturable nonlinearity. By using the generalized discrete nonlinear Schrödinger equation, we calculate two different physical quantities as a function of time, which are the participation number and the mean square displacement from the excitation site. From detailed numerical analysis, we find that the saturable nonlinearity can promote a sub-diffusive spreading of the wave packet even in the presence of diagonal disorder for a long time. In addition, we also investigate the effect of the saturated nonlinearity for initial times of the electronic evolution thus showing the possibility of mobile breather-like modes.
Exact closed-form solutions of a fully nonlinear asymptotic two-fluid model

NASA Astrophysics Data System (ADS)

Cheviakov, Alexei F.

2018-05-01

A fully nonlinear model of Choi and Camassa (1999) describing one-dimensional incompressible dynamics of two non-mixing fluids in a horizontal channel, under a shallow water approximation, is considered. An equivalence transformation is presented, leading to a special dimensionless form of the system, involving a single dimensionless constant physical parameter, as opposed to five parameters present in the original model. A first-order dimensionless ordinary differential equation describing traveling wave solutions is analyzed. Several multi-parameter families of physically meaningful exact closed-form solutions of the two-fluid model are derived, corresponding to periodic, solitary, and kink-type bidirectional traveling waves; specific examples are given, and properties of the exact solutions are analyzed.

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