A phase space approach to wave propagation with dispersion.

PubMed

Ben-Benjamin, Jonathan S; Cohen, Leon; Loughlin, Patrick J

2015-08-01

A phase space approximation method for linear dispersive wave propagation with arbitrary initial conditions is developed. The results expand on a previous approximation in terms of the Wigner distribution of a single mode. In contrast to this previously considered single-mode case, the approximation presented here is for the full wave and is obtained by a different approach. This solution requires one to obtain (i) the initial modal functions from the given initial wave, and (ii) the initial cross-Wigner distribution between different modal functions. The full wave is the sum of modal functions. The approximation is obtained for general linear wave equations by transforming the equations to phase space, and then solving in the new domain. It is shown that each modal function of the wave satisfies a Schrödinger-type equation where the equivalent "Hamiltonian" operator is the dispersion relation corresponding to the mode and where the wavenumber is replaced by the wavenumber operator. Application to the beam equation is considered to illustrate the approach.

Nonlinear and linear wave equations for propagation in media with frequency power law losses

NASA Astrophysics Data System (ADS)

Szabo, Thomas L.

2003-10-01

The Burgers, KZK, and Westervelt wave equations used for simulating wave propagation in nonlinear media are based on absorption that has a quadratic dependence on frequency. Unfortunately, most lossy media, such as tissue, follow a more general frequency power law. The authors first research involved measurements of loss and dispersion associated with a modification to Blackstock's solution to the linear thermoviscous wave equation [J. Acoust. Soc. Am. 41, 1312 (1967)]. A second paper by Blackstock [J. Acoust. Soc. Am. 77, 2050 (1985)] showed the loss term in the Burgers equation for plane waves could be modified for other known instances of loss. The authors' work eventually led to comprehensive time-domain convolutional operators that accounted for both dispersion and general frequency power law absorption [Szabo, J. Acoust. Soc. Am. 96, 491 (1994)]. Versions of appropriate loss terms were developed to extend the standard three nonlinear wave equations to these more general losses. Extensive experimental data has verified the predicted phase velocity dispersion for different power exponents for the linear case. Other groups are now working on methods suitable for solving wave equations numerically for these types of loss directly in the time domain for both linear and nonlinear media.

Low-frequency surface waves on semi-bounded magnetized quantum plasma

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

Moradi, Afshin, E-mail: a.moradi@kut.ac.ir

2016-08-15

The propagation of low-frequency electrostatic surface waves on the interface between a vacuum and an electron-ion quantum plasma is studied in the direction perpendicular to an external static magnetic field which is parallel to the interface. A new dispersion equation is derived by employing both the quantum magnetohydrodynamic and Poisson equations. It is shown that the dispersion equations for forward and backward-going surface waves are different from each other.

Dispersive shock waves in systems with nonlocal dispersion of Benjamin-Ono type

NASA Astrophysics Data System (ADS)

El, G. A.; Nguyen, L. T. K.; Smyth, N. F.

2018-04-01

We develop a general approach to the description of dispersive shock waves (DSWs) for a class of nonlinear wave equations with a nonlocal Benjamin-Ono type dispersion term involving the Hilbert transform. Integrability of the governing equation is not a pre-requisite for the application of this method which represents a modification of the DSW fitting method previously developed for dispersive-hydrodynamic systems of Korteweg-de Vries (KdV) type (i.e. reducible to the KdV equation in the weakly nonlinear, long wave, unidirectional approximation). The developed method is applied to the Calogero-Sutherland dispersive hydrodynamics for which the classification of all solution types arising from the Riemann step problem is constructed and the key physical parameters (DSW edge speeds, lead soliton amplitude, intermediate shelf level) of all but one solution type are obtained in terms of the initial step data. The analytical results are shown to be in excellent agreement with results of direct numerical simulations.

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.

Conservation laws and rogue waves for a higher-order nonlinear Schrödinger equation with variable coefficients in the inhomogeneous fiber

NASA Astrophysics Data System (ADS)

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

2017-07-01

Subpicosecond or femtosecond optical pulse propagation in the inhomogeneous fiber can be described by a higher-order nonlinear Schrödinger equation with variable coefficients, which is investigated in the paper. Via the Ablowitz-Kaup-Newell-Segur system and symbolic computation, the Lax pair and infinitely-many conservation laws are deduced. Based on the Lax pair and a modified Darboux transformation technique, the first- and second-order rogue wave solutions are constructed. Effects of the groupvelocity dispersion and third-order dispersion on the properties of the first- and second-order rouge waves are graphically presented and analyzed: The groupvelocity dispersion and third-order dispersion both affect the ranges and shapes of the first- and second-order rogue waves: The third-order dispersion can produce a skew angle of the first-order rogue wave and the skew angle rotates counterclockwise with the increase of the groupvelocity dispersion, when the groupvelocity dispersion and third-order dispersion are chosen as the constants; When the groupvelocity dispersion and third-order dispersion are taken as the functions of the propagation distance, the linear, X-shaped and parabolic trajectories of the rogue waves are obtained.

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.

Local-in-space blow-up criteria for a class of nonlinear dispersive wave equations

NASA Astrophysics Data System (ADS)

Novruzov, Emil

2017-11-01

This paper is concerned with blow-up phenomena for the nonlinear dispersive wave equation on the real line, ut -uxxt +[ f (u) ] x -[ f (u) ] xxx +[ g (u) + f″/(u) 2 ux2 ] x = 0 that includes the Camassa-Holm equation as well as the hyperelastic-rod wave equation (f (u) = ku2 / 2 and g (u) = (3 - k) u2 / 2) as special cases. We establish some a local-in-space blow-up criterion (i.e., a criterion involving only the properties of the data u0 in a neighborhood of a single point) simplifying and precising earlier blow-up criteria for this equation.

Transverse instability of solitary waves in the generalized kadomtsev-petviashvili equation

PubMed

Kataoka; Tsutahara; Negoro

2000-04-03

The linear stability of planar solitary waves with respect to long-wavelength transverse perturbations is studied in the framework of the generalized Kadomtsev-Petviashvili equation. It is newly discovered that for some nonlinearities in this family, the solitary waves could be transversely unstable even in a medium with negative dispersion. In the case of positive dispersion, they are found to be always unstable.

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.

Nonlinear Mechanisms for the Generation of Nearshore Wave Phenomena.

DTIC Science & Technology

1988-04-01

Kadomtsev - Petviashvili equation . Numerical solutions of this equation indicate that steady state is reached only if dispersion is negative; otherwise...leads to a forced Kadomtsev - Petviashvili equation . Numerical solutions of this equation indicate that steady state is reached only if dispersion is

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.

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.

Multiple and exact soliton solutions of the perturbed Korteweg-de Vries equation of long surface waves in a convective fluid via Painlevé analysis, factorization, and simplest equation methods.

PubMed

Selima, Ehab S; Yao, Xiaohua; Wazwaz, Abdul-Majid

2017-06-01

In this research, the surface waves of a horizontal fluid layer open to air under gravity field and vertical temperature gradient effects are studied. The governing equations of this model are reformulated and converted to a nonlinear evolution equation, the perturbed Korteweg-de Vries (pKdV) equation. We investigate the latter equation, which includes dispersion, diffusion, and instability effects, in order to examine the evolution of long surface waves in a convective fluid. Dispersion relation of the pKdV equation and its properties are discussed. The Painlevé analysis is applied not only to check the integrability of the pKdV equation but also to establish the Bäcklund transformation form. In addition, traveling wave solutions and a general form of the multiple-soliton solutions of the pKdV equation are obtained via Bäcklund transformation, the simplest equation method using Bernoulli, Riccati, and Burgers' equations as simplest equations, and the factorization method.

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).

Finite volume treatment of dispersion-relation-preserving and optimized prefactored compact schemes for wave propagation

NASA Astrophysics Data System (ADS)

Popescu, Mihaela; Shyy, Wei; Garbey, Marc

2005-12-01

In developing suitable numerical techniques for computational aero-acoustics, the dispersion-relation-preserving (DRP) scheme by Tam and co-workers and the optimized prefactored compact (OPC) scheme by Ashcroft and Zhang have shown desirable properties of reducing both dissipative and dispersive errors. These schemes, originally based on the finite difference, attempt to optimize the coefficients for better resolution of short waves with respect to the computational grid while maintaining pre-determined formal orders of accuracy. In the present study, finite volume formulations of both schemes are presented to better handle the nonlinearity and complex geometry encountered in many engineering applications. Linear and nonlinear wave equations, with and without viscous dissipation, have been adopted as the test problems. Highlighting the principal characteristics of the schemes and utilizing linear and nonlinear wave equations with different wavelengths as the test cases, the performance of these approaches is documented. For the linear wave equation, there is no major difference between the DRP and OPC schemes. For the nonlinear wave equations, the finite volume version of both DRP and OPC schemes offers substantially better solutions in regions of high gradient or discontinuity.

Lamb wave extraction of dispersion curves in micro/nano-plates using couple stress theories

NASA Astrophysics Data System (ADS)

Ghodrati, Behnam; Yaghootian, Amin; Ghanbar Zadeh, Afshin; Mohammad-Sedighi, Hamid

2018-01-01

In this paper, Lamb wave propagation in a homogeneous and isotropic non-classical micro/nano-plates is investigated. To consider the effect of material microstructure on the wave propagation, three size-dependent models namely indeterminate-, modified- and consistent couple stress theories are used to extract the dispersion equations. In the mentioned theories, a parameter called 'characteristic length' is used to consider the size of material microstructure in the governing equations. To generalize the parametric studies and examine the effect of thickness, propagation wavelength, and characteristic length on the behavior of miniature plate structures, the governing equations are nondimensionalized by defining appropriate dimensionless parameters. Then the dispersion curves for phase and group velocities are plotted in terms of a wide frequency-thickness range to study the lamb waves propagation considering microstructure effects in very high frequencies. According to the illustrated results, it was observed that the couple stress theories in the Cosserat type material predict more rigidity than the classical theory; so that in a plate with constant thickness, by increasing the thickness to characteristic length ratio, the results approach to the classical theory, and by reducing this ratio, wave propagation speed in the plate is significantly increased. In addition, it is demonstrated that for high-frequency Lamb waves, it converges to dispersive Rayleigh wave velocity.

On a hierarchy of nonlinearly dispersive generalized Korteweg - de Vries evolution equations

DOE PAGES

Christov, Ivan C.

2015-08-20

We propose a hierarchy of nonlinearly dispersive generalized Korteweg–de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. Two recent nonlinear evolution equations describing wave propagation in certain generalized continua with an inherent material length scale are members of the proposed hierarchy. Like KdV, the equations from the proposed hierarchy possess Hamiltonian structure. Unlike KdV, the solutions to these equations can be compact (i.e., they vanish outside of some open interval) and, in addition, peaked. Implicit solutions for these peaked, compact traveling waves (“peakompactons”) are presented.

Applications of the ETEM for obtaining optical soliton solutions for the Lakshmanan-Porsezian-Daniel model

NASA Astrophysics Data System (ADS)

Manafian, Jalil; Foroutan, Mohammadreza; Guzali, Aref

2017-11-01

This paper examines the effectiveness of an integration scheme which is called the extended trial equation method (ETEM) for solving a well-known nonlinear equation of partial differential equations (PDEs). In this respect, the Lakshmanan-Porsezian-Daniel (LPD) equation with Kerr and power laws of nonlinearity which describes higher-order dispersion, full nonlinearity and spatiotemporal dispersion is considered, and as an achievement, a series of exact travelling-wave solutions for the aforementioned equation is formally extracted. Explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of LPD equation. The movement of obtained solutions is shown graphically, which helps to understand the physical phenomena of this optical soliton equation. Many other such types of nonlinear equations arising in basic fabric of communications network technology and nonlinear optics can also be solved by this method.

Bright, dark and W-shaped solitons with extended nonlinear Schrödinger's equation for odd and even higher-order terms

NASA Astrophysics Data System (ADS)

Bendahmane, Issam; Triki, Houria; Biswas, Anjan; Saleh Alshomrani, Ali; Zhou, Qin; Moshokoa, Seithuti P.; Belic, Milivoj

2018-02-01

We present solitary wave solutions of an extended nonlinear Schrödinger equation with higher-order odd (third-order) and even (fourth-order) terms by using an ansatz method. The including high-order dispersion terms have significant physical applications in fiber optics, the Heisenberg spin chain, and ocean waves. Exact envelope solutions comprise bright, dark and W-shaped solitary waves, illustrating the potentially rich set of solitary wave solutions of the extended model. Furthermore, we investigate the properties of these solitary waves in nonlinear and dispersive media. Moreover, specific constraints on the system parameters for the existence of these structures are discussed exactly. The results show that the higher-order dispersion and nonlinear effects play a crucial role for the formation and properties of propagating waves.

Nonlocal Symmetries, Conservation Laws and Interaction Solutions of the Generalised Dispersive Modified Benjamin-Bona-Mahony Equation

NASA Astrophysics Data System (ADS)

Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Wang, Xiu-Bin; Zhang, Tian-Tian

2018-05-01

We consider the generalised dispersive modified Benjamin-Bona-Mahony equation, which describes an approximation status for long surface wave existed in the non-linear dispersive media. By employing the truncated Painlevé expansion method, we derive its non-local symmetry and Bäcklund transformation. The non-local symmetry is localised by a new variable, which provides the corresponding non-local symmetry group and similarity reductions. Moreover, a direct method can be provided to construct a kind of finite symmetry transformation via the classic Lie point symmetry of the normal prolonged system. Finally, we find that the equation is a consistent Riccati expansion solvable system. With the help of the Jacobi elliptic function, we get its interaction solutions between solitary waves and cnoidal periodic waves.

Bifurcation of rupture path by linear and cubic damping force

NASA Astrophysics Data System (ADS)

Dennis L. C., C.; Chew X., Y.; Lee Y., C.

2014-06-01

Bifurcation of rupture path is studied for the effect of linear and cubic damping. Momentum equation with Rayleigh factor was transformed into ordinary differential form. Bernoulli differential equation was obtained and solved by the separation of variables. Analytical or exact solutions yielded the bifurcation was visible at imaginary part when the wave was non dispersive. For the dispersive wave, bifurcation of rupture path was invisible.

Preserving the Helmholtz dispersion relation: One-way acoustic wave propagation using matrix square roots

NASA Astrophysics Data System (ADS)

Keefe, Laurence

2016-11-01

Parabolized acoustic propagation in transversely inhomogeneous media is described by the operator update equation U (x , y , z + Δz) =eik0 (- 1 +√{ 1 + Z }) U (x , y , z) for evolution of the envelope of a wavetrain solution to the original Helmholtz equation. Here the operator, Z =∇T2 + (n2 - 1) , involves the transverse Laplacian and the refractive index distribution. Standard expansion techniques (on the assumption Z << 1)) produce pdes that approximate, to greater or lesser extent, the full dispersion relation of the original Helmholtz equation, except that none of them describe evanescent/damped waves without special modifications to the expansion coefficients. Alternatively, a discretization of both the envelope and the operator converts the operator update equation into a matrix multiply, and existing theorems on matrix functions demonstrate that the complete (discrete) Helmholtz dispersion relation, including evanescent/damped waves, is preserved by this discretization. Propagation-constant/damping-rates contour comparisons for the operator equation and various approximations demonstrate this point, and how poorly the lowest-order, textbook, parabolized equation describes propagation in lined ducts.

Finite Difference Modeling of Wave Progpagation in Acoustic TiltedTI Media

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

Zhang, Linbin; Rector III, James W.; Hoversten, G. Michael

2005-03-21

Based on an acoustic assumption (shear wave velocity is zero) and a dispersion relation, we derive an acoustic wave equation for P-waves in tilted transversely isotropic (TTI) media (transversely isotropic media with a tilted symmetry axis). This equation has fewer parameters than an elastic wave equation in TTI media and yields an accurate description of P-wave traveltimes and spreading-related attenuation. Our TTI acoustic wave equation is a fourth-order equation in time and space. We demonstrate that the acoustic approximation allows the presence of shear waves in the solution. The substantial differences in traveltime and amplitude between data created using VTImore » and TTI assumptions is illustrated in examples.« less

Symmetries of the TDNLS equations for weakly nonlinear dispersive MHD waves

NASA Technical Reports Server (NTRS)

Webb, G. M.; Brio, M.; Zank, G. P.

1995-01-01

In this paper we consider the symmetries and conservation laws for the TDNLS equations derived by Hada (1993) and Brio, Hunter and Johnson, to describe the propagation of weakly nonlinear dispersive MHD waves in beta approximately 1 plasmas. The equations describe the interaction of the Alfven and magnetoacoustic modes near the triple umbilic, where the fast magnetosonic, slow magnetosonic and Alfven speeds coincide and a(g)(exp 2) = V(A)(exp 2) where a(g) is the gas sound speed and V(A) is the Alfven speed. We discuss Lagrangian and Hamiltonian formulations, and similarity solutions for the equations.

Power-law spatial dispersion from fractional Liouville equation

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

Tarasov, Vasily E.

2013-10-15

A microscopic model in the framework of fractional kinetics to describe spatial dispersion of power-law type is suggested. The Liouville equation with the Caputo fractional derivatives is used to obtain the power-law dependence of the absolute permittivity on the wave vector. The fractional differential equations for electrostatic potential in the media with power-law spatial dispersion are derived. The particular solutions of these equations for the electric potential of point charge in this media are considered.

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.

Dispersive optical soliton solutions for higher order nonlinear Sasa-Satsuma equation in mono mode fibers via new auxiliary equation method

NASA Astrophysics Data System (ADS)

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

2018-01-01

In this research, we apply new technique for higher order nonlinear Schrödinger equation which is representing the propagation of short light pulses in the monomode optical fibers and the evolution of slowly varying packets of quasi-monochromatic waves in weakly nonlinear media that have dispersion. Nonlinear Schrödinger equation is one of the basic model in fiber optics. We apply new auxiliary equation method for nonlinear Sasa-Satsuma equation to obtain a new optical forms of solitary traveling wave solutions. Exact and solitary traveling wave solutions are obtained in different kinds like trigonometric, hyperbolic, exponential, rational functions, …, etc. These forms of solutions that we represent in this research prove the superiority of our new technique on almost thirteen powerful methods. The main merits of this method over the other methods are that it gives more general solutions with some free parameters.

Generation of zonal magnetic fields by low-frequency dispersive electromagnetic waves in a nonuniform dusty magnetoplasma.

PubMed

Shukla, P K

2004-04-01

It is shown that zonal magnetic fields can be parametrically excited by low-frequency dispersive driftlike compressional electromagnetic (DDCEM) modes in a nonuniform dusty magnetoplasma. For this purpose, we derive a pair of coupled equations which exhibits the nonlinear coupling between DDCEM modes and zonal magnetic fields. The coupled mode equations are Fourier analyzed to derive a nonlinear dispersion relation. The latter depicts that zonal magnetic fields are nonlinearly generated at the expense of the low-frequency DDCEM wave energy. The relevance of our investigation to the transfer of energy from short scale DDCEM waves to long scale zonal magnetic field structures in dark molecular clouds is discussed.

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

An improvement of convergence of a dispersion-relation preserving method for the classical Boussinesq equation

NASA Astrophysics Data System (ADS)

Jang, T. S.

2018-03-01

A dispersion-relation preserving (DRP) method, as a semi-analytic iterative procedure, has been proposed by Jang (2017) for integrating the classical Boussinesq equation. It has been shown to be a powerful numerical procedure for simulating a nonlinear dispersive wave system because it preserves the dispersion-relation, however, there still exists a potential flaw, e.g., a restriction on nonlinear wave amplitude and a small region of convergence (ROC) and so on. To remedy the flaw, a new DRP method is proposed in this paper, aimed at improving convergence performance. The improved method is proved to have convergence properties and dispersion-relation preserving nature for small waves; of course, unique existence of the solutions is also proved. In addition, by a numerical experiment, the method is confirmed to be good at observing nonlinear wave phenomena such as moving solitary waves and their binary collision with different wave amplitudes. Especially, it presents a ROC (much) wider than that of the previous method by Jang (2017). Moreover, it gives the numerical simulation of a high (or large-amplitude) nonlinear dispersive wave. In fact, it is demonstrated to simulate a large-amplitude solitary wave and the collision of two solitary waves with large-amplitudes that we have failed to simulate with the previous method. Conclusively, it is worth noting that better convergence results are achieved compared to Jang (2017); i.e., they represent a major improvement in practice over the previous method.

Radiating dispersive shock waves in non-local optical media

PubMed Central

El, Gennady A.

2016-01-01

We consider the step Riemann problem for the system of equations describing the propagation of a coherent light beam in nematic liquid crystals, which is a general system describing nonlinear wave propagation in a number of different physical applications. While the equation governing the light beam is of defocusing nonlinear Schrödinger (NLS) equation type, the dispersive shock wave (DSW) generated from this initial condition has major differences from the standard DSW solution of the defocusing NLS equation. In particular, it is found that the DSW has positive polarity and generates resonant radiation which propagates ahead of it. Remarkably, the velocity of the lead soliton of the DSW is determined by the classical shock velocity. The solution for the radiative wavetrain is obtained using the Wentzel–Kramers–Brillouin approximation. It is shown that for sufficiently small initial jumps the nematic DSW is asymptotically governed by a Korteweg–de Vries equation with the fifth-order dispersion, which explicitly shows the resonance generating the radiation ahead of the DSW. The constructed asymptotic theory is shown to be in good agreement with the results of direct numerical simulations. PMID:27118911

The modulational instability for the TDNLS equations for weakly nonlinear dispersive MHD waves

NASA Technical Reports Server (NTRS)

Webb, G. M.; Brio, M.; Zank, G. P.

1995-01-01

In this paper we study the modulational instability for the TDNLS equations derived by Hada (1993) and Brio, Hunter, and Johnson to describe the propagation of weakly nonlinear dispersive MHD waves in beta approximately 1 plasmas. We employ Whitham's averaged Lagrangian method to study the modulational instability. This complements studies of the modulational instability by Hada (1993) and Hollweg (1994), who did not use the averaged Lagrangian approach.

Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves

NASA Astrophysics Data System (ADS)

El, G. A.; Khamis, E. G.; Tovbis, A.

2016-09-01

We propose a novel, analytically tractable, scenario of the rogue wave formation in the framework of the small-dispersion focusing nonlinear Schrödinger (NLS) equation with the initial condition in the form of a rectangular barrier (a ‘box’). We use the Whitham modulation theory combined with the nonlinear steepest descent for the semi-classical inverse scattering transform, to describe the evolution and interaction of two counter-propagating nonlinear wave trains—the dispersive dam break flows—generated in the NLS box problem. We show that the interaction dynamics results in the emergence of modulated large-amplitude quasi-periodic breather lattices whose amplitude profiles are closely approximated by the Akhmediev and Peregrine breathers within certain space-time domain. Our semi-classical analytical results are shown to be in excellent agreement with the results of direct numerical simulations of the small-dispersion focusing NLS equation.

Effect of small floating disks on the propagation of gravity waves

NASA Astrophysics Data System (ADS)

De Santi, F.; Olla, P.

2017-04-01

A dispersion relation for gravity waves in water covered by disk-like impurities embedded in a viscous matrix is derived. The macroscopic equations are obtained by ensemble-averaging the fluid equations at the disk scale in the asymptotic limit of long waves and low disk surface fraction. Various regimes are identified depending on the disk radii and the thickness and viscosity of the top layer. Semi-quantitative analysis in the close-packing regime suggests dramatic modification of the dynamics, with orders of magnitude increase in wave damping and wave dispersion. A simplified model working in this regime is proposed. Possible applications to wave propagation in an ice-covered ocean are discussed and comparison with field data is provided.

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

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.; Manafian, Jalil

2018-03-01

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

Simple equations guide high-frequency surface-wave investigation techniques

USGS Publications Warehouse

Xia, J.; Xu, Y.; Chen, C.; Kaufmann, R.D.; Luo, Y.

2006-01-01

We discuss five useful equations related to high-frequency surface-wave techniques and their implications in practice. These equations are theoretical results from published literature regarding source selection, data-acquisition parameters, resolution of a dispersion curve image in the frequency-velocity domain, and the cut-off frequency of high modes. The first equation suggests Rayleigh waves appear in the shortest offset when a source is located on the ground surface, which supports our observations that surface impact sources are the best source for surface-wave techniques. The second and third equations, based on the layered earth model, reveal a relationship between the optimal nearest offset in Rayleigh-wave data acquisition and seismic setting - the observed maximum and minimum phase velocities, and the maximum wavelength. Comparison among data acquired with different offsets at one test site confirms the better data were acquired with the suggested optimal nearest offset. The fourth equation illustrates that resolution of a dispersion curve image at a given frequency is directly proportional to the product of a length of a geophone array and the frequency. We used real-world data to verify the fourth equation. The last equation shows that the cut-off frequency of high modes of Love waves for a two-layer model is determined by shear-wave velocities and the thickness of the top layer. We applied this equation to Rayleigh waves and multi-layer models with the average velocity and obtained encouraging results. This equation not only endows with a criterion to distinguish high modes from numerical artifacts but also provides a straightforward means to resolve the depth to the half space of a layered earth model. ?? 2005 Elsevier Ltd. All rights reserved.

Effect of surface wave propagation in a four-layered oceanic crust model

NASA Astrophysics Data System (ADS)

Paul, Pasupati; Kundu, Santimoy; Mandal, Dinbandhu

2017-12-01

Dispersion of Rayleigh type surface wave propagation has been discussed in four-layered oceanic crust. It includes a sandy layer over a crystalline elastic half-space and over it there are two more layers—on the top inhomogeneous liquid layer and under it a liquid-saturated porous layer. Frequency equation is obtained in the form of determinant. The effects of the width of different layers as well as the inhomogeneity of liquid layer, sandiness of sandy layer on surface waves are depicted and shown graphically by considering all possible case of the particular model. Some special cases have been deduced, few special cases give the dispersion equation of Scholte wave and Stoneley wave, some of which have already been discussed elsewhere.

On solutions of the fifth-order dispersive equations with porous medium type non-linearity

NASA Astrophysics Data System (ADS)

Kocak, Huseyin; Pinar, Zehra

2018-07-01

In this work, we focus on obtaining the exact solutions of the fifth-order semi-linear and non-linear dispersive partial differential equations, which have the second-order diffusion-like (porous-type) non-linearity. The proposed equations were not studied in the literature in the sense of the exact solutions. We reveal solutions of the proposed equations using the classical Riccati equations method. The obtained exact solutions, which can play a key role to simulate non-linear waves in the medium with dispersion and diffusion, are illustrated and discussed in details.

Dark and grey compressional dispersive Alfven solitons in plasmas

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

Shukla, P. K.; Eliasson, B.; Stenflo, L.

2011-06-15

The amplitude modulation of compressional dispersive Alfven (CDA) waves in a low-{beta} plasma is considered. It is shown that the dynamics of modulated CDA waves is governed by a cubic nonlinear Schroedinger equation, which depicts the formation of a dark/grey envelope CDA soliton.

Mathematical Modeling of Torsional Surface Wave Propagation in a Non-Homogeneous Transverse Isotropic Elastic Solid Semi-Infinite Medium Under a Layer

NASA Astrophysics Data System (ADS)

Sethi, M.; Sharma, A.; Vasishth, A.

2017-05-01

The present paper deals with the mathematical modeling of the propagation of torsional surface waves in a non-homogeneous transverse isotropic elastic half-space under a rigid layer. Both rigidities and density of the half-space are assumed to vary inversely linearly with depth. Separation of variable method has been used to get the analytical solutions for the dispersion equation of the torsional surface waves. Also, the effects of nonhomogeneities on the phase velocity of torsional surface waves have been shown graphically. Also, dispersion equations have been derived for some particular cases, which are in complete agreement with some classical results.

On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation.

PubMed

Khusnutdinova, K R; Klein, C; Matveev, V B; Smirnov, A O

2013-03-01

There exist two versions of the Kadomtsev-Petviashvili (KP) equation, related to the Cartesian and cylindrical geometries of the waves. In this paper, we derive and study a new version, related to the elliptic cylindrical geometry. The derivation is given in the context of surface waves, but the derived equation is a universal integrable model applicable to generic weakly nonlinear weakly dispersive waves. We also show that there exist nontrivial transformations between all three versions of the KP equation associated with the physical problem formulation, and use them to obtain new classes of approximate solutions for water waves.

New Similarity Reductions and Compacton Solutions for Boussinesq-Like Equations with Fully Nonlinear Dispersion

NASA Astrophysics Data System (ADS)

Yan, Zhen-Ya

2001-10-01

In this paper, similarity reductions of Boussinesq-like equations with nonlinear dispersion (simply called B(m,n) equations) utt=(u^n)xx+(u^m)xxxx, which is a generalized model of Boussinesq equation utt=(u^2)xx+uxxxx and modified Bousinesq equation utt=(u^3)xx+uxxxx, are considered by using the direct reduction method. As a result, several new types of similarity reductions are found. Based on the reduction equations and some simple transformations, we obtain the solitary wave solutions and compacton solutions (which are solitary waves with the property that after colliding with other compacton solutions, they re-emerge with the same coherent shape) of B(1,n) equations and B(m,m) equations, respectively. The project supported by National Key Basic Research Development Project Program of China under Grant No. G1998030600 and Doctoral Foundation of China under Grant No. 98014119

Low-Dispersion Scheme for Nonlinear Acoustic Waves in Nonuniform Flow

NASA Technical Reports Server (NTRS)

Baysal, Oktay; Kaushik, Dinesh K.; Idres, Moumen

1997-01-01

The linear dispersion-relation-preserving scheme and its boundary conditions have been extended to the nonlinear Euler equations. This allowed computing, a nonuniform flowfield and a nonlinear acoustic wave propagation in such a medium, by the same scheme. By casting all the equations, boundary conditions, and the solution scheme in generalized curvilinear coordinates, the solutions were made possible for non-Cartesian domains and, for the better deployment of the grid points, nonuniform grid step sizes could be used. It has been tested for a number of simple initial-value and periodic-source problems. A simple demonstration of the difference between a linear and nonlinear propagation was conducted. The wall boundary condition, derived from the momentum equations and implemented through a pressure at a ghost point, and the radiation boundary condition, derived from the asymptotic solution to the Euler equations, have proven to be effective for the nonlinear equations and nonuniform flows. The nonreflective characteristic boundary conditions also have shown success but limited to the nonlinear waves in no mean flow, and failed for nonlinear waves in nonuniform flow.

The General Fishbone Like Dispersion Relation

NASA Astrophysics Data System (ADS)

Zonca, Fulvio

2015-12-01

The following sections are included: * Introduction * Motivation and outline * Fundamental equations * The collisionless gyrokinetic equation * Vorticity equation * Quasi-neutrality condition * Perpendicular Ampère's law * Studying collective modes in burning plasmas * Ideal plasma equilibrium in the low-β limit * Approximations for the energetic population * Characteristic frequencies of particle motions * Alfvén wave frequency and wavelength orderings * Applications of the general theoretical framework * The general fishbone like dispersion relation * Properties of the fishbone like dispersion relation * Derivation of the fishbone like dispersion relation * Special cases of the fishbone like dispersion relation * Toroidal Alfvén Eigenmodes (TAE) * Alfvén Cascades * Summary and discussions * Acknowledgments * References

Wave theory in rotating systems: Schrödinger equations bridge the gaps between the equatorial β-plane and the spherical earth

NASA Astrophysics Data System (ADS)

Paldor, N.

2017-12-01

The concise and elegant wave theory developed on the equatorial β-plane by Matsuno (1966, M66 hereafter) is based on the formulation of a Schrödinger equation associated with the governing Linear Rotating Shallow Water Equations (LRSWE). The theory yields explicit expressions for the dispersion relations and meridional amplitude structures of all zonally propagating waves - Rossby, Inertia-Gravity, Kelvin and Yanai. In contrast, the spherical wave theory of Longuet-Higgins (1968) is a collection of asymptotic expansions in many sub-ranges e.g. large, small (and even negative) Lamb Number; high and low frequency; low-latitudes, etc. that rests upon extensive numerical solutions of several Ordinary Differential Equations. The difference between the two theories is highlighted by their lengths. The essential elements of the former planar study are completely revealed in just 3-4 pages including the derivation of explicit formulae for the phase speeds and amplitude meridional structures. In comtrast, the latter spherical theory contains 97 pages and the results of the numerical calculations are summarized in 30 pages of tables filled with numerical values and about 31 figures, each of which containing many separate curves! In my talk I will re-visit the wave problem on a sphere by developing several Schrödinger equations that approximate the governing eigenvalue equation associated with zonally propagating waves. Each of the Schrödinger equations approximates the original second order Ordinary Differential Equation in a different range of the 3 parameters: Lamb-Number, frequency and zonal wavenumber. As in M66, each of the Schrödinger equations yields explicit expressions for the dispersion relations and meridional amplitude structure of Rossby and Inertia-Gravity waves. In addition, the analysis shows that Yanai wave exists on a sphere even tough the zonal velocity is regular everywhere there (in contrast to the β-plane where the zonal velocity is singular everywhere) and that Kelvin waves do not exist as a separate mode (but the eastward propagating n=0 Inertia-Gravity is nearly non-dispersive). References Longuet-Higgins, M. S. Phil. Trans. Roy. Soc. London; 262, 511-607; 1968 Matsuno, T.; J. Met. Soc. Japan. 44(1), 25-43; 1966

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.

A space-time discretization procedure for wave propagation problems

NASA Technical Reports Server (NTRS)

Davis, Sanford

1989-01-01

Higher order compact algorithms are developed for the numerical simulation of wave propagation by using the concept of a discrete dispersion relation. The dispersion relation is the imprint of any linear operator in space-time. The discrete dispersion relation is derived from the continuous dispersion relation by examining the process by which locally plane waves propagate through a chosen grid. The exponential structure of the discrete dispersion relation suggests an efficient splitting of convective and diffusive terms for dissipative waves. Fourth- and eighth-order convection schemes are examined that involve only three or five spatial grid points. These algorithms are subject to the same restrictions that govern the use of dispersion relations in the constructions of asymptotic expansions to nonlinear evolution equations. A new eighth-order scheme is developed that is exact for Courant numbers of 1, 2, 3, and 4. Examples are given of a pulse and step wave with a small amount of physical diffusion.

Nonlinear dispersive waves in repulsive lattices

NASA Astrophysics Data System (ADS)

Mehrem, A.; Jiménez, N.; Salmerón-Contreras, L. J.; García-Andrés, X.; García-Raffi, L. M.; Picó, R.; Sánchez-Morcillo, V. J.

2017-07-01

The propagation of nonlinear waves in a lattice of repelling particles is studied theoretically and experimentally. A simple experimental setup is proposed, consisting of an array of coupled magnetic dipoles. By driving harmonically the lattice at one boundary, we excite propagating waves and demonstrate different regimes of mode conversion into higher harmonics, strongly influenced by dispersion and discreteness. The phenomenon of acoustic dilatation of the chain is also predicted and discussed. The results are compared with the theoretical predictions of the α -Fermi-Pasta-Ulam equation, describing a chain of masses connected by nonlinear quadratic springs and numerical simulations. The results can be extrapolated to other systems described by this equation.

Photon polarizability and its effect on the dispersion of plasma waves

NASA Astrophysics Data System (ADS)

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

2017-04-01

High-frequency photons travelling in plasma exhibit a linear polarizability that can influence the dispersion of linear plasma waves. We present a detailed calculation of this effect for Langmuir waves as a characteristic example. Two alternative formulations are given. In the first formulation, we calculate the modified dispersion of Langmuir waves by solving the governing equations for the electron fluid, where the photon contribution enters as a ponderomotive force. In the second formulation, we provide a derivation based on the photon polarizability. Then, the calculation of ponderomotive forces is not needed, and the result is more general.

Photon polarizability and its effect on the dispersion of plasma waves

DOE PAGES

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

2017-03-06

High-frequency photons travelling in plasma exhibit a linear polarizability that can influence the dispersion of linear plasma waves. We present a detailed calculation of this effect for Langmuir waves as a characteristic example. Here, two alternative formulations are given. In the first formulation, we calculate the modified dispersion of Langmuir waves by solving the governing equations for the electron fluid, where the photon contribution enters as a ponderomotive force. In the second formulation, we provide a derivation based on the photon polarizability. Then, the calculation of ponderomotive forces is not needed, and the result is more general.

Influence of the dispersive and dissipative scales alpha and beta on the energy spectrum of the Navier-Stokes alphabeta equations.

PubMed

Chen, Xuemei; Fried, Eliot

2008-10-01

Lundgren's vortex model for the intermittent fine structure of high-Reynolds-number turbulence is applied to the Navier-Stokes alphabeta equations and specialized to the Navier-Stokes alpha equations. The Navier-Stokes alphabeta equations involve dispersive and dissipative length scales alpha and beta, respectively. Setting beta equal to alpha reduces the Navier-Stokes alphabeta equations to the Navier-Stokes alpha equations. For the Navier-Stokes alpha equations, the energy spectrum is found to obey Kolmogorov's -5/3 law in a range of wave numbers identical to that determined by Lundgren for the Navier-Stokes equations. For the Navier-Stokes alphabeta equations, Kolmogorov's -5/3 law is also recovered. However, granted that beta < alpha, the range of wave numbers for which this law holds is extended by a factor of alphabeta . This suggests that simulations based on the Navier-Stokes alphabeta equations may have the potential to resolve features smaller than those obtainable using the Navier-Stokes alpha equations.

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.

Undular bore theory for the Gardner equation

NASA Astrophysics Data System (ADS)

Kamchatnov, A. M.; Kuo, Y.-H.; Lin, T.-C.; Horng, T.-L.; Gou, S.-C.; Clift, R.; El, G. A.; Grimshaw, R. H. J.

2012-09-01

We develop modulation theory for undular bores (dispersive shock waves) in the framework of the Gardner, or extended Korteweg-de Vries (KdV), equation, which is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation, when effects of higher order nonlinearity become important. Using a reduced version of the finite-gap integration method we derive the Gardner-Whitham modulation system in a Riemann invariant form and show that it can be mapped onto the well-known modulation system for the Korteweg-de Vries equation. The transformation between the two counterpart modulation systems is, however, not invertible. As a result, the study of the resolution of an initial discontinuity for the Gardner equation reveals a rich phenomenology of solutions which, along with the KdV-type simple undular bores, include nonlinear trigonometric bores, solibores, rarefaction waves, and composite solutions representing various combinations of the above structures. We construct full parametric maps of such solutions for both signs of the cubic nonlinear term in the Gardner equation. Our classification is supported by numerical simulations.

Guided elastic waves in a pre-stressed compressible interlayer

PubMed

Sotiropoulos

2000-03-01

The propagation of guided elastic waves in a pre-stressed elastic compressible layer embedded in a different compressible material is examined. The waves propagate parallel to the planar layer interfaces as a superposed dynamic stress state on the statically pre-stressed layer and host material. The underlying stress condition in the two materials is characterized by equibiaxial in-plane deformations with common principal axes of strain, one of the axes being perpendicular to the layering. Both materials have arbitrary strain energy functions. The dispersion equation is derived in explicit form. Analysis of the dispersion equation reveals the propagation characteristics and their dependence on frequency, material parameters and stress parameters. Combinations of these parameters are also defined for which guided waves cannot propagate.

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.

Optical Kerr spatiotemporal dark extreme waves

NASA Astrophysics Data System (ADS)

Wabnitz, Stefan; Kodama, Yuji; Baronio, Fabio

2018-02-01

We study the existence and propagation of multidimensional dark non-diffractive and non-dispersive spatiotemporal optical wave-packets in nonlinear Kerr media. We report analytically and confirm numerically the properties of spatiotemporal dark lines, X solitary waves and lump solutions of the (2 + 1)D nonlinear Schr odinger equation (NLSE). Dark lines, X waves and lumps represent holes of light on a continuous wave background. These solitary waves are derived by exploiting the connection between the (2 + 1)D NLSE and a well-known equation of hydrodynamics, namely the (2+1)D Kadomtsev-Petviashvili (KP) equation. This finding opens a novel path for the excitation and control of spatiotemporal optical solitary and rogue waves, of hydrodynamic nature.

Rogue wave solutions for the infinite integrable nonlinear Schrödinger equation hierarchy.

PubMed

Ankiewicz, A; Akhmediev, N

2017-07-01

We present rogue wave solutions of the integrable nonlinear Schrödinger equation hierarchy with an infinite number of higher-order terms. The latter include higher-order dispersion and higher-order nonlinear terms. In particular, we derive the fundamental rogue wave solutions for all orders of the hierarchy, with exact expressions for velocities, phase, and "stretching factors" in the solutions. We also present several examples of exact solutions of second-order rogue waves, including rogue wave triplets.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Time-Reversal Generation of Rogue Waves

NASA Astrophysics Data System (ADS)

Chabchoub, Amin; Fink, Mathias

2014-03-01

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

Dispersion relation and growth rate of a relativistic electron beam propagating through a Langmuir wave wiggler

NASA Astrophysics Data System (ADS)

Zirak, H.; Jafari, S.

2015-06-01

In this study, a theory of free-electron laser (FEL) with a Langmuir wave wiggler in the presence of an axial magnetic field has been presented. The small wavelength of the plasma wave (in the sub-mm range) allows obtaining higher frequency than conventional wiggler FELs. Electron trajectories have been obtained by solving the equations of motion for a single electron. In addition, a fourth-order Runge-Kutta method has been used to simulate the electron trajectories. Employing a perturbation analysis, the dispersion relation for an electromagnetic and space-charge waves has been derived by solving the momentum transfer, continuity, and wave equations. Numerical calculations show that the growth rate increases with increasing the e-beam energy and e-beam density, while it decreases with increasing the strength of the axial guide magnetic field.

Evolution of initial discontinuities in the Riemann problem for the Kaup-Boussinesq equation with positive dispersion

NASA Astrophysics Data System (ADS)

Congy, T.; Ivanov, S. K.; Kamchatnov, A. M.; Pavloff, N.

2017-08-01

We consider the space-time evolution of initial discontinuities of depth and flow velocity for an integrable version of the shallow water Boussinesq system introduced by Kaup. We focus on a specific version of this "Kaup-Boussinesq model" for which a flat water surface is modulationally stable, we speak below of "positive dispersion" model. This model also appears as an approximation to the equations governing the dynamics of polarisation waves in two-component Bose-Einstein condensates. We describe its periodic solutions and the corresponding Whitham modulation equations. The self-similar, one-phase wave structures are composed of different building blocks, which are studied in detail. This makes it possible to establish a classification of all the possible wave configurations evolving from initial discontinuities. The analytic results are confirmed by numerical simulations.

Evolution of initial discontinuities in the Riemann problem for the Kaup-Boussinesq equation with positive dispersion.

PubMed

Congy, T; Ivanov, S K; Kamchatnov, A M; Pavloff, N

2017-08-01

We consider the space-time evolution of initial discontinuities of depth and flow velocity for an integrable version of the shallow water Boussinesq system introduced by Kaup. We focus on a specific version of this "Kaup-Boussinesq model" for which a flat water surface is modulationally stable, we speak below of "positive dispersion" model. This model also appears as an approximation to the equations governing the dynamics of polarisation waves in two-component Bose-Einstein condensates. We describe its periodic solutions and the corresponding Whitham modulation equations. The self-similar, one-phase wave structures are composed of different building blocks, which are studied in detail. This makes it possible to establish a classification of all the possible wave configurations evolving from initial discontinuities. The analytic results are confirmed by numerical simulations.

PARTICLE SCATTERING OFF OF RIGHT-HANDED DISPERSIVE WAVES

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

Schreiner, C.; Kilian, P.; Spanier, F., E-mail: cschreiner@astro.uni-wuerzburg.de

Resonant scattering of fast particles off low frequency plasma waves is a major process determining transport characteristics of energetic particles in the heliosphere and contributing to their acceleration. Usually, only Alfvén waves are considered for this process, although dispersive waves are also present throughout the heliosphere. We investigate resonant interaction of energetic electrons with dispersive, right-handed waves. For the interaction of particles and a single wave a variable transformation into the rest frame of the wave can be performed. Here, well-established analytic models derived in the framework of magnetostatic quasi-linear theory can be used as a reference to validate simulationmore » results. However, this approach fails as soon as several dispersive waves are involved. Based on analytic solutions modeling the scattering amplitude in the magnetostatic limit, we present an approach to modify these equations for use in the plasma frame. Thereby we aim at a description of particle scattering in the presence of several waves. A particle-in-cell code is employed to study wave–particle scattering on a micro-physically correct level and to test the modified model equations. We investigate the interactions of electrons at different energies (from 1 keV to 1 MeV) and right-handed waves with various amplitudes. Differences between model and simulation arise in the case of high amplitudes or several waves. Analyzing the trajectories of single particles we find no microscopic diffusion in the case of a single plasma wave, although a broadening of the particle distribution can be observed.« less

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.

Influence of nonlinear detuning at plasma wavebreaking threshold on backward Raman compression of non-relativistic laser pulses

NASA Astrophysics Data System (ADS)

Balakin, A. A.; Fraiman, G. M.; Jia, Q.; Fisch, N. J.

2018-06-01

Taking into account the nonlinear dispersion of the plasma wave, the fluid equations for the three-wave (Raman) interaction in plasmas are derived. It is found that, in some parameter regimes, the nonlinear detuning resulting from the plasma wave dispersion during Raman compression limits the plasma wave amplitude to noticeably below the generally recognized wavebreaking threshold. Particle-in-cell simulations confirm the theoretical estimates. For weakly nonlinear dispersion, the detuning effect can be counteracted by pump chirping or, equivalently, by upshifting slightly the pump frequency, so that the frequency-upshifted pump interacts with the seed at the point where the plasma wave enters the nonlinear stage.

Nonlinear coupling of left and right handed circularly polarized dispersive Alfvén wave

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

Sharma, R. P., E-mail: rpsharma@ces.iitd.ac.in; Sharma, Swati, E-mail: swati.sharma704@gmail.com; Gaur, Nidhi, E-mail: nidhiphysics@gmail.com

2014-07-15

The nonlinear phenomena are of prominent interests in understanding the particle acceleration and transportation in the interplanetary space. The ponderomotive nonlinearity causing the filamentation of the parallel propagating circularly polarized dispersive Alfvén wave having a finite frequency may be one of the mechanisms that contribute to the heating of the plasmas. The contribution will be different of the left (L) handed mode, the right (R) handed mode, and the mix mode. The contribution also depends upon the finite frequency of the circularly polarized waves. In the present paper, we have investigated the effect of the nonlinear coupling of the Lmore » and R circularly polarized dispersive Alfvén wave on the localized structures formation and the respective power spectra. The dynamical equations are derived in the presence of the ponderomotive nonlinearity of the L and R pumps and then studied semi-analytically as well as numerically. The ponderomotive nonlinearity accounts for the nonlinear coupling between both the modes. In the presence of the adiabatic response of the density fluctuations, the nonlinear dynamical equations satisfy the modified nonlinear Schrödinger equation. The equations thus obtained are solved in solar wind regime to study the coupling effect on localization and the power spectra. The effect of coupling is also studied on Faraday rotation and ellipticity of the wave caused due to the difference in the localization of the left and the right modes with the distance of propagation.« less

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.

Wave propagation in strongly dispersive superthermal dusty plasma

NASA Astrophysics Data System (ADS)

El-Labany, S. K.; El-Shewy, E. K.; Abd El-Razek, H. N.; El-Rahman, A. A.

2017-04-01

The attributes of acoustic envelope waves in a collisionless dust ion unmagnetized plasmas model composed of cold ions, superthermal electrons and positive-negative dust grains have been studied. Using the derivative expansion technique in a strong dispersive medium, the system model is reduced to a nonlinearly form of Schrodinger equation (NLSE). Rational solution of NLSE in unstable region is responsible for the creation of large shape waves; namely rogue waves. The subjection of instability regions upon electron superthermality (via κ), carrier wave number and dusty grains charge is discussed.

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.

Power loss of an oscillating electric dipole in a quantum plasma

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

Ghaderipoor, L.; Mehramiz, A.

2012-12-15

A system of linearized quantum plasma equations (quantum hydrodynamic model) has been used for investigating the dispersion equation for electrostatic waves in the plasma. Furthermore, dispersion relations and their modifications due to quantum effects are used for calculating the power loss of an oscillating electric dipole. Finally, the results are compared in quantum and classical regimes.

Stability of transition waves and positive entire solutions of Fisher-KPP equations with time and space dependence

NASA Astrophysics Data System (ADS)

Shen, Wenxian

2017-09-01

This paper is concerned with the stability of transition waves and strictly positive entire solutions of random and nonlocal dispersal evolution equations of Fisher-KPP type with general time and space dependence, including time and space periodic or almost periodic dependence as special cases. We first show the existence, uniqueness, and stability of strictly positive entire solutions of such equations. Next, we show the stability of uniformly continuous transition waves connecting the unique strictly positive entire solution and the trivial solution zero and satisfying certain decay property at the end close to the trivial solution zero (if it exists). The existence of transition waves has been studied in Liang and Zhao (2010 J. Funct. Anal. 259 857-903), Nadin (2009 J. Math. Pures Appl. 92 232-62), Nolen et al (2005 Dyn. PDE 2 1-24), Nolen and Xin (2005 Discrete Contin. Dyn. Syst. 13 1217-34) and Weinberger (2002 J. Math. Biol. 45 511-48) for random dispersal Fisher-KPP equations with time and space periodic dependence, in Nadin and Rossi (2012 J. Math. Pures Appl. 98 633-53), Nadin and Rossi (2015 Anal. PDE 8 1351-77), Nadin and Rossi (2017 Arch. Ration. Mech. Anal. 223 1239-67), Shen (2010 Trans. Am. Math. Soc. 362 5125-68), Shen (2011 J. Dynam. Differ. Equ. 23 1-44), Shen (2011 J. Appl. Anal. Comput. 1 69-93), Tao et al (2014 Nonlinearity 27 2409-16) and Zlatoš (2012 J. Math. Pures Appl. 98 89-102) for random dispersal Fisher-KPP equations with quite general time and/or space dependence, and in Coville et al (2013 Ann. Inst. Henri Poincare 30 179-223), Rawal et al (2015 Discrete Contin. Dyn. Syst. 35 1609-40) and Shen and Zhang (2012 Comm. Appl. Nonlinear Anal. 19 73-101) for nonlocal dispersal Fisher-KPP equations with time and/or space periodic dependence. The stability result established in this paper implies that the transition waves obtained in many of the above mentioned papers are asymptotically stable for well-fitted perturbation. Up to the author’s knowledge, it is the first time that the stability of transition waves of Fisher-KPP equations with general time and space dependence is studied.

Influence of the electromagnetic parameters on the surface wave attenuation in thin absorbing layers

NASA Astrophysics Data System (ADS)

Li, Yinrui; Li, Dongmeng; Wang, Xian; Nie, Yan; Gong, Rongzhou

2018-05-01

This paper describes the relationships between the surface wave attenuation properties and the electromagnetic parameters of radar absorbing materials (RAMs). In order to conveniently obtain the attenuation constant of TM surface waves over a wide frequency range, the simplified dispersion equations in thin absorbing materials were firstly deduced. The validity of the proposed method was proved by comparing with the classical dispersion equations. Subsequently, the attenuation constants were calculated separately for the absorbing layers with hypothetical relative permittivity and permeability. It is found that the surface wave attenuation properties can be strongly tuned by the permeability of RAM. Meanwhile, the permittivity should be appropriate so as to maintain high cutoff frequency. The present work provides specific methods and designs to improve the attenuation performances of radar absorbing materials.

Dark- and bright-rogue-wave solutions for media with long-wave-short-wave resonance.

PubMed

Chen, Shihua; Grelu, Philippe; Soto-Crespo, J M

2014-01-01

Exact explicit rogue-wave solutions of intricate structures are presented for the long-wave-short-wave resonance equation. These vector parametric solutions feature coupled dark- and bright-field counterparts of the Peregrine soliton. Numerical simulations show the robustness of dark and bright rogue waves in spite of the onset of modulational instability. Dark fields originate from the complex interplay between anomalous dispersion and the nonlinearity driven by the coupled long wave. This unusual mechanism, not available in scalar nonlinear wave equation models, can provide a route to the experimental realization of dark rogue waves in, for instance, negative index media or with capillary-gravity waves.

Theory and observation of electromagnetic ion cyclotron triggered emissions in the magnetosphere

NASA Astrophysics Data System (ADS)

Omura, Yoshiharu; Pickett, Jolene; Grison, Benjamin; Santolik, Ondrej; Dandouras, Iannis; Engebretson, Mark; Décréau, Pierrette M. E.; Masson, Arnaud

2010-07-01

We develop a nonlinear wave growth theory of electromagnetic ion cyclotron (EMIC) triggered emissions observed in the inner magnetosphere. We first derive the basic wave equations from Maxwell's equations and the momentum equations for the electrons and ions. We then obtain equations that describe the nonlinear dynamics of resonant protons interacting with an EMIC wave. The frequency sweep rate of the wave plays an important role in forming the resonant current that controls the wave growth. Assuming an optimum condition for the maximum growth rate as an absolute instability at the magnetic equator and a self-sustaining growth condition for the wave propagating from the magnetic equator, we obtain a set of ordinary differential equations that describe the nonlinear evolution of a rising tone emission generated at the magnetic equator. Using the physical parameters inferred from the wave, particle, and magnetic field data measured by the Cluster spacecraft, we determine the dispersion relation for the EMIC waves. Integrating the differential equations numerically, we obtain a solution for the time variation of the amplitude and frequency of a rising tone emission at the equator. Assuming saturation of the wave amplitude, as is found in the observations, we find good agreement between the numerical solutions and the wave spectrum of the EMIC triggered emissions.

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.

Coupling of Coastal Wave Transformation and Computational Fluid Dynamics Models for Seakeeping Analysis

DTIC Science & Technology

2017-04-03

setup in terms of temporal and spatial discretization . The second component was an extension of existing depth-integrated wave models to describe...equations (Abbott, 1976). Discretization schemes involve numerical dispersion and dissipation that distort the true character of the governing equations...represent a leading-order approximation of the Boussinesq-type equations. Tam and Webb (1993) proposed a wavenumber-based discretization scheme to preserve

Inversion of Surface-wave Dispersion Curves due to Low-velocity-layer Models

NASA Astrophysics Data System (ADS)

Shen, C.; Xia, J.; Mi, B.

2016-12-01

A successful inversion relies on exact forward modeling methods. It is a key step to accurately calculate multi-mode dispersion curves of a given model in high-frequency surface-wave (Rayleigh wave and Love wave) methods. For normal models (shear (S)-wave velocity increasing with depth), their theoretical dispersion curves completely match the dispersion spectrum that is generated based on wave equation. For models containing a low-velocity-layer, however, phase velocities calculated by existing forward-modeling algorithms (e.g. Thomson-Haskell algorithm, Knopoff algorithm, fast vector-transfer algorithm and so on) fail to be consistent with the dispersion spectrum at a high frequency range. They will approach a value that close to the surface-wave velocity of the low-velocity-layer under the surface layer, rather than that of the surface layer when their corresponding wavelengths are short enough. This phenomenon conflicts with the characteristics of surface waves, which results in an erroneous inverted model. By comparing the theoretical dispersion curves with simulated dispersion energy, we proposed a direct and essential solution to accurately compute surface-wave phase velocities due to low-velocity-layer models. Based on the proposed forward modeling technique, we can achieve correct inversion for these types of models. Several synthetic data proved the effectiveness of our method.

Spatiotemporal optical dark X solitary waves.

PubMed

Baronio, Fabio; Chen, Shihua; Onorato, Miguel; Trillo, Stefano; Wabnitz, Stefan; Kodama, Yuji

2016-12-01

We introduce spatiotemporal optical dark X solitary waves of the (2+1)D hyperbolic nonlinear Schrödinger equation (NLSE), which rules wave propagation in a self-focusing and normally dispersive medium. These analytical solutions are derived by exploiting the connection between the NLSE and a well-known equation of hydrodynamics, namely the type II Kadomtsev-Petviashvili (KP-II) equation. As a result, families of shallow water X soliton solutions of the KP-II equation are mapped into optical dark X solitary wave solutions of the NLSE. Numerical simulations show that optical dark X solitary waves may propagate for long distances (tens of nonlinear lengths) before they eventually break up, owing to the modulation instability of the continuous wave background. This finding opens a novel path for the excitation and control of X solitary waves in nonlinear optics.

On Richardson extrapolation for low-dissipation low-dispersion diagonally implicit Runge-Kutta schemes

NASA Astrophysics Data System (ADS)

Havasi, Ágnes; Kazemi, Ehsan

2018-04-01

In the modeling of wave propagation phenomena it is necessary to use time integration methods which are not only sufficiently accurate, but also properly describe the amplitude and phase of the propagating waves. It is not clear if amending the developed schemes by extrapolation methods to obtain a high order of accuracy preserves the qualitative properties of these schemes in the perspective of dissipation, dispersion and stability analysis. It is illustrated that the combination of various optimized schemes with Richardson extrapolation is not optimal for minimal dissipation and dispersion errors. Optimized third-order and fourth-order methods are obtained, and it is shown that the proposed methods combined with Richardson extrapolation result in fourth and fifth orders of accuracy correspondingly, while preserving optimality and stability. The numerical applications include the linear wave equation, a stiff system of reaction-diffusion equations and the nonlinear Euler equations with oscillatory initial conditions. It is demonstrated that the extrapolated third-order scheme outperforms the recently developed fourth-order diagonally implicit Runge-Kutta scheme in terms of accuracy and stability.

Vanishing characteristic speeds and critical dispersive points in nonlinear interfacial wave problems

NASA Astrophysics Data System (ADS)

Ratliff, Daniel J.

2017-11-01

Criticality plays a central role in the study of reductions and stability of hydrodynamical systems. At critical points, it is often the case that nonlinear reductions with dispersion arise to govern solution behavior. By considering when such models become bidirectional and lose their initial dispersive properties, it will be shown that higher order dispersive models may be supported in hydrodynamical systems. Precisely, this equation is a two-way Boussinesq equation with sixth order dispersion. The case of two layered shallow water is considered to illustrate this, and it is reasoned why such an environment is natural for such a system to emerge. Further, it is demonstrated that the regions in the parameter space for nontrivial flow, which admit this reduction, are vast and in fact form a continuum. The reduced model is then numerically simulated to illustrate how the two-way and higher dispersive properties suggest more exotic families of solitary wave solutions can emerge in stratified flows.

Formation of undular bores and solitary waves in the Strait of Malacca caused by the 26 December 2004 Indian Ocean tsunami

NASA Astrophysics Data System (ADS)

Grue, J.; Pelinovsky, E. N.; Fructus, D.; Talipova, T.; Kharif, C.

2008-05-01

Deformation of the Indian Ocean tsunami moving into the shallow Strait of Malacca and formation of undular bores and solitary waves in the strait are simulated in a model study using the fully nonlinear dispersive method (FNDM) and the Korteweg-deVries (KdV) equation. Two different versions of the incoming wave are studied where the waveshape is the same but the amplitude is varied: full amplitude and half amplitude. While moving across three shallow bottom ridges, the back face of the leading depression wave steepens until the wave slope reaches a level of 0.0036-0.0038, when short waves form, resembling an undular bore for both full and half amplitude. The group of short waves has very small amplitude in the beginning, behaving like a linear dispersive wave train, the front moving with the shallow water speed and the tail moving with the linear group velocity. Energy transfer from long to short modes is similar for the two input waves, indicating the fundamental role of the bottom topography to the formation of short waves. The dominant period becomes about 20 s in both cases. The train of short waves, emerging earlier for the larger input wave than for the smaller one, eventually develops into a sequence of rank-ordered solitary waves moving faster than the leading depression wave and resembles a fission of the mother wave. The KdV equation has limited capacity in resolving dispersion compared to FNDM.

Optical soliton solutions for the higher-order dispersive cubic-quintic nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

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

2017-12-01

In this paper, we analyze new optical soliton solutions to the higher-order dispersive cubic-quintic nonlinear Schrödinger equation (NLSE) using three integration schemes. The schemes used in this paper are modified tanh-coth (MTC), extended Jacobi elliptic function expansion (EJEF), and two variable (G‧ / G , 1 / G) -expansion methods. We obtain new solutions that to the best of our knowledge do not exist previously. The obtained solutions includes bright, dark, combined bright-dark, singular as well as periodic waves solitons. The obtained solutions may be used to explain and understand the physical nature of the wave spreads in the most dispersive optical medium. Some interesting figures for the physical interpretation of the obtained solutions are also presented.

Theory of wave propagation in partially saturated double-porosity rocks: a triple-layer patchy model

NASA Astrophysics Data System (ADS)

Sun, Weitao; Ba, Jing; Carcione, José M.

2016-04-01

Wave-induced local fluid flow is known as a key mechanism to explain the intrinsic wave dissipation in fluid-saturated rocks. Understanding the relationship between the acoustic properties of rocks and fluid patch distributions is important to interpret the observed seismic wave phenomena. A triple-layer patchy (TLP) model is proposed to describe the P-wave dissipation process in a double-porosity media saturated with two immiscible fluids. The double-porosity rock consists of a solid matrix with unique host porosity and inclusions which contain the second type of pores. Two immiscible fluids are considered in concentric spherical patches, where the inner pocket and the outer sphere are saturated with different fluids. The kinetic and dissipation energy functions of local fluid flow (LFF) in the inner pocket are formulated through oscillations in spherical coordinates. The wave propagation equations of the TLP model are based on Biot's theory and the corresponding Lagrangian equations. The P-wave dispersion and attenuation caused by the Biot friction mechanism and the local fluid flow (related to the pore structure and the fluid distribution) are obtained by a plane-wave analysis from the Christoffel equations. Numerical examples and laboratory measurements indicate that P-wave dispersion and attenuation are significantly influenced by the spatial distributions of both, the solid heterogeneity and the fluid saturation distribution. The TLP model is in reasonably good agreement with White's and Johnson's models. However, differences in phase velocity suggest that the heterogeneities associated with double-porosity and dual-fluid distribution should be taken into account when describing the P-wave dispersion and attenuation in partially saturated rocks.

Quasi-optical simulation of the electron cyclotron plasma heating in a mirror magnetic trap

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

Shalashov, A. G., E-mail: ags@appl.sci-nnov.ru; Balakin, A. A.; Khusainov, T. A.

The resonance microwave plasma heating in a large-scale open magnetic trap is simulated taking into account all the basic wave effects during the propagation of short-wavelength wave beams (diffraction, dispersion, and aberration) within the framework of the consistent quasi-optical approximation of Maxwell’s equations. The quasi-optical method is generalized to the case of inhomogeneous media with absorption dispersion, a new form of the quasi-optical equation is obtained, the efficient method for numerical integration is found, and simulation results are verified on the GDT facility (Novosibirsk).

A dispersion relationship governing incompressible wall turbulence

NASA Technical Reports Server (NTRS)

Tsuge, S.

1978-01-01

The method of separation of variables is shown to make turbulent correlation equations of Karman-Howarth type tractable for shear turbulence as well under the condition of neglected triple correlation. The separated dependent variable obeys an Orr-Sommerfeld equation. A new analytical method is developed using a scaling law different from the classical one due to Heisenberg and Lin and more appropriate for wall turbulent profiles. A dispersion relationship between the wave number and the separation constant which has the dimension of a frequency is derived in support of experimental observations of wave or coherent structure of wall turbulence.

Approximation method for a spherical bound system in the quantum plasma

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

Mehramiz, A.; Sobhanian, S.; Mahmoodi, J.

2010-08-15

A system of quantum hydrodynamic equations has been used for investigating the dielectric tensor and dispersion equation of a semiconductor as a quantum magnetized plasma. Dispersion relations and their modifications due to quantum effects are derived for both longitudinal and transverse waves. The number of states and energy levels are analytically estimated for a spherical bound system embedded in a semiconductor quantum plasma. The results show that longitudinal waves decay rapidly and do not interact with the spherical bound system. The energy shifts caused by the spin-orbit interaction and the Zeeman effect are calculated.

Mathematical nonlinear optics

NASA Astrophysics Data System (ADS)

McLaughlin, David W.

1995-08-01

The principal investigator, together with a post-doctoral fellows Tetsuji Ueda and Xiao Wang, several graduate students, and colleagues, has applied the modern mathematical theory of nonlinear waves to problems in nonlinear optics and to equations directly relevant to nonlinear optics. Projects included the interaction of laser light with nematic liquid crystals and chaotic, homoclinic, small dispersive, and random behavior of solutions of the nonlinear Schroedinger equation. In project 1, the extremely strong nonlinear response of a continuous wave laser beam in a nematic liquid crystal medium has produced striking undulation and filamentation of the laser beam which has been observed experimentally and explained theoretically. In project 2, qualitative properties of the nonlinear Schroedinger equation (which is the fundamental equation for nonlinear optics) have been identified and studied. These properties include optical shocking behavior in the limit of very small dispersion, chaotic and homoclinic behavior in discretizations of the partial differential equation, and random behavior.

Pressure evolution equation for the particulate phase in inhomogeneous compressible disperse multiphase flows

NASA Astrophysics Data System (ADS)

Annamalai, Subramanian; Balachandar, S.; Sridharan, P.; Jackson, T. L.

2017-02-01

An analytical expression describing the unsteady pressure evolution of the dispersed phase driven by variations in the carrier phase is presented. In this article, the term "dispersed phase" represents rigid particles, droplets, or bubbles. Letting both the dispersed and continuous phases be inhomogeneous, unsteady, and compressible, the developed pressure equation describes the particle response and its eventual equilibration with that of the carrier fluid. The study involves impingement of a plane traveling wave of a given frequency and subsequent volume-averaged particle pressure calculation due to a single wave. The ambient or continuous fluid's pressure and density-weighted normal velocity are identified as the source terms governing the particle pressure. Analogous to the generalized Faxén theorem, which is applicable to the particle equation of motion, the pressure expression is also written in terms of the surface average of time-varying incoming flow properties. The surface average allows the current formulation to be generalized for any complex incident flow, including situations where the particle size is comparable to that of the incoming flow. Further, the particle pressure is also found to depend on the dispersed-to-continuous fluid density ratio and speed of sound ratio in addition to dynamic viscosities of both fluids. The model is applied to predict the unsteady pressure variation inside an aluminum particle subjected to normal shock waves. The results are compared against numerical simulations and found to be in good agreement. Furthermore, it is shown that, although the analysis is conducted in the limit of negligible flow Reynolds and Mach numbers, it can be used to compute the density and volume of the dispersed phase to reasonable accuracy. Finally, analogous to the pressure evolution expression, an equation describing the time-dependent particle radius is deduced and is shown to reduce to the Rayleigh-Plesset equation in the linear limit.

Nonlinear and Dissipation Characteristics of Ocean Surface Waves in Estuarine Environments

DTIC Science & Technology

2013-09-30

developed models while using the general framework of operational wave models. We will conduct robustness tests of the system to determine the...and Guza (1984) model is weakly dispersive, in line with the assumptions behind the Boussinesq equations from which it was derived. The Kaihatu and...interactions across both frequency and directions. This system of equations is solved over a 2D frequency (f) and shore parallel wave number (κ) space. The

Pure quasi-P-wave calculation in transversely isotropic media using a hybrid method

NASA Astrophysics Data System (ADS)

Wu, Zedong; Liu, Hongwei; Alkhalifah, Tariq

2018-07-01

The acoustic approximation for anisotropic media is widely used in current industry imaging and inversion algorithms mainly because Pwaves constitute the majority of the energy recorded in seismic exploration. The resulting acoustic formulae tend to be simpler, resulting in more efficient implementations, and depend on fewer medium parameters. However, conventional solutions of the acoustic wave equation with higher-order derivatives suffer from shear wave artefacts. Thus, we derive a new acoustic wave equation for wave propagation in transversely isotropic (TI) media, which is based on a partially separable approximation of the dispersion relation for TI media and free of shear wave artefacts. Even though our resulting equation is not a partial differential equation, it is still a linear equation. Thus, we propose to implement this equation efficiently by combining the finite difference approximation with spectral evaluation of the space-independent parts. The resulting algorithm provides solutions without the constraint ɛ ≥ δ. Numerical tests demonstrate the effectiveness of the approach.

The nonlinear Schrödinger equation and the propagation of weakly nonlinear waves in optical fibers and on the water surface

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

Chabchoub, A., E-mail: achabchoub@swin.edu.au; Kibler, B.; Finot, C.

2015-10-15

The dynamics of waves in weakly nonlinear dispersive media can be described by the nonlinear Schrödinger equation (NLSE). An important feature of the equation is that it can be derived in a number of different physical contexts; therefore, analogies between different fields, such as for example fiber optics, water waves, plasma waves and Bose–Einstein condensates, can be established. Here, we investigate the similarities between wave propagation in optical Kerr media and water waves. In particular, we discuss the modulation instability (MI) in both media. In analogy to the water wave problem, we derive for Kerr-media the Benjamin–Feir index, i.e. amore » nondimensional parameter related to the probability of formation of rogue waves in incoherent wave trains.« less

Propagation estimates for dispersive wave equations: Application to the stratified wave equation

NASA Astrophysics Data System (ADS)

Pravica, David W.

1999-01-01

The plane-stratified wave equation (∂t2+H)ψ=0 with H=-c(y)2∇z2 is studied, where z=x⊕y, x∈Rk, y∈R1 and |c(y)-c∞|→0 as |y|→∞. Solutions to such an equation are solved for the propagation of waves through a layered medium and can include waves which propagate in the x-directions only (i.e., trapped modes). This leads to a consideration of the pseudo-differential wave equation (∂t2+ω(-Δx))ψ=0 such that the dispersion relation ω(ξ2) is analytic and satisfies c1⩽ω'(ξ2)⩽c2 for c*>0. Uniform propagation estimates like ∫|x|⩽|t|αE(UtP±φ0)dkx⩽Cα,β(1+|t|)-β∫E(φ0)dkx are obtained where Ut is the evolution group, P± are projection operators onto the Hilbert space of initial conditions φ∈H and E(ṡ) is the local energy density. In special cases scattering of trapped modes off a local perturbation satisfies the causality estimate ||P+ρΛjSP-ρΛk||⩽Cνρ-ν for each ν<1/2. Here P+ρΛj (P-ρΛk) are remote outgoing/detector (incoming/transmitter) projections for the jth (kth) trapped mode. Also Λ⋐R+ is compact, so the projections localize onto formally-incoming (eventually-outgoing) states.

On the evolution of perturbations to solutions of the Kadomtsev-Petviashvilli equation using the Benney-Luke equation

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Curtis, Christopher W.

2011-05-01

The Benney-Luke equation, which arises as a long wave asymptotic approximation of water waves, contains the Kadomtsev-Petviashvilli (KP) equation as a leading-order maximal balanced approximation. The question analyzed is how the Benney-Luke equation modifies the so-called web solutions of the KP equation. It is found that the Benney-Luke equation introduces dispersive radiation which breaks each of the symmetric soliton-like humps well away from the interaction region of the KP web solution into a tail of multi-peaked oscillating profiles behind the main solitary hump. Computation indicates that the wave structure is modified near the center of the interaction region. Both analytical and numerical techniques are employed for working with non-periodic, non-decaying solutions on unbounded domains.

A discontinuous Galerkin approach for conservative modeling of fully nonlinear and weakly dispersive wave transformations

NASA Astrophysics Data System (ADS)

Sharifian, Mohammad Kazem; Kesserwani, Georges; Hassanzadeh, Yousef

2018-05-01

This work extends a robust second-order Runge-Kutta Discontinuous Galerkin (RKDG2) method to solve the fully nonlinear and weakly dispersive flows, within a scope to simultaneously address accuracy, conservativeness, cost-efficiency and practical needs. The mathematical model governing such flows is based on a variant form of the Green-Naghdi (GN) equations decomposed as a hyperbolic shallow water system with an elliptic source term. Practical features of relevance (i.e. conservative modeling over irregular terrain with wetting and drying and local slope limiting) have been restored from an RKDG2 solver to the Nonlinear Shallow Water (NSW) equations, alongside new considerations to integrate elliptic source terms (i.e. via a fourth-order local discretization of the topography) and to enable local capturing of breaking waves (i.e. via adding a detector for switching off the dispersive terms). Numerical results are presented, demonstrating the overall capability of the proposed approach in achieving realistic prediction of nearshore wave processes involving both nonlinearity and dispersion effects within a single model.

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.

Galerkin Spectral Method for the 2D Solitary Waves of Boussinesq Paradigm Equation

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

Christou, M. A.; Christov, C. I.

2009-10-29

We consider the 2D stationary propagating solitary waves of the so-called Boussinesq Paradigm equation. The fourth- order elliptic boundary value problem on infinite interval is solved by a Galerkin spectral method. An iterative procedure based on artificial time ('false transients') and operator splitting is used. Results are obtained for the shapes of the solitary waves for different values of the dispersion parameters for both subcritical and supercritical phase speeds.

The picosecond structure of ultra-fast rogue waves

NASA Astrophysics Data System (ADS)

Klein, Avi; Shahal, Shir; Masri, Gilad; Duadi, Hamootal; Sulimani, Kfir; Lib, Ohad; Steinberg, Hadar; Kolpakov, Stanislav A.; Fridman, Moti

2018-02-01

We investigated ultrafast rogue waves in fiber lasers and found three different patterns of rogue waves: single- peaks, twin-peaks, and triple-peaks. The statistics of the different patterns as a function of the pump power of the laser reveals that the probability for all rogue waves patterns increase close to the laser threshold. We developed a numerical model which prove that the ultrafast rogue waves patterns result from both the polarization mode dispersion in the fiber and the non-instantaneous nature of the saturable absorber. This discovery reveals that there are three different types of rogue waves in fiber lasers: slow, fast, and ultrafast, which relate to three different time-scales and are governed by three different sets of equations: the laser rate equations, the nonlinear Schrodinger equation, and the saturable absorber equations, accordingly. This discovery is highly important for analyzing rogue waves and other extreme events in fiber lasers and can lead to realizing types of rogue waves which were not possible so far such as triangular rogue waves.

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.

Long-Time Asymptotics of a Box-Type Initial Condition in a Viscous Fluid Conduit

NASA Astrophysics Data System (ADS)

Franco, Nevil; Webb, Emily; Maiden, Michelle; Hoefer, Mark; El, Gennady

2017-11-01

The initial value problem for a localized hump disturbance is fundamental to dispersive nonlinear waves, beginning with studies of the celebrated, completely integrable Korteweg-de Vries equation. However, understanding responses to similar disturbances in many realistic dispersive wave systems is more complicated because they lack the mathematical property of complete integrability. This project applies Whitham nonlinear wave modulation theory to estimate how a viscous fluid conduit evolves this classic initial value problem. Comparisons between theory, numerical simulations, and experiments are presented. The conduit system consists of a viscous fluid column (glycerol) and a diluted, dyed version of the same fluid introduced to the column through a nozzle at the bottom. Steady injection and the buoyancy of the injected fluid leads to the eventual formation of a stable fluid conduit. Within this structure, a one hump disturbance is introduced and is observed to break up into a quantifiable number of solitons. This structure's experimental evolution is to Whitham theory and numerical simulations of a long-wave interfacial model equation. The method presented is general and can be applied to other dispersive nonlinear wave systems. Please email me, as I am the submitter.

Non-autonomous multi-rogue waves for spin-1 coupled nonlinear Gross-Pitaevskii equation and management by external potentials.

PubMed

Li, Li; Yu, Fajun

2017-09-06

We investigate non-autonomous multi-rogue wave solutions in a three-component(spin-1) coupled nonlinear Gross-Pitaevskii(GP) equation with varying dispersions, higher nonlinearities, gain/loss and external potentials. The similarity transformation allows us to relate certain class of multi-rogue wave solutions of the spin-1 coupled nonlinear GP equation to the solutions of integrable coupled nonlinear Schrödinger(CNLS) equation. We study the effect of time-dependent quadratic potential on the profile and dynamic of non-autonomous rogue waves. With certain requirement on the backgrounds, some non-autonomous multi-rogue wave solutions exhibit the different shapes with two peaks and dip in bright-dark rogue waves. Then, the managements with external potential and dynamic behaviors of these solutions are investigated analytically. The results could be of interest in such diverse fields as Bose-Einstein condensates, nonlinear fibers and super-fluids.

An exact solution for the Hawking effect in a dispersive fluid

NASA Astrophysics Data System (ADS)

Philbin, T. G.

2016-09-01

We consider the wave equation for sound in a moving fluid with a fourth-order anomalous dispersion relation. The velocity of the fluid is a linear function of position, giving two points in the flow where the fluid velocity matches the group velocity of low-frequency waves. We find the exact solution for wave propagation in the flow. The scattering shows amplification of classical waves, leading to spontaneous emission when the waves are quantized. In the dispersionless limit the system corresponds to a 1 +1 -dimensional black-hole or white-hole binary and there is a thermal spectrum of Hawking radiation from each horizon. Dispersion changes the scattering coefficients so that the quantum emission is no longer thermal. The scattering coefficients were previously obtained by Busch and Parentani in a study of dispersive fields in de Sitter space [Phys. Rev. D 86, 104033 (2012)]. Our results give further details of the wave propagation in this exactly solvable case, where our focus is on laboratory systems.

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

New envelope solitons for Gerdjikov-Ivanov model in nonlinear fiber optics

NASA Astrophysics Data System (ADS)

Triki, Houria; Alqahtani, Rubayyi T.; Zhou, Qin; Biswas, Anjan

2017-11-01

Exact soliton solutions in a class of derivative nonlinear Schrödinger equations including a pure quintic nonlinearity are investigated. By means of the coupled amplitude-phase formulation, we derive a nonlinear differential equation describing the evolution of the wave amplitude in the non-Kerr quintic media. The resulting amplitude equation is then solved to get exact analytical chirped bright, kink, antikink, and singular soliton solutions for the model. It is also shown that the nonlinear chirp associated with these solitons is crucially dependent on the wave intensity and related to self-steepening and group velocity dispersion parameters. Parametric conditions on physical parameters for the existence of chirped solitons are also presented. These localized structures exist due to a balance among quintic nonlinearity, group velocity dispersion, and self-steepening effects.

Nonlinear Waves In A Stenosed Elastic Tube Filled With Viscous Fluid: Forced Perturbed Korteweg-De Vries Equation

NASA Astrophysics Data System (ADS)

Gaik*, Tay Kim; Demiray, Hilmi; Tiong, Ong Chee

In the present work, treating the artery as a prestressed thin-walled and long circularly cylindrical elastic tube with a mild symmetrical stenosis and the blood as an incompressible Newtonian fluid, we have studied the pro pagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method. By intro ducing a set of stretched coordinates suitable for the boundary value type of problems and expanding the field variables into asymptotic series of the small-ness parameter of nonlinearity and dispersion, we obtained a set of nonlinear differential equations governing the terms at various order. By solving these nonlinear differential equations, we obtained the forced perturbed Korteweg-de Vries equation with variable coefficient as the nonlinear evolution equation. By use of the coordinate transformation, it is shown that this type of nonlinear evolution equation admits a progressive wave solution with variable wave speed.

One-step leapfrog ADI-FDTD method for simulating electromagnetic wave propagation in general dispersive media.

PubMed

Wang, Xiang-Hua; Yin, Wen-Yan; Chen, Zhi Zhang David

2013-09-09

The one-step leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is reformulated for simulating general electrically dispersive media. It models material dispersive properties with equivalent polarization currents. These currents are then solved with the auxiliary differential equation (ADE) and then incorporated into the one-step leapfrog ADI-FDTD method. The final equations are presented in the form similar to that of the conventional FDTD method but with second-order perturbation. The adapted method is then applied to characterize (a) electromagnetic wave propagation in a rectangular waveguide loaded with a magnetized plasma slab, (b) transmission coefficient of a plane wave normally incident on a monolayer graphene sheet biased by a magnetostatic field, and (c) surface plasmon polaritons (SPPs) propagation along a monolayer graphene sheet biased by an electrostatic field. The numerical results verify the stability, accuracy and computational efficiency of the proposed one-step leapfrog ADI-FDTD algorithm in comparison with analytical results and the results obtained with the other methods.

Peakompactons: Peaked compact nonlinear waves

DOE PAGES

Christov, Ivan C.; Kress, Tyler; Saxena, Avadh

2017-04-20

This paper is meant as an accessible introduction to/tutorial on the analytical construction and numerical simulation of a class of nonstandard solitary waves termed peakompactons. We present that these peaked compactly supported waves arise as solutions to nonlinear evolution equations from a hierarchy of nonlinearly dispersive Korteweg–de Vries-type models. Peakompactons, like the now-well-known compactons and unlike the soliton solutions of the Korteweg–de Vries equation, have finite support, i.e., they are of finite wavelength. However, unlike compactons, peakompactons are also peaked, i.e., a higher spatial derivative suffers a jump discontinuity at the wave’s crest. Here, we construct such solutions exactly bymore » reducing the governing partial differential equation to a nonlinear ordinary differential equation and employing a phase-plane analysis. Lastly, a simple, but reliable, finite-difference scheme is also designed and tested for the simulation of collisions of peakompactons. In addition to the peakompacton class of solutions, the general physical features of the so-called K #(n,m) hierarchy of nonlinearly dispersive Korteweg–de Vries-type models are discussed as well.« less

A coupled "AB" system: Rogue waves and modulation instabilities.

PubMed

Wu, C F; Grimshaw, R H J; Chow, K W; Chan, H N

2015-10-01

Rogue waves are unexpectedly large and localized displacements from an equilibrium position or an otherwise calm background. For the nonlinear Schrödinger (NLS) model widely used in fluid mechanics and optics, these waves can occur only when dispersion and nonlinearity are of the same sign, a regime of modulation instability. For coupled NLS equations, rogue waves will arise even if dispersion and nonlinearity are of opposite signs in each component as new regimes of modulation instability will appear in the coupled system. The same phenomenon will be demonstrated here for a coupled "AB" system, a wave-current interaction model describing baroclinic instability processes in geophysical flows. Indeed, the onset of modulation instability correlates precisely with the existence criterion for rogue waves for this system. Transitions from "elevation" rogue waves to "depression" rogue waves are elucidated analytically. The dispersion relation as a polynomial of the fourth order may possess double pairs of complex roots, leading to multiple configurations of rogue waves for a given set of input parameters. For special parameter regimes, the dispersion relation reduces to a cubic polynomial, allowing the existence criterion for rogue waves to be computed explicitly. Numerical tests correlating modulation instability and evolution of rogue waves were conducted.

Parametric instabilities of finite-amplitude, circularly polarized Alfven waves in an anisotropic plasma

NASA Technical Reports Server (NTRS)

Hamabata, Hiromitsu

1993-01-01

A class of parametric instabilities of finite-amplitude, circularly polarized Alfven waves in a plasma with pressure anisotropy is studied by application of the CGL equations. A linear perturbation analysis is used to find the dispersion relation governing the instabilities, which is a fifth-order polynomial and is solved numerically. A large-amplitude, circularly polarized wave is unstable with respect to decay into three waves: one sound-like wave and two side-band Alfven-like waves. It is found that, in addition to the decay instability, two new instabilities that are absent in the framework of the MHD equations can occur, depending on the plasma parameters.

Interface waves in multilayered plates.

PubMed

Li, Bing; Li, Ming-Hang; Lu, Tong

2018-04-01

In this paper, the characteristic equation of interface waves in multilayered plates is derived. With a reasonable assumption undertaken for the potential functions of longitudinal and shear waves in the nth layer medium, the characteristic equation of interface waves in the N-layered plate is derived and presented in a determinant form. The particle displacement and stress components are further presented in explicit forms. The dispersion curves and wave structures of interface waves in both a three-layered Al-Steel-Ti and a four-layered Steel-Al-Steel-Ti plate are displayed subsequently. It is observed in dispersion curves that obvious dispersion occurs on the low frequency band, whereas the phase velocities converge to the corresponding true Stoneley wave mode velocities at high frequency, and the number of interface wave modes equals the number of interfaces in multilayered plates (if all individual interfaces satisfy the existence condition of Stoneley waves). The wave structures reveal that the displacement components of interface waves are relatively high at interfaces, and the amplitude distribution varies from frequency to frequency. In the end, a similarly structured three-layered Al-Steel-Ti plate is tested. In this experiment, theoretical group velocity and experimental group velocity are compared. According to the discussion and comparison, the predicted group velocities are in good agreement with the experimental results. Thus, the theory of interface wave in multilayered plates is proved. As a result, the proposed theoretical approach represents a leap forward in the understanding of how to promote the characteristic study and practical applications of interface waves in multilayered structures.

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

Quantum revival for elastic waves in thin plate

NASA Astrophysics Data System (ADS)

Dubois, Marc; Lefebvre, Gautier; Sebbah, Patrick

2017-05-01

Quantum revival is described as the time-periodic reconstruction of a wave packet initially localized in space and time. This effect is expected in finite-size systems which exhibit commensurable discrete spectrum such as the infinite quantum well. Here, we report on the experimental observation of full and fractional quantum revival for classical waves in a two dimensional cavity. We consider flexural waves propagating in thin plates, as their quadratic dispersion at low frequencies mimics the dispersion relation of quantum systems governed by Schrödinger equation. Time-dependent excitation and measurement are performed at ultrasonic frequencies and reveal a periodic reconstruction of the initial elastic wave packet.

Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials.

PubMed

Kourakis, I; Shukla, P K

2005-07-01

We investigate the nonlinear propagation of electromagnetic waves in left-handed materials. For this purpose, we consider a set of coupled nonlinear Schrödinger (CNLS) equations, which govern the dynamics of coupled electric and magnetic field envelopes. The CNLS equations are used to obtain a nonlinear dispersion, which depicts the modulational stability profile of the coupled plane-wave solutions in left-handed materials. An exact (in)stability criterion for modulational interactions is derived, and analytical expressions for the instability growth rate are obtained.

Magnetoelastic shear wave propagation in pre-stressed anisotropic media under gravity

NASA Astrophysics Data System (ADS)

Kumari, Nirmala; Chattopadhyay, Amares; Singh, Abhishek K.; Sahu, Sanjeev A.

2017-03-01

The present study investigates the propagation of shear wave (horizontally polarized) in two initially stressed heterogeneous anisotropic (magnetoelastic transversely isotropic) layers in the crust overlying a transversely isotropic gravitating semi-infinite medium. Heterogeneities in both the anisotropic layers are caused due to exponential variation (case-I) and linear variation (case-II) in the elastic constants with respect to the space variable pointing positively downwards. The dispersion relations have been established in closed form using Whittaker's asymptotic expansion and were found to be in the well-agreement to the classical Love wave equations. The substantial effects of magnetoelastic coupling parameters, heterogeneity parameters, horizontal compressive initial stresses, Biot's gravity parameter, and wave number on the phase velocity of shear waves have been computed and depicted by means of a graph. As a special case, dispersion equations have been deduced when the two layers and half-space are isotropic and homogeneous. The comparative study for both cases of heterogeneity of the layers has been performed and also depicted by means of graphical illustrations.

Convective wave breaking in the KdV equation

NASA Astrophysics Data System (ADS)

Brun, Mats K.; Kalisch, Henrik

2018-03-01

The KdV equation is a model equation for waves at the surface of an inviscid incompressible fluid, and it is well known that the equation describes the evolution of unidirectional waves of small amplitude and long wavelength fairly accurately if the waves fall into the Boussinesq regime. The KdV equation allows a balance of nonlinear steepening effects and dispersive spreading which leads to the formation of steady wave profiles in the form of solitary waves and cnoidal waves. While these wave profiles are solutions of the KdV equation for any amplitude, it is shown here that there for both the solitary and the cnoidal waves, there are critical amplitudes for which the horizontal component of the particle velocity matches the phase velocity of the wave. Solitary or cnoidal solutions of the KdV equation which surpass these amplitudes feature incipient wave breaking as the particle velocity exceeds the phase velocity near the crest of the wave, and the model breaks down due to violation of the kinematic surface boundary condition. The condition for breaking can be conveniently formulated as a convective breaking criterion based on the local Froude number at the wave crest. This breaking criterion can also be applied to time-dependent situations, and one case of interest is the development of an undular bore created by an influx at a lateral boundary. It is shown that this boundary forcing leads to wave breaking in the leading wave behind the bore if a certain threshold is surpassed.

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.

Observation of Self-Cavitating Envelope Dispersive Shock Waves in Yttrium Iron Garnet Thin Films

NASA Astrophysics Data System (ADS)

Janantha, P. A. Praveen; Sprenger, Patrick; Hoefer, Mark A.; Wu, Mingzhong

2017-07-01

The formation and properties of envelope dispersive shock wave (DSW) excitations from repulsive nonlinear waves in a magnetic film are studied. Experiments involve the excitation of a spin wave step pulse in a low-loss magnetic Y3Fe5O12 thin film strip, in which the spin wave amplitude increases rapidly, realizing the canonical Riemann problem of shock theory. Under certain conditions, the envelope of the spin wave pulse evolves into a DSW that consists of an expanding train of nonlinear oscillations with amplitudes increasing from front to back, terminated by a black soliton. The onset of DSW self-cavitation, indicated by a point of zero power and a concomitant 180° phase jump, is observed for sufficiently large steps, indicative of the bidirectional dispersive hydrodynamic nature of the DSW. The experimental observations are interpreted with theory and simulations of the nonlinear Schrödinger equation.

Soliton, rational, and periodic solutions for the infinite hierarchy of defocusing nonlinear Schrödinger equations.

PubMed

Ankiewicz, Adrian

2016-07-01

Analysis of short-pulse propagation in positive dispersion media, e.g., in optical fibers and in shallow water, requires assorted high-order derivative terms. We present an infinite-order "dark" hierarchy of equations, starting from the basic defocusing nonlinear Schrödinger equation. We present generalized soliton solutions, plane-wave solutions, and periodic solutions of all orders. We find that "even"-order equations in the set affect phase and "stretching factors" in the solutions, while "odd"-order equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are complex. There are various applications in optics and water waves.

Dispersion relations with crossing symmetry for {pi}{pi} D- and F-wave amplitudes

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

Kaminski, R.

A set of once subtracted dispersion relations with imposed crossing symmetry condition for the {pi}{pi} D- and F-wave amplitudes is derived and analyzed. An example of numerical calculations in the effective two-pion mass range from the threshold to 1.1 GeV is presented. It is shown that these new dispersion relations impose quite strong constraints on the analyzed {pi}{pi} interactions and are very useful tools to test the {pi}{pi} amplitudes. One of the goals of this work is to provide a complete set of equations required for easy use. Full analytical expressions are presented. Along with the well-known dispersion relations successfulmore » in testing the {pi}{pi} S- and P-wave amplitudes, those presented here for the D and F waves give a complete set of tools for analyses of the {pi}{pi} interactions.« less

Dispersive shock waves and modulation theory

NASA Astrophysics Data System (ADS)

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

2016-10-01

There is growing physical and mathematical interest in the hydrodynamics of dissipationless/dispersive media. Since G.B. Whitham's seminal publication fifty years ago that ushered in the mathematical study of dispersive hydrodynamics, there has been a significant body of work in this area. However, there has been no comprehensive survey of the field of dispersive hydrodynamics. Utilizing Whitham's averaging theory as the primary mathematical tool, we review the rich mathematical developments over the past fifty years with an emphasis on physical applications. The fundamental, large scale, coherent excitation in dispersive hydrodynamic systems is an expanding, oscillatory dispersive shock wave or DSW. Both the macroscopic and microscopic properties of DSWs are analyzed in detail within the context of the universal, integrable, and foundational models for uni-directional (Korteweg-de Vries equation) and bi-directional (Nonlinear Schrödinger equation) dispersive hydrodynamics. A DSW fitting procedure that does not rely upon integrable structure yet reveals important macroscopic DSW properties is described. DSW theory is then applied to a number of physical applications: superfluids, nonlinear optics, geophysics, and fluid dynamics. Finally, we survey some of the more recent developments including non-classical DSWs, DSW interactions, DSWs in perturbed and inhomogeneous environments, and two-dimensional, oblique DSWs.

White-light parametric instabilities in plasmas.

PubMed

Santos, J E; Silva, L O; Bingham, R

2007-06-08

Parametric instabilities driven by partially coherent radiation in plasmas are described by a generalized statistical Wigner-Moyal set of equations, formally equivalent to the full wave equation, coupled to the plasma fluid equations. A generalized dispersion relation for stimulated Raman scattering driven by a partially coherent pump field is derived, revealing a growth rate dependence, with the coherence width sigma of the radiation field, scaling with 1/sigma for backscattering (three-wave process), and with 1/sigma1/2 for direct forward scattering (four-wave process). Our results demonstrate the possibility to control the growth rates of these instabilities by properly using broadband pump radiation fields.

Estimation of near-surface shear-wave velocity by inversion of Rayleigh waves

USGS Publications Warehouse

Xia, J.; Miller, R.D.; Park, C.B.

1999-01-01

The shear-wave (S-wave) velocity of near-surface materials (soil, rocks, pavement) and its effect on seismic-wave propagation are of fundamental interest in many groundwater, engineering, and environmental studies. Rayleigh-wave phase velocity of a layered-earth model is a function of frequency and four groups of earth properties: P-wave velocity, S-wave velocity, density, and thickness of layers. Analysis of the Jacobian matrix provides a measure of dispersion-curve sensitivity to earth properties. S-wave velocities are the dominant influence on a dispersion curve in a high-frequency range (>5 Hz) followed by layer thickness. An iterative solution technique to the weighted equation proved very effective in the high-frequency range when using the Levenberg-Marquardt and singular-value decomposition techniques. Convergence of the weighted solution is guaranteed through selection of the damping factor using the Levenberg-Marquardt method. Synthetic examples demonstrated calculation efficiency and stability of inverse procedures. We verify our method using borehole S-wave velocity measurements.Iterative solutions to the weighted equation by the Levenberg-Marquardt and singular-value decomposition techniques are derived to estimate near-surface shear-wave velocity. Synthetic and real examples demonstrate the calculation efficiency and stability of the inverse procedure. The inverse results of the real example are verified by borehole S-wave velocity measurements.

Dynamics of nonautonomous discrete rogue wave solutions for an Ablowitz-Musslimani equation with PT-symmetric potential.

PubMed

Yu, Fajun

2017-02-01

Starting from a discrete spectral problem, we derive a hierarchy of nonlinear discrete equations which include the Ablowitz-Ladik (AL) equation. We analytically study the discrete rogue-wave (DRW) solutions of AL equation with three free parameters. The trajectories of peaks and depressions of profiles for the first- and second-order DRWs are produced by means of analytical and numerical methods. In particular, we study the solutions with dispersion in parity-time ( PT) symmetric potential for Ablowitz-Musslimani equation. And we consider the non-autonomous DRW solutions, parameters controlling and their interactions with variable coefficients, and predict the long-living rogue wave solutions. Our results might provide useful information for potential applications of synthetic PT symmetric systems in nonlinear optics and condensed matter physics.

Effects of electromagnetic wiggler and ion channel guiding on equilibrium orbits and waves propagation in a free electron laser

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

Amri, Hassan Ehsani; Mohsenpour, Taghi, E-mail: mohsenpour@umz.ac.ir

2016-02-15

In this paper, an analysis of equilibrium orbits for electrons by a simultaneous solution of the equation of motion and the dispersion relation for electromagnetic wave wiggler in a free-electron laser (FEL) with ion-channel guiding has been presented. A fluid model has been used to investigate interactions among all possible waves. The dispersion relation has been derived for electrostatic and electromagnetic waves with all relativistic effects included. This dispersion relation has been solved numerically. For group I and II orbits, when the transverse velocity is small, only the FEL instability is found. In group I and II orbits with relativelymore » large transverse velocity, new couplings between other modes are found.« less

Fisher equation for anisotropic diffusion: simulating South American human dispersals.

PubMed

Martino, Luis A; Osella, Ana; Dorso, Claudio; Lanata, José L

2007-09-01

The Fisher equation is commonly used to model population dynamics. This equation allows describing reaction-diffusion processes, considering both population growth and diffusion mechanism. Some results have been reported about modeling human dispersion, always assuming isotropic diffusion. Nevertheless, it is well-known that dispersion depends not only on the characteristics of the habitats where individuals are but also on the properties of the places where they intend to move, then isotropic approaches cannot adequately reproduce the evolution of the wave of advance of populations. Solutions to a Fisher equation are difficult to obtain for complex geometries, moreover, when anisotropy has to be considered and so few studies have been conducted in this direction. With this scope in mind, we present in this paper a solution for a Fisher equation, introducing anisotropy. We apply a finite difference method using the Crank-Nicholson approximation and analyze the results as a function of the characteristic parameters. Finally, this methodology is applied to model South American human dispersal.

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.

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.

Lie Symmetry Analysis, Analytical Solutions, and Conservation Laws of the Generalised Whitham-Broer-Kaup-Like Equations

NASA Astrophysics Data System (ADS)

Wang, Xiu-Bin; Tian, Shou-Fu; Qin, Chun-Yan; Zhang, Tian-Tian

2017-03-01

In this article, a generalised Whitham-Broer-Kaup-Like (WBKL) equations is investigated, which can describe the bidirectional propagation of long waves in shallow water. The equations can be reduced to the dispersive long wave equations, variant Boussinesq equations, Whitham-Broer-Kaup-Like equations, etc. The Lie symmetry analysis method is used to consider the vector fields and optimal system of the equations. The similarity reductions are given on the basic of the optimal system. Furthermore, the power series solutions are derived by using the power series theory. Finally, based on a new theorem of conservation laws, the conservation laws associated with symmetries of this equations are constructed with a detailed derivation.

Full thermomechanical coupling in modelling of micropolar thermoelasticity

NASA Astrophysics Data System (ADS)

Murashkin, E. V.; Radayev, Y. N.

2018-04-01

The present paper is devoted to plane harmonic waves of displacements and microrotations propagating in fully coupled thermoelastic continua. The analysis is carried out in the framework of linear conventional thermoelastic micropolar continuum model. The reduced energy balance equation and the special form of the Helmholtz free energy are discussed. The constitutive constants providing fully coupling of equations of motion and heat conduction are considered. The dispersion equation is derived and analysed in the form bi-cubic and bi-quadratic polynoms product. The equation are analyzed by the computer algebra system Mathematica. Algebraic forms expressed by complex multivalued square and cubic radicals are obtained for wavenumbers of transverse and longitudinal waves. The exact forms of wavenumbers of a plane harmonic coupled thermoelastic waves are computed.

Interactions of solitary waves and compression/expansion waves in core-annular flows

NASA Astrophysics Data System (ADS)

Maiden, Michelle; Anderson, Dalton; El, Gennady; Franco, Nevil; Hoefer, Mark

2017-11-01

The nonlinear hydrodynamics of an initial step leads to the formation of rarefaction waves and dispersive shock waves in dispersive media. Another hallmark of these media is the soliton, a localized traveling wave whose speed is amplitude dependent. Although compression/expansion waves and solitons have been well-studied individually, there has been no mathematical description of their interaction. In this talk, the interaction of solitons and shock/rarefaction waves for interfacial waves in viscous, miscible core-annular flows are modeled mathematically and explored experimentally. If the interior fluid is continuously injected, a deformable conduit forms whose interfacial dynamics are well-described by a scalar, dispersive nonlinear partial differential equation. The main focus is on interactions of solitons with dispersive shock waves and rarefaction waves. Theory predicts that a soliton can either be transmitted through or trapped by the extended hydrodynamic state. The notion of reciprocity is introduced whereby a soliton interacts with a shock wave in a reciprocal or dual fashion as with the rarefaction. Soliton reciprocity, trapping, and transmission are observed experimentally and are found to agree with the modulation theory and numerical simulations. This work was partially supported by NSF CAREER DMS-1255422 (M.A.H.) and NSF GRFP (M.D.M.).

4-wave dynamics in kinetic wave turbulence

NASA Astrophysics Data System (ADS)

Chibbaro, Sergio; Dematteis, Giovanni; Rondoni, Lamberto

2018-01-01

A general Hamiltonian wave system with quartic resonances is considered, in the standard kinetic limit of a continuum of weakly interacting dispersive waves with random phases. The evolution equation for the multimode characteristic function Z is obtained within an ;interaction representation; and a perturbation expansion in the small nonlinearity parameter. A frequency renormalization is performed to remove linear terms that do not appear in the 3-wave case. Feynman-Wyld diagrams are used to average over phases, leading to a first order differential evolution equation for Z. A hierarchy of equations, analogous to the Boltzmann hierarchy for low density gases is derived, which preserves in time the property of random phases and amplitudes. This amounts to a general formalism for both the N-mode and the 1-mode PDF equations for 4-wave turbulent systems, suitable for numerical simulations and for investigating intermittency. Some of the main results which are developed here in detail have been tested numerically in a recent work.

Nonlinear coherent structures of Alfvén wave in a collisional plasma

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

Jana, Sayanee; Chakrabarti, Nikhil; Ghosh, Samiran

2016-07-15

The Alfvén wave dynamics is investigated in the framework of two-fluid approach in a compressible collisional magnetized plasma. In the finite amplitude limit, the dynamics of the nonlinear Alfvén wave is found to be governed by a modified Korteweg-de Vries Burgers equation (mKdVB). In this mKdVB equation, the electron inertia is found to act as a source of dispersion, and the electron-ion collision serves as a dissipation. The collisional dissipation is eventually responsible for the Burgers term in mKdVB equation. In the long wavelength limit, this weakly nonlinear Alfvén wave is shown to be governed by a damped nonlinear Schrödingermore » equation. Furthermore, these nonlinear equations are analyzed by means of analytical calculation and numerical simulation to elucidate the various aspects of the phase-space dynamics of the nonlinear wave. Results reveal that nonlinear Alfvén wave exhibits the dissipation mediated shock, envelope, and breather like structures. Numerical simulations also predict the formation of dissipative Alfvénic rogue wave, giant breathers, and rogue wave holes. These results are discussed in the context of the space plasma.« less

Ultrasonic waves in classical gases

NASA Astrophysics Data System (ADS)

Magner, A. G.; Gorenstein, M. I.; Grygoriev, U. V.

2017-12-01

The velocity and absorption coefficient for the plane sound waves in a classical gas are obtained by solving the Boltzmann kinetic equation, which describes the reaction of the single-particle distribution function to a periodic external field. Within the linear response theory, the nonperturbative dispersion equation valid for all sound frequencies is derived and solved numerically. The results are in agreement with the approximate analytical solutions found for both the frequent- and rare-collision regimes. These results are also in qualitative agreement with the experimental data for ultrasonic waves in dilute gases.

Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials.

PubMed

Scalora, Michael; Syrchin, Maxim S; Akozbek, Neset; Poliakov, Evgeni Y; D'Aguanno, Giuseppe; Mattiucci, Nadia; Bloemer, Mark J; Zheltikov, Aleksei M

2005-07-01

A new generalized nonlinear Schrödinger equation describing the propagation of ultrashort pulses in bulk media exhibiting frequency dependent dielectric susceptibility and magnetic permeability is derived and used to characterize wave propagation in a negative index material. The equation has new features that are distinct from ordinary materials (mu=1): the linear and nonlinear coefficients can be tailored through the linear properties of the medium to attain any combination of signs unachievable in ordinary matter, with significant potential to realize a wide class of solitary waves.

Surface plasmon oscillations in a semi-bounded semiconductor plasma

NASA Astrophysics Data System (ADS)

M, SHAHMANSOURI; A, P. MISRA

2018-02-01

We study the dispersion properties of surface plasmon (SP) oscillations in a semi-bounded semiconductor plasma with the effects of the Coulomb exchange (CE) force associated with the spin polarization of electrons and holes as well as the effects of the Fermi degenerate pressure and the quantum Bohm potential. Starting from a quantum hydrodynamic model coupled to the Poisson equation, we derive the general dispersion relation for surface plasma waves. Previous results in this context are recovered. The dispersion properties of the surface waves are analyzed in some particular cases of interest and the relative influence of the quantum forces on these waves are also studied for a nano-sized GaAs semiconductor plasma. It is found that the CE effects significantly modify the behaviors of the SP waves. The present results are applicable to understand the propagation characteristics of surface waves in solid density plasmas.

Kinematic parameters of internal waves of the second mode in the South China Sea

NASA Astrophysics Data System (ADS)

Kurkina, Oxana; Talipova, Tatyana; Soomere, Tarmo; Giniyatullin, Ayrat; Kurkin, Andrey

2017-10-01

Spatial distributions of the main properties of the mode function and kinematic and non-linear parameters of internal waves of the second mode are derived for the South China Sea for typical summer conditions in July. The calculations are based on the Generalized Digital Environmental Model (GDEM) climatology of hydrological variables, from which the local stratification is evaluated. The focus is on the phase speed of long internal waves and the coefficients at the dispersive, quadratic and cubic terms of the weakly non-linear Gardner model. Spatial distributions of these parameters, except for the coefficient at the cubic term, are qualitatively similar for waves of both modes. The dispersive term of Gardner's equation and phase speed for internal waves of the second mode are about a quarter and half, respectively, of those for waves of the first mode. Similarly to the waves of the first mode, the coefficients at the quadratic and cubic terms of Gardner's equation are practically independent of water depth. In contrast to the waves of the first mode, for waves of the second mode the quadratic term is mostly negative. The results can serve as a basis for expressing estimates of the expected parameters of internal waves for the South China Sea.

Modeling RF Fields in Hot Plasmas with Parallel Full Wave Code

NASA Astrophysics Data System (ADS)

Spencer, Andrew; Svidzinski, Vladimir; Zhao, Liangji; Galkin, Sergei; Kim, Jin-Soo

2016-10-01

FAR-TECH, Inc. is developing a suite of full wave RF plasma codes. It is based on a meshless formulation in configuration space with adapted cloud of computational points (CCP) capability and using the hot plasma conductivity kernel to model the nonlocal plasma dielectric response. The conductivity kernel is calculated by numerically integrating the linearized Vlasov equation along unperturbed particle trajectories. Work has been done on the following calculations: 1) the conductivity kernel in hot plasmas, 2) a monitor function based on analytic solutions of the cold-plasma dispersion relation, 3) an adaptive CCP based on the monitor function, 4) stencils to approximate the wave equations on the CCP, 5) the solution to the full wave equations in the cold-plasma model in tokamak geometry for ECRH and ICRH range of frequencies, and 6) the solution to the wave equations using the calculated hot plasma conductivity kernel. We will present results on using a meshless formulation on adaptive CCP to solve the wave equations and on implementing the non-local hot plasma dielectric response to the wave equations. The presentation will include numerical results of wave propagation and absorption in the cold and hot tokamak plasma RF models, using DIII-D geometry and plasma parameters. Work is supported by the U.S. DOE SBIR program.

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.

Model Equation for Acoustic Nonlinear Measurement of Dispersive Specimens at High Frequency

NASA Astrophysics Data System (ADS)

Zhang, Dong; Kushibiki, Junichi; Zou, Wei

2006-10-01

We present a theoretical model for acoustic nonlinearity measurement of dispersive specimens at high frequency. The nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation governs the nonlinear propagation in the SiO2/specimen/SiO2 multi-layer medium. The dispersion effect is considered in a special manner by introducing the frequency-dependant sound velocity in the KZK equation. Simple analytic solutions are derived by applying the superposition technique of Gaussian beams. The solutions are used to correct the diffraction and dispersion effects in the measurement of acoustic nonlinearity of cottonseed oil in the frequency range of 33-96 MHz. Regarding two different ultrasonic devices, the accuracies of the measurements are improved to ±2.0% and ±1.3% in comparison with ±9.8% and ±2.9% obtained from the previous plane wave model.

Rayleigh-type waves in nonlocal micropolar solid half-space.

PubMed

Khurana, Aarti; Tomar, S K

2017-01-01

Propagation of Rayleigh type surface waves in nonlocal micropolar elastic solid half-space has been investigated. Two modes of Rayleigh-type waves are found to propagate under certain approximations. Frequency equations of these Rayleigh type modes and their conditions of existence have been derived. These frequency equations are found to be dispersive in character due to the presence of micropolarity and nonlocality parameters in the medium. One of the frequency equations is a counterpart of the classical Rayleigh waves and the other is new and has appeared due to micropolarity of the medium. Phase speeds of these waves are computed numerically for Magnesium crystal and their variation against wavenumber are presented graphically. Comparisons have been made between the phase speeds of Rayleigh type waves through nonlocal micropolar, local micropolar and elastic solid half-spaces. Copyright © 2016 Elsevier B.V. All rights reserved.

Ion acoustic waves in pair-ion plasma: Linear and nonlinear analyses

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

Saeed, R.; Mushtaq, A.

2009-03-15

Linear and nonlinear properties of low frequency ion acoustic wave (IAW) in pair-ion plasma in the presence of electrons are investigated. The dispersion relation and Kadomtsev-Petviashvili equation for linear/nonlinear IAW are derived from sets of hydrodynamic equations where the ion pairs are inertial while electrons are Boltzmannian. The dispersion curves for various concentrations of electrons are discussed and compared with experimental results. The predicted linear IAW propagates at the same frequencies as those of the experimentally observed IAW if n{sub e0}{approx}10{sup 4} cm{sup -3}. It is found that nonlinear profile of the ion acoustic solitary waves is significantly affected bymore » the percentage ratio of electron number density and temperature. It is also determined that rarefactive solitary waves can propagate in this system. It is hoped that the results presented in this study would be helpful in understanding the salient features of the finite amplitude localized ion acoustic solitary pulses in a laboratory fullerene plasma.« less

Modulation stability and optical soliton solutions of nonlinear Schrödinger equation with higher order dispersion and nonlinear terms and its applications

NASA Astrophysics Data System (ADS)

Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen

2017-12-01

In optical fibers, the higher order non-linear Schrödinger equation (NLSE) with cubic quintic nonlinearity describes the propagation of extremely short pulses. We constructed bright and dark solitons, solitary wave and periodic solitary wave solutions of generalized higher order NLSE in cubic quintic non Kerr medium by applying proposed modified extended mapping method. These obtained solutions have key applications in physics and mathematics. Moreover, we have also presented the formation conditions on solitary wave parameters in which dark and bright solitons can exist for this media. We also gave graphically the movement of constructed solitary wave and soliton solutions, that helps to realize the physical phenomena's of this model. The stability of the model in normal dispersion and anomalous regime is discussed by using the modulation instability analysis, which confirms that all constructed solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method.

Spectrum of spin waves in cold polarized gases

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

Andreeva, T. L., E-mail: phdocandreeva@yandex.ru

2017-02-15

The spin dynamics of cold polarized gases are investigated using the Boltzmann equation. The dispersion relation for spin waves (transverse component of the magnetic moment) and the spin diffusion coefficient of the longitudinal component of the magnetic moment are calculated without using fitting parameters. The spin wave frequency and the diffusion coefficient for rubidium atoms are estimated numerically.

Stability properties of solitary waves for fractional KdV and BBM equations

NASA Astrophysics Data System (ADS)

Angulo Pava, Jaime

2018-03-01

This paper sheds new light on the stability properties of solitary wave solutions associated with Korteweg-de Vries-type models when the dispersion is very low. Using a compact, analytic approach and asymptotic perturbation theory, we establish sufficient conditions for the existence of exponentially growing solutions to the linearized problem and so a criterium of spectral instability of solitary waves is obtained for both models. Moreover, the nonlinear stability and spectral instability of the ground state solutions for both models is obtained for some specific regimen of parameters. Via a Lyapunov strategy and a variational analysis, we obtain the stability of the blow-up of solitary waves for the critical fractional KdV equation. The arguments presented in this investigation show promise for use in the study of the instability of traveling wave solutions of other nonlinear evolution equations.

Solitary waves and nonlinear dynamic coherent structures in magnetic metamaterials

NASA Astrophysics Data System (ADS)

Tankeyev, A. P.; Smagin, V. V.; Borich, M. A.; Zhuravlev, A. S.

2009-03-01

Within the framework of the extended nonlinear Schrödinger equation (ENSE), two types of nonlinear states of magnetization in a ferromagnet-dielectric-metal metamagnetic structure have been obtained and investigated. These states have an internal structure; e.g., a periodic sequence of compound solitons is formed by kink-antikink pairs (shock waves), and coherent periodic breather structures are formed by “bright” quasi-solitons. Conditions have been found under which the envelope of these states is described by a modified Korteweg-de Vries (mKdV) equation. It is shown that the compound solitons are described by an mKdV equation with repulsion, and the breather structures, by an mKdV equation with attraction. It is shown also that the characteristic properties of the solutions are determined by the sign of the group-velocity dispersion rather than by the sign of the group velocity itself. The results obtained can be used for searching new nonlinear dynamic coherent structures, e.g., compound solitons and breathers in high-dispersion magnetic metamaterials.

Dispersion features of complex waves in a graphene-coated semiconductor nanowire

NASA Astrophysics Data System (ADS)

Yu, Pengchao; Fesenko, Volodymyr I.; Tuz, Vladimir R.

2018-05-01

The dispersion features of a graphene-coated semiconductor nanowire operating in the terahertz frequency band are consistently studied in the framework of a special theory of complex waves. Detailed classification of the waveguide modes was carried out based on the analysis of characteristics of the phase and attenuation constants obtained from the complex roots of characteristic equation. With such a treatment, the waves are attributed to the group of either "proper" or "improper" waves, wherein their type is determined as the trapped surface waves, fast and slow leaky waves, and surface plasmons. The dispersion curves of axially symmetric TM0n and TE0n modes, as well as nonsymmetric hybrid EH1n and HE1n modes, were plotted and analyzed in detail, and both radiative regime of leaky waves and guided regime of trapped surface waves are identified. The peculiarities of propagation of the TM modes of surface plasmons were revealed. Two subregions of existence of surface plasmons were found out where they appear as propagating and reactive waves. The cutoff conditions for higher-order TM modes of surface plasmons were correctly determined.

Comment on “Surface electromagnetic wave equations in a warm magnetized quantum plasma” [Phys. Plasmas 21, 072114 (2014)

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

Moradi, Afshin, E-mail: a.moradi@kut.ac.ir

2016-07-15

In a recent article [C. Li et al., Phys. Plasmas 21, 072114 (2014)], Li et al. studied the propagation of surface waves on a magnetized quantum plasma half-space in the Voigt configuration (in this case, the magnetic field is parallel to the surface but is perpendicular to the direction of propagation). Here, we present a fresh look at the problem and obtain a new form of dispersion relation of surface waves of the system. We find that our new dispersion relation does not agree with the result obtained by Li et al.

Effects of dust size distribution on dust acoustic waves in two-dimensional unmagnetized dusty plasma

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

He Guangjun; Duan Wenshan; Tian Duoxiang

2008-04-15

For unmagnetized dusty plasma with many different dust grain species containing both hot isothermal electrons and ions, both the linear dispersion relation and the Kadomtsev-Petviashvili equation for small, but finite amplitude dust acoustic waves are obtained. The linear dispersion relation is investigated numerically. Furthermore, the variations of amplitude, width, and propagation velocity of the nonlinear solitary wave with an arbitrary dust size distribution function are studied as well. Moreover, both the power law distribution and the Gaussian distribution are approximately simulated by using appropriate arbitrary dust size distribution functions.

Interaction of solitons for obliquely propagating magnetoacoustic waves in stellar atmosphere

NASA Astrophysics Data System (ADS)

Jahangir, R.; Masood, W.; Siddiq, M.; Batool, Nazia

2016-12-01

We study here the nonlinear oblique propagation of magnetoacoustic waves in dense plasmas with degenerate electrons by deriving Kadomtsev-Petviashvili (KP) equation for small but finite amplitude perturbations. The two soliton interaction has been studied by finding the solution of the KP equation using the Hirota bilinear formalism. For illustrative purposes, we have used the plasma parameters typically found in white dwarf stars for both the fast and slow modes of magnetoacoustic waves. It has been observed that the soliton interaction in the fast and slow modes is strongly influenced by the predominant and weak dispersive coefficients of the KP equation. The single soliton behavior has also been explained for the fast and slow magnetoacoustic modes.

Traveling wave and exact solutions for the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity

NASA Astrophysics Data System (ADS)

Akram, Ghazala; Mahak, Nadia

2018-06-01

The nonlinear Schrödinger equation (NLSE) with the aid of three order dispersion terms is investigated to find the exact solutions via the extended (G'/G2)-expansion method and the first integral method. Many exact traveling wave solutions, such as trigonometric, hyperbolic, rational, soliton and complex function solutions, are characterized with some free parameters of the problem studied. It is corroborated that the proposed techniques are manageable, straightforward and powerful tools to find the exact solutions of nonlinear partial differential equations (PDEs). Some figures are plotted to describe the propagation of traveling wave solutions expressed by the hyperbolic functions, trigonometric functions and rational functions.

Wave-induced fluid flow in random porous media: Attenuation and dispersion of elastic waves

NASA Astrophysics Data System (ADS)

Müller, Tobias M.; Gurevich, Boris

2005-05-01

A detailed analysis of the relationship between elastic waves in inhomogeneous, porous media and the effect of wave-induced fluid flow is presented. Based on the results of the poroelastic first-order statistical smoothing approximation applied to Biot's equations of poroelasticity, a model for elastic wave attenuation and dispersion due to wave-induced fluid flow in 3-D randomly inhomogeneous poroelastic media is developed. Attenuation and dispersion depend on linear combinations of the spatial correlations of the fluctuating poroelastic parameters. The observed frequency dependence is typical for a relaxation phenomenon. Further, the analytic properties of attenuation and dispersion are analyzed. It is shown that the low-frequency asymptote of the attenuation coefficient of a plane compressional wave is proportional to the square of frequency. At high frequencies the attenuation coefficient becomes proportional to the square root of frequency. A comparison with the 1-D theory shows that attenuation is of the same order but slightly larger in 3-D random media. Several modeling choices of the approach including the effect of cross correlations between fluid and solid phase properties are demonstrated. The potential application of the results to real porous materials is discussed. .

Localized light waves: Paraxial and exact solutions of the wave equation (a review)

NASA Astrophysics Data System (ADS)

Kiselev, A. P.

2007-04-01

Simple explicit localized solutions are systematized over the whole space of a linear wave equation, which models the propagation of optical radiation in a linear approximation. Much attention has been paid to exact solutions (which date back to the Bateman findings) that describe wave beams (including Bessel-Gauss beams) and wave packets with a Gaussian localization with respect to the spatial variables and time. Their asymptotics with respect to free parameters and at large distances are presented. A similarity between these exact solutions and harmonic in time fields obtained in the paraxial approximation based on the Leontovich-Fock parabolic equation has been studied. Higher-order modes are considered systematically using the separation of variables method. The application of the Bateman solutions of the wave equation to the construction of solutions to equations with dispersion and nonlinearity and their use in wavelet analysis, as well as the summation of Gaussian beams, are discussed. In addition, solutions localized at infinity known as the Moses-Prosser “acoustic bullets”, as well as their harmonic in time counterparts, “ X waves”, waves from complex sources, etc., have been considered. Everywhere possible, the most elementary mathematical formalism is used.

Rogue waves of the Kundu-Eckhaus equation in a chaotic wave field.

PubMed

Bayindir, Cihan

2016-03-01

In this paper we study the properties of the chaotic wave fields generated in the frame of the Kundu-Eckhaus equation (KEE). Modulation instability results in a chaotic wave field which exhibits small-scale filaments with a free propagation constant, k. The average velocity of the filaments is approximately given by the average group velocity calculated from the dispersion relation for the plane-wave solution; however, direction of propagation is controlled by the β parameter, the constant in front of the Raman-effect term. We have also calculated the probabilities of the rogue wave occurrence for various values of propagation constant k and showed that the probability of rogue wave occurrence depends on k. Additionally, we have showed that the probability of rogue wave occurrence significantly depends on the quintic and the Raman-effect nonlinear terms of the KEE. Statistical comparisons between the KEE and the cubic nonlinear Schrödinger equation have also been presented.

Modeling ultrasonic transient scattering from biological tissues including their dispersive properties directly in the time domain.

PubMed

Norton, G V; Novarini, J C

2007-06-01

Ultrasonic imaging in medical applications involves propagation and scattering of acoustic waves within and by biological tissues that are intrinsically dispersive. Analytical approaches for modeling propagation and scattering in inhomogeneous media are difficult and often require extremely simplifying approximations in order to achieve a solution. To avoid such approximations, the direct numerical solution of the wave equation via the method of finite differences offers the most direct tool, which takes into account diffraction and refraction. It also allows for detailed modeling of the real anatomic structure and combination/layering of tissues. In all cases the correct inclusion of the dispersive properties of the tissues can make the difference in the interpretation of the results. However, the inclusion of dispersion directly in the time domain proved until recently to be an elusive problem. In order to model the transient signal a convolution operator that takes into account the dispersive characteristics of the medium is introduced to the linear wave equation. To test the ability of this operator to handle scattering from localized scatterers, in this work, two-dimensional numerical modeling of scattering from an infinite cylinder with physical properties associated with biological tissue is calculated. The numerical solutions are compared with the exact solution synthesized from the frequency domain for a variety of tissues having distinct dispersive properties. It is shown that in all cases, the use of the convolutional propagation operator leads to the correct solution for the scattered field.

Temperature and porosity effects on wave propagation in nanobeams using bi-Helmholtz nonlocal strain-gradient elasticity

NASA Astrophysics Data System (ADS)

Reza Barati, Mohammad

2018-05-01

In this paper, applying a general nonlocal strain-gradient elasticity model with two nonlocal and one strain-gradient parameters, wave dispersion behavior of thermally affected and elastically bonded nanobeams is investigated. The two nanobeams are considered to have material imperfections or porosities evenly dispersed across the thickness. Each nanobeam has uniform thickness and is modeled by refined shear deformation beam theory with sinusoidal transverse shear strains. The governing equations of the system are derived by Hamilton's rule and are analytically solved to obtain wave frequencies and the velocity of wave propagation. In the presented graphs, one can see that porosities, temperature, nonlocal, strain gradient and bonding springs have great influences on the wave characteristics of the system.

Modelling Bathymetric Control of Near Coastal Wave Climate: Report 3

DTIC Science & Technology

1992-02-01

complexity would occur if we were to make the full set of restrictions appropriate to the parabolic approximation of the KP equation ( Kadomtsev ... Kadomtsev , B.B. and Petviashvili , V.I., 1970, "On the stability of solitary waves in weakly dispersing media", Soy. Phys. Dokl., 15, 539-541. 24 Kirby...bar theory. Theory for Small Amplitude Bars The theory which provides the framework for analysis here is given by an extended mild-slope equation

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.

Modal analysis of wave propagation in dispersive media

NASA Astrophysics Data System (ADS)

Abdelrahman, M. Ismail; Gralak, B.

2018-01-01

Surveys on wave propagation in dispersive media have been limited since the pioneering work of Sommerfeld [Ann. Phys. 349, 177 (1914), 10.1002/andp.19143491002] by the presence of branches in the integral expression of the wave function. In this article a method is proposed to eliminate these critical branches and hence to establish a modal expansion of the time-dependent wave function. The different components of the transient waves are physically interpreted as the contributions of distinct sets of modes and characterized accordingly. Then, the modal expansion is used to derive a modified analytical expression of the Sommerfeld precursor improving significantly the description of the amplitude and the oscillating period up to the arrival of the Brillouin precursor. The proposed method and results apply to all waves governed by the Helmholtz equations.

Two modified symplectic partitioned Runge-Kutta methods for solving the elastic wave equation

NASA Astrophysics Data System (ADS)

Su, Bo; Tuo, Xianguo; Xu, Ling

2017-08-01

Based on a modified strategy, two modified symplectic partitioned Runge-Kutta (PRK) methods are proposed for the temporal discretization of the elastic wave equation. The two symplectic schemes are similar in form but are different in nature. After the spatial discretization of the elastic wave equation, the ordinary Hamiltonian formulation for the elastic wave equation is presented. The PRK scheme is then applied for time integration. An additional term associated with spatial discretization is inserted into the different stages of the PRK scheme. Theoretical analyses are conducted to evaluate the numerical dispersion and stability of the two novel PRK methods. A finite difference method is used to approximate the spatial derivatives since the two schemes are independent of the spatial discretization technique used. The numerical solutions computed by the two new schemes are compared with those computed by a conventional symplectic PRK. The numerical results, which verify the new method, are superior to those generated by traditional conventional methods in seismic wave modeling.

Spatial dispersion effects upon local excitation of extrinsic plasmons in a graphene micro-disk

NASA Astrophysics Data System (ADS)

Mencarelli, D.; Bellucci, S.; Sindona, A.; Pierantoni, L.

2015-11-01

Excitation of surface plasmon waves in extrinsic graphene is studied using a full-wave electromagnetic field solver as analysis engine. Particular emphasis is placed on the role played by spatial dispersion due to the finite size of the two-dimensional material at the micro-scale. A simple instructive set up is considered where the near field of a wire antenna is held at sub-micrometric distance from a disk-shaped graphene patch. The key-input of the simulation is the graphene conductivity tensor at terahertz frequencies, being modeled by the Boltzmann transport equation for the valence and conduction electrons at the Dirac points (where a linear wave-vector dependence of the band energies is assumed). The conductivity equation is worked out in different levels of approximations, based on the relaxation time ansatz with an additional constraint for particle number conservation. Both drift and diffusion currents are shown to significantly contribute to the spatially dispersive anisotropic features of micro-scale graphene. More generally, spatial dispersion effects are predicted to influence not only plasmon propagation free of external sources, but also typical scanning probe microscopy configurations. The paper sets the focus on plasmon excitation phenomena induced by near field probes, being a central issue for the design of optical devices and photonic circuits.

Propagation of SH waves in an infinite/semi-infinite piezoelectric/piezomagnetic periodically layered structure.

PubMed

Pang, Yu; Liu, Yu-Shan; Liu, Jin-Xi; Feng, Wen-Jie

2016-04-01

In this paper, SH bulk/surface waves propagating in the corresponding infinite/semi-infinite piezoelectric (PE)/piezomagnetic (PM) and PM/PE periodically layered composites are investigated by two methods, the stiffness matrix method and the transfer matrix method. For a semi-infinite PE/PM or PM/PE medium, the free surface is parallel to the layer interface. Both PE and PM materials are assumed to be transversely isotropic solids. Dispersion equations are derived by the stiffness/transfer matrix methods, respectively. The effects of electric-magnetic (ME) boundary conditions at the free surface and the layer thickness ratios on dispersion curves are considered in detail. Numerical examples show that the results calculated by the two methods are the same. The dispersion curves of SH surface waves are below the bulk bands or inside the frequency gaps. The ratio of the layer thickness has an important effect not only on the bulk bands but also on the dispersion curves of SH surface waves. Electric and magnetic boundary conditions, respectively, determine the dispersion curves of SH surface waves for the PE/PM and PM/PE semi-infinite structures. The band structures of SH bulk waves are consistent for the PE/PM and PM/PE structures, however, the dispersive behaviors of SH surface waves are indeed different for the two composites. The realization of the above-mentioned characteristics of SH waves will make it possible to design PE/PM acoustic wave devices with periodical structures and achieve the better performance. Copyright © 2016 Elsevier B.V. All rights reserved.

Canonical structures for dispersive waves in shallow water

NASA Astrophysics Data System (ADS)

Neyzi, Fahrünisa; Nutku, Yavuz

1987-07-01

The canonical Hamiltonian structure of the equations of fluid dynamics obtained in the Boussinesq approximation are considered. New variational formulations of these equations are proposed and it is found that, as in the case of the KdV equation and the equations governing long waves in shallow water, they are degenerate Lagrangian systems. Therefore, in order to cast these equations into canonical form it is again necessary to use Dirac's theory of constraints. It is found that there are primary and secondary constraints which are second class and it is possible to construct the Hamiltonian in terms of canonical variables. Among the examples of Boussinesq equations that are discussed are the equations of Whitham-Broer-Kaup which Kupershmidt has recently expressed in symmetric form and shown to admit tri-Hamiltonian structure.

Internally driven inertial waves in geodynamo simulations

NASA Astrophysics Data System (ADS)

Ranjan, A.; Davidson, P. A.; Christensen, U. R.; Wicht, J.

2018-05-01

Inertial waves are oscillations in a rotating fluid, such as the Earth's outer core, which result from the restoring action of the Coriolis force. In an earlier work, it was argued by Davidson that inertial waves launched near the equatorial regions could be important for the α2 dynamo mechanism, as they can maintain a helicity distribution which is negative (positive) in the north (south). Here, we identify such internally driven inertial waves, triggered by buoyant anomalies in the equatorial regions in a strongly forced geodynamo simulation. Using the time derivative of vertical velocity, ∂uz/∂t, as a diagnostic for traveling wave fronts, we find that the horizontal movement in the buoyancy field near the equator is well correlated with a corresponding movement of the fluid far from the equator. Moreover, the azimuthally averaged spectrum of ∂uz/∂t lies in the inertial wave frequency range. We also test the dispersion properties of the waves by computing the spectral energy as a function of frequency, ϖ, and the dispersion angle, θ. Our results suggest that the columnar flow in the rotation-dominated core, which is an important ingredient for the maintenance of a dipolar magnetic field, is maintained despite the chaotic evolution of the buoyancy field on a fast timescale by internally driven inertial waves.

Phase-Shifted Based Numerical Method for Modeling Frequency-Dependent Effects on Seismic Reflections

NASA Astrophysics Data System (ADS)

Chen, Xuehua; Qi, Yingkai; He, Xilei; He, Zhenhua; Chen, Hui

2016-08-01

The significant velocity dispersion and attenuation has often been observed when seismic waves propagate in fluid-saturated porous rocks. Both the magnitude and variation features of the velocity dispersion and attenuation are frequency-dependent and related closely to the physical properties of the fluid-saturated porous rocks. To explore the effects of frequency-dependent dispersion and attenuation on the seismic responses, in this work, we present a numerical method for seismic data modeling based on the diffusive and viscous wave equation (DVWE), which introduces the poroelastic theory and takes into account diffusive and viscous attenuation in diffusive-viscous-theory. We derive a phase-shift wave extrapolation algorithm in frequencywavenumber domain for implementing the DVWE-based simulation method that can handle the simultaneous lateral variations in velocity, diffusive coefficient and viscosity. Then, we design a distributary channels model in which a hydrocarbon-saturated sand reservoir is embedded in one of the channels. Next, we calculated the synthetic seismic data to analytically and comparatively illustrate the seismic frequency-dependent behaviors related to the hydrocarbon-saturated reservoir, by employing DVWE-based and conventional acoustic wave equation (AWE) based method, respectively. The results of the synthetic seismic data delineate the intrinsic energy loss, phase delay, lower instantaneous dominant frequency and narrower bandwidth due to the frequency-dependent dispersion and attenuation when seismic wave travels through the hydrocarbon-saturated reservoir. The numerical modeling method is expected to contribute to improve the understanding of the features and mechanism of the seismic frequency-dependent effects resulted from the hydrocarbon-saturated porous rocks.

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.

Propagation phenomena in monostable integro-differential equations: Acceleration or not?

NASA Astrophysics Data System (ADS)

Alfaro, Matthieu; Coville, Jérôme

2017-11-01

We consider the homogeneous integro-differential equation ∂t u = J * u - u + f (u) with a monostable nonlinearity f. Our interest is twofold: we investigate the existence/nonexistence of travelling waves, and the propagation properties of the Cauchy problem. When the dispersion kernel J is exponentially bounded, travelling waves are known to exist and solutions of the Cauchy problem typically propagate at a constant speed [7,10,11,22,26,27]. On the other hand, when the dispersion kernel J has heavy tails and the nonlinearity f is nondegenerate, i.e. f‧ (0) > 0, travelling waves do not exist and solutions of the Cauchy problem propagate by accelerating [14,20,27]. For a general monostable nonlinearity, a dichotomy between these two types of propagation behaviour is still not known. The originality of our work is to provide such dichotomy by studying the interplay between the tails of the dispersion kernel and the Allee effect induced by the degeneracy of f, i.e. f‧ (0) = 0. First, for algebraic decaying kernels, we prove the exact separation between existence and nonexistence of travelling waves. This in turn provides the exact separation between nonacceleration and acceleration in the Cauchy problem. In the latter case, we provide a first estimate of the position of the level sets of the solution.

Dispersion of doppleron-phonon modes in strong coupling regime.

PubMed

Gudkov, V V; Zhevstovskikh, I V

2004-04-01

The dispersion equation for doppleron-phonon modes was constructed and solved analytically in the strong coupling regime. The Fermi surface model proposed previously for calculating the doppleron spectrum in an indium crystal was used. It was shown that in the vicinity of doppleron-phonon resonance, the dispersion curves of coupled modes form a gap qualitatively different from the one observed under helicon-phonon resonance: there is a frequency interval forbidden for existence of waves of definite circular polarization depending upon direction of the external DC magnetic field. The physical reason for it is interaction of the waves which have oppositely directed group velocities.

Propagation of Electromagnetic Waves in Slab Waveguide Structure Consisting of Chiral Nihility Claddings and Negative-Index Material Core Layer

NASA Astrophysics Data System (ADS)

Helal, Alaa N. Abu; Taya, Sofyan A.; Elwasife, Khitam Y.

2018-06-01

The dispersion equation of an asymmetric three-layer slab waveguide, in which all layers are chiral materials is presented. Then, the dispersion equation of a symmetric slab waveguide, in which the claddings are chiral materials and the core layer is negative index material, is derived. Normalized cut-off frequencies, field profile, and energies flow of right-handed and left-handed circularly polarized modes are derived and plotted. We consider both odd and even guided modes. Numerical results of guided low-order modes are provided. Some novel features, such as abnormal dispersion curves, are found.

S-Wave Normal Mode Propagation in Aluminum Cylinders

USGS Publications Warehouse

Lee, Myung W.; Waite, William F.

2010-01-01

Large amplitude waveform features have been identified in pulse-transmission shear-wave measurements through cylinders that are long relative to the acoustic wavelength. The arrival times and amplitudes of these features do not follow the predicted behavior of well-known bar waves, but instead they appear to propagate with group velocities that increase as the waveform feature's dominant frequency increases. To identify these anomalous features, the wave equation is solved in a cylindrical coordinate system using an infinitely long cylinder with a free surface boundary condition. The solution indicates that large amplitude normal-mode propagations exist. Using the high-frequency approximation of the Bessel function, an approximate dispersion relation is derived. The predicted amplitude and group velocities using the approximate dispersion relation qualitatively agree with measured values at high frequencies, but the exact dispersion relation should be used to analyze normal modes for full ranges of frequency of interest, particularly at lower frequencies.

Controlling Wavebreaking in a Viscous Fluid Conduit

NASA Astrophysics Data System (ADS)

Anderson, Dalton; Maiden, Michelle; Hoefer, Mark

2015-11-01

This poster will present a new technique in the experimental investigation of dispersive hydrodynamics. In shallow water flows, internal ocean waves, superfluids, and optical media, wave breaking can be resolved by a dispersive shock wave (DSW). In this work, an experimental method to control the location of DSW formation (gradient catastrophe) is explained. The central idea is to convert an initial value problem (Riemann problem) into an equivalent boundary value problem. The system to which this technique is applied is a fluid conduit resulting from high viscosity contrast between a buoyant interior and heavier exterior fluid. The conduit cross-sectional area is modeled by a nonlinear, conservative, dispersive, third order partial differential equation. Using this model, the aim is to predict the breaking location of a DSW by controlling one boundary condition. An analytical expression for this boundary condition is derived by solving the dispersionless equation backward in time from the desired step via the method of characteristics. This is used in experiment to generate an injection rate profile for a high precision piston pump. This translates to the desired conduit shape. Varying the jump height and desired breaking location indicates good control of DSW formation. This result can be improved by deriving a conduit profile by numerical simulation of the full model equation. Controlling the breaking location of a DSW allows for the investigation of dynamics independent of the boundary. Support provided by NSF CAREER DMS-1255422 , NSF EXTREEMS.

A low-dispersion, exactly energy-charge-conserving semi-implicit relativistic particle-in-cell algorithm

NASA Astrophysics Data System (ADS)

Chen, Guangye; Luis, Chacon; Bird, Robert; Stark, David; Yin, Lin; Albright, Brian

2017-10-01

Leap-frog based explicit algorithms, either ``energy-conserving'' or ``momentum-conserving'', do not conserve energy discretely. Time-centered fully implicit algorithms can conserve discrete energy exactly, but introduce large dispersion errors in the light-wave modes, regardless of timestep sizes. This can lead to intolerable simulation errors where highly accurate light propagation is needed (e.g. laser-plasma interactions, LPI). In this study, we selectively combine the leap-frog and Crank-Nicolson methods to produce a low-dispersion, exactly energy-and-charge-conserving PIC algorithm. Specifically, we employ the leap-frog method for Maxwell equations, and the Crank-Nicolson method for particle equations. Such an algorithm admits exact global energy conservation, exact local charge conservation, and preserves the dispersion properties of the leap-frog method for the light wave. The algorithm has been implemented in a code named iVPIC, based on the VPIC code developed at LANL. We will present numerical results that demonstrate the properties of the scheme with sample test problems (e.g. Weibel instability run for 107 timesteps, and LPI applications.

Control of propagation of spatially localized polariton wave packets in a Bragg mirror with embedded quantum wells

NASA Astrophysics Data System (ADS)

Sedova, I. E.; Chestnov, I. Yu.; Arakelian, S. M.; Kavokin, A. V.; Sedov, E. S.

2018-01-01

We considered the nonlinear dynamics of Bragg polaritons in a specially designed stratified semiconductor structure with embedded quantum wells, which possesses a convex dispersion. The model for the ensemble of single periodically arranged quantum wells coupled with the Bragg photon fields has been developed. In particular, the generalized Gross-Pitaevskii equation with the non-parabolic dispersion has been obtained for the Bragg polariton wave function. We revealed a number of dynamical regimes for polariton wave packets resulting from competition of the convex dispersion and the repulsive nonlinearity effects. Among the regimes are spreading, breathing and soliton propagation. When the control parameters including the exciton-photon detuning, the matter-field coupling and the nonlinearity are manipulated, the dynamical regimes switch between themselves.

Chirped solitary pulses for a nonic nonlinear Schrödinger equation on a continuous-wave background

NASA Astrophysics Data System (ADS)

Triki, Houria; Porsezian, K.; Choudhuri, Amitava; Dinda, P. Tchofo

2016-06-01

A class of derivative nonlinear Schrödinger equation with cubic-quintic-septic-nonic nonlinear terms describing the propagation of ultrashort optical pulses through a nonlinear medium with higher-order Kerr responses is investigated. An intensity-dependent chirp ansatz is adopted for solving the two coupled amplitude-phase nonlinear equations of the propagating wave. We find that the dynamics of field amplitude in this system is governed by a first-order nonlinear ordinary differential equation with a tenth-degree nonlinear term. We demonstrate that this system allows the propagation of a very rich variety of solitary waves (kink, dark, bright, and gray solitary pulses) which do not coexist in the conventional nonlinear systems that have appeared so far in the literature. The stability of the solitary wave solution under some violation on the parametric conditions is investigated. Moreover, we show that, unlike conventional systems, the nonlinear Schrödinger equation considered here meets the special requirements for the propagation of a chirped solitary wave on a continuous-wave background, involving a balance among group velocity dispersion, self-steepening, and higher-order nonlinearities of different nature.

The numerical simulation of Lamb wave propagation in laser welding of stainless steel

NASA Astrophysics Data System (ADS)

Zhang, Bo; Liu, Fang; Liu, Chang; Li, Jingming; Zhang, Baojun; Zhou, Qingxiang; Han, Xiaohui; Zhao, Yang

2017-12-01

In order to explore the Lamb wave propagation in laser welding of stainless steel, the numerical simulation is used to show the feature of Lamb wave. In this paper, according to Lamb dispersion equation, excites the Lamb wave on the edge of thin stainless steel plate, and presents the reflection coefficient for quantizing the Lamb wave energy, the results show that the reflection coefficient is increased with the welding width increasing,

Anisotropic metamaterial waveguide driven by a cold and relativistic electron beam

NASA Astrophysics Data System (ADS)

Torabi, Mahmoud; Shokri, Babak

2018-03-01

We study the interaction of a cold and relativistic electron beam with a cylindrical waveguide loaded by an anisotropic and dispersive metamaterial layer. The general dispersion relation for the transverse magnetic (TM) mode, through the linear fluid model and Maxwell equations decomposition method, is derived. The effects of some metamaterial parameters on dispersion relation are presented. A qualitative discussion shows the possibility of monomodal propagation band widening and obtaining more control on dispersion relation behavior. Especially for epsilon negative near zero metamaterials, these effects are considerable. Finally, the anisotropy and metamaterial layer thickness impacts on wave growth rate for different metamaterials are considered. The results demonstrate that we can control both wave growth rate and voltage of saturation peak by metamaterial parameters.

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.

Modification of 2-D Time-Domain Shallow Water Wave Equation using Asymptotic Expansion Method

NASA Astrophysics Data System (ADS)

Khairuman, Teuku; Nasruddin, MN; Tulus; Ramli, Marwan

2018-01-01

Generally, research on the tsunami wave propagation model can be conducted by using a linear model of shallow water theory, where a non-linear side on high order is ignored. In line with research on the investigation of the tsunami waves, the Boussinesq equation model underwent a change aimed to obtain an improved quality of the dispersion relation and non-linearity by increasing the order to be higher. To solve non-linear sides at high order is used a asymptotic expansion method. This method can be used to solve non linear partial differential equations. In the present work, we found that this method needs much computational time and memory with the increase of the number of elements.

Focusing Leaky Waves: A Class of Electromagnetic Localized Waves with Complex Spectra

NASA Astrophysics Data System (ADS)

Fuscaldo, Walter; Comite, Davide; Boesso, Alessandro; Baccarelli, Paolo; Burghignoli, Paolo; Galli, Alessandro

2018-05-01

Localized waves, i.e., the wide class of limited-diffraction, limited-dispersion solutions to the wave equation are generally characterized by real wave numbers. We consider the role played by localized waves with generally complex "leaky" wave numbers. First, the impact of the imaginary part of the wave number (i.e., the leakage constant) on the diffractive (spatial broadening) features of monochromatic localized solutions (i.e., beams) is rigorously evaluated. Then general conditions are derived to show that only a restricted class of spectra (either real or complex) allows for generating a causal localized wave. It turns out that backward leaky waves fall into this category. On this ground, several criteria for the systematic design of wideband radiators, namely, periodic radial waveguides based on backward leaky waves, are established in the framework of leaky-wave theory. An effective design method is proposed to minimize the frequency dispersion of the proposed class of devices and the impact of the "leakage" on the dispersive (temporal broadening) features of polychromatic localized solutions (i.e., pulses) is accounted for. Numerical results corroborate the concept, clearly highlighting the advantages and limitations of the leaky-wave approach for the generation of localized pulses at millimeter-wave frequencies, where energy focusing is in high demand in modern applications.

Integral Equation Method for Electromagnetic Wave Propagation in Stratified Anisotropic Dielectric-Magnetic Materials

NASA Astrophysics Data System (ADS)

Shu, Wei-Xing; Fu, Na; Lü, Xiao-Fang; Luo, Hai-Lu; Wen, Shuang-Chun; Fan, Dian-Yuan

2010-11-01

We investigate the propagation of electromagnetic waves in stratified anisotropic dielectric-magnetic materials using the integral equation method (IEM). Based on the superposition principle, we use Hertz vector formulations of radiated fields to study the interaction of wave with matter. We derive in a new way the dispersion relation, Snell's law and reflection/transmission coefficients by self-consistent analyses. Moreover, we find two new forms of the generalized extinction theorem. Applying the IEM, we investigate the wave propagation through a slab and disclose the underlying physics, which are further verified by numerical simulations. The results lead to a unified framework of the IEM for the propagation of wave incident either from a medium or vacuum in stratified dielectric-magnetic materials.

Expansion shock waves in regularized shallow-water theory

NASA Astrophysics Data System (ADS)

El, Gennady A.; Hoefer, Mark A.; Shearer, Michael

2016-05-01

We identify a new type of shock wave by constructing a stationary expansion shock solution of a class of regularized shallow-water equations that include the Benjamin-Bona-Mahony and Boussinesq equations. An expansion shock exhibits divergent characteristics, thereby contravening the classical Lax entropy condition. The persistence of the expansion shock in initial value problems is analysed and justified using matched asymptotic expansions and numerical simulations. The expansion shock's existence is traced to the presence of a non-local dispersive term in the governing equation. We establish the algebraic decay of the shock as it is gradually eroded by a simple wave on either side. More generally, we observe a robustness of the expansion shock in the presence of weak dissipation and in simulations of asymmetric initial conditions where a train of solitary waves is shed from one side of the shock.

Rogue wave modes for a derivative nonlinear Schrödinger model.

PubMed

Chan, Hiu Ning; Chow, Kwok Wing; Kedziora, David Jacob; Grimshaw, Roger Hamilton James; Ding, Edwin

2014-03-01

Rogue waves in fluid dynamics and optical waveguides are unexpectedly large displacements from a background state, and occur in the nonlinear Schrödinger equation with positive linear dispersion in the regime of positive cubic nonlinearity. Rogue waves of a derivative nonlinear Schrödinger equation are calculated in this work as a long-wave limit of a breather (a pulsating mode), and can occur in the regime of negative cubic nonlinearity if a sufficiently strong self-steepening nonlinearity is also present. This critical magnitude is shown to be precisely the threshold for the onset of modulation instabilities of the background plane wave, providing a strong piece of evidence regarding the connection between a rogue wave and modulation instability. The maximum amplitude of the rogue wave is three times that of the background plane wave, a result identical to that of the Peregrine breather in the classical nonlinear Schrödinger equation model. This amplification ratio and the resulting spectral broadening arising from modulation instability correlate with recent experimental results of water waves. Numerical simulations in the regime of marginal stability are described.

Expressions to Rayleigh circumferential phase velocity and dispersion relation for a cylindrical surface under mechanical pressure

NASA Astrophysics Data System (ADS)

Sebold, Jean Eduardo; de Lacerda, Luiz Alkimin

2018-04-01

This paper describes a substantiated mathematical theory for Rayleigh waves propagated on some types of metal cylinders. More specifically, it presents not only a new way to express the dispersion relation of Rayleigh waves propagated on the cylindrical surface, but also how it can be used to construct a mathematical equation showing that the applied static mechanical pressure affects the shear modulus of the metal cylinder. All steps, required to conclude the process, consider the equation of motion as a function of radial and circumferential coordinates only, while the axial component can be overlooked without causing any problems. Some numerical experiments are done to illustrate the changes in the Rayleigh circumferential phase velocity in a metal cylindrical section due to static mechanical pressure around its external surface.

Wave propagation in piezoelectric layered structures of film bulk acoustic resonators.

PubMed

Zhu, Feng; Qian, Zheng-Hua; Wang, Bin

2016-04-01

In this paper, we studied the wave propagation in a piezoelectric layered plate consisting of a piezoelectric thin film on an electroded elastic substrate with or without a driving electrode. Both plane-strain and anti-plane waves were taken into account for the sake of completeness. Numerical results on dispersion relations, cut-off frequencies and vibration distributions of selected modes were given. The effects of mass ratio of driving electrode layer to film layer on the dispersion curve patterns and cut-off frequencies of the plane-strain waves were discussed in detail. Results show that the mass ratio does not change the trend of dispersion curves but larger mass ratio lowers corresponding frequency at a fixed wave number and may extend the frequency range for energy trapping. Those results are of fundamental importance and can be used as a reference to develop effective two-dimensional plate equations for structural analysis and design of film bulk acoustic resonators. Copyright © 2016 Elsevier B.V. All rights reserved.

Wave instabilities in the presence of non vanishing background in nonlinear Schrödinger systems

PubMed Central

Trillo, S.; Gongora, J. S. Totero; Fratalocchi, A.

2014-01-01

We investigate wave collapse ruled by the generalized nonlinear Schrödinger (NLS) equation in 1+1 dimensions, for localized excitations with non-zero background, establishing through virial identities a new criterion for blow-up. When collapse is arrested, a semiclassical approach allows us to show that the system can favor the formation of dispersive shock waves. The general findings are illustrated with a model of interest to both classical and quantum physics (cubic-quintic NLS equation), demonstrating a radically novel scenario of instability, where solitons identify a marginal condition between blow-up and occurrence of shock waves, triggered by arbitrarily small mass perturbations of different sign. PMID:25468032

Quantum effects on compressional Alfven waves in compensated semiconductors

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

Amin, M. R.

2015-03-15

Amplitude modulation of a compressional Alfven wave in compensated electron-hole semiconductor plasmas is considered in the quantum magnetohydrodynamic regime in this paper. The important ingredients of this study are the inclusion of the particle degeneracy pressure, exchange-correlation potential, and the quantum diffraction effects via the Bohm potential in the momentum balance equations of the charge carriers. A modified nonlinear Schrödinger equation is derived for the evolution of the slowly varying amplitude of the compressional Alfven wave by employing the standard reductive perturbation technique. Typical values of the parameters for GaAs, GaSb, and GaN semiconductors are considered in analyzing the linearmore » and nonlinear dispersions of the compressional Alfven wave. Detailed analysis of the modulation instability in the long-wavelength regime is presented. For typical parameter ranges of the semiconductor plasmas and at the long-wavelength regime, it is found that the wave is modulationally unstable above a certain critical wavenumber. Effects of the exchange-correlation potential and the Bohm potential in the wave dynamics are also studied. It is found that the effect of the Bohm potential may be neglected in comparison with the effect of the exchange-correlation potential in the linear and nonlinear dispersions of the compressional Alfven wave.« less

Broken degeneracy of low frequency surface waves in semi-bounded quantum plasmas including the quantum recoil effect

NASA Astrophysics Data System (ADS)

Lee, Myoung-Jae; Jung, Young-Dae

2018-02-01

We present a derivation of the dispersion relation for electrostatic waves propagating at the interface of semi-bounded quantum plasma in which degenerate electrons are governed by the Wigner-Poisson system, while non-degenerate ions follow the classical fluid equations. We consider parameters for metallic plasmas in terms of the ratio of plasmon energy to Fermi energy. The dispersion relation is solved numerically and analyzed for various plasmon energies. The result shows that two-mode of waves can be possible: high- and low-mode. We have found that the degeneracy for high-mode wave would be broken when the plasmon energy is larger than the Fermi energy. We also discuss the characteristics of group velocities for high- and low-mode waves.

Modulation stability analysis of exact multidimensional solutions to the generalized nonlinear Schrödinger equation and the Gross-Pitaevskii equation using a variational approach.

PubMed

Petrović, Nikola Z; Aleksić, Najdan B; Belić, Milivoj

2015-04-20

We analyze the modulation stability of spatiotemporal solitary and traveling wave solutions to the multidimensional nonlinear Schrödinger equation and the Gross-Pitaevskii equation with variable coefficients that were obtained using Jacobi elliptic functions. For all the solutions we obtain either unconditional stability, or a conditional stability that can be furnished through the use of dispersion management.

Interactions of large amplitude solitary waves in viscous fluid conduits

NASA Astrophysics Data System (ADS)

Lowman, Nicholas K.; Hoefer, M. A.; El, G. A.

2014-07-01

The free interface separating an exterior, viscous fluid from an intrusive conduit of buoyant, less viscous fluid is known to support strongly nonlinear solitary waves due to a balance between viscosity-induced dispersion and buoyancy-induced nonlinearity. The overtaking, pairwise interaction of weakly nonlinear solitary waves has been classified theoretically for the Korteweg-de Vries equation and experimentally in the context of shallow water waves, but a theoretical and experimental classification of strongly nonlinear solitary wave interactions is lacking. The interactions of large amplitude solitary waves in viscous fluid conduits, a model physical system for the study of one-dimensional, truly dissipationless, dispersive nonlinear waves, are classified. Using a combined numerical and experimental approach, three classes of nonlinear interaction behavior are identified: purely bimodal, purely unimodal, and a mixed type. The magnitude of the dispersive radiation due to solitary wave interactions is quantified numerically and observed to be beyond the sensitivity of our experiments, suggesting that conduit solitary waves behave as "physical solitons." Experimental data are shown to be in excellent agreement with numerical simulations of the reduced model. Experimental movies are available with the online version of the paper.

Dispersive wave propagation in two-dimensional rigid periodic blocky materials with elastic interfaces

NASA Astrophysics Data System (ADS)

Bacigalupo, Andrea; Gambarotta, Luigi

2017-05-01

Dispersive waves in two-dimensional blocky materials with periodic microstructure made up of equal rigid units, having polygonal centro-symmetric shape with mass and gyroscopic inertia, connected with each other through homogeneous linear interfaces, have been analyzed. The acoustic behavior of the resulting discrete Lagrangian model has been obtained through a Floquet-Bloch approach. From the resulting eigenproblem derived by the Euler-Lagrange equations for harmonic wave propagation, two acoustic branches and an optical branch are obtained in the frequency spectrum. A micropolar continuum model to approximate the Lagrangian model has been derived based on a second-order Taylor expansion of the generalized macro-displacement field. The constitutive equations of the equivalent micropolar continuum have been obtained, with the peculiarity that the positive definiteness of the second-order symmetric tensor associated to the curvature vector is not guaranteed and depends both on the ratio between the local tangent and normal stiffness and on the block shape. The same results have been obtained through an extended Hamiltonian derivation of the equations of motion for the equivalent continuum that is related to the Hill-Mandel macro homogeneity condition. Moreover, it is shown that the hermitian matrix governing the eigenproblem of harmonic wave propagation in the micropolar model is exact up to the second order in the norm of the wave vector with respect to the same matrix from the discrete model. To appreciate the acoustic behavior of some relevant blocky materials and to understand the reliability and the validity limits of the micropolar continuum model, some blocky patterns have been analyzed: rhombic and hexagonal assemblages and running bond masonry. From the results obtained in the examples, the obtained micropolar model turns out to be particularly accurate to describe dispersive functions for wavelengths greater than 3-4 times the characteristic dimension of the block. Finally, in consideration that the positive definiteness of the second order elastic tensor of the micropolar model is not guaranteed, the hyperbolicity of the equation of motion has been investigated by considering the Legendre-Hadamard ellipticity conditions requiring real values for the wave velocity.

Hydroelectromechanical modelling of a piezoelectric wave energy converter

NASA Astrophysics Data System (ADS)

Renzi, E.

2016-11-01

We investigate the hydroelectromechanical-coupled dynamics of a piezoelectric wave energy converter. The converter is made of a flexible bimorph plate, clamped at its ends and forced to motion by incident ocean surface waves. The piezoceramic layers are connected in series and transform the elastic motion of the plate into useful electricity by means of the piezoelectric effect. By using a distributed-parameter analytical approach, we couple the linear piezoelectric constitutive equations for the plate with the potential-flow equations for the surface water waves. The resulting system of governing partial differential equations yields a new hydroelectromechanical dispersion relation, whose complex roots are determined with a numerical approach. The effect of the piezoelectric coupling in the hydroelastic domain generates a system of short- and long-crested weakly damped progressive waves travelling along the plate. We show that the short-crested flexural wave component gives a dominant contribution to the generated power. We determine the hydroelectromechanical resonant periods of the device, at which the power output is significant.

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

Choi, Cheong R.

The structural changes of kinetic Alfvén solitary waves (KASWs) due to higher-order terms are investigated. While the first-order differential equation for KASWs provides the dispersion relation for kinetic Alfvén waves, the second-order differential equation describes the structural changes of the solitary waves due to higher-order nonlinearity. The reductive perturbation method is used to obtain the second-order and third-order partial differential equations; then, Kodama and Taniuti's technique [J. Phys. Soc. Jpn. 45, 298 (1978)] is applied in order to remove the secularities in the third-order differential equations and derive a linear second-order inhomogeneous differential equation. The solution to this new second-ordermore » equation indicates that, as the amplitude increases, the hump-type Korteweg-de Vries solution is concentrated more around the center position of the soliton and that dip-type structures form near the two edges of the soliton. This result has a close relationship with the interpretation of the complex KASW structures observed in space with satellites.« less

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.

Kuznetsov-Ma waves train generation in a left-handed material

NASA Astrophysics Data System (ADS)

Atangana, Jacques; Giscard Onana Essama, Bedel; Biya-Motto, Frederick; Mokhtari, Bouchra; Cherkaoui Eddeqaqi, Noureddine; Crépin Kofane, Timoléon

2015-03-01

We analyze the behavior of an electromagnetic wave which propagates in a left-handed material. Second-order dispersion and cubic-quintic nonlinearities are considered. This behavior of an electromagnetic wave is modeled by a nonlinear Schrödinger equation which is solved by collective coordinates theory in order to characterize the light pulse intensity profile. More so, a specific frequency range has been outlined where electromagnetic wave behavior will be investigated. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton. When the quintic nonlinearity comes into play, it provokes strong and long internal perturbations which lead to Benjamin-Feir instability. This phenomenon, also called modulational instability, induces appearance of a Kuznetsov-Ma waves train. We numerically verify the validity of Kuznetsov-Ma theory by presenting physical conditions which lead to Kuznetsov-Ma waves train generation. Thereafter, some properties of such waves train are also verified.

Spectral modification of seismic waves propagating through solids exhibiting a resonance frequency: a 1-D coupled wave propagation-oscillation model

NASA Astrophysics Data System (ADS)

Frehner, Marcel; Schmalholz, Stefan M.; Podladchikov, Yuri

2009-02-01

A 1-D model is presented that couples the microscale oscillations of non-wetting fluid blobs in a partially saturated poroelastic medium with the macroscale wave propagation through the elastic skeleton. The fluid oscillations are caused by surface tension forces that act as the restoring forces driving the oscillations. The oscillations are described mathematically with the equation for a linear oscillator and the wave propagation is described with the 1-D elastic wave equation. Coupling is done using Hamilton's variational principle for continuous systems. The resulting linear system of two partial differential equations is solved numerically with explicit finite differences. Numerical simulations are used to analyse the effect of solids exhibiting internal oscillations, and consequently a resonance frequency, on seismic waves propagating through such media. The phase velocity dispersion relation shows a higher phase velocity in the high-frequency limit and a lower phase velocity in the low-frequency limit. At the resonance frequency a singularity in the dispersion relation occurs. Seismic waves can initiate oscillations of the fluid by transferring energy from solid to fluid at the resonance frequency. Due to this transfer, the spectral amplitude of the solid particle velocity decreases at the resonance frequency. After initiation, the oscillatory movement of the fluid continuously transfers energy at the resonance frequency back to the solid. Therefore, the spectral amplitude of the solid particle velocity is increased at the resonance frequency. Once initiated, fluid oscillations decrease in amplitude with increasing time. Consequently, the spectral peak of the solid particle velocity at the resonance frequency decreases with time.

Stimulated scattering of electromagnetic waves carrying orbital angular momentum in quantum plasmas.

PubMed

Shukla, P K; Eliasson, B; Stenflo, L

2012-07-01

We investigate stimulated scattering instabilities of coherent circularly polarized electromagnetic (CPEM) waves carrying orbital angular momentum (OAM) in dense quantum plasmas with degenerate electrons and nondegenerate ions. For this purpose, we employ the coupled equations for the CPEM wave vector potential and the driven (by the ponderomotive force of the CPEM waves) equations for the electron and ion plasma oscillations. The electrons are significantly affected by the quantum forces (viz., the quantum statistical pressure, the quantum Bohm potential, as well as the electron exchange and electron correlations due to electron spin), which are included in the framework of the quantum hydrodynamical description of the electrons. Furthermore, our investigation of the stimulated Brillouin instability of coherent CPEM waves uses the generalized ion momentum equation that includes strong ion coupling effects. The nonlinear equations for the coupled CPEM and quantum plasma waves are then analyzed to obtain nonlinear dispersion relations which exhibit stimulated Raman, stimulated Brillouin, and modulational instabilities of CPEM waves carrying OAM. The present results are useful for understanding the origin of scattered light off low-frequency density fluctuations in high-energy density plasmas where quantum effects are eminent.

Wave turbulence in shallow water models.

PubMed

Clark di Leoni, P; Cobelli, P J; Mininni, P D

2014-06-01

We study wave turbulence in shallow water flows in numerical simulations using two different approximations: the shallow water model and the Boussinesq model with weak dispersion. The equations for both models were solved using periodic grids with up to 2048{2} points. In all simulations, the Froude number varies between 0.015 and 0.05, while the Reynolds number and level of dispersion are varied in a broader range to span different regimes. In all cases, most of the energy in the system remains in the waves, even after integrating the system for very long times. For shallow flows, nonlinear waves are nondispersive and the spectrum of potential energy is compatible with ∼k{-2} scaling. For deeper (Boussinesq) flows, the nonlinear dispersion relation as directly measured from the wave and frequency spectrum (calculated independently) shows signatures of dispersion, and the spectrum of potential energy is compatible with predictions of weak turbulence theory, ∼k{-4/3}. In this latter case, the nonlinear dispersion relation differs from the linear one and has two branches, which we explain with a simple qualitative argument. Finally, we study probability density functions of the surface height and find that in all cases the distributions are asymmetric. The probability density function can be approximated by a skewed normal distribution as well as by a Tayfun distribution.

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.

The Complex-Step-Finite-Difference method

NASA Astrophysics Data System (ADS)

Abreu, Rafael; Stich, Daniel; Morales, Jose

2015-07-01

We introduce the Complex-Step-Finite-Difference method (CSFDM) as a generalization of the well-known Finite-Difference method (FDM) for solving the acoustic and elastic wave equations. We have found a direct relationship between modelling the second-order wave equation by the FDM and the first-order wave equation by the CSFDM in 1-D, 2-D and 3-D acoustic media. We present the numerical methodology in order to apply the introduced CSFDM and show an example for wave propagation in simple homogeneous and heterogeneous models. The CSFDM may be implemented as an extension into pre-existing numerical techniques in order to obtain fourth- or sixth-order accurate results with compact three time-level stencils. We compare advantages of imposing various types of initial motion conditions of the CSFDM and demonstrate its higher-order accuracy under the same computational cost and dispersion-dissipation properties. The introduced method can be naturally extended to solve different partial differential equations arising in other fields of science and engineering.

Convectively Coupled Equatorial Waves in Reanalysis and CMIP5 Simulations

NASA Astrophysics Data System (ADS)

Castanheira, J. M.; Marques, C. A. F.

2014-12-01

Convectively coupled equatorial waves (CCEWs) are a result of the interplay between the physics and dynamics in the tropical atmosphere. As a result of such interplay, tropical convection appears often organized into synoptic to planetary-scale disturbances with time scales matching those of equatorial shallow water waves. CCEWs have broad impacts within the tropics, and their simulation in general circulation models is still problematic. Several studies showed that dispersion of those waves characteristics fit the dispersion curves derived from the Matsuno's (1966) solutions of the shallow water equations on the equatorial beta plane, namely, Kelvin, equatorial Rossby, mixed Rossby-gravity, and inertio-gravity waves. However, the more common methodology used to identify those waves is yet controversial. In this communication a new methodology for the diagnosis of CCEWs will be presented. It is based on a pre-filtering of the geopotential and horizontal wind, using 3--D normal modes functions of the adiabatic linearized equations of a resting atmosphere, followed by a space--time spectral analysis to identify the spectral regions of coherence. The methodology permits a direct detection of various types of equatorial waves, compares the dispersion characteristics of the coupled waves with the theoretical dispersion curves and allows an identification of which vertical modes are more involved in the convection. Moreover, the proposed methodology is able to show the existence of free dry waves and moist coupled waves with a common vertical structure, which is in conformity with the effect of convective heating/cooling on the effective static stability, as traduced in the gross moist stability concept. The methodology is also sensible to Doppler shifting effects. The methodology has been applied to the ERA-Interim horizontal wind and geopotential height fields and to the interpolated Outgoing Longwave Radiation (OLR) data produced by the National Oceanic and Atmospheric Administration. The same type of data (i.e. u, v, Φ and OLR) from CMIP5 historical experiments (1976-2005) were analyzed. The obtained results provide examples of the aforementioned effects and points deficiencies in the models.

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.

Electromagnetic Ion Cyclotron Wavefields in a Realistic Dipole Field

NASA Astrophysics Data System (ADS)

Denton, R. E.

2018-02-01

The latitudinal distribution and properties of electromagnetic ion cyclotron (EMIC) waves determine the total effect of those waves on relativistic electrons. Here we describe the latitudinal variation of EMIC waves simulated self-consistently in a dipole magnetic field for a plasmasphere or plume-like plasma at geostationary orbit with cold H+, He+, and O+ and hot protons with temperature anisotropy. The waves grow as they propagate away from the magnetic equator to higher latitude, while the wave vector turns outward radially and the polarization becomes linear. We calculate the detailed wave spectrum in four latitudinal ranges varying from magnetic latitude (MLAT) close to 0° (magnetic equator) up to 21°. The strongest waves are propagating away from the magnetic equator, but some wave power propagating toward the magnetic equator is observed due to local generation (especially close to the magnetic equator) or reflection. The He band waves, which are generated relatively high up on their dispersion surface, are able to propagate all the way to MLAT = 21°, but the H band waves experience frequency filtering, with no equatorial waves propagating to MLAT = 21° and only the higher-frequency waves propagating to MLAT = 14°. The result is that the wave power averaged k∥, which determines the relativistic electron minimum resonance energy, scales like the inverse of the local magnetic field for the He mode, whereas it is almost constant for the H mode. While the perpendicular wave vector turns outward, it broadens. These wavefields should be useful for simulations of radiation belt particle dynamics.

Parametric instabilities of the circularly polarized Alfven waves including dispersion. [for solar wind

NASA Technical Reports Server (NTRS)

Wong, H. K.; Goldstein, M. L.

1986-01-01

A class of parametric instabilities of large-amplitude, circularly polarized Alfven waves is considered in which finite frequency (dispersive) effects are included. The dispersion equation governing the instabilities is a sixth-order polynomial which is solved numerically. As a function of K identically equal to k/k-sub-0 (where k-sub-0 and k are the wave number of the 'pump' wave and unstable sound wave, respectively), there are three regionals of instability: a modulation instability at K less than 1, a decay instability at K greater than 1, and a relatively weak and narrow instability at K close to squared divided by v-sub-A squared (where c-sub-s and v-sub-A are the sound and Alfven speeds respectively), the modulational instability occurs when beta is less than 1 (more than 1) for left-hand (right-hand) pump waves, in agreement with the previous results of Sakai and Sonnerup (1983). The growth rate of the decay instability of left-hand waves is greater than the modulational instability at all values of beta. Applications to large-amplitude wave observed in the solar wind, in computer simulations, and in the vicinity of planetary and interplanetary collisionless shocks are discussed.

Lamb wave dispersion ultrasound vibrometry (LDUV) method for quantifying mechanical properties of viscoelastic solids.

PubMed

Nenadic, Ivan Z; Urban, Matthew W; Mitchell, Scott A; Greenleaf, James F

2011-04-07

Diastolic dysfunction is the inability of the left ventricle to supply sufficient stroke volumes under normal physiological conditions and is often accompanied by stiffening of the left-ventricular myocardium. A noninvasive technique capable of quantifying viscoelasticity of the myocardium would be beneficial in clinical settings. Our group has been investigating the use of shear wave dispersion ultrasound vibrometry (SDUV), a noninvasive ultrasound-based method for quantifying viscoelasticity of soft tissues. The primary motive of this study is the design and testing of viscoelastic materials suitable for validation of the Lamb wave dispersion ultrasound vibrometry (LDUV), an SDUV-based technique for measuring viscoelasticity of tissues with plate-like geometry. We report the results of quantifying viscoelasticity of urethane rubber and gelatin samples using LDUV and an embedded sphere method. The LDUV method was used to excite antisymmetric Lamb waves and measure the dispersion in urethane rubber and gelatin plates. An antisymmetric Lamb wave model was fitted to the wave speed dispersion data to estimate elasticity and viscosity of the materials. A finite element model of a viscoelastic plate submerged in water was used to study the appropriateness of the Lamb wave dispersion equations. An embedded sphere method was used as an independent measurement of the viscoelasticity of the urethane rubber and gelatin. The FEM dispersion data were in excellent agreement with the theoretical predictions. Viscoelasticity of the urethane rubber and gelatin obtained using the LDUV and embedded sphere methods agreed within one standard deviation. LDUV studies on excised porcine myocardium sample were performed to investigate the feasibility of the approach in preparation for open-chest in vivo studies. The results suggest that the LDUV technique can be used to quantify the mechanical properties of soft tissues with a plate-like geometry.

Dissipative nonlinear waves in a gravitating quantum fluid

NASA Astrophysics Data System (ADS)

Sahu, Biswajit; Sinha, Anjana; Roychoudhury, Rajkumar

2018-02-01

Nonlinear wave propagation is studied in a dissipative, self-gravitating Bose-Einstein condensate, starting from the Gross-Pitaevskii equation. In the absence of an exact analytical result, approximate methods like the linear analysis and perturbative approach are applied. The linear dispersion relation puts a restriction on the permissible range of the dissipation parameter. The waves get damped due to dissipation. The small amplitude analysis using reductive perturbation technique is found to yield a modified form of KdV equation, which is solved both analytically as well as numerically. Interestingly, the analytical and numerical plots match excellently with each other, in the realm of weak dissipation.

High-frequency solitons in media with induced scattering from damped low-frequency waves with nonuniform dispersion and nonlinearity

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

Aseeva, N. V., E-mail: vtyutin@hse.ru; Gromov, E. M.; Tyutin, V. V.

2015-12-15

The dynamics of high-frequency field solitons is considered using the extended nonhomogeneous nonlinear Schrödinger equation with induced scattering from damped low-frequency waves (pseudoinduced scattering). This scattering is a 3D analog of the stimulated Raman scattering from temporal spatially homogeneous damped low-frequency modes, which is well known in optics. Spatial inhomogeneities of secondorder linear dispersion and cubic nonlinearity are also taken into account. It is shown that the shift in the 3D spectrum of soliton wavenumbers toward the short-wavelength region is due to nonlinearity increasing in coordinate and to decreasing dispersion. Analytic results are confirmed by numerical calculations.

Scattering of Lamb waves by cracks in a composite graphite fiber-reinforced epoxy plate

NASA Technical Reports Server (NTRS)

Bratton, Robert; Datta, Subhendu K.; Shah, Arvind

1990-01-01

Recent investigations of space construction techniques have explored the used of composite materials in the construction of space stations and platforms. These composites offer superior strength to weight ratio and are thermally stable. For example, a composite material being considered is laminates of graphite fibers in an epoxy matrix. The overall effective elastic constants of such a medium can be calculated from fiber and matrix properties by using an effective modulus theory as shown in Datta, el. al. The investigation of propagation and scattering of elastic waves in composite materials is necessary in order to develop an ability to characterize cracks and predict the reliability of composite structures. The objective of this investigation is the characterization of a surface breaking crack by ultrasonic techniques. In particular, the use of Lamb waves for this purpose is studied here. The Lamb waves travel through the plate, encountering a crack, and scatter. Of interest is the modeling of the scattered wave in terms of the Lamb wave modes. The direct problem of propagation and scattering of Lamb waves by a surface breaking crack has been analyzed. This would permit an experimentalist to characterize the crack by comparing the measured response to the analytical model. The plate is assumed to be infinite in the x and y directions with a constant thickness in the z direction. The top and bottom surfaces are traction free. Solving the governing wave equations and using the stress-free boundary conditions results in the dispersion equation. This equation yields the guided modes in the homogeneous plate. The theoretical model is a hybrid method that combines analytical and finite elements techniques to describe the scattered displacements. A finite region containing the defects is discretized by finite elements. Outside the local region, the far field solution is expressed as a Fourier summation of the guided modes obtained from the dispersion equation. Continuity of tractions and displacements at the boundaries of the two regions provides the necessary equations to determine the expansion coefficients and the nodal displacements. In the hybrid method used here these defects can be of arbitrary shapes as well as inclusions of different materials.

Stability and instability of periodic travelling wave solutions for the critical Korteweg-de Vries and nonlinear Schrödinger equations

NASA Astrophysics Data System (ADS)

Angulo Pava, Jaime; Natali, Fábio M. Amorin

2009-04-01

In this paper we establish new results about the existence, stability, and instability of periodic travelling wave solutions related to the critical Korteweg-de Vries equation ut+5u4ux+u=0, and the critical nonlinear Schrödinger equation ivt+v+|v=0. The periodic travelling wave solutions obtained in our study tend to the classical solitary wave solutions in the infinite wavelength scenario. The stability approach is based on the theory developed by Angulo & Natali in [J. Angulo, F. Natali, Positivity properties of the Fourier transform and the stability of periodic travelling wave solutions, SIAM J. Math. Anal. 40 (2008) 1123-1151] for positive periodic travelling wave solutions associated to dispersive evolution equations of Korteweg-de Vries type. The instability approach is based on an extension to the periodic setting of arguments found in Bona & Souganidis & Strauss [J.L. Bona, P.E. Souganidis, W.A. Strauss, Stability and instability of solitary waves of Korteweg-de Vries type, Proc. Roy. Soc. London Ser. A 411 (1987) 395-412]. Regarding the critical Schrödinger equation stability/instability theories similar to the critical Korteweg-de Vries equation are obtained by using the classical Grillakis & Shatah & Strauss theory in [M. Grillakis, J. Shatah, W. Strauss, Stability theory of solitary waves in the presence of symmetry II, J. Funct. Anal. 94 (1990) 308-348; M. Grillakis, J. Shatah, W. Strauss, Stability theory of solitary waves in the presence of symmetry I, J. Funct. Anal. 74 (1987) 160-197]. The arguments presented in this investigation have prospects for the study of the stability of periodic travelling wave solutions of other nonlinear evolution equations.

Expansion shock waves in regularized shallow-water theory

PubMed Central

El, Gennady A.; Shearer, Michael

2016-01-01

We identify a new type of shock wave by constructing a stationary expansion shock solution of a class of regularized shallow-water equations that include the Benjamin–Bona–Mahony and Boussinesq equations. An expansion shock exhibits divergent characteristics, thereby contravening the classical Lax entropy condition. The persistence of the expansion shock in initial value problems is analysed and justified using matched asymptotic expansions and numerical simulations. The expansion shock's existence is traced to the presence of a non-local dispersive term in the governing equation. We establish the algebraic decay of the shock as it is gradually eroded by a simple wave on either side. More generally, we observe a robustness of the expansion shock in the presence of weak dissipation and in simulations of asymmetric initial conditions where a train of solitary waves is shed from one side of the shock. PMID:27279780

Excitation of turbulence by density waves

NASA Technical Reports Server (NTRS)

Tichen, C. M.

1985-01-01

A nonlinear system describes the microdynamical state of turbulence that is excited by density waves. It consists of an equation of propagation and a master equation. A group-scaling generates the scaled equations of many interacting groups of distribution functions. The two leading groups govern the transport processes of evolution and eddy diffusivity. The remaining sub-groups represent the relaxation for the approach of diffusivity to equilibrium. In strong turbulence, the sub-groups disperse themselves and the ensemble acts like a medium that offers an effective damping to close the hierarchy. The kinetic equation of turbulence is derived. It calculates the eddy viscosity and identifies the effective damping of the assumed medium self-consistently. It formulates the coupling mechanism for the intensification of the turbulent energy at the expense of the wave energy, and the transfer mechanism for the cascade. The spectra of velocity and density fluctuations find the power law k sup-2 and k sup-4, respectively.

Absorbing boundary conditions for second-order hyperbolic equations

NASA Technical Reports Server (NTRS)

Jiang, Hong; Wong, Yau Shu

1989-01-01

A uniform approach to construct absorbing artificial boundary conditions for second-order linear hyperbolic equations is proposed. The nonlocal boundary condition is given by a pseudodifferential operator that annihilates travelling waves. It is obtained through the dispersion relation of the differential equation by requiring that the initial-boundary value problem admits the wave solutions travelling in one direction only. Local approximation of this global boundary condition yields an nth-order differential operator. It is shown that the best approximations must be in the canonical forms which can be factorized into first-order operators. These boundary conditions are perfectly absorbing for wave packets propagating at certain group velocities. A hierarchy of absorbing boundary conditions is derived for transonic small perturbation equations of unsteady flows. These examples illustrate that the absorbing boundary conditions are easy to derive, and the effectiveness is demonstrated by the numerical experiments.

Dielectric permeability tensor and linear waves in spin-1/2 quantum kinetics with non-trivial equilibrium spin-distribution functions

NASA Astrophysics Data System (ADS)

Andreev, Pavel A.; Kuz'menkov, L. S.

2017-11-01

A consideration of waves propagating parallel to the external magnetic field is presented. The dielectric permeability tensor is derived from the quantum kinetic equations with non-trivial equilibrium spin-distribution functions in the linear approximation on the amplitude of wave perturbations. It is possible to consider the equilibrium spin-distribution functions with nonzero z-projection proportional to the difference of the Fermi steps of electrons with the chosen spin direction, while x- and y-projections are equal to zero. It is called the trivial equilibrium spin-distribution functions. In the general case, x- and y-projections of the spin-distribution functions are nonzero which is called the non-trivial regime. A corresponding equilibrium solution is found in Andreev [Phys. Plasmas 23, 062103 (2016)]. The contribution of the nontrivial part of the spin-distribution function appears in the dielectric permeability tensor in the additive form. It is explicitly found here. A corresponding modification in the dispersion equation for the transverse waves is derived. The contribution of the nontrivial part of the spin-distribution function in the spectrum of transverse waves is calculated numerically. It is found that the term caused by the nontrivial part of the spin-distribution function can be comparable with the classic terms for the relatively small wave vectors and frequencies above the cyclotron frequency. In a majority of regimes, the extra spin caused term dominates over the spin term found earlier, except the small frequency regime, where their contributions in the whistler spectrum are comparable. A decrease of the left-hand circularly polarized wave frequency, an increase of the high-frequency right-hand circularly polarized wave frequency, and a decrease of frequency changing by an increase of frequency at the growth of the wave vector for the whistler are found. A considerable decrease of the spin wave frequency is found either. It results in an increase of module of the negative group velocity of the spin wave. The found dispersion equations are used for obtaining of an effective quantum hydrodynamics reproducing these results. This generalization requires the introduction of the corresponding equation of state for the thermal part of the spin current in the spin evolution equation.

Models for short-wave instability in inviscid shear flows

NASA Astrophysics Data System (ADS)

Grimshaw, Roger

1999-11-01

The generation of instability in an invsicid fluid occurs by a resonance between two wave modes, where here the resonance occurs by a coincidence of phase speeds for a finite, non-zero wavenumber. We show that in the weakly nonlinear limit, the appropriate model consists of two coupled equations for the envelopes of the wave modes, in which the nonlinear terms are balanced with low-order cross-coupling linear dispersive terms rather than the more familiar high-order terms which arise in the nonlinear Schrodinger equation, for instance. We will show that this system may either contain gap solitons as solutions in the linearly stable case, or wave breakdown in the linearly unstable case. In this latter circumstance, the system either exhibits wave collapse in finite time, or disintegration into fine-scale structures.

Electromagnetic van Kampen waves

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

Ignatov, A. M., E-mail: aign@fpl.gpi.ru

2017-01-15

The theory of van Kampen waves in plasma with an arbitrary anisotropic distribution function is developed. The obtained solutions are explicitly expressed in terms of the permittivity tensor. There are three types of perturbations, one of which is characterized by the frequency dependence on the wave vector, while for the other two, the dispersion relation is lacking. Solutions to the conjugate equations allowing one to solve the initial value problem are analyzed.

Green's function and Bloch theory for the analysis of the dynamic response of a periodically supported beam to a moving load

NASA Astrophysics Data System (ADS)

Lassoued, R.; Lecheheb, M.; Bonnet, G.

2012-08-01

This paper describes an analytical method for the wave field induced by a moving load on a periodically supported beam. The Green's function for an Euler beam without support is evaluated by using the direct integration. Afterwards, it introduces the supports into the model established by using the superposition principle which states that the response from all the sleeper points and from the external point force add up linearly to give a total response. The periodicity of the supports is described by Bloch's theorem. The homogeneous system thus obtained represents a linear differential equation which governs rail response. It is initially solved in the homogeneous case, and it admits a no null solution if its determinant is null, this permits the establishment the dispersion equation to Bloch waves and wave bands. The Bloch waves and dispersion curves contain all the physics of the dynamic problem and the wave field induced by a dynamic load applied to the system is finally obtained by decomposition into Bloch waves, similarly to the usual decomposition into dynamic modes on a finite structure. The method is applied to obtain the field induced by a load moving at constant velocity on a thin beam supported by periodic elastic supports.

Theory of the lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability

NASA Technical Reports Server (NTRS)

Lallemand, Pierre; Luo, Li-Shi

2000-01-01

The generalized hydrodynamics (the wave vector dependence of the transport coefficients) of a generalized lattice Boltzmann equation (LBE) is studied in detail. The generalized lattice Boltzmann equation is constructed in moment space rather than in discrete velocity space. The generalized hydrodynamics of the model is obtained by solving the dispersion equation of the linearized LBE either analytically by using perturbation technique or numerically. The proposed LBE model has a maximum number of adjustable parameters for the given set of discrete velocities. Generalized hydrodynamics characterizes dispersion, dissipation (hyper-viscosities), anisotropy, and lack of Galilean invariance of the model, and can be applied to select the values of the adjustable parameters which optimize the properties of the model. The proposed generalized hydrodynamic analysis also provides some insights into stability and proper initial conditions for LBE simulations. The stability properties of some 2D LBE models are analyzed and compared with each other in the parameter space of the mean streaming velocity and the viscous relaxation time. The procedure described in this work can be applied to analyze other LBE models. As examples, LBE models with various interpolation schemes are analyzed. Numerical results on shear flow with an initially discontinuous velocity profile (shock) with or without a constant streaming velocity are shown to demonstrate the dispersion effects in the LBE model; the results compare favorably with our theoretical analysis. We also show that whereas linear analysis of the LBE evolution operator is equivalent to Chapman-Enskog analysis in the long wave-length limit (wave vector k = 0), it can also provide results for large values of k. Such results are important for the stability and other hydrodynamic properties of the LBE method and cannot be obtained through Chapman-Enskog analysis.

Propagation of thickness-twist waves in a piezoelectric ceramic plate with unattached electrodes.

PubMed

Qian, Zheng-Hua; Kishimoto, Kikuo; Yang, Jiashi

2009-06-01

We analyze the propagation of thickness-twist waves in an unbounded piezoelectric ceramic plate with air gaps between the plate surfaces and two electrodes. These waves are also called anti-plane or shear-horizontal waves with one displacement component only. An exact solution is obtained from the equations of the linear theory of piezoelectricity. Dispersion relations of the waves are obtained and plotted. Results show that the wave frequency or speed is sensitive to the air gap thickness. This effect can be used to manipulate the behavior of the waves and has implications in acoustic wave devices.

Classical relativistic model for spin dependence in a magnetized electron gas

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

Melrose, D. B.; Mushtaq, A.; TPPD, PINSTECH, P. O. Nilore Islamabad 44000

2011-05-15

The response of a cold electron gas is generalized to include the spin of the electron described by the relativistically correct quasiclassical Bargmann-Michel-Telegdi (BMT) equation. The magnetization of the electron gas is assumed to be along the background magnetic field B and the spin-dependent contribution to the response tensor is proportional to the magnitude of the magnetization. The dispersion equation is shown to be quadratic in the refractive index squared, and dispersion curves for the two wave modes are plotted for cases where the magnetic field associated with magnetization is comparable with B. Two intrinsically spin-dependent wave modes are identified:more » one bounded by two resonances and the other by two cutoffs. The counterpart of the z mode can escape without encountering a resonance or a cutoff.« less

Dispersion relation in oscillatory reaction-diffusion systems with self-consistent flow in true slime mold.

PubMed

Yamada, H; Nakagaki, T; Baker, R E; Maini, P K

2007-06-01

In the large amoeboid organism Physarum, biochemical oscillators are spatially distributed throughout the organism and their collective motion exhibits phase waves, which carry physiological signals. The basic nature of this wave behaviour is not well-understood because, to date, an important effect has been neglected, namely, the shuttle streaming of protoplasm which accompanies the biochemical rhythms. Here we study the effects of self-consistent flow on the wave behaviour of oscillatory reaction-diffusion models proposed for the Physarum plasmodium, by means of numerical simulation for the dispersion relation and weakly nonlinear analysis for derivation of the phase equation. We conclude that the flow term is able to increase the speed of phase waves (similar to elongation of wave length). We compare the theoretical consequences with real waves observed in the organism and also point out the physiological roles of these effects on control mechanisms of intracellular communication.

Nonlinear surface waves at ferrite-metamaterial waveguide structure

NASA Astrophysics Data System (ADS)

Hissi, Nour El Houda; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Shabat, Mohammed Musa; Atangana, Jacques

2016-09-01

A new ferrite slab made of a metamaterial (MTM), surrounded by a nonlinear cover cladding and a ferrite substrate, was shown to support unusual types of electromagnetic surface waves. We impose the boundary conditions to derive the dispersion relation and others necessary to formulate the proposed structure. We analyse the dispersion properties of the nonlinear surface waves and we calculate the associated propagation index and the film-cover interface nonlinearity. In the calculation, several sets of the permeability of the MTM are considered. Results show that the waves behaviour depends on the values of the permeability of the MTM, the thickness of the waveguide and the film-cover interface nonlinearity. It is also shown that the use of the singular solutions to the electric field equation allows to identify several new properties of surface waves which do not exist in conventional waveguide.

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.

Transformation of apparent ocean wave spectra observed from an aircraft sensor platform

NASA Technical Reports Server (NTRS)

Poole, L. R.

1976-01-01

The problem considered was transformation of a unidirectional apparent ocean wave spectrum observed from an aircraft sensor platform into the true spectrum that would be observed from a stationary platform. Spectral transformation equations were developed in terms of the linear wave dispersion relationship and the wave group speed. An iterative solution to the equations was outlined and used to transform reference theoretical apparent spectra for several assumed values of average water depth. Results show that changing the average water depth leads to a redistribution of energy density among the various frequency bands of the transformed spectrum. This redistribution is most severe when much of the energy density is expected, a priori, to reside at relatively low true frequencies.

Generation of localized patterns in anharmonic lattices with cubic-quintic nonlinearities and fourth-order dispersion via a variational approach

NASA Astrophysics Data System (ADS)

Wamba, Etienne; Tchakoutio Nguetcho, Aurélien S.

2018-05-01

We use the time-dependent variational method to examine the formation of localized patterns in dynamically unstable anharmonic lattices with cubic-quintic nonlinearities and fourth-order dispersion. The governing equation is an extended nonlinear Schrödinger equation known for modified Frankel-Kontorova models of atomic lattices and here derived from an extended Bose-Hubbard model of bosonic lattices with local three-body interactions. In presence of modulated waves, we derive and investigate the ordinary differential equations for the time evolution of the amplitude and phase of dynamical perturbation. Through an effective potential, we find the modulationally unstable domains of the lattice and discuss the effect of the fourth-order dispersion in the dynamics. Direct numerical simulations are performed to support our analytical results, and a good agreement is found. Various types of localized patterns, including breathers and solitonic chirped-like pulses, form in the system as a result of interplay between the cubic-quintic nonlinearities and the second- and fourth-order dispersions.

Initial-value problem for the Gardner equation applied to nonlinear internal waves

NASA Astrophysics Data System (ADS)

Rouvinskaya, Ekaterina; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim

2017-04-01

The Gardner equation is a fundamental mathematical model for the description of weakly nonlinear weakly dispersive internal waves, when cubic nonlinearity cannot be neglected. Within this model coefficients of quadratic and cubic nonlinearity can both be positive as well as negative, depending on background conditions of the medium, where waves propagate (sea water density stratification, shear flow profile) [Rouvinskaya et al., 2014, Kurkina et al., 2011, 2015]. For the investigation of weakly dispersive behavior in the framework of nondimensional Gardner equation with fixed (positive) sign of quadratic nonlinearity and positive or negative cubic nonlinearity {eq1} partial η/partial t+6η( {1± η} )partial η/partial x+partial ^3η/partial x^3=0, } the series of numerical experiments of initial-value problem was carried out for evolution of a bell-shaped impulse of negative polarity (opposite to the sign of quadratic nonlinear coefficient): {eq2} η(x,t=0)=-asech2 ( {x/x0 } ), for which amplitude a and width x0 was varied. Similar initial-value problem was considered in the paper [Trillo et al., 2016] for the Korteweg - de Vries equation. For the Gardner equation with different signs of cubic nonlinearity the initial-value problem for piece-wise constant initial condition was considered in detail in [Grimshaw et al., 2002, 2010]. It is widely known, for example, [Pelinovsky et al., 2007], that the Gardner equation (1) with negative cubic nonlinearity has a family of classic solitary wave solutions with only positive polarity,and with limiting amplitude equal to 1. Therefore evolution of impulses (2) of negative polarity (whose amplitudes a were varied from 0.1 to 3, and widths at the level of a/2 were equal to triple width of solitons with the same amplitude for a 1) was going on a universal scenario with the generation of nonlinear Airy wave. For the Gardner equation (1) with the positive cubic nonlinearity coefficient there exist two one-parametric families of solitons (family with positive polarity, and family with negative polarity bounded below by the amplitude of 2) and two-parametric family of breathers (oscillatory wave packets). In this case varying amplitude and width of bell-shaped initial impulse leads to plenty of different evolutionary scenarios with the generation of solitary waves, breathers, solibores and nonlinear Airy wave in their various combinations. Statistical analysis of the wave field in time shows almost permanent substantial exceedance of the level of the significant wave height in some position in spatial coordinate. Evolution of Fourier spectrum of the wave field is also analyzed, and its behavior after a long time of initial wave evolution demonstrates the power asymptotic for small wave numbers and exponential asymptotic for large wave numbers. The presented results of research are obtained with the support of the grant of the President of the Russian Federation for state support of the young Russian scientists - Candidates of Sciences (MK-5208.2016.5) and Russian Foundation for Basic Research grant 16-05-00049. References: Grimshaw R., Pelinovsky D., Pelinovsky E and Slunyaev A. Generation of large-amplitude solitons in the extended Korteweg-de Vries equation // Chaos, 2002. - V.12. - No 4. - 1070-1076. Grimshaw, R., Slunyaev, A., and Pelinovsky, E. Generation of solitons and breathers in the extended Korteweg-de Vries equation with positive cubic nonlinearity //Chaos, 2010. - vol. 20.-013102. Kurkina O.E., Kurkin A.A., Soomere T., Pelinovsky E.N., Rouvinskaya E.A. Higher-order (2+4) Korteweg-de Vries - like equation for interfacial waves in a symmetric three-layer fluid // Physics of Fluids, 2011. - Volume 23. - Issue 11. - p.116602--1--13. Kurkina O., Rouvinskaya E., Talipova T., Kurkin A., Pelinovsky E. Nonlinear disintegration of sine wave in the framework of the Gardner equation // Physica D: Nonlinear Phenomena, 2015. - doi:10.1016/j.physd.2015.12.007. Pelinovsky E., Polukhina O., Slunyaev A., Talipova T. Internal solitary waves // Chapter 4 in the book ``Solitary Waves in Fluids''. WIT Press. Southampton, Boston. 2007. P. 85 - 110. Rouvinskaya E., Kurkina O., Kurkin A. Dynamics of nonlinear internal gravity waves in layered fluids // NNSTU n.a. R.E. Alekseev Press - Nizhny Novgorod, 2014 - 160 p. [In Russian] Trillo S., Klein M., Clauss G., Onorato M. Observation of dispersive shock waves developing from initial depressions in shallow water // Physica D, 2016. - http://dx.doi.org/10.1016/j.physd.2016.01.007.

Comment on "Dynamics and properties of waves in a modified Noguchi electrical transmission line"

NASA Astrophysics Data System (ADS)

Kenmogne, Fabien; Yemélé, David; Marquié, Patrick

2016-09-01

A recent paper [Phys. Rev. E 91, 022925 (2015), 10.1103/PhysRevE.91.022925] presents the derivation of the nonlinear equation modeling envelope waves in a specific case of band passed filter discrete nonlinear electrical transmission line (NLTL), called "A modified Noguchi electrical transmission line" according to the authors. Using the reductive perturbation approach in the semidiscrete approximation, they showed that the modulated waves propagating in this NLTL are described by the ordinary nonlinear Schrödinger (NLS) equation. On the basis of their results, the authors claimed that all previous works on the band passed filter NLTL, which considered the vanishing of the dc component of the signal voltage, are incorrect, and this dc term is nonzero. As a consequence, the dispersion and nonlinearity coefficients of the NLS equation are strongly different from those usually obtained, and they found, according to the sign of the product P Q , the existence of one more region (compared to the work of Marquié et al. [Phys. Rev. E 49, 828 (1994)], 10.1103/PhysRevE.49.828) in the dispersion curve that allows the motion of envelope solitons of higher frequency in the system. In this Comment we provide sufficient theoretical and numerical evidence showing that the evidence obtained by the authors otherwise is due to certain terms missed in their mathematical developments when they derived the NLS equation. Our results also suggest that the previous work of Marquié and co-workers correctly predict the fact that the dc term of the signal voltage does not exist and there exist only two regions in the dispersion curve according to the sign of the product P Q .

Effective orthorhombic anisotropic models for wavefield extrapolation

NASA Astrophysics Data System (ADS)

Ibanez-Jacome, Wilson; Alkhalifah, Tariq; Waheed, Umair bin

2014-09-01

Wavefield extrapolation in orthorhombic anisotropic media incorporates complicated but realistic models to reproduce wave propagation phenomena in the Earth's subsurface. Compared with the representations used for simpler symmetries, such as transversely isotropic or isotropic, orthorhombic models require an extended and more elaborated formulation that also involves more expensive computational processes. The acoustic assumption yields more efficient description of the orthorhombic wave equation that also provides a simplified representation for the orthorhombic dispersion relation. However, such representation is hampered by the sixth-order nature of the acoustic wave equation, as it also encompasses the contribution of shear waves. To reduce the computational cost of wavefield extrapolation in such media, we generate effective isotropic inhomogeneous models that are capable of reproducing the first-arrival kinematic aspects of the orthorhombic wavefield. First, in order to compute traveltimes in vertical orthorhombic media, we develop a stable, efficient and accurate algorithm based on the fast marching method. The derived orthorhombic acoustic dispersion relation, unlike the isotropic or transversely isotropic ones, is represented by a sixth order polynomial equation with the fastest solution corresponding to outgoing P waves in acoustic media. The effective velocity models are then computed by evaluating the traveltime gradients of the orthorhombic traveltime solution, and using them to explicitly evaluate the corresponding inhomogeneous isotropic velocity field. The inverted effective velocity fields are source dependent and produce equivalent first-arrival kinematic descriptions of wave propagation in orthorhombic media. We extrapolate wavefields in these isotropic effective velocity models using the more efficient isotropic operator, and the results compare well, especially kinematically, with those obtained from the more expensive anisotropic extrapolator.

Direct measurement of nonlinear dispersion relation for water surface waves

NASA Astrophysics Data System (ADS)

Magnus Arnesen Taklo, Tore; Trulsen, Karsten; Elias Krogstad, Harald; Gramstad, Odin; Nieto Borge, José Carlos; Jensen, Atle

2013-04-01

The linear dispersion relation for water surface waves is often taken for granted for the interpretation of wave measurements. High-resolution spatiotemporal measurements suitable for direct validation of the linear dispersion relation are on the other hand rarely available. While the imaging of the ocean surface with nautical radar does provide the desired spatiotemporal coverage, the interpretation of the radar images currently depends on the linear dispersion relation as a prerequisite, (Nieto Borge et al., 2004). Krogstad & Trulsen (2010) carried out numerical simulations with the nonlinear Schrödinger equation and its generalizations demonstrating that the nonlinear evolution of wave fields may render the linear dispersion relation inadequate for proper interpretation of observations, the reason being that the necessary domain of simultaneous coverage in space and time would allow significant nonlinear evolution. They found that components above the spectral peak can have larger phase and group velocities than anticipated by linear theory, and that the spectrum does not maintain a thin dispersion surface. We have run laboratory experiments and accurate numerical simulations designed to have sufficient resolution in space and time to deduce the dispersion relation directly. For a JONSWAP spectrum we find that the linear dispersion relation can be appropriate for the interpretation of spatiotemporal measurements. For a Gaussian spectrum with narrower bandwidth we find that the dynamic nonlinear evolution in space and time causes the directly measured dispersion relation to deviate from the linear dispersion surface in good agreement with our previous numerical predictions. This work has been supported by RCN grant 214556/F20. Krogstad, H. E. & Trulsen, K. (2010) Interpretations and observations of ocean wave spectra. Ocean Dynamics 60:973-991. Nieto Borge, J. C., Rodríguez, G., Hessner, K., Izquierdo, P. (2004) Inversion of marine radar images for surface wave analysis. J. Atmos. Ocean. Tech. 21:1291-1300.

Plasma waves produced by the xenon ion beam experiment on the Porcupine sounding rocket

NASA Technical Reports Server (NTRS)

Kintner, P. M.; Kelley, M.

1982-01-01

The production of electrostatic ion cyclotron waves by a perpendicular ion beam in the F-region ionosphere is described. The ion beam experiment was part of the Porcupine program and produced electrostatic hydrogen cyclotron waves just above harmonics of the hydrogen cyclotron frequency. The plasma process may be thought of as a magnetized background ionosphere through which an unmagnetized beam is flowing. The dispersion equation for this hypothesis is constructed and solved. Preliminary solutions agree well with the observed plasma waves.

Stationary Shock Waves with Oscillating Front in Dislocation Systems of Semiconductors

NASA Astrophysics Data System (ADS)

Gestrin, S. G.; Shchukina, E. V.

2018-05-01

The paper presents a study of weakly nonlinear wave processes in the cylindrical region of a hole gas surrounding a negatively charged dislocation in an n-type semiconductor crystal. It is shown that shock waves propagating along the dislocation are the solutions of the Korteweg-de Vries-Burgers equation when the dispersion and dissipation of medium are taken into account. Estimates are obtained for the basic physical parameters characterizing the shock wave and the region inside the Reed cylinder.

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.

Two dimensional modelling of flood flows and suspended sedimenttransport: the case of the Brenta River, Veneto (Italy)

NASA Astrophysics Data System (ADS)

Martini, P.; Carniello, L.; Avanzi, C.

2004-03-01

The paper presents a numerical model for the simulation of flood waves and suspended sediment transport in a lowland river basin of North Eastern Italy. The two dimensional depth integrated momentum and continuity equations are modified to take into account the bottom irregularities that strongly affect the hydrodynamics in partially dry areas, as for example, in the first stages of an inundation process or in tidal flow. The set of equations are solved with a standard Galerkin finite element method using a semi-implicit numerical scheme where the effects of both the small channel network and the regulation devices on the flood wave propagation are accounted for. Transport of suspended sediment and bed evolution are coupled with the hydrodynamics using an appropriate form of the advection-dispersion equation and Exner's equation. Applications to a case study are presented in which the effects of extreme flooding on the Brenta River (Italy) are examined. Urban and rural flood risk areas are identified and the effects of a alleviating action based on a diversion channel flowing into Venice Lagoon are simulated. The results show that this solution strongly reduces the flood risk in the downstream areas and can provide an important source of sediment for the Venice Lagoon. Finally, preliminary results of the sediment dispersion due to currents and waves in the Venice Lagoon are presented.

Advances in wave turbulence: rapidly rotating flows

NASA Astrophysics Data System (ADS)

Cambon, C.; Rubinstein, R.; Godeferd, F. S.

2004-07-01

At asymptotically high rotation rates, rotating turbulence can be described as a field of interacting dispersive waves by the general theory of weak wave turbulence. However, rotating turbulence has some complicating features, including the anisotropy of the wave dispersion relation and the vanishing of the wave frequency on a non-vanishing set of 'slow' modes. These features prevent straightforward application of existing theories and lead to some interesting properties, including the transfer of energy towards the slow modes. This transfer competes with, and might even replace, the transfer to small scales envisioned in standard turbulence theories. In this paper, anisotropic spectra for rotating turbulence are proposed based on weak turbulence theory; some evidence for their existence is given based on numerical calculations of the wave turbulence equations. Previous arguments based on the properties of resonant wave interactions suggest that the slow modes decouple from the others. Here, an extended wave turbulence theory with non-resonant interactions is proposed in which all modes are coupled; these interactions are possible only because of the anisotropy of the dispersion relation. Finally, the vanishing of the wave frequency on the slow modes implies that these modes cannot be described by weak turbulence theory. A more comprehensive approach to rotating turbulence is proposed to overcome this limitation.

Wave excitation by inhomogeneous suprathermal electron beams

NASA Technical Reports Server (NTRS)

Freund, H. P.; Dillenburg, D.; Wu, C. S.

1982-01-01

Wave excitation by an inhomogeneous suprathermal electron beam in a homogeneous magnetized plasma is studied. Not only is the beam density nonuniform, but the beam electrons possess a sheared bulk velocity. The general dispersion equation encompassing both electrostatic and electromagnetic effects is derived. Particular attention is given to the whistler mode. It is established that the density-gradient and velocity-shear effects are important for waves with frequencies close to the lower-hybrid resonance frequency.

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.

Lamb Wave Dispersion Ultrasound Vibrometry (LDUV) Method for Quantifying Mechanical Properties of Viscoelastic Solids

PubMed Central

Nenadic, Ivan Z.; Urban, Matthew W.; Mitchell, Scott A.; Greenleaf, James F.

2011-01-01

Diastolic dysfunction is the inability of the left ventricle to supply sufficient stroke volumes under normal physiological conditions and is often accompanied by stiffening of the left-ventricular myocardium. A noninvasive technique capable of quantifying viscoelasticity of the myocardium would be beneficial in clinical settings. Our group has been investigating the use of Shearwave Dispersion Ultrasound Vibrometry (SDUV), a noninvasive ultrasound based method for quantifying viscoelasticity of soft tissues. The primary motive of this study is the design and testing of viscoelastic materials suitable for validation of the Lamb wave Dispersion Ultrasound Vibrometry (LDUV), an SDUV-based technique for measuring viscoelasticity of tissues with plate-like geometry. We report the results of quantifying viscoelasticity of urethane rubber and gelatin samples using LDUV and an embedded sphere method. The LDUV method was used to excite antisymmetric Lamb waves and measure the dispersion in urethane rubber and gelatin plates. An antisymmetric Lamb wave model was fitted to the wave speed dispersion data to estimate elasticity and viscosity of the materials. A finite element model of a viscoelastic plate submerged in water was used to study the appropriateness of the Lamb wave dispersion equations. An embedded sphere method was used as an independent measurement of the viscoelasticity of the urethane rubber and gelatin. The FEM dispersion data were in excellent agreement with the theoretical predictions. Viscoelasticity of the urethane rubber and gelatin obtained using the LDUV and embedded sphere methods agreed within one standard deviation. LDUV studies on excised porcine myocardium sample were performed to investigate the feasibility of the approach in preparation for open-chest in vivo studies. The results suggest that the LDUV technique can be used to quantify mechanical properties of soft tissues with a plate-like geometry. PMID:21403186

Photon wave function formalism for analysis of Mach–Zehnder interferometer and sum-frequency generation

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

Ritboon, Atirach, E-mail: atirach.3.14@gmail.com; Department of Physics, Faculty of Science, Prince of Songkla University, Hat Yai 90112; Daengngam, Chalongrat, E-mail: chalongrat.d@psu.ac.th

2016-08-15

Biakynicki-Birula introduced a photon wave function similar to the matter wave function that satisfies the Schrödinger equation. Its second quantization form can be applied to investigate nonlinear optics at nearly full quantum level. In this paper, we applied the photon wave function formalism to analyze both linear optical processes in the well-known Mach–Zehnder interferometer and nonlinear optical processes for sum-frequency generation in dispersive and lossless medium. Results by photon wave function formalism agree with the well-established Maxwell treatments and existing experimental verifications.

Roy-Steiner equations for πN scattering

NASA Astrophysics Data System (ADS)

de Elvira, J. Ruiz; Ditsche, C.; Hoferichter, M.; Kubis, B.; Meißner, U.-G.

2015-10-01

In this talk, we briefly review our ongoing collaboration to precisely determine the low-energy πN scattering amplitude by means of Roy-Steiner equations. After giving a brief overview of this system of dispersive equations and their application to πN scattering, we proceed to solve for the lower partial waves of the s-channel (πN → πN) and the t-channel l( {π π to bar NN} right) sub-problems.

Reflection coefficient of qP, qS and SH at a plane boundary between viscoelastic TTI media

NASA Astrophysics Data System (ADS)

Wang, Hongwei; Peng, Suping

2016-01-01

This paper introduces a calculation method for the effective elastic stiffness tensor matrix of the viscous-elastic TTI medium based on the Chapman theory. We then obtain the phase velocity formula and seismic wave polarization formula of the viscous-elastic TTI medium, by solving the Christoffel equation; solve the phase angle of reflection and transmission wave through the numerical method in accordance with the wave slowness ellipsoid; on the basis of this assumption, and assuming that qP, qS and SH waves occurred simultaneously at the viscous-elastic anisotropic interface, establish the sixth-order Zoeppritz equation in accordance with the boundary conditions; establish the models for the upper and lower media which are viscous-elastic HTI, TTI, etc., on the basis of the sixth-order Zoeppritz equation; and study the impact of fracture dip angle, azimuth angle and frequency on the reflection coefficient. From this we obtain the following conclusions: the reflection coefficient can identify the fracture strike and dip when any information pertaining to the media is unknown; dispersion phenomenon is obvious on the axial plane of symmetry and weakened in the plane vertical to the axial plane of symmetry; the vertical-incidence longitudinal wave can stimulate the qS wave when the dip angle is not 0° or 90° under the condition of coincidence between the symmetry planes of the upper and lower media; when the symmetry planes of the upper and lower media do not coincide and the dip angle is not 0° or 90°, then the vertical-incidence qP will stimulate the qS and SH waves at the same time; the dip angle can cause the reflection coefficient curve to have a more obvious dispersion phenomenon, while the included angle between the symmetry planes of the upper and lower media will weaken the dispersion except SH; and the intercept of reflection coefficient is affected by the fracture dip and included angle between the symmetry planes of the upper and lower media.

Modeling of Nonlinear Hydrodynamics of the Coastal Areas of the Black Sea by the Chain of the Proprietary and Open Source Models

NASA Astrophysics Data System (ADS)

Kantardgi, Igor; Zheleznyak, Mark; Demchenko, Raisa; Dykyi, Pavlo; Kivva, Sergei; Kolomiets, Pavlo; Sorokin, Maxim

2014-05-01

The nearshore hydrodynamic fields are produced by the nonlinear interactions of the shoaling waves of different time scales and currents. To simulate the wind wave and swells propagated to the coasts, wave generated near shore currents, nonlinear-dispersive wave transformation and wave diffraction in interaction with coastal and port structure, sediment transport and coastal erosion the chains of the models should be used. The objective of this presentation is to provide an overview of the results of the application of the model chains for the assessment of the wave impacts on new construction designed at the Black Sea coasts and the impacts of these constructions on the coastal erosion/ accretion processes to demonstrate needs for further development of the nonlinear models for the coastal engineering applications. The open source models Wave Watch III and SWAN has been used to simulate wave statistics of the dedicated areas of the Black Sea in high resolution to calculated the statistical parameters of the extreme wave approaching coastal zone construction in accordance with coastal engineering standards. As the main tool for the costal hydrodynamic simulations the modeling system COASTOX-MORPHO has been used, that includes the following models. HWAVE -code based on hyperbolic version of mild slope equations., HWAVE-S - spectral version of HWAVE., BOUSS-FNL - fully nonlinear system of Boussinesq equations for simulation wave nonlinear -dispersive wave transformation in coastal areas. COASTOX-CUR - the code provided the numerical solution of the Nonlinear Shallow Water Equations (NLSWE) by finite-volume methods on the unstructured grid describing the long wave transformation in the coastal zone with the efficient drying -wetting algorithms to simulate the inundation of the coastal areas including tsunami wave runup. Coastox -Cur equations with the radiation stress term calculated via near shore wave fields simulate the wave generated nearhore currents. COASTOX-SED - the module of the simulation of the sediment transport in which the suspended sediments are simulated on the basis of the solution of 2-D advection -diffusion equation and the bottom sediment transport calculations are provided the basis of a library of the most popular semi-empirical formulas. MORPH - the module of the simulation of the morphological transformation of coastal zone based on the mass balance equation, on the basis of the sediment fluxes, calculated in the SED module. MORPH management submodel is responsible for the execution of the model chain "waves- current- sediments - morphodynamics- waves". The open source model SWASH has been used to simulate nonlinear resonance phenomena in coastal waters. The model chain was applied to simulate the potential impact of the designed shore protection structures at the Sochi Olympic Park on coastal morphodynamics, the wave parameters and nonlinear oscillations in the new ports designed in Gelenddjik and Taman at North-East coast of the Black Sea. The modeling results are compared with the results of the physical modeling in the hydraulic flumes of Moscow University of Civil Engineering.

Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media: II. The nonlinear theory

NASA Astrophysics Data System (ADS)

Bona, J. L.; Chen, M.; Saut, J.-C.

2004-05-01

In part I of this work (Bona J L, Chen M and Saut J-C 2002 Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media I: Derivation and the linear theory J. Nonlinear Sci. 12 283-318), a four-parameter family of Boussinesq systems was derived to describe the propagation of surface water waves. Similar systems are expected to arise in other physical settings where the dominant aspects of propagation are a balance between the nonlinear effects of convection and the linear effects of frequency dispersion. In addition to deriving these systems, we determined in part I exactly which of them are linearly well posed in various natural function classes. It was argued that linear well-posedness is a natural necessary requirement for the possible physical relevance of the model in question. In this paper, it is shown that the first-order correct models that are linearly well posed are in fact locally nonlinearly well posed. Moreover, in certain specific cases, global well-posedness is established for physically relevant initial data. In part I, higher-order correct models were also derived. A preliminary analysis of a promising subclass of these models shows them to be well posed.

Efficient computation of photonic crystal waveguide modes with dispersive material.

PubMed

Schmidt, Kersten; Kappeler, Roman

2010-03-29

The optimization of PhC waveguides is a key issue for successfully designing PhC devices. Since this design task is computationally expensive, efficient methods are demanded. The available codes for computing photonic bands are also applied to PhC waveguides. They are reliable but not very efficient, which is even more pronounced for dispersive material. We present a method based on higher order finite elements with curved cells, which allows to solve for the band structure taking directly into account the dispersiveness of the materials. This is accomplished by reformulating the wave equations as a linear eigenproblem in the complex wave-vectors k. For this method, we demonstrate the high efficiency for the computation of guided PhC waveguide modes by a convergence analysis.

Nonparaxial rogue waves in optical Kerr media.

PubMed

Temgoua, D D Estelle; Kofane, T C

2015-06-01

We consider the inhomogeneous nonparaxial nonlinear Schrödinger (NLS) equation with varying dispersion, nonlinearity, and nonparaxiality coefficients, which governs the nonlinear wave propagation in an inhomogeneous optical fiber system. We present the similarity and Darboux transformations and for the chosen specific set of parameters and free functions, the first- and second-order rational solutions of the nonparaxial NLS equation are generated. In particular, the features of rogue waves throughout polynomial and Jacobian elliptic functions are analyzed, showing the nonparaxial effects. It is shown that the nonparaxiality increases the intensity of rogue waves by increasing the length and reducing the width simultaneously, by the way it increases their speed and penalizes interactions between them. These properties and the characteristic controllability of the nonparaxial rogue waves may give another opportunity to perform experimental realizations and potential applications in optical fibers.

Quantum propagation in single mode fiber

NASA Technical Reports Server (NTRS)

Joneckis, Lance G.; Shapiro, Jeffrey H.

1994-01-01

This paper presents a theory for quantum light propagation in a single-mode fiber which includes the effects of the Kerr nonlinearity, group-velocity dispersion, and linear loss. The theory reproduces the results of classical self-phase modulation, quantum four-wave mixing, and classical solution physics, within their respective regions of validity. It demonstrates the crucial role played by the Kerr-effect material time constant, in limiting the quantum phase shifts caused by the broadband zero-point fluctuations that accompany any quantized input field. Operator moment equations - approximated, numerically, via a terminated cumulant expansion - are used to obtain results for homodyne-measurement noise spectra when dispersion is negligible. More complicated forms of these equations can be used to incorporate dispersion into the noise calculations.

Nonlinear modulation near the Lighthill instability threshold in 2+1 Whitham theory

NASA Astrophysics Data System (ADS)

Bridges, Thomas J.; Ratliff, Daniel J.

2018-04-01

The dispersionless Whitham modulation equations in 2+1 (two space dimensions and time) are reviewed and the instabilities identified. The modulation theory is then reformulated, near the Lighthill instability threshold, with a slow phase, moving frame and different scalings. The resulting nonlinear phase modulation equation near the Lighthill surfaces is a geometric form of the 2+1 two-way Boussinesq equation. This equation is universal in the same sense as Whitham theory. Moreover, it is dispersive, and it has a wide range of interesting multi-periodic, quasi-periodic and multi-pulse localized solutions. For illustration the theory is applied to a complex nonlinear 2+1 Klein-Gordon equation which has two Lighthill surfaces in the manifold of periodic travelling waves. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1994-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

New integrable model of propagation of the few-cycle pulses in an anisotropic microdispersed medium

NASA Astrophysics Data System (ADS)

Sazonov, S. V.; Ustinov, N. V.

2018-03-01

We investigate the propagation of the few-cycle electromagnetic pulses in the anisotropic microdispersed medium. The effects of the anisotropy and spatial dispersion of the medium are created by the two sorts of the two-level atoms. The system of the material equations describing an evolution of the states of the atoms and the wave equations for the ordinary and extraordinary components of the pulses is derived. By applying the approximation of the sudden excitation to exclude the material variables, we reduce this system to the single nonlinear wave equation that generalizes the modified sine-Gordon equation and the Rabelo-Fokas equation. It is shown that this equation is integrable by means of the inverse scattering transformation method if an additional restriction on the parameters is imposed. The multisoliton solutions of this integrable generalization are constructed and investigated.

Numerical Simulations of Light Bullets, Using The Full Vector, Time Dependent, Nonlinear Maxwell Equations

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1995-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that we currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Karr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations.

Surface Wave Propagation on a Laterally Heterogeneous Earth

NASA Astrophysics Data System (ADS)

Tromp, Jeroen

1992-01-01

Love and Rayleigh waves propagating on the surface of the Earth exhibit path, phase and amplitude anomalies as a result of the lateral heterogeneity of the mantle. In the JWKB approximation, these anomalies can be determined by tracing surface wave trajectories, and calculating phase and amplitude anomalies along them. A time- or frequency -domain JWKB analysis yields local eigenfunctions, local dispersion relations, and conservation laws for the surface wave energy. The local dispersion relations determine the surface wave trajectories, and the energy equations determine the surface wave amplitudes. On an anisotrophic Earth model the local dispersion relation and the local vertical eigenfunctions depend explicitly on the direction of the local wavevector. Apart from the usual dynamical phase, which is the integral of the local wavevector along a raypath, there is an additional variation is phase. This additional phase, which is an analogue of the Berry phase in adiabatic quantum mechanics, vanishes in a waveguide with a local vertical two-fold symmetry axis or a local horizontal mirror plane. JWKB theory breaks down in the vicinity of caustics, where neighboring rays merge and the surface wave amplitude diverges. Based upon a potential representation of the surface wave field, a uniformly valid Maslov theory can be obtained. Surface wave trajectories are determined by a system of four ordinary differential equations which define a three-dimensional manifold in four-dimensional phase space (theta,phi,k_theta,k _phi), where theta is colatitude, phi is longitude, and k_theta and k _phi are the covariant components of the wavevector. There are no caustics in phase space; it is only when the rays in phase space are projected onto configuration space (theta,phi), the mixed spaces (k_theta,phi ) and (theta,k_phi), or onto momentum space (k_theta,k _phi), that caustics occur. The essential strategy is to employ a mixed or momentum space representation of the wavefield in the vicinity of a configuration space caustic.

Particle Simulations in Magnetospheric Plasmas

DTIC Science & Technology

1989-12-18

Foreshock As an application of the simulation method used in the proposed research (Broadband electrostatic noise), the beam instability in the... foreshock has been investigated. Electrons backstreaming into the Earth’s foreshock generate waves near the plasma frequency by the beam instability. Two...results and numerical solutions of the dispersion equation indicate that the center frequency of the intense narrowband waves near the foreshock boundary

Resonant excitation of coupled Rayleigh waves in a short and narrow fluid channel clad between two identical metal plates

DOE PAGES

García-Chocano, Victor M.; López-Rios, Tomás; Krokhin, Arkadii; ...

2011-12-23

Transmission of ultrasonic waves through a slit between two water immersed brass plates is studied for sub-wavelength plate thicknesses and slit apertures. Extraordinary high absorption is observed at discrete frequencies corresponding to resonant excitation of Rayleigh waves on the both sides of the channel. The coupling of the Rayleigh waves occurs through the fluid and the corresponding contribution to the dispersion has been theoretically derived and also experimentally confirmed. Symmetric and anti-symmetric modes are predicted but only the symmetric mode resonances have been observed. It follows from the dispersion equation that the coupled Rayleigh waves cannot be excited in amore » channel with apertures less than the critical one. The calculated critical aperture is in a good agreement with the measured acoustic spectra. These findings could be applied to design a broadband absorptive metamaterial.« less

Chiral Anomalous Dispersion

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

Sadofyev, Andrey; Sen, Srimoyee

The linearized Einstein equation describing graviton propagation through a chiral medium appears to be helicity dependent. We analyze features of the corresponding spectrum in a collision-less regime above a flat background. In the long wave-length limit, circularly polarized metric perturbations travel with a helicity dependent group velocity that can turn negative giving rise to a new type of an anomalous dispersion. We further show that this chiral anomalous dispersion is a general feature of polarized modes propagating through chiral plasmas extending our result to the electromagnetic sector.

Chiral Anomalous Dispersion

DOE PAGES

Sadofyev, Andrey; Sen, Srimoyee

2018-02-16

The linearized Einstein equation describing graviton propagation through a chiral medium appears to be helicity dependent. We analyze features of the corresponding spectrum in a collision-less regime above a flat background. In the long wave-length limit, circularly polarized metric perturbations travel with a helicity dependent group velocity that can turn negative giving rise to a new type of an anomalous dispersion. We further show that this chiral anomalous dispersion is a general feature of polarized modes propagating through chiral plasmas extending our result to the electromagnetic sector.

Propagation behavior of two transverse surface waves in a three-layer piezoelectric/piezomagnetic structure

NASA Astrophysics Data System (ADS)

Nie, Guoquan; Liu, Jinxi; Liu, Xianglin

2017-10-01

Propagation of transverse surface waves in a three-layer system consisting of a piezoelectric/piezomagnetic (PE/PM) bi-layer bonded on an elastic half-space is theoretically investigated in this paper. Dispersion relations and mode shapes for transverse surface waves are obtained in closed form under electrically open and shorted boundary conditions at the upper surface. Two transverse surface waves related both to Love-type wave and Bleustein-Gulyaev (B-G) type wave propagating in corresponding three-layer structure are discussed through numerically solving the derived dispersion equation. The results show that Love-type wave possesses the property of multiple modes, it can exist all of the values of wavenumber for every selected thickness ratios regardless of the electrical boundary conditions. The presence of PM interlayer makes the phase velocity of Love-type wave decrease. There exist two modes allowing the propagation of B-G type wave under electrically shorted circuit, while only one mode appears in the case of electrically open circuit. The modes of B-G type wave are combinations of partly normal dispersion and partly anomalous dispersion whether the electrically open or shorted. The existence range of mode for electrically open case is greatly related to the thickness ratios, with the thickness of PM interlayer increasing the wavenumber range for existence of B-G type wave quickly shortened. When the thickness ratio is large enough, the wavenumber range of the second mode for electrically shorted circuit is extremely narrow which can be used to remove as an undesired mode. The propagation behaviors and mode shapes of transverse surface waves can be regulated by the modification of the thickness of PM interlayer. The obtained results provide a theoretical prediction and basis for applications of PE-PM composites and acoustic wave devices.

Solitary waves with weak transverse perturbations in quantum dusty plasmas

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

Ur-Rehman, H.; Masood, W.; Siddiq, M.

2008-12-15

Using the quantum hydrodynamic model, quantum dust ion-acoustic solitary waves are investigated in the presence of weak transverse perturbations. The linear dispersion relation is obtained using the Fourier analysis. The two-dimensional (2D) propagation of small amplitude nonlinear waves is studied by deriving the Kadomtsev-Petviashvili (KP) equation. The traveling wave solution of the KP equation is obtained by employing the tanh method. By dint of this solution, the effects of quantum Bohm pressure and the dust concentration on the 2D solitary structure are studied. The effect of quantum Bohm potential on the stability of the KP soliton is also investigated. Themore » results are supported by the numerical analysis and the relevance of the present investigation in dense astrophysical environments is also pointed out.« less

Compacton solutions in a class of generalized fifth-order Korteweg-de Vries equations.

PubMed

Cooper, F; Hyman, J M; Khare, A

2001-08-01

Solitons play a fundamental role in the evolution of general initial data for quasilinear dispersive partial differential equations, such as the Korteweg-de Vries (KdV), nonlinear Schrödinger, and the Kadomtsev-Petviashvili equations. These integrable equations have linear dispersion and the solitons have infinite support. We have derived and investigate a new KdV-like Hamiltonian partial differential equation from a four-parameter Lagrangian where the nonlinear dispersion gives rise to solitons with compact support (compactons). The new equation does not seem to be integrable and only mass, momentum, and energy seem to be conserved; yet, the solitons display almost the same modal decompositions and structural stability observed in integrable partial differential equations. The compactons formed from arbitrary initial data, are nonlinearly self-stabilizing, and maintain their coherence after multiple collisions. The robustness of these compactons and the inapplicability of the inverse scattering tools, that worked so well for the KdV equation, make it clear that there is a fundamental mechanism underlying the processes beyond integrability. We have found explicit formulas for multiple classes of compact traveling wave solutions. When there are more than one compacton solution for a particular set of parameters, the wider compacton is the minimum of a reduced Hamiltonian and is the only one that is stable.

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.

Dispersion relation for electromagnetic propagation in stochastic dielectric and magnetic helical photonic crystals

NASA Astrophysics Data System (ADS)

Avendaño, Carlos G.; Reyes, Arturo

2017-03-01

We theoretically study the dispersion relation for axially propagating electromagnetic waves throughout a one-dimensional helical structure whose pitch and dielectric and magnetic properties are spatial random functions with specific statistical characteristics. In the system of coordinates rotating with the helix, by using a matrix formalism, we write the set of differential equations that governs the expected value of the electromagnetic field amplitudes and we obtain the corresponding dispersion relation. We show that the dispersion relation depends strongly on the noise intensity introduced in the system and the autocorrelation length. When the autocorrelation length increases at fixed fluctuation and when the fluctuation augments at fixed autocorrelation length, the band gap widens and the attenuation coefficient of electromagnetic waves propagating in the random medium gets larger. By virtue of the degeneracy in the imaginary part of the eigenvalues associated with the propagating modes, the random medium acts as a filter for circularly polarized electromagnetic waves, in which only the propagating backward circularly polarized wave can propagate with no attenuation. Our results are valid for any kind of dielectric and magnetic structures which possess a helical-like symmetry such as cholesteric and chiral smectic-C liquid crystals, structurally chiral materials, and stressed cholesteric elastomers.

Kinetic Alfvén solitary and rogue waves in superthermal plasmas

NASA Astrophysics Data System (ADS)

Bains, A. S.; Li, Bo; Xia, Li-Dong

2014-03-01

We investigate the small but finite amplitude solitary Kinetic Alfvén waves (KAWs) in low β plasmas with superthermal electrons modeled by a kappa-type distribution. A nonlinear Korteweg-de Vries (KdV) equation describing the evolution of KAWs is derived by using the standard reductive perturbation method. Examining the dependence of the nonlinear and dispersion coefficients of the KdV equation on the superthermal parameter κ, plasma β, and obliqueness of propagation, we show that these parameters may change substantially the shape and size of solitary KAW pulses. Only sub-Alfvénic, compressive solitons are supported. We then extend the study to examine kinetic Alfvén rogue waves by deriving a nonlinear Schrödinger equation from the KdV equation. Rational solutions that form rogue wave envelopes are obtained. We examine how the behavior of rogue waves depends on the plasma parameters in question, finding that the rogue envelopes are lowered with increasing electron superthermality whereas the opposite is true when the plasma β increases. The findings of this study may find applications to low β plasmas in astrophysical environments where particles are superthermally distributed.

Generalized thermoelastic diffusive waves in heat conducting materials

NASA Astrophysics Data System (ADS)

Sharma, J. N.

2007-04-01

Keeping in view the applications of diffusion processes in geophysics and electronics industry, the aim of the present paper is to give a detail account of the plane harmonic generalized thermoelastic diffusive waves in heat conducting solids. According to the characteristic equation, three longitudinal waves namely, elastodiffusive (ED), mass diffusion (MD-mode) and thermodiffusive (TD-mode), can propagate in such solids in addition to transverse waves. The transverse waves get decoupled from rest of the fields and hence remain unaffected due to temperature change and mass diffusion effects. These waves travel without attenuation and dispersion. The other generalized thermoelastic diffusive waves are significantly influenced by the interacting fields and hence suffer both attenuation and dispersion. At low frequency mass diffusion and thermal waves do not exist but at high-frequency limits these waves propagate with infinite velocity being diffusive in character. Moreover, in the low-frequency regions, the disturbance is mainly dominant by mechanical process of transportation of energy and at high-frequency regions it is significantly dominated by a close to diffusive process (heat conduction or mass diffusion). Therefore, at low-frequency limits the waves like modes are identifiable with small amplitude waves in elastic materials that do not conduct heat. The general complex characteristic equation is solved by using irreducible case of Cardano's method with the help of DeMoivre's theorem in order to obtain phase speeds, attenuation coefficients and specific loss factor of energy dissipation of various modes. The propagation of waves in case of non-heat conducting solids is also discussed. Finally, the numerical solution is carried out for copper (solvent) and zinc (solute) materials and the obtained phase velocities, attenuation coefficients and specific loss factor of various thermoelastic diffusive waves are presented graphically.

Dispersion analysis of leaky guided waves in fluid-loaded waveguides of generic shape.

PubMed

Mazzotti, M; Marzani, A; Bartoli, I

2014-01-01

A fully coupled 2.5D formulation is proposed to compute the dispersive parameters of waveguides with arbitrary cross-section immersed in infinite inviscid fluids. The discretization of the waveguide is performed by means of a Semi-Analytical Finite Element (SAFE) approach, whereas a 2.5D BEM formulation is used to model the impedance of the surrounding infinite fluid. The kernels of the boundary integrals contain the fundamental solutions of the space Fourier-transformed Helmholtz equation, which governs the wave propagation process in the fluid domain. Numerical difficulties related to the evaluation of singular integrals are avoided by using a regularization procedure. To improve the numerical stability of the discretized boundary integral equations for the external Helmholtz problem, the so called CHIEF method is used. The discrete wave equation results in a nonlinear eigenvalue problem in the complex axial wavenumbers that is solved at the frequencies of interest by means of a contour integral algorithm. In order to separate physical from non-physical solutions and to fulfill the requirement of holomorphicity of the dynamic stiffness matrix inside the complex wavenumber contour, the phase of the radial bulk wavenumber is uniquely defined by enforcing the Snell-Descartes law at the fluid-waveguide interface. Three numerical applications are presented. The computed dispersion curves for a circular bar immersed in oil are in agreement with those extracted using the Global Matrix Method. Novel results are presented for viscoelastic steel bars of square and L-shaped cross-section immersed in water. Copyright © 2013 Elsevier B.V. All rights reserved.

Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert Problem approach

NASA Astrophysics Data System (ADS)

Tovbis, Alexander; El, Gennady A.

2016-10-01

The main goal of this paper is to put together: a) the Whitham theory applicable to slowly modulated N-phase nonlinear wave solutions to the focusing nonlinear Schrödinger (fNLS) equation, and b) the Riemann-Hilbert Problem approach to particular solutions of the fNLS in the semiclassical (small dispersion) limit that develop slowly modulated N-phase nonlinear wave in the process of evolution. Both approaches have their own merits and limitations. Understanding of the interrelations between them could prove beneficial for a broad range of problems involving the semiclassical fNLS.

Linear and nonlinear ion-acoustic waves in nonrelativistic quantum plasmas with arbitrary degeneracy.

PubMed

Haas, Fernando; Mahmood, Shahzad

2015-11-01

Linear and nonlinear ion-acoustic waves are studied in a fluid model for nonrelativistic, unmagnetized quantum plasma with electrons with an arbitrary degeneracy degree. The equation of state for electrons follows from a local Fermi-Dirac distribution function and applies equally well both to fully degenerate and classical, nondegenerate limits. Ions are assumed to be cold. Quantum diffraction effects through the Bohm potential are also taken into account. A general coupling parameter valid for dilute and dense plasmas is proposed. The linear dispersion relation of the ion-acoustic waves is obtained and the ion-acoustic speed is discussed for the limiting cases of extremely dense or dilute systems. In the long-wavelength limit, the results agree with quantum kinetic theory. Using the reductive perturbation method, the appropriate Korteweg-de Vries equation for weakly nonlinear solutions is obtained and the corresponding soliton propagation is analyzed. It is found that soliton hump and dip structures are formed depending on the value of the quantum parameter for the degenerate electrons, which affect the phase velocities in the dispersive medium.

Linear and nonlinear ion-acoustic waves in nonrelativistic quantum plasmas with arbitrary degeneracy

NASA Astrophysics Data System (ADS)

Haas, Fernando; Mahmood, Shahzad

2015-11-01

Linear and nonlinear ion-acoustic waves are studied in a fluid model for nonrelativistic, unmagnetized quantum plasma with electrons with an arbitrary degeneracy degree. The equation of state for electrons follows from a local Fermi-Dirac distribution function and applies equally well both to fully degenerate and classical, nondegenerate limits. Ions are assumed to be cold. Quantum diffraction effects through the Bohm potential are also taken into account. A general coupling parameter valid for dilute and dense plasmas is proposed. The linear dispersion relation of the ion-acoustic waves is obtained and the ion-acoustic speed is discussed for the limiting cases of extremely dense or dilute systems. In the long-wavelength limit, the results agree with quantum kinetic theory. Using the reductive perturbation method, the appropriate Korteweg-de Vries equation for weakly nonlinear solutions is obtained and the corresponding soliton propagation is analyzed. It is found that soliton hump and dip structures are formed depending on the value of the quantum parameter for the degenerate electrons, which affect the phase velocities in the dispersive medium.

SPREADING SPEEDS AND TRAVELING WAVES FOR NON-COOPERATIVE INTEGRO-DIFFERENCE SYSTEMS

PubMed Central

Wang, Haiyan; Castillo-Chavez, Carlos

2014-01-01

The study of spatially explicit integro-difference systems when the local population dynamics are given in terms of discrete-time generations models has gained considerable attention over the past two decades. These nonlinear systems arise naturally in the study of the spatial dispersal of organisms. The brunt of the mathematical research on these systems, particularly, when dealing with cooperative systems, has focused on the study of the existence of traveling wave solutions and the characterization of their spreading speed. Here, we characterize the minimum propagation (spreading) speed, via the convergence of initial data to wave solutions, for a large class of non cooperative nonlinear systems of integro-difference equations. The spreading speed turns out to be the slowest speed from a family of non-constant traveling wave solutions. The applicability of these theoretical results is illustrated through the explicit study of an integro-difference system with local population dynamics governed by Hassell and Comins’ non-cooperative competition model (1976). The corresponding integro-difference nonlinear systems that results from the redistribution of individuals via a dispersal kernel is shown to satisfy conditions that guarantee the existence of minimum speeds and traveling waves. This paper is dedicated to Avner Friedman as we celebrate his immense contributions to the fields of partial differential equations, integral equations, mathematical biology, industrial mathematics and applied mathematics in general. His leadership in the mathematical sciences and his mentorship of students and friends over several decades has made a huge difference in the personal and professional lives of many, including both of us. PMID:24899868

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.

Traveltime delay relative to the maximum energy of the wave train for dispersive tsunamis propagating across the Pacific Ocean: the case of 2010 and 2015 Chilean Tsunamis

NASA Astrophysics Data System (ADS)

Poupardin, A.; Heinrich, P.; Hébert, H.; Schindelé, F.; Jamelot, A.; Reymond, D.; Sugioka, H.

2018-05-01

This paper evaluates the importance of frequency dispersion in the propagation of recent trans-Pacific tsunamis. Frequency dispersion induces a time delay for the most energetic waves, which increases for long propagation distances and short source dimensions. To calculate this time delay, propagation of tsunamis is simulated and analyzed from spectrograms of time-series at specific gauges in the Pacific Ocean. One- and two-dimensional simulations are performed by solving either shallow water or Boussinesq equations and by considering realistic seismic sources. One-dimensional sensitivity tests are first performed in a constant-depth channel to study the influence of the source width. Two-dimensional tests are then performed in a simulated Pacific Ocean with a 4000-m constant depth and by considering tectonic sources of 2010 and 2015 Chilean earthquakes. For these sources, both the azimuth and the distance play a major role in the frequency dispersion of tsunamis. Finally, simulations are performed considering the real bathymetry of the Pacific Ocean. Multiple reflections, refractions as well as shoaling of waves result in much more complex time series for which the effects of the frequency dispersion are hardly discernible. The main point of this study is to evaluate frequency dispersion in terms of traveltime delays by calculating spectrograms for a time window of 6 hours after the arrival of the first wave. Results of the spectral analysis show that the wave packets recorded by pressure and tide sensors in the Pacific Ocean seem to be better reproduced by the Boussinesq model than the shallow water model and approximately follow the theoretical dispersion relationship linking wave arrival times and frequencies. Additionally, a traveltime delay is determined above which effects of frequency dispersion are considered to be significant in terms of maximum surface elevations.

Modulation instability induced by cross-phase modulation with higher-order dispersions and cubic-quintic nonlinearities in metamaterials

NASA Astrophysics Data System (ADS)

Yu, Chuanxi; Xue, Yan Ling; Liu, Ying

2014-07-01

Based on the dispersive Drude model in metamaterials (MMs), coupled nonlinear Schodinger equations are derived for two co-propagating optical waves with higher-order dispersions and cubic-quintic nonlinearities. And modulation instabilities induced by the cross -phase modulation (XMI) are studied. The impact of 3rd-, 4th-order of dispersion and quintic nonlinearity on the gain spectra of XMI is analyzed. It is shown that the 3rd-order dispersion has no effect on XMI and its gain spectra. With the increment of 4th-order dispersion, the gain spectra appear in higher frequency region (2nd spectrum region) and gain peaks become smaller.

Magnetosonic solitons in semiconductor plasmas in the presence of quantum tunneling and exchange correlation effects

NASA Astrophysics Data System (ADS)

Hussain, S.; Mahmood, S.

2018-01-01

Low frequency magnetosonic wave excitations are investigated in semiconductor hole-electron plasmas. The quantum mechanical effects such as Fermi pressure, quantum tunneling, and exchange-correlation of holes and electrons in the presence of the magnetic field are considered. The two fluid quantum magnetohydrodynamic model is used to study magnetosonic wave dynamics, while electric and magnetic fields are coupled via Maxwell equations. The dispersion relation of the magnetosonic wave in electron-hole semiconductor plasma propagating in the perpendicular direction of the magnetic field is obtained, and its dispersion effects are discussed. The Korteweg-de Vries equation (KdV) for magnetosonic solitons is derived by employing the reductive perturbation method. For numerical analysis, the plasma parameters are taken from the semiconductors such as GaAs, GaSb, GaN, and InP already existing in the literature. It is found that the phase velocity of the magnetosonic wave is increased with the inclusion of exchange-correlation force in the model. The soliton dip structures of the magnetosonic wave in GaN semiconductor plasma are obtained, which satisfy the quantum plasma conditions for electron and hole fluids. The magnetosonic soliton dip structures move with speed less than the magnetosonic wave phase speed in the lab frame. The effects of exchange-correlation force in the model and variations of magnetic field intensity and electron/hole density on the magnetosonic wave dip structures are also investigated numerically for illustration.

Two types of nonlinear wave equations for diffractive beams in bubbly liquids with nonuniform bubble number density.

PubMed

Kanagawa, Tetsuya

2015-05-01

This paper theoretically treats the weakly nonlinear propagation of diffracted sound beams in nonuniform bubbly liquids. The spatial distribution of the number density of the bubbles, initially in a quiescent state, is assumed to be a slowly varying function of the spatial coordinates; the amplitude of variation is assumed to be small compared to the mean number density. A previous derivation method of nonlinear wave equations for plane progressive waves in uniform bubbly liquids [Kanagawa, Yano, Watanabe, and Fujikawa (2010). J. Fluid Sci. Technol. 5(3), 351-369] is extended to handle quasi-plane beams in weakly nonuniform bubbly liquids. The diffraction effect is incorporated by adding a relation that scales the circular sound source diameter to the wavelength into the original set of scaling relations composed of nondimensional physical parameters. A set of basic equations for bubbly flows is composed of the averaged equations of mass and momentum, the Keller equation for bubble wall, and supplementary equations. As a result, two types of evolution equations, a nonlinear Schrödinger equation including dissipation, diffraction, and nonuniform effects for high-frequency short-wavelength case, and a Khokhlov-Zabolotskaya-Kuznetsov equation including dispersion and nonuniform effects for low-frequency long-wavelength case, are derived from the basic set.

Nucleon-nucleon interactions from dispersion relations: Elastic partial waves

NASA Astrophysics Data System (ADS)

Albaladejo, M.; Oller, J. A.

2011-11-01

We consider nucleon-nucleon (NN) interactions from chiral effective field theory. In this work we restrict ourselves to the elastic NN scattering. We apply the N/D method to calculate the NN partial waves taking as input the one-pion exchange discontinuity along the left-hand cut. This discontinuity is amenable to a chiral power counting as discussed by Lacour, Oller, and Meißner [Ann. Phys. (NY)APNYA60003-491610.1016/j.aop.2010.06.012 326, 241 (2011)], with one-pion exchange as its leading order contribution. The resulting linear integral equation for a partial wave with orbital angular momentum ℓ≥2 is solved in the presence of ℓ-1 constraints, so as to guarantee the right behavior of the D- and higher partial waves near threshold. The calculated NN partial waves are based on dispersion relations and are independent of regulator. This method can also be applied to higher orders in the calculation of the discontinuity along the left-hand cut and extended to triplet coupled partial waves.

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.

Roy-Steiner equations for pion-nucleon scattering

NASA Astrophysics Data System (ADS)

Ditsche, C.; Hoferichter, M.; Kubis, B.; Meißner, U.-G.

2012-06-01

Starting from hyperbolic dispersion relations, we derive a closed system of Roy-Steiner equations for pion-nucleon scattering that respects analyticity, unitarity, and crossing symmetry. We work out analytically all kernel functions and unitarity relations required for the lowest partial waves. In order to suppress the dependence on the high energy regime we also consider once- and twice-subtracted versions of the equations, where we identify the subtraction constants with subthreshold parameters. Assuming Mandelstam analyticity we determine the maximal range of validity of these equations. As a first step towards the solution of the full system we cast the equations for the π π to overline N N partial waves into the form of a Muskhelishvili-Omnès problem with finite matching point, which we solve numerically in the single-channel approximation. We investigate in detail the role of individual contributions to our solutions and discuss some consequences for the spectral functions of the nucleon electromagnetic form factors.

Solution of the Riemann problem for polarization waves in a two-component Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Ivanov, S. K.; Kamchatnov, A. M.; Congy, T.; Pavloff, N.

2017-12-01

We provide a classification of the possible flows of two-component Bose-Einstein condensates evolving from initially discontinuous profiles. We consider the situation where the dynamics can be reduced to the consideration of a single polarization mode (also denoted as "magnetic excitation") obeying a system of equations equivalent to the Landau-Lifshitz equation for an easy-plane ferromagnet. We present the full set of one-phase periodic solutions. The corresponding Whitham modulation equations are obtained together with formulas connecting their solutions with the Riemann invariants of the modulation equations. The problem is not genuinely nonlinear, and this results in a non-single-valued mapping of the solutions of the Whitham equations with physical wave patterns as well as the appearance of interesting elements—contact dispersive shock waves—that are absent in more standard, genuinely nonlinear situations. Our analytic results are confirmed by numerical simulations.

On a theory of surface waves in a smoothly inhomogeneous plasma in an external magnetic field

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

Kuzelev, M. V., E-mail: kuzelev@mail.ru; Orlikovskaya, N. G.

2016-12-15

A theory of surface waves in a magnetoactive plasma with smooth boundaries has been developed. A dispersion equation for surface waves has been derived for a linear law of density change at the plasma boundary. The frequencies of surface waves and their collisionless damping rates have been determined. A generalization to an arbitrary density profile at the plasma boundary is given. The collisions have been taken into account, and the application of the Landau rule in the theory of surface wave damping in a spatially inhomogeneous magnetoactive collisional plasma has been clarified.

Acceleration of stable TTI P-wave reverse-time migration with GPUs

NASA Astrophysics Data System (ADS)

Kim, Youngseo; Cho, Yongchae; Jang, Ugeun; Shin, Changsoo

2013-03-01

When a pseudo-acoustic TTI (tilted transversely isotropic) coupled wave equation is used to implement reverse-time migration (RTM), shear wave energy is significantly included in the migration image. Because anisotropy has intrinsic elastic characteristics, coupling P-wave and S-wave modes in the pseudo-acoustic wave equation is inevitable. In RTM with only primary energy or the P-wave mode in seismic data, the S-wave energy is regarded as noise for the migration image. To solve this problem, we derive a pure P-wave equation for TTI media that excludes the S-wave energy. Additionally, we apply the rapid expansion method (REM) based on a Chebyshev expansion and a pseudo-spectral method (PSM) to calculate spatial derivatives in the wave equation. When REM is incorporated with the PSM for the spatial derivatives, wavefields with high numerical accuracy can be obtained without grid dispersion when performing numerical wave modeling. Another problem in the implementation of TTI RTM is that wavefields in an area with high gradients of dip or azimuth angles can be blown up in the progression of the forward and backward algorithms of the RTM. We stabilize the wavefields by applying a spatial-frequency domain high-cut filter when calculating the spatial derivatives using the PSM. In addition, to increase performance speed, the graphic processing unit (GPU) architecture is used instead of traditional CPU architecture. To confirm the degree of acceleration compared to the CPU version on our RTM, we then analyze the performance measurements according to the number of GPUs employed.

Complete spatial and temporal locking in phase-mismatched second-harmonic generation.

PubMed

Fazio, Eugenio; Pettazzi, Federico; Centini, Marco; Chauvet, Mathieu; Belardini, Alessandro; Alonzo, Massimo; Sibilia, Concita; Bertolotti, Mario; Scalora, Micheal

2009-03-02

We experimentally demonstrate simultaneous phase and group velocity locking of fundamental and generated second harmonic pulses in Lithium Niobate, under conditions of material phase mismatch. In phase-mismatched, pulsed second harmonic generation in addition to a reflected signal two forward-propagating pulses are also generated at the interface between a linear and a second order nonlinear material: the first pulse results from the solution of the homogeneous wave equation, and propagates at the group velocity expected from material dispersion; the second pulse is the solution of the inhomogeneous wave equation, is phase-locked and trapped by the pump pulse, and follows the pump trajectory. At normal incidence, the normal and phase locked pulses simply trail each other. At oblique incidence, the consequences can be quite dramatic. The homogeneous pulse refracts as predicted by material dispersion and Snell's law, yielding at least two spatially separate second harmonic spots at the medium's exit. We thus report the first experimental results showing that, at oblique incidence, fundamental and phase-locked second harmonic pulses travel with the same group velocity and follow the same trajectory. This is direct evidence that, at least up to first order, the effective dispersion of the phase-locked pulse is similar to the dispersion of the pump pulse.

Gravitational instability in isotropic MHD plasma waves

NASA Astrophysics Data System (ADS)

Cherkos, Alemayehu Mengesha

2018-04-01

The effect of compressive viscosity, thermal conductivity and radiative heat-loss functions on the gravitational instability of infinitely extended homogeneous MHD plasma has been investigated. By taking in account these parameters we developed the six-order dispersion relation for magnetohydrodynamic (MHD) waves propagating in a homogeneous and isotropic plasma. The general dispersion relation has been developed from set of linearized basic equations and solved analytically to analyse the conditions of instability and instability of self-gravitating plasma embedded in a constant magnetic field. Our result shows that the presence of viscosity and thermal conductivity in a strong magnetic field substantially modifies the fundamental Jeans criterion of gravitational instability.

A Landau fluid model for dispersive magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Passot, T.; Sulem, P. L.

2004-11-01

A monofluid model with Landau damping is presented for strongly magnetized electron-proton collisionless plasmas whose distribution functions are close to bi-Maxwellians. This description that includes dynamical equations for the gyrotropic components of the pressure and heat flux tensors, extends the Landau-fluid model of Snyder, Hammett, and Dorland [Phys. Plasmas 4, 3974 (1997)] by retaining Hall effect and finite Larmor radius corrections. It accurately reproduces the weakly nonlinear dynamics of dispersive Alfvén waves whose wavelengths are large compared to the ion inertial length, whatever their direction of propagation, and also the rapid Landau dissipation of long magnetosonic waves in a warm plasma.

Exact axisymmetric solutions of the Maxwell equations in a nonlinear nondispersive medium.

PubMed

Petrov, E Yu; Kudrin, A V

2010-05-14

The features of propagation of intense waves are of great interest for theory and experiment in electrodynamics and acoustics. The behavior of nonlinear waves in a bounded volume is of special importance and, at the same time, is an extremely complicated problem. It seems almost impossible to find a rigorous solution to such a problem even for any model of nonlinearity. We obtain the first exact solution of this type. We present a new method for deriving exact solutions of the Maxwell equations in a nonlinear medium without dispersion and give examples of the obtained solutions that describe propagation of cylindrical electromagnetic waves in a nonlinear nondispersive medium and free electromagnetic oscillations in a cylindrical cavity resonator filled with such a medium.

Computational procedures for mixed equations with shock waves

NASA Technical Reports Server (NTRS)

Yu, N. J.; Seebass, R.

1974-01-01

This paper discusses the procedures we have developed to treat a canonical problem involving a mixed nonlinear equation with boundary data that imply a discontinuous solution. This equation arises in various physical contexts and is basic to the description of the nonlinear acoustic behavior of a shock wave near a caustic. The numerical scheme developed is of second order, treats discontinuities as such by applying the appropriate jump conditions across them, and eliminates the numerical dissipation and dispersion associated with large gradients. Our results are compared with the results of a first-order scheme and with those of a second-order scheme we have developed. The algorithm used here can easily be generalized to more complicated problems, including transonic flows with imbedded shocks.

Nonlinear tunneling of bright and dark rogue waves in combined nonlinear Schrödinger and Maxwell-Bloch systems

NASA Astrophysics Data System (ADS)

Raju, Thokala Soloman; Pal, Ritu

2018-05-01

We derive the analytical rogue wave solutions for the generalized inhomogeneous nonlinear Schrödinger-Maxwell-Bloch (GINLS-MB) equation describing the pulse propagation in erbium-doped fibre system. Then by suitably choosing the inhomogeneous parameters, we delineate the tunneling properties of rogue waves through dispersion and nonlinearity barriers or wells. Finally, we demonstrate the propagating characteristics of optical solitons by considering their tunneling through periodic barriers by the proper choice of external potential.

Pseudospectral modeling and dispersion analysis of Rayleigh waves in viscoelastic media

USGS Publications Warehouse

Zhang, K.; Luo, Y.; Xia, J.; Chen, C.

2011-01-01

Multichannel Analysis of Surface Waves (MASW) is one of the most widely used techniques in environmental and engineering geophysics to determine shear-wave velocities and dynamic properties, which is based on the elastic layered system theory. Wave propagation in the Earth, however, has been recognized as viscoelastic and the propagation of Rayleigh waves presents substantial differences in viscoelastic media as compared with elastic media. Therefore, it is necessary to carry out numerical simulation and dispersion analysis of Rayleigh waves in viscoelastic media to better understand Rayleigh-wave behaviors in the real world. We apply a pseudospectral method to the calculation of the spatial derivatives using a Chebyshev difference operator in the vertical direction and a Fourier difference operator in the horizontal direction based on the velocity-stress elastodynamic equations and relations of linear viscoelastic solids. This approach stretches the spatial discrete grid to have a minimum grid size near the free surface so that high accuracy and resolution are achieved at the free surface, which allows an effective incorporation of the free surface boundary conditions since the Chebyshev method is nonperiodic. We first use an elastic homogeneous half-space model to demonstrate the accuracy of the pseudospectral method comparing with the analytical solution, and verify the correctness of the numerical modeling results for a viscoelastic half-space comparing the phase velocities of Rayleigh wave between the theoretical values and the dispersive image generated by high-resolution linear Radon transform. We then simulate three types of two-layer models to analyze dispersive-energy characteristics for near-surface applications. Results demonstrate that the phase velocity of Rayleigh waves in viscoelastic media is relatively higher than in elastic media and the fundamental mode increases by 10-16% when the frequency is above 10. Hz due to the velocity dispersion of P and S waves. ?? 2011 Elsevier Ltd.

Algorithmic Extensions of Low-Dispersion Scheme and Modeling Effects for Acoustic Wave Simulation. Revised

NASA Technical Reports Server (NTRS)

Kaushik, Dinesh K.; Baysal, Oktay

1997-01-01

Accurate computation of acoustic wave propagation may be more efficiently performed when their dispersion relations are considered. Consequently, computational algorithms which attempt to preserve these relations have been gaining popularity in recent years. In the present paper, the extensions to one such scheme are discussed. By solving the linearized, 2-D Euler and Navier-Stokes equations with such a method for the acoustic wave propagation, several issues were investigated. Among them were higher-order accuracy, choice of boundary conditions and differencing stencils, effects of viscosity, low-storage time integration, generalized curvilinear coordinates, periodic series, their reflections and interference patterns from a flat wall and scattering from a circular cylinder. The results were found to be promising en route to the aeroacoustic simulations of realistic engineering problems.

Elementary dispersion analysis of some mimetic discretizations on triangular C-grids

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

Korn, P., E-mail: peter.korn@mpimet.mpg.de; Danilov, S.; A.M. Obukhov Institute of Atmospheric Physics, Moscow

2017-02-01

Spurious modes supported by triangular C-grids limit their application for modeling large-scale atmospheric and oceanic flows. Their behavior can be modified within a mimetic approach that generalizes the scalar product underlying the triangular C-grid discretization. The mimetic approach provides a discrete continuity equation which operates on an averaged combination of normal edge velocities instead of normal edge velocities proper. An elementary analysis of the wave dispersion of the new discretization for Poincaré, Rossby and Kelvin waves shows that, although spurious Poincaré modes are preserved, their frequency tends to zero in the limit of small wavenumbers, which removes the divergence noisemore » in this limit. However, the frequencies of spurious and physical modes become close on shorter scales indicating that spurious modes can be excited unless high-frequency short-scale motions are effectively filtered in numerical codes. We argue that filtering by viscous dissipation is more efficient in the mimetic approach than in the standard C-grid discretization. Lumping of mass matrices appearing with the velocity time derivative in the mimetic discretization only slightly reduces the accuracy of the wave dispersion and can be used in practice. Thus, the mimetic approach cures some difficulties of the traditional triangular C-grid discretization but may still need appropriately tuned viscosity to filter small scales and high frequencies in solutions of full primitive equations when these are excited by nonlinear dynamics.« less

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.

Frenkel versus charge-transfer exciton dispersion in molecular crystals

NASA Astrophysics Data System (ADS)

Cudazzo, Pierluigi; Gatti, Matteo; Rubio, Angel; Sottile, Francesco

2013-11-01

By solving the many-body Bethe-Salpeter equation at finite momentum transfer, we characterize the exciton dispersion in two prototypical molecular crystals, picene and pentacene, in which localized Frenkel excitons compete with delocalized charge-transfer excitons. We explain the exciton dispersion on the basis of the interplay between electron and hole hopping and electron-hole exchange interaction, unraveling a simple microscopic description to distinguish Frenkel and charge-transfer excitons. This analysis is general and can be applied to other systems in which the electron wave functions are strongly localized, as in strongly correlated insulators.

Approximation of wave action flux velocity in strongly sheared mean flows

NASA Astrophysics Data System (ADS)

Banihashemi, Saeideh; Kirby, James T.; Dong, Zhifei

2017-08-01

Spectral wave models based on the wave action equation typically use a theoretical framework based on depth uniform current to account for current effects on waves. In the real world, however, currents often have variations over depth. Several recent studies have made use of a depth-weighted current U˜ due to [Skop, R. A., 1987. Approximate dispersion relation for wave-current interactions. J. Waterway, Port, Coastal, and Ocean Eng. 113, 187-195.] or [Kirby, J. T., Chen, T., 1989. Surface waves on vertically sheared flows: approximate dispersion relations. J. Geophys. Res. 94, 1013-1027.] in order to account for the effect of vertical current shear. Use of the depth-weighted velocity, which is a function of wavenumber (or frequency and direction) has been further simplified in recent applications by only utilizing a weighted current based on the spectral peak wavenumber. These applications do not typically take into account the dependence of U˜ on wave number k, as well as erroneously identifying U˜ as the proper choice for current velocity in the wave action equation. Here, we derive a corrected expression for the current component of the group velocity. We demonstrate its consistency using analytic results for a current with constant vorticity, and numerical results for a measured, strongly-sheared current profile obtained in the Columbia River. The effect of choosing a single value for current velocity based on the peak wave frequency is examined, and we suggest an alternate strategy, involving a Taylor series expansion about the peak frequency, which should significantly extend the range of accuracy of current estimates available to the wave model with minimal additional programming and data transfer.

Wave propagation in a plate after impact by a projectile

NASA Technical Reports Server (NTRS)

El-Raheb, M.; Wagner, P.

1987-01-01

The wave propagation in a circular plate after impact by a cylindrical projectile is studied. In the vicinity of impact, the pressure is computed numerically. An intense pressure pulse is generated that peaks 0.2 microns after impact, then drops sharply to a plateau. The response of the plate is determined adopting a modal solution of Mindlin's equations. Velocity and acceleration histories display both propagating and dispersive features.

SPM of nonlinear surface plasmon waveguides

NASA Astrophysics Data System (ADS)

Li, Yuee; Zhang, Xiaoping

2008-10-01

Pulse propagation equation of nonlinear dispersion surface plasmon waveguide is educed strictly from wave equation. The nonlinear coefficient is defined and then used to assess and compare the nonlinear characteristic of three popular 1-D surface plasmon waveguides: the single metal-dielectric interface, the metal slab bounded by dielectric and the dielectric slab bounded by metal. SPM (self-phase modulation) of the typical surface plasmon waveguide is predicted and discussed.

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

Sibiryakov, B. P., E-mail: sibiryakovbp@ipgg.sbras.ru; Novosibirsk State University, Novosibirsk, 630090

This paper studies properties of a continuum with structure. The characteristic size of the structure governs the fact that difference relations are nonautomatically transformed into differential ones. It is impossible to consider an infinitesimal volume of a body, to which the major conservation laws could be applied, because the minimum representative volume of the body must contain at least a few elementary microstructures. The corresponding equations of motion are equations of infinite order, solutions of which include, along with usual sound waves, unusual waves with abnormally low velocities without a lower limit. It is shown that in such media weakmore » perturbations can increase or decrease outside the limits. The number of complex roots of the corresponding dispersion equation, which can be interpreted as the number of unstable solutions, depends on the specific surface of cracks and is an almost linear dependence on a logarithmic scale, as in the seismological Gutenberg–Richter law. If the distance between one pore (crack) to another one is a random value with some distribution, we must write another dispersion equation and examine different scenarios depending on the statistical characteristics of the random distribution. In this case, there are sufficient deviations from the Gutenberg–Richter law and this theoretical result corresponds to some field and laboratory observations.« less

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.

Vorticity Transport and Wave Emission in the Protoplanetary Nebula

NASA Technical Reports Server (NTRS)

Davis, S. S.; DeVincenzi, Donald (Technical Monitor)

2001-01-01

Higher order numerical algorithms (4th order in time, 3rd order in space) are applied to the Euler/Energy equations and are used to examine vorticity transport and wave motion in a non-self gravitating, initially isentropic Keplerian disk. In this talk we will examine the response of the nebula to an isolated vortex with a circulation about equal to the rotation rate of Jupiter. The vortex is located on the 4 AU circle and the nebula is simulated from 1 to 24 AU. We show that the vortex emits pressure-supported density and Rossby-type wave packets before it decays within a few orbits. The acoustic density waves evolve into weak (non entropy preserving) shock waves that propagate over the entire disk. The Rossby waves remain in the vicinity of the initial vortex disturbance, but are rapidly damped. Temporal frequencies and spatial wavenumbers are derived using the simulation data and compared with analytical dispersion relations from the linearized Euler/Energy equations.

Vorticity Transport and Wave Emission In A Protoplanetary Disk

NASA Technical Reports Server (NTRS)

Davis, S. S.; Davis, Sanford (Technical Monitor)

2002-01-01

Higher order numerical algorithms (4th order in time, 3rd order in space) are applied to the Euler equations and are used to examine vorticity transport and wave motion in a non-self gravitating, initially isentropic Keplerian disk. In this talk we will examine the response of the disk to an isolated vortex with a circulation about equal to the rotation rate of Jupiter. The vortex is located on the 4 AU circle and the nebula is simulated from 1 to 24 AU. We show that the vortex emits pressure-supported density and Rossby-type wave packets before it decays within a few orbits. The acoustic density waves evolve into weak (non entropy preserving) shock waves that propagate over the entire disk. The Rossby waves remain in the vicinity of the initial vortex disturbance, but are rapidly damped. Temporal frequencies and spatial wavenumbers are derived from the nonlinear simulation data and correlated with analytical dispersion relations from the linearized Euler and energy equations.

The cosmic-ray shock structure problem for relativistic shocks

NASA Technical Reports Server (NTRS)

Webb, G. M.

1985-01-01

The time asymptotic behaviour of a relativistic (parallel) shock wave significantly modified by the diffusive acceleration of cosmic-rays is investigated by means of relativistic hydrodynamical equations for both the cosmic-rays and thermal gas. The form of the shock structure equation and the dispersion relation for both long and short wavelength waves in the system are obtained. The dependence of the shock acceleration efficiency on the upstream fluid spped, long wavelength Mach number and the ratio N = P sub co/cP sub co+P sub go)(Psub co and P sub go are the upstream cosmic-ray and thermal gas pressures respectively) are studied.

Capillary-wave dynamics and interface structure modulation in binary Bose-Einstein condensate mixtures

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Van Thu, Nguyen; Lin, Chang-You; Phat, Tran Huu

2018-04-01

The localized low-energy interfacial excitations, or interfacial Nambu-Goldstone modes, of phase-segregated binary mixtures of Bose-Einstein condensates are investigated analytically. To this end a double-parabola approximation (DPA) is performed on the Lagrangian density in Gross-Pitaevskii theory for a system in a uniform potential. This DPA entails a model in which analytic expressions are obtained for the excitations underlying capillary waves or ripplons for arbitrary strength K (>1 ) of the phase segregation. The dispersion relation ω (k ) ∝k3 /2 is derived directly from the Bogoliubov-de Gennes equations in the limit that the wavelength 2 π /k is much larger than the interface width. The proportionality constant in the dispersion relation provides the static interfacial tension. A correction term in ω (k ) of order k5 /2 is calculated analytically within the DPA model. The combined result is tested against numerical diagonalization of the exact Bogoliubov-de Gennes equations. Satisfactory agreement is obtained in the range of physically relevant wavelengths. The ripplon dispersion relation is relevant to state-of-the-art experiments using (quasi)uniform optical-box traps. Furthermore, within the DPA model explicit expressions are obtained for the structural deformation of the interface due to the passing of the capillary wave. It is found that the amplitude of the wave is enhanced by an amount that is quadratic in the ratio of the phase velocity ω /k to the sound velocity c . For generic mixtures consisting of condensates with unequal healing lengths, an additional modulation is predicted of the common value of the condensate densities at the interface.

Ion temperature effects on magnetotail Alfvén wave propagation and electron energization: ION TEMPERATURE EFFECTS ON ALFVÉN WAVES

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

Damiano, P. A.; Johnson, J. R.; Chaston, C. C.

2015-07-01

A new 2-D self-consistent hybrid gyrofluid-kinetic electron model in dipolar coordinates is presented and used to simulate dispersive-scale Alfvén wave pulse propagation from the equator to the ionosphere along an L = 10 magnetic field line. The model is an extension of the hybrid MHD-kinetic electron model that incorporates ion Larmor radius corrections via the kinetic fluid model of Cheng and Johnson (1999). It is found that consideration of a realistic ion to electron temperature ratio decreases the propagation time of the wave from the plasma sheet to the ionosphere by several seconds relative to a ρi=0 case (which alsomore » implies shorter timing for a substorm onset signal) and leads to significant dispersion of wave energy perpendicular to the ambient magnetic field. Additionally, ion temperature effects reduce the parallel current and electron energization all along the field line for the same magnitude perpendicular electric field perturbation.« less

On the nonintegrability of equations for long- and short-wave interactions

NASA Astrophysics Data System (ADS)

Deconinck, Bernard; Upsal, Jeremy

2018-07-01

We examine the integrability of two models used for the interaction of long and short waves in dispersive media. One is more classical but arguably cannot be derived from the underlying water wave equations, while the other one was recently derived. We use the method of Zakharov and Schulman to attempt to construct conserved quantities for these systems at different orders in the magnitude of the solutions. The coupled KdV-NLS model is shown to be nonintegrable, due to the presence of fourth-order resonances. A coupled real KdV-complex KdV system is shown to suffer the same fate, except for three special choices of the coefficients, where higher-order calculations or a different approach are necessary to conclude integrability or the absence thereof.

Interesting features of nonlinear shock equations in dissipative pair-ion-electron plasmas

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

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

2011-09-15

Two dimensional nonlinear electrostatic waves are studied in unmagnetized, dissipative pair-ion-electron plasmas in the presence of weak transverse perturbation. The dissipation in the system is taken into account by incorporating the kinematic viscosity of both positive and negative ions. In the linear case, a biquadratic dispersion relation is obtained, which yields the fast and slow modes in a pair-ion-electron plasma. It is shown that the limiting cases of electron-ion and pair-ion can be retrieved from the general biquadratic dispersion relation, and the differences in the characters of the waves propagating in both the cases are also highlighted. Using the smallmore » amplitude approximation method, the nonlinear Kadomtsev Petviashvili Burgers as well as Burgers-Kadomtsev Petviashvili equations are derived and their applicability for pair-ion-electron plasma is explained in detail. The present study may have relevance to understand the formation of two dimensional electrostatic shocks in laboratory produced pair-ion-electron plasmas.« less

Kinetic theory for electrostatic waves due to transverse velocity shears

NASA Technical Reports Server (NTRS)

Ganguli, G.; Lee, Y. C.; Palmadesso, P. J.

1988-01-01

A kinetic theory in the form of an integral equation is provided to study the electrostatic oscillations in a collisionless plasma immersed in a uniform magnetic field and a nonuniform transverse electric field. In the low temperature limit the dispersion differential equation is recovered for the transverse Kelvin-Helmholtz modes for arbitrary values of K parallel, where K parallel is the component of the wave vector in the direction of the external magnetic field assumed in the z direction. For higher temperatures the ion-cyclotron-like modes described earlier in the literature by Ganguli, Lee and Plamadesso are recovered. In this article, the integral equation is reduced to a second-order differential equation and a study is made of the kinetic Kelvin-Helmholtz and ion-cyclotron-like modes that constitute the two branches of oscillation in a magnetized plasma including a transverse inhomogeneous dc electric field.

Two dimensional modelling of flood flows and suspended sediment transport: the case of Brenta River

NASA Astrophysics Data System (ADS)

D'Alpaos, L.; Martini, P.; Carniello, L.

2003-04-01

The paper deals with numerical modelling of flood waves and suspended sediment in plain river basins. The two dimensional depth integrated momentum and continuity equations, modified to take into account of the bottom irregularities that strongly affect the hydrodynamic and the continuity in partially dry areas (for example, during the first stages of a plain flooding and in tidal flows), are solved with a standard Galerkin finite element method using a semi-implicit numerical scheme and considering the role both of the small channel network and the regulation dispositive on the flooding wave propagation. Transport of suspended sediment and bed evolution are coupled with the flood propagation through the convection-dispersion equation and the Exner's equation. Results of a real case study are presented in which the effects of extreme flood of Brenta River (Italy) are examinated. The flooded areas (urban and rural areas) are identified and a mitigation solution based on a diversion channel flowing into Venice Lagoon is proposed. We show that this solution strongly reduces the flood risk in the downstream areas and can provide an important sediment source to the Venice Lagoon. Finally, preliminary results of the sediment dispersion in the Venice Lagoon are presented.

Acoustic waves in polydispersed bubbly liquids

NASA Astrophysics Data System (ADS)

Gubaidullin, D. A.; Gubaidullina, D. D.; Fedorov, Yu V.

2014-11-01

The propagation of acoustic waves in polydispersed mixtures of liquid with two sorts of gas bubbles each of which has its own bubble size distribution function is studied. The system of the differential equations of the perturbed motion of a mixture is presented, the dispersion relation is obtained. Equilibrium speed of sound, low-frequency and high-frequency asymptotes of the attenuation coefficient are found. Comparison of the developed theory with known experimental data is presented.

An Analysis of an Implicit Factored Scheme for Simulating Shock Waves

DTIC Science & Technology

1988-05-01

can cope with a wide range of boundary conditions and equations of state, For modelling -( shock waves in solids, elastic- plastic terms must also be...positive caracteristic speeds. One-sided schemes have superior dissipative and dispersive properties compared to those of centered schemes (Steger and...Elastic- plastic con. ditions must be- incorporated into the problem and usually the addition of suitable bource or sink terms to c-’ustion (1

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

Development of full wave code for modeling RF fields in hot non-uniform plasmas

NASA Astrophysics Data System (ADS)

Zhao, Liangji; Svidzinski, Vladimir; Spencer, Andrew; Kim, Jin-Soo

2016-10-01

FAR-TECH, Inc. is developing a full wave RF modeling code to model RF fields in fusion devices and in general plasma applications. As an important component of the code, an adaptive meshless technique is introduced to solve the wave equations, which allows resolving plasma resonances efficiently and adapting to the complexity of antenna geometry and device boundary. The computational points are generated using either a point elimination method or a force balancing method based on the monitor function, which is calculated by solving the cold plasma dispersion equation locally. Another part of the code is the conductivity kernel calculation, used for modeling the nonlocal hot plasma dielectric response. The conductivity kernel is calculated on a coarse grid of test points and then interpolated linearly onto the computational points. All the components of the code are parallelized using MPI and OpenMP libraries to optimize the execution speed and memory. The algorithm and the results of our numerical approach to solving 2-D wave equations in a tokamak geometry will be presented. Work is supported by the U.S. DOE SBIR program.

Nonlinear dynamics of electromagnetic turbulence in a nonuniform magnetized plasma

NASA Astrophysics Data System (ADS)

Shukla, P. K.; Mirza, Arshad M.; Faria, R. T.

1998-03-01

By using the hydrodynamic electron response with fixed (kinetic) ions along with Poisson's equation as well as Ampère's law, a system of nonlinear equations for low-frequency (in comparison with the electron gyrofrequency) long-(short-) wavelength electromagnetic waves in a nonuniform resistive magnetoplasma has been derived. The plasma contains equilibrium density gradient and sheared equilibrium plasma flows. In the linear limit, local dispersion relations are obtained and analyzed. It is found that sheared equilibrium flows can cause instability of Alfvén-like electromagnetic waves even in the absence of a density gradient. Furthermore, it is shown that possible stationary solutions of the nonlinear equations without dissipation can be represented in the form of various types of vortices. On the other hand, the temporal behavior of our nonlinear dissipative systems without the equilibrium density inhomogeneity can be described by the generalized Lorenz equations which admit chaotic trajectories. The density inhomogeneity may lead to even qualitative changes in the chaotic dynamics. The results of our investigation should be useful in understanding the linear and nonlinear properties of nonthermal electromagnetic waves in space and laboratory plasmas.

Dispersive analysis of the scalar form factor of the nucleon

NASA Astrophysics Data System (ADS)

Hoferichter, M.; Ditsche, C.; Kubis, B.; Meißner, U.-G.

2012-06-01

Based on the recently proposed Roy-Steiner equations for pion-nucleon ( πN) scattering [1], we derive a system of coupled integral equations for the π π to overline N N and overline K K to overline N N S-waves. These equations take the form of a two-channel Muskhelishvili-Omnès problem, whose solution in the presence of a finite matching point is discussed. We use these results to update the dispersive analysis of the scalar form factor of the nucleon fully including overline K K intermediate states. In particular, we determine the correction {Δ_{σ }} = σ ( {2M_{π }^2} ) - {σ_{{π N}}} , which is needed for the extraction of the pion-nucleon σ term from πN scattering, as a function of pion-nucleon subthreshold parameters and the πN coupling constant.

Multidimensional Solitons in Complex Media with Variable Dispersion: Structure and Evolution

DTIC Science & Technology

2003-07-20

the results of numerical experiments on Kadomtsev - Petviashvili (KP) equation study of structure and evolution of the nonlinear waves Sx described by...the KP equation with 13 = 3 (t,r) are con- at + auaxu + 03’u =K fAjudx, (1) sidered distracting from a concrete type of media. The -o• numerical...0i)(cot 0- mIM). It is well known that cluding the solutions of the mixed "soliton - non-soliton" the ID solutions of the KdV equation with 3 = const

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

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

Green-Naghdi dynamics of surface wind waves in finite depth

NASA Astrophysics Data System (ADS)

Manna, M. A.; Latifi, A.; Kraenkel, R. A.

2018-04-01

The Miles’ quasi laminar theory of waves generation by wind in finite depth h is presented. In this context, the fully nonlinear Green-Naghdi model equation is derived for the first time. This model equation is obtained by the non perturbative Green-Naghdi approach, coupling a nonlinear evolution of water waves with the atmospheric dynamics which works as in the classic Miles’ theory. A depth-dependent and wind-dependent wave growth γ is drawn from the dispersion relation of the coupled Green-Naghdi model with the atmospheric dynamics. Different values of the dimensionless water depth parameter δ = gh/U 1, with g the gravity and U 1 a characteristic wind velocity, produce two families of growth rate γ in function of the dimensionless theoretical wave-age c 0: a family of γ with h constant and U 1 variable and another family of γ with U 1 constant and h variable. The allowed minimum and maximum values of γ in this model are exhibited.

Dirac electron in a chiral space-time crystal created by counterpropagating circularly polarized plane electromagnetic waves

NASA Astrophysics Data System (ADS)

Borzdov, G. N.

2017-10-01

The family of solutions to the Dirac equation for an electron moving in an electromagnetic lattice with the chiral structure created by counterpropagating circularly polarized plane electromagnetic waves is obtained. At any nonzero quasimomentum, the dispersion equation has two solutions which specify bispinor wave functions describing electron states with different energies and mean values of momentum and spin operators. The inversion of the quasimomentum results in two other linearly independent solutions. These four basic wave functions are uniquely defined by eight complex scalar functions (structural functions), which serve as convenient building blocks of the relations describing the electron properties. These properties are illustrated in graphical form over a wide range of quasimomenta. The superpositions of two basic wave functions describing different spin states and corresponding to (i) the same quasimomentum (unidirectional electron states with the spin precession) and (ii) the two equal-in-magnitude but oppositely directed quasimomenta (bidirectional electron states) are also treated.

High-Frequency Normal Mode Propagation in Aluminum Cylinders

USGS Publications Warehouse

Lee, Myung W.; Waite, William F.

2009-01-01

Acoustic measurements made using compressional-wave (P-wave) and shear-wave (S-wave) transducers in aluminum cylinders reveal waveform features with high amplitudes and with velocities that depend on the feature's dominant frequency. In a given waveform, high-frequency features generally arrive earlier than low-frequency features, typical for normal mode propagation. To analyze these waveforms, the elastic equation is solved in a cylindrical coordinate system for the high-frequency case in which the acoustic wavelength is small compared to the cylinder geometry, and the surrounding medium is air. Dispersive P- and S-wave normal mode propagations are predicted to exist, but owing to complex interference patterns inside a cylinder, the phase and group velocities are not smooth functions of frequency. To assess the normal mode group velocities and relative amplitudes, approximate dispersion relations are derived using Bessel functions. The utility of the normal mode theory and approximations from a theoretical and experimental standpoint are demonstrated by showing how the sequence of P- and S-wave normal mode arrivals can vary between samples of different size, and how fundamental normal modes can be mistaken for the faster, but significantly smaller amplitude, P- and S-body waves from which P- and S-wave speeds are calculated.

Dissipation-preserving spectral element method for damped seismic wave equations

NASA Astrophysics Data System (ADS)

Cai, Wenjun; Zhang, Huai; Wang, Yushun

2017-12-01

This article describes the extension of the conformal symplectic method to solve the damped acoustic wave equation and the elastic wave equations in the framework of the spectral element method. The conformal symplectic method is a variation of conventional symplectic methods to treat non-conservative time evolution problems, which has superior behaviors in long-time stability and dissipation preservation. To reveal the intrinsic dissipative properties of the model equations, we first reformulate the original systems in their equivalent conformal multi-symplectic structures and derive the corresponding conformal symplectic conservation laws. We thereafter separate each system into a conservative Hamiltonian system and a purely dissipative ordinary differential equation system. Based on the splitting methodology, we solve the two subsystems respectively. The dissipative one is cheaply solved by its analytic solution. While for the conservative system, we combine a fourth-order symplectic Nyström method in time and the spectral element method in space to cover the circumstances in realistic geological structures involving complex free-surface topography. The Strang composition method is adopted thereby to concatenate the corresponding two parts of solutions and generate the completed conformal symplectic method. A relative larger Courant number than that of the traditional Newmark scheme is found in the numerical experiments in conjunction with a spatial sampling of approximately 5 points per wavelength. A benchmark test for the damped acoustic wave equation validates the effectiveness of our proposed method in precisely capturing dissipation rate. The classical Lamb problem is used to demonstrate the ability of modeling Rayleigh wave in elastic wave propagation. More comprehensive numerical experiments are presented to investigate the long-time simulation, low dispersion and energy conservation properties of the conformal symplectic methods in both the attenuating homogeneous and heterogeneous media.

Asymptotics for Large Time of Global Solutions to the Generalized Kadomtsev-Petviashvili Equation

NASA Astrophysics Data System (ADS)

Hayashi, Nakao; Naumkin, Pavel I.; Saut, Jean-Claude

We study the large time asymptotic behavior of solutions to the generalized Kadomtsev-Petviashvili (KP) equations where σ= 1 or σ=- 1. When ρ= 2 and σ=- 1, (KP) is known as the KPI equation, while ρ= 2, σ=+ 1 corresponds to the KPII equation. The KP equation models the propagation along the x-axis of nonlinear dispersive long waves on the surface of a fluid, when the variation along the y-axis proceeds slowly [10]. The case ρ= 3, σ=- 1 has been found in the modeling of sound waves in antiferromagnetics [15]. We prove that if ρ>= 3 is an integer and the initial data are sufficiently small, then the solution u of (KP) satisfies the following estimates: for all t∈R, where κ= 1 if ρ= 3 and κ= 0 if ρ>= 4. We also find the large time asymptotics for the solution.

A new analysis of the Fornberg-Whitham equation pertaining to a fractional derivative with Mittag-Leffler-type kernel

NASA Astrophysics Data System (ADS)

Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru

2018-02-01

The mathematical model of breaking of non-linear dispersive water waves with memory effect is very important in mathematical physics. In the present article, we examine a novel fractional extension of the non-linear Fornberg-Whitham equation occurring in wave breaking. We consider the most recent theory of differentiation involving the non-singular kernel based on the extended Mittag-Leffler-type function to modify the Fornberg-Whitham equation. We examine the existence of the solution of the non-linear Fornberg-Whitham equation of fractional order. Further, we show the uniqueness of the solution. We obtain the numerical solution of the new arbitrary order model of the non-linear Fornberg-Whitham equation with the aid of the Laplace decomposition technique. The numerical outcomes are displayed in the form of graphs and tables. The results indicate that the Laplace decomposition algorithm is a very user-friendly and reliable scheme for handling such type of non-linear problems of fractional order.

Perfectly Matched Layer for Linearized Euler Equations in Open and Ducted Domains

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Auriault, Laurent; Cambuli, Francesco

1998-01-01

Recently, perfectly matched layer (PML) as an absorbing boundary condition has widespread applications. The idea was first introduced by Berenger for electromagnetic waves computations. In this paper, it is shown that the PML equations for the linearized Euler equations support unstable solutions when the mean flow has a component normal to the layer. To suppress such unstable solutions so as to render the PML concept useful for this class of problems, it is proposed that artificial selective damping terms be added to the discretized PML equations. It is demonstrated that with a proper choice of artificial mesh Reynolds number, the PML equations can be made stable. Numerical examples are provided to illustrate that the stabilized PML performs well as an absorbing boundary condition. In a ducted environment, the wave mode are dispersive. It will be shown that the group velocity and phase velocity of these modes can have opposite signs. This results in a confined environment, PML may not be suitable as an absorbing boundary condition.

Electron acoustic-Langmuir solitons in a two-component electron plasma

NASA Astrophysics Data System (ADS)

McKenzie, J. F.

2003-04-01

We investigate the conditions under which ‘high-frequency’ electron acoustic Langmuir solitons can be constructed in a plasma consisting of protons and two electron populations: one ‘cold’ and the other ‘hot’. Conservation of total momentum can be cast as a structure equation either for the ‘cold’ or ‘hot’ electron flow speed in a stationary wave using the Bernoulli energy equations for each species. The linearized version of the governing equations gives the dispersion equation for the stationary waves of the system, from which follows the necessary but not sufficient conditions for the existence of soliton structures; namely that the wave speed must be less than the acoustic speed of the ‘hot’ electron component and greater than the low-frequency compound acoustic speed of the two electron populations. In this wave speed regime linear waves are ‘evanescent’, giving rise to the exponential growth or decay, which readily can give rise to non-linear effects that may balance dispersion and allow soliton formation. In general the ‘hot’ component must be more abundant than the ‘cold’ one and the wave is characterized by a compression of the ‘cold’ component and an expansion in the ‘hot’ component necessitating a potential dip. Both components are driven towards their sonic points; the ‘cold’ from above and the ‘hot’ from below. It is this transonic feature which limits the amplitude of the soliton. If the ‘hot’ component is not sufficiently abundant the window for soliton formation shrinks to a narrow speed regime which is quasi-transonic relative to the ‘hot’ electron acoustic speed, and it is shown that smooth solitons cannot be constructed. In the special case of a very cold electron population (i.e. ‘highly supersonic’) and the other population being very hot (i.e. ‘highly subsonic’) with adiabatic index 2, the structure equation simplifies and can be integrated in terms of elementary transcendental functions that provide the fully non-linear counterpart to the weakly non-linear sech(2) -type solitons. In this case the limiting soliton is comprised of an infinite compression in the cold component, a weak rarefaction in the ‘hot’ electrons and a modest potential dip.

Nonlinear structure formation in ion-temperature-gradient driven drift waves in pair-ion plasma with nonthermal electron distribution

NASA Astrophysics Data System (ADS)

Razzaq, Javaria; Haque, Q.; Khan, Majid; Bhatti, Adnan Mehmood; Kamran, M.; Mirza, Arshad M.

2018-02-01

Nonlinear structure formation in ion-temperature-gradient (ITG) driven waves is investigated in pair-ion plasma comprising ions and nonthermal electrons (kappa, Cairns). By using the transport equations of the Braginskii model, a new set of nonlinear equations are derived. A linear dispersion relation is obtained and discussed analytically as well as numerically. It is shown that the nonthermal population of electrons affects both the linear and nonlinear characteristics of the ITG mode in pair-ion plasma. This work will be useful in tokamaks and stellarators where non-Maxwellian population of electrons may exist due to resonant frequency heating, electron cyclotron heating, runaway electrons, etc.

Reverse time migration in tilted transversely isotropic media

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

Zhang, Linbing; Rector III, James W.; Hoversten, G. Michael

2004-07-01

This paper presents a reverse time migration (RTM) method for the migration of shot records in tilted transversely isotropic (TTI) media. It is based on the tilted TI acoustic wave equation that was derived from the dispersion relation. The RTM is a full depth migration allowing for velocity to vary laterally as well as vertically and has no dip limitations. The wave equation is solved by a tenth-order finite difference scheme. Using 2D numerical models, we demonstrate that ignoring the tilt angle will introduce both lateral and vertical shifts in imaging. The shifts can be larger than 0.5 wavelength inmore » the vertical direction and 1.5 wavelength in the lateral direction.« less

Longitudinal dielectric function and dispersion relation of electrostatic waves in relativistic plasmas

NASA Astrophysics Data System (ADS)

Touil, B.; Bendib, A.; Bendib-Kalache, K.

2017-02-01

The longitudinal dielectric function is derived analytically from the relativistic Vlasov equation for arbitrary values of the relevant parameters z = m c 2 / T , where m is the rest electron mass, c is the speed of light, and T is the electron temperature in energy units. A new analytical approach based on the Legendre polynomial expansion and continued fractions was used. Analytical expression of the electron distribution function was derived. The real part of the dispersion relation and the damping rate of electron plasma waves are calculated both analytically and numerically in the whole range of the parameter z . The results obtained improve significantly the previous results reported in the literature. For practical purposes, explicit expressions of the real part of the dispersion relation and the damping rate in the range z > 30 and strongly relativistic regime are also proposed.

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.

Integrodifference equations in patchy landscapes : II: population level consequences.

PubMed

Musgrave, Jeffrey; Lutscher, Frithjof

2014-09-01

We analyze integrodifference equations (IDEs) in patchy landscapes. Movement is described by a dispersal kernel that arises from a random walk model with patch dependent diffusion, settling, and mortality rates, and it incorporates individual behavior at an interface between two patch types. Growth follows a simple Beverton-Holt growth or linear decay. We obtain explicit formulae for the critical domain-size problem, and we illustrate how different individual behavior at the boundary between two patch types affects this quantity. We also study persistence conditions on an infinite, periodic, patchy landscape. We observe that if the population can persist on the landscape, the spatial profile of the invasion evolves into a discontinuous traveling periodic wave that moves with constant speed. Assuming linear determinacy, we calculate the dispersion relation and illustrate how movement behavior affects invasion speed. Numerical simulations justify our approach by showing a close correspondence between the spread rate obtained from the dispersion relation and from numerical simulations.

Thickness resonances dispersion characteristics of a lossy piezoceramic plate with electrodes of arbitrary conductivity.

PubMed

Mezheritsky, Alex A; Mezheritsky, Alex V

2007-12-01

A theoretical description of the dissipative phenomena in the wave dispersion related to the "energytrap" effect in a thickness-vibrating, infinite thicknesspolarized piezoceramic plate with resistive electrodes is presented. The three-dimensional (3-D) equations of linear piezoelectricity were used to obtain symmetric and antisymmetric solutions of plane harmonic waves and investigate the eigen-modes of thickness longitudinal (TL) up to third harmonic and shear (TSh) up to ninth harmonic vibrations of odd- and even-orders. The effects of internal and electrode energy dissipation parameters on the wave propagation under regimes ranging from a short-circuit (sc) condition through RC-type relaxation dispersion to an opencircuit (oc) condition are examined in detail for PZT piezoceramics with three characteristic T -mode energy-trap figure-of-merit c-(D)(33)/c-(E)(44) values - less, near equal and higher 4 - when the second harmonic spurious TSh resonance lies below, inside, and above the fundamental TL resonanceantiresonance frequency interval. Calculated complex lateral wave number dispersion dependences on frequency and electrode resistance are found to follow the universal scaling formula similar to those for dielectrics characterization. Formally represented as a Cole-Cole diagram, the dispersion branches basically exhibit Debye-like and modified Davidson Cole dependences. Varying the dissipation parameters of internal loss and electrode conductivity, the interaction of different branches was demonstrated by analytical and numerical analysis. For the purposes of dispersion characterization of at least any thickness resonance, the following theorem was stated: the ratio of two characteristic determinants, specifically constructed from the oc and sc boundary conditions, in the limit of zero lateral wave number, is equal to the basic elementary-mode normalized admittance. As was found based on the theorem, the dispersion near the basic and nonbasic TL and TSh resonances reveal some simple representations related to the respective elementary admittance and showing the connection between the propagation and excitation problems in a continuous piezoactive medium.

Parametric decay of an extraordinary electromagnetic wave in relativistic plasma

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

Dorofeenko, V. G.; Krasovitskiy, V. B., E-mail: krasovit@mail.ru; Turikov, V. A.

2015-03-15

Parametric instability of an extraordinary electromagnetic wave in plasma preheated to a relativistic temperature is considered. A set of self-similar nonlinear differential equations taking into account the electron “thermal” mass is derived and investigated. Small perturbations of the parameters of the heated plasma are analyzed in the linear approximation by using the dispersion relation determining the phase velocities of the fast and slow extraordinary waves. In contrast to cold plasma, the evanescence zone in the frequency range above the electron upper hybrid frequency vanishes and the asymptotes of both branches converge. Theoretical analysis of the set of nonlinear equations showsmore » that the growth rate of decay instability increases with increasing initial temperature of plasma electrons. This result is qualitatively confirmed by numerical simulations of plasma heating by a laser pulse injected from vacuum.« less

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

Lee, Wonjung; Kovacic, Gregor; Cai, David

Using the (1+1)D Majda-McLaughlin-Tabak model as an example, we present an extension of the wave turbulence (WT) theory to systems with strong nonlinearities. We demonstrate that nonlinear wave interactions renormalize the dynamics, leading to (i) a possible destruction of scaling structures in the bare wave systems and a drastic deformation of the resonant manifold even at weak nonlinearities, and (ii) creation of nonlinear resonance quartets in wave systems for which there would be no resonances as predicted by the linear dispersion relation. Finally, we derive an effective WT kinetic equation and show that our prediction of the renormalized Rayleigh-Jeans distributionmore » is in excellent agreement with the simulation of the full wave system in equilibrium.« less

Faraday waves in a Hele-Shaw cell

NASA Astrophysics Data System (ADS)

Li, Jing; Li, Xiaochen; Chen, Kaijie; Xie, Bin; Liao, Shijun

2018-04-01

We investigate Faraday waves in a Hele-Shaw cell via experimental, numerical, and theoretical studies. Inspired by the Kelvin-Helmholtz-Darcy theory, we develop the gap-averaged Navier-Stokes equations and end up with the stable standing waves with half frequency of the external forced vibration. To overcome the dependency of a numerical model on the experimental parameter of wave length, we take two-phase flow into consideration and a novel dispersion relation is derived. The numerical results compare well with our experimental data, which effectively validates our proposed mathematical model. Therefore, this model can produce robust solutions of Faraday wave patterns and resolve related physical phenomena, which demonstrates the practical importance of the present study.

Stabilization of the Peregrine soliton and Kuznetsov-Ma breathers by means of nonlinearity and dispersion management

NASA Astrophysics Data System (ADS)

Cuevas-Maraver, J.; Malomed, Boris A.; Kevrekidis, P. G.; Frantzeskakis, D. J.

2018-04-01

We demonstrate a possibility to make rogue waves (RWs) in the form of the Peregrine soliton (PS) and Kuznetsov-Ma breathers (KMBs) effectively stable objects, with the help of properly defined dispersion or nonlinearity management applied to the continuous-wave (CW) background supporting the RWs. In particular, it is found that either management scheme, if applied along the longitudinal coordinate, making the underlying nonlinear Schrödinger equation (NLSE) self-defocusing in the course of disappearance of the PS, indeed stabilizes the global solution with respect to the modulational instability of the background. In the process, additional excitations are generated, namely, dispersive shock waves and, in some cases, also a pair of slowly separating dark solitons. Further, the nonlinearity-management format, which makes the NLSE defocusing outside of a finite domain in the transverse direction, enables the stabilization of the KMBs, in the form of confined oscillating states. On the other hand, a nonlinearity-management format applied periodically along the propagation direction, creates expanding patterns featuring multiplication of KMBs through their cascading fission.

Propagation and stability of wavelike solutions of finite difference equations with variable coefficients

NASA Technical Reports Server (NTRS)

Giles, M. B.; Thompkins, W. T., Jr.

1985-01-01

The propagation and dissipation of wavelike solutions to finite difference equations is analyzed on the basis of an asymptotic approach in which a wave solution is expressed as a product of a complex amplitude and an oscillatory phase function whose frequency and wavenumber may also be complex. An asymptotic expansion leads to a local dispersion relation for wavenumber and frequency; the first-order terms produce an equation for the amplitude in which the local group velocity appears as the convection velocity of the amplitude. Equations for the motion of wavepackets and their interaction at boundaries are derived, and a global stability analysis is carried out.

SMALL-SCALE SOLAR WIND TURBULENCE DUE TO NONLINEAR ALFVÉN WAVES

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

Kumar, Sanjay; Moon, Y.-J.; Sharma, R. P., E-mail: sanjaykumar@khu.ac.kr

We present an evolution of wave localization and magnetic power spectra in solar wind plasma using kinetic Alfvén waves (AWs) and fast AWs. We use a two-fluid model to derive the dynamical equations of these wave modes and then numerically solve these nonlinear dynamical equations to analyze the power spectra and wave localization at different times. The ponderomotive force associated with the kinetic AW (or pump) is responsible for the wave localization, and these thin slabs (or sheets) become more chaotic as the system evolves with time until the modulational instability (or oscillating two-stream instability) saturates. From our numerical results,more » we notice a steepening of the spectra from the inertial range (k{sup −1.67}) to the dispersion range (k{sup −3.0}). The steepening of the spectra could be described as the energy transference from longer to smaller scales. The formation of complex magnetic thin slabs and the change of the spectral index may be considered to be the main reason for the charged particles acceleration in solar wind plasma.« less

Asymptotic Approach to the Problem of Boundary Layer Instability in Transonic Flow

NASA Astrophysics Data System (ADS)

Zhuk, V. I.

2018-03-01

Tollmien-Schlichting waves can be analyzed using the Prandtl equations involving selfinduced pressure. This circumstance was used as a starting point to examine the properties of the dispersion relation and the eigenmode spectrum, which includes modes with amplitudes increasing with time. The fact that the asymptotic equations for a nonclassical boundary layer (near the lower branch of the neutral curve) have unstable fluctuation solutions is well known in the case of subsonic and transonic flows. At the same time, similar solutions for supersonic external flows do not contain unstable modes. The bifurcation pattern of the behavior of dispersion curves in complex domains gives a mathematical explanation of the sharp change in the stability properties occurring in the transonic range.

Numerical Simulations of Self-Focused Pulses Using the Nonlinear Maxwell Equations

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Silberberg, Yaron; Kwak, Dochan (Technical Monitor)

1994-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that solves the full vector nonlinear Maxwell's equations exactly without the approximations that are currently made. Present methods solve a reduced scalar wave equation, namely the nonlinear Schrodinger equation, and neglect the optical carrier. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of 'light bullet' like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit modeling 2-D and 3-D optical soliton propagation, scattering, and switching directly from the full-vector Maxwell's equations. Abstract of a proposed paper for presentation at the meeting NONLINEAR OPTICS: Materials, Fundamentals, and Applications, Hyatt Regency Waikaloa, Waikaloa, Hawaii, July 24-29, 1994, Cosponsored by IEEE/Lasers and Electro-Optics Society and Optical Society of America

Dissipative behavior of some fully non-linear KdV-type equations

NASA Astrophysics Data System (ADS)

Brenier, Yann; Levy, Doron

2000-03-01

The KdV equation can be considered as a special case of the general equation u t+f(u) x-δg(u xx) x=0, δ>0, where f is non-linear and g is linear, namely f( u)= u2/2 and g( v)= v. As the parameter δ tends to 0, the dispersive behavior of the KdV equation has been throughly investigated (see, e.g., [P.G. Drazin, Solitons, London Math. Soc. Lect. Note Ser. 85, Cambridge University Press, Cambridge, 1983; P.D. Lax, C.D. Levermore, The small dispersion limit of the Korteweg-de Vries equation, III, Commun. Pure Appl. Math. 36 (1983) 809-829; G.B. Whitham, Linear and Nonlinear Waves, Wiley/Interscience, New York, 1974] and the references therein). We show through numerical evidence that a completely different, dissipative behavior occurs when g is non-linear, namely when g is an even concave function such as g( v)=-∣ v∣ or g( v)=- v2. In particular, our numerical results hint that as δ→0 the solutions strongly converge to the unique entropy solution of the formal limit equation, in total contrast with the solutions of the KdV equation.

Nonlinear propagation analysis of few-optical-cycle pulses for subfemtosecond compression and carrier envelope phase effect

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

Mizuta, Yo; Nagasawa, Minoru; Ohtani, Morimasa

2005-12-15

A numerical approach called Fourier direct method (FDM) is applied to nonlinear propagation of optical pulses with the central wavelength 800 nm, the width 2.67-12.00 fs, and the peak power 25-6870 kW in a fused-silica fiber. Bidirectional propagation, delayed Raman response, nonlinear dispersion (self-steepening, core dispersion), as well as correct linear dispersion are incorporated into 'bidirectional propagation equations' which are derived directly from Maxwell's equations. These equations are solved for forward and backward waves, instead of the electric-field envelope as in the nonlinear Schroedinger equation (NLSE). They are integrated as multidimensional simultaneous evolution equations evolved in space. We investigate, bothmore » theoretically and numerically, the validity and the limitation of assumptions and approximations used for deriving the NLSE. Also, the accuracy and the efficiency of the FDM are compared quantitatively with those of the finite-difference time-domain numerical approach. The time-domain size 500 fs and the number of grid points in time 2048 are chosen to investigate numerically intensity spectra, spectral phases, and temporal electric-field profiles up to the propagation distance 1.0 mm. On the intensity spectrum of a few-optical-cycle pulses, the self-steepening, core dispersion, and the delayed Raman response appear as dominant, middle, and slight effects, respectively. The delayed Raman response and the core dispersion reduce the effective nonlinearity. Correct linear dispersion is important since it affects the intensity spectrum sensitively. For the compression of femtosecond optical pulses by the complete phase compensation, the shortness and the pulse quality of compressed pulses are remarkably improved by the intense initial peak power rather than by the short initial pulse width or by the propagation distance longer than 0.1 mm. They will be compressed as short as 0.3 fs below the damage threshold of fused-silica fiber 6 MW. It is demonstrated that the carrier envelope phase (CEP) causes the difference on the temporal electric-field profile and the intensity spectrum for the initial peak power of the order of megawatts. At the propagation distance longer than the coherence length for third-order harmonics, the difference grows in the spectral components around the third-order and higher-order harmonics. The CEP can be a sensitive marker to monitor the evolution of nonlinear optical process by a few-optical-cycle electric-field wave-packet source.« less

On the estimation of heating effects in the atmosphere because of seismic activities

NASA Astrophysics Data System (ADS)

Meister, Claudia-Veronika; Hoffmann, Dieter H. H.

2014-05-01

The dielectric model for waves in the Earth's ionosphere is further developed and applied to possible electro-magnetic phenomena in seismic regions. In doing so, in comparison to the well-known dielectric wave model by R.O. Dendy [Plasma dynamics, Oxford University Press, 1990] for homogeneous systems, the stratification of the atmosphere is taken into account. Moreover, within the frame of many-fluid magnetohydrodynamics also the momentum transfer between the charged and neutral particles is considered. Discussed are the excitation of Alfvén and magnetoacoustic waves, but also their variations by the neutral gas winds. Further, also other current driven waves like Farley-Buneman ones are studied. In the work, models of the altitudinal scales of the plasma parameters and the electromagnetic wave field are derived. In case of the electric wave field, a method is given to calculate the altitudinal scale based on the Poisson equation for the electric field and the magnetohydrodynamic description of the particles. Further, expressions are derived to estimate density, pressure, and temperatur changes in the E-layer because of the generation of the electromagnetic waves. Last not least, formulas are obtained to determine the dispersion and polarisation of the excited electromagnetic waves. These are applied to find quantitative results for the turbulent heating of the ionospheric E-layer. Concerning the calculation of the dispersion relation, in comparison to a former work by Meister et al. [Contr. Plasma Phys. 53 (4-5), 406-413, 2013], where a numerical double-iteration method was suggested to obtain results for the wave dispersion relations, now further analytical calculations are performed. In doing so, different polynomial dependencies of the wave frequencies from the wave vectors are treated. This helped to restrict the numerical calculations to only one iteration process.

Integrability of the coupled cubic-quintic complex Ginzburg-Landau equations and multiple-soliton solutions via mathematical methods

NASA Astrophysics Data System (ADS)

Selima, Ehab S.; Seadawy, Aly R.; Yao, Xiaohua; Essa, F. A.

2018-02-01

This paper is devoted to study the (1+1)-dimensional coupled cubic-quintic complex Ginzburg-Landau equations (cc-qcGLEs) with complex coefficients. This equation can be used to describe the nonlinear evolution of slowly varying envelopes of periodic spatial-temporal patterns in a convective binary fluid. Dispersion relation and properties of cc-qcGLEs are constructed. Painlevé analysis is used to check the integrability of cc-qcGLEs and to establish the Bäcklund transformation form. New traveling wave solutions and a general form of multiple-soliton solutions of cc-qcGLEs are obtained via the Bäcklund transformation and simplest equation method with Bernoulli, Riccati and Burgers’ equations as simplest equations.

Cluster observations of EMIC triggered emissions in association with Pc1 waves near Earth's plasmapause

NASA Astrophysics Data System (ADS)

Pickett, J. S.; Grison, B.; Omura, Y.; Engebretson, M. J.; Dandouras, I.; Masson, A.; Adrian, M. L.; Santolík, O.; Décréau, P. M. E.; Cornilleau-Wehrlin, N.; Constantinescu, D.

2010-05-01

The Cluster spacecraft were favorably positioned on the nightside near the equatorial plasmapause of Earth at L ˜ 4.3 on 30 March 2002 to observe electromagnetic ion cyclotron (EMIC) rising tone emissions in association with Pc1 waves at 1.5 Hz. The EMIC rising tone emissions were found to be left-hand, circularly polarized, dispersive, and propagating away from the equator. Their burstiness and dispersion of ˜30s/Hz rising out of the 1.5 Hz Pc1 waves are consistent with their identification as EMIC triggered chorus emissions, the first to be reported through in situ observations near the plasmapause. Along with the expected H+ ring current ions seen at higher energies (>300 eV), lower energy ions (300 eV and less) were observed during the most intense EMIC triggered emission events. Nonlinear wave-particle interactions via cyclotron resonance between the ˜2-10 keV H+ ions with temperature anisotropy and the linearly-amplified Pc1 waves are suggested as a possible generation mechanism for the EMIC triggered emissions.

Current driven instabilities of an electromagnetically accelerated plasma

NASA Technical Reports Server (NTRS)

Chouetri, E. Y.; Kelly, A. J.; Jahn, R. G.

1988-01-01

A plasma instability that strongly influences the efficiency and lifetime of electromagnetic plasma accelerators was quantitatively measured. Experimental measurements of dispersion relations (wave phase velocities), spatial growth rates, and stability boundaries are reported. The measured critical wave parameters are in excellent agreement with theoretical instability boundary predictions. The instability is current driven and affects a wide spectrum of longitudinal (electrostatic) oscillations. Current driven instabilities, which are intrinsic to the high-current-carrying magnetized plasma of the magnetoplasmadynmic (MPD) accelerator, were investigated with a kinetic theoretical model based on first principles. Analytical limits of the appropriate dispersion relation yield unstable ion acoustic waves for T(i)/T(e) much less than 1 and electron acoustic waves for T(i)/T(e) much greater than 1. The resulting set of nonlinear equations for the case of T(i)/T(e) = 1, of most interest to the MPD thruster Plasma Wave Experiment, was numerically solved to yield a multiparameter set of stability boundaries. Under certain conditions, marginally stable waves traveling almost perpendicular to the magnetic field would travel at a velocity equal to that of the electron current. Such waves were termed current waves. Unstable current waves near the upper stability boundary were observed experimentally and are in accordance with theoretical predictions. This provides unambiguous proof of the existence of such instabilites in electromagnetic plasma accelerators.

On the stability of lumps and wave collapse in water waves.

PubMed

Akylas, T R; Cho, Yeunwoo

2008-08-13

In the classical water-wave problem, fully localized nonlinear waves of permanent form, commonly referred to as lumps, are possible only if both gravity and surface tension are present. While much attention has been paid to shallow-water lumps, which are generalizations of Korteweg-de Vries solitary waves, the present study is concerned with a distinct class of gravity-capillary lumps recently found on water of finite or infinite depth. In the near linear limit, these lumps resemble locally confined wave packets with envelope and wave crests moving at the same speed, and they can be approximated in terms of a particular steady solution (ground state) of an elliptic equation system of the Benney-Roskes-Davey-Stewartson (BRDS) type, which governs the coupled evolution of the envelope along with the induced mean flow. According to the BRDS equations, however, initial conditions above a certain threshold develop a singularity in finite time, known as wave collapse, due to nonlinear focusing; the ground state, in fact, being exactly at the threshold for collapse suggests that the newly discovered lumps are unstable. In an effort to understand the role of this singularity in the dynamics of lumps, here we consider the fifth-order Kadomtsev-Petviashvili equation, a model for weakly nonlinear gravity-capillary waves on water of finite depth when the Bond number is close to one-third, which also admits lumps of the wave packet type. It is found that an exchange of stability occurs at a certain finite wave steepness, lumps being unstable below but stable above this critical value. As a result, a small-amplitude lump, which is linearly unstable and according to the BRDS equations would be prone to wave collapse, depending on the perturbation, either decays into dispersive waves or evolves into an oscillatory state near a finite-amplitude stable lump.

Layering, interface and edge effects in multi-layered composite medium

NASA Technical Reports Server (NTRS)

Datta, S. K.; Shah, A. H.; Karunesena, W.

1990-01-01

Guided waves in a cross-ply laminated plate are studied. Because of the complexity of the exact dispersion equation that governs the wave propagation in a multi-layered fiber-reinforced plate, a stiffness method that can be applied to any number of layers is presented. It is shown that, for a sufficiently large number of layers, the plate can be modeled as a homogeneous anisotropic plate. Also studied is the reflection of guided waves from the edge of a multilayered plate. These results are quite different than in the case of a single homogeneous plate.

Investigation of computational and spectral analysis methods for aeroacoustic wave propagation

NASA Technical Reports Server (NTRS)

Vanel, Florence O.

1995-01-01

Most computational fluid dynamics (CFD) schemes are not adequately accurate for solving aeroacoustics problems, which have wave amplitudes several orders of magnitude smaller yet with frequencies larger than the flow field variations generating the sound. Hence, a computational aeroacoustics (CAA) algorithm should have minimal dispersion and dissipation features. A dispersion relation preserving (DRP) scheme is, therefore, applied to solve the linearized Euler equations in order to simulate the propagation of three types of waves, namely: acoustic, vorticity, and entropy waves. The scheme is derived using an optimization procedure to ensure that the numerical derivatives preserve the wave number and angular frequency of the partial differential equations being discretized. Consequently, simulated waves propagate with the correct wave speeds and exhibit their appropriate properties. A set of radiation and outflow boundary conditions, compatible with the DRP scheme and derived from the asymptotic solutions of the governing equations, are also implemented. Numerical simulations are performed to test the effectiveness of the DRP scheme and its boundary conditions. The computed solutions are shown to agree favorably with the exact solutions. The major restriction appears to be that the dispersion relations can be preserved only for waves with wave lengths longer than four or five spacings. The boundary conditions are found to be transparent to the outgoing disturbances. However, when the disturbance source is placed closer to a boundary, small acoustic reflections start appearing. CAA generates enormous amounts of temporal data which needs to be reduced to understand the physical problem being simulated. Spectral analysis is one approach that helps us in extracting information which often can not be easily interpreted in the time domain. Thus, three different methods for the spectral analysis of numerically generated aeroacoustic data are studied. First, the capabilities of two traditional methods for spectral analysis, namely, the Blackman-Tukey method and periodogram method, are compared in estimating the spectra of a simple-periodic process. The periodogram is then applied to analyze transitory-deterministic processes. Finally, these two methods are compared with a more recent method, referred as the Weighted-Overlapped-Segment-Averaging (WOSA) method, in estimating the spectra of a chaotic (random-like) process. From the demonstrative case for the spectral analyses of data generated by simple-periodic process, the periodogram method is found to give a better estimate of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window is found to perform better with the periodogram method than with the Blackman-Tukey method. Finally, for the spectral analysis of data generated by the chaotic process, the periodogram method does not perform well, whereas, the WOSA and Blackman-Tukey methods give equivalently good results.

Modeling Tsunami Wave Generation Using a Two-layer Granular Landslide Model

NASA Astrophysics Data System (ADS)

Ma, G.; Kirby, J. T., Jr.; Shi, F.; Grilli, S. T.; Hsu, T. J.

2016-12-01

Tsunamis can be generated by subaerial or submarine landslides in reservoirs, lakes, fjords, bays and oceans. Compared to seismogenic tsunamis, landslide or submarine mass failure (SMF) tsunamis are normally characterized by relatively shorter wave lengths and stronger wave dispersion, and potentially may generate large wave amplitudes locally and high run-up along adjacent coastlines. Due to a complex interplay between the landslide and tsunami waves, accurate simulation of landslide motion as well as tsunami generation is a challenging task. We develop and test a new two-layer model for granular landslide motion and tsunami wave generation. The landslide is described as a saturated granular flow, accounting for intergranular stresses governed by Coulomb friction. Tsunami wave generation is simulated by the three-dimensional non-hydrostatic wave model NHWAVE, which is capable of capturing wave dispersion efficiently using a small number of discretized vertical levels. Depth-averaged governing equations for the granular landslide are derived in a slope-oriented coordinate system, taking into account the dynamic interaction between the lower-layer granular landslide and upper-layer water motion. The model is tested against laboratory experiments on impulsive wave generation by subaerial granular landslides. Model results illustrate a complex interplay between the granular landslide and tsunami waves, and they reasonably predict not only the tsunami wave generation but also the granular landslide motion from initiation to deposition.

Structure-preserving spectral element method in attenuating seismic wave modeling

NASA Astrophysics Data System (ADS)

Cai, Wenjun; Zhang, Huai

2016-04-01

This work describes the extension of the conformal symplectic method to solve the damped acoustic wave equation and the elastic wave equations in the framework of the spectral element method. The conformal symplectic method is a variation of conventional symplectic methods to treat non-conservative time evolution problems which has superior behaviors in long-time stability and dissipation preservation. To construct the conformal symplectic method, we first reformulate the damped acoustic wave equation and the elastic wave equations in their equivalent conformal multi-symplectic structures, which naturally reveal the intrinsic properties of the original systems, especially, the dissipation laws. We thereafter separate each structures into a conservative Hamiltonian system and a purely dissipative ordinary differential equation system. Based on the splitting methodology, we solve the two subsystems respectively. The dissipative one is cheaply solved by its analytic solution. While for the conservative system, we combine a fourth-order symplectic Nyström method in time and the spectral element method in space to cover the circumstances in realistic geological structures involving complex free-surface topography. The Strang composition method is adopted thereby to concatenate the corresponding two parts of solutions and generate the completed numerical scheme, which is conformal symplectic and can therefore guarantee the numerical stability and dissipation preservation after a large time modeling. Additionally, a relative larger Courant number than that of the traditional Newmark scheme is found in the numerical experiments in conjunction with a spatial sampling of approximately 5 points per wavelength. A benchmark test for the damped acoustic wave equation validates the effectiveness of our proposed method in precisely capturing dissipation rate. The classical Lamb problem is used to demonstrate the ability of modeling Rayleigh-wave propagation. More comprehensive numerical experiments are presented to investigate the long-time simulation, low dispersion and energy conservation properties of the conformal symplectic method in both the attenuating homogeneous and heterogeneous mediums.

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.

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

Garifullin, R. N., E-mail: rustem@matem.anrb.ru; Suleimanov, B. I., E-mail: bisul@mail.r

An analysis is presented of the effect of weak dispersion on transitions from weak to strong discontinuities in inviscid fluid dynamics. In the neighborhoods of transition points, this effect is described by simultaneous solutions to the Korteweg-de Vries equation u{sub t}'+ uu{sub x}' + u{sub xxx}' = 0 and fifth-order nonautonomous ordinary differential equations. As x{sup 2} + t{sup 2} {yields}{infinity}, the asymptotic behavior of these simultaneous solutions in the zone of undamped oscillations is given by quasi-simple wave solutions to Whitham equations of the form r{sub i}(t, x) = tl{sub i} x/t{sup 2}.

A numerical study on weak-dissipative two-mode perturbed Burgers' and Ostrovsky models: right-left moving waves

NASA Astrophysics Data System (ADS)

Jaradat, Imad; Alquran, Marwan; Ali, Mohammed

2018-04-01

The purpose of this study is threefold. First, it derives newly developed two-mode nonlinear equations, two-mode perturbed Burgers' and two-mode Ostrovsky models. Second, it investigates the values of the nonlinearity and dispersion parameters that support the existence of two right-left (R-L) moving wave solutions to these models. Finally, it provides a graphical analysis of the "two-mode" concept and the impact of its phase velocity on the field function.

Effect of Liquid Viscosity on Dispersion of Quasi-Lamb Waves in an Elastic-Layer-Viscous-Liquid-Layer System

NASA Astrophysics Data System (ADS)

Guz, A. N.; Bagno, A. M.

2017-07-01

The dispersion curves are constructed and propagation of quasi-Lamb waves are studied for wide range of frequencies based on the Navier -Stokes three-dimensional linearized equations for a viscous liquid and linear equations of the classical theory of elasticity for an elastic layer. For a thick liquid layer, the effect of the viscosity of the liquid and the thickness of elastic and liquid layers on the phase velocities and attenuation coefficients of quasi-Lamb modes is analyzed. It is shown that in the case of a thick liquid layer for all modes, there are elastic layers of certain thickness with minimal effect of liquid viscosity on the phase velocities and attenuation coefficients of modes. It is also discovered that for some modes, there are both certain thicknesses and certain ranges of thickness where the effect of liquid viscosity on the phase velocities and attenuation coefficients of these modes is considerable. We ascertain that liquid viscosity promotes decrease of the penetration depth of the lowest quasi-Lamb mode into the liquid. The developed approach and the obtained results make it possible to ascertain for wave processes the limits of applicability of the model of ideal compressible fluid. Numerical results in the form of graphs are adduced and analyzed.

Natural oscillations of a gas bubble in a liquid-filled cavity located in a viscoelastic medium

NASA Astrophysics Data System (ADS)

Doinikov, Alexander A.; Marmottant, Philippe

2018-04-01

The present study is motivated by cavitation phenomena that occur in the stems of trees. The internal pressure in tree conduits can drop down to significant negative values. This drop gives rise to cavitation bubbles, which undergo high-frequency eigenmodes. The aim of the present study is to determine the parameters of the bubble natural oscillations. To this end, a theory is developed that describes the pulsation of a spherical bubble located at the center of a spherical cavity surrounded by an infinite solid medium. It is assumed that the medium inside the bubble is a gas-vapor mixture, the cavity is filled with a compressible viscous liquid, and the medium surrounding the cavity behaves as a viscoelastic solid. The theoretical solution takes into account the outgoing acoustic wave produced by the bubble pulsation, the incoming wave caused by reflection from the liquid-solid boundary, and the outgoing wave propagating in the solid. A dispersion equation for the calculation of complex wavenumbers of the bubble eigenmodes is derived. Approximate analytical solutions to the dispersion equation are found. Numerical simulations are performed to reveal the effect of different physical parameters on the resonance frequency and the attenuation coefficient of the bubble oscillations.

Dielectric function and plasmons in graphene: A self-consistent-field calculation within a Markovian master equation formalism

DOE PAGES

Karimi, F.; Davoody, A. H.; Knezevic, I.

2016-05-12

We introduce a method for calculating the dielectric function of nanostructures with an arbitrary band dispersion and Bloch wave functions. The linear response of a dissipative electronic system to an external electromagnetic field is calculated by a self-consistent-field approach within a Markovian master equation formalism (SCF-MMEF) coupled with full-wave electromagnetic equations. The SCF-MMEF accurately accounts for several concurrent scattering mechanisms. The method captures interband electron-hole-pair generation, as well as the interband and intraband electron scattering with phonons and impurities. We employ the SCF-MMEF to calculate the dielectric function, complex conductivity, and loss function for supported graphene. From the loss-function maximum,more » we obtain plasmon dispersion and propagation length for different substrate types [nonpolar diamondlike carbon (DLC) and polar SiO 2 and hBN], impurity densities, carrier densities, and temperatures. Plasmons on the two polar substrates are suppressed below the highest surface phonon energy, while the spectrum is broad on the nonpolar DLC. Plasmon propagation lengths are comparable on polar and nonpolar substrates and are on the order of tens of nanometers, considerably shorter than previously reported. As a result, they improve with fewer impurities, at lower temperatures, and at higher carrier densities.« less

Absorbing Boundary Conditions For Optical Pulses In Dispersive, Nonlinear Materials

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.; Kwak, Dochan (Technical Monitor)

1995-01-01

This paper will present results in computational nonlinear optics. An algorithm will be described that provides absorbing boundary conditions for optical pulses in dispersive, nonlinear materials. A new numerical absorber at the boundaries has been developed that is responsive to the spectral content of the pulse. Also, results will be shown of calculations of 2-D electromagnetic nonlinear waves computed by directly integrating in time the nonlinear vector Maxwell's equations. The results will include simulations of "light bullet" like pulses. Here diffraction and dispersion will be counteracted by nonlinear effects. Comparisons will be shown of calculations that use the standard boundary conditions and the new ones.

Experimental Observation and Theoretical Description of Multisoliton Fission in Shallow Water

NASA Astrophysics Data System (ADS)

Trillo, S.; Deng, G.; Biondini, G.; Klein, M.; Clauss, G. F.; Chabchoub, A.; Onorato, M.

2016-09-01

We observe the dispersive breaking of cosine-type long waves [Phys. Rev. Lett. 15, 240 (1965)] in shallow water, characterizing the highly nonlinear "multisoliton" fission over variable conditions. We provide new insight into the interpretation of the results by analyzing the data in terms of the periodic inverse scattering transform for the Korteweg-de Vries equation. In a wide range of dispersion and nonlinearity, the data compare favorably with our analytical estimate, based on a rigorous WKB approach, of the number of emerging solitons. We are also able to observe experimentally the universal Fermi-Pasta-Ulam recurrence in the regime of moderately weak dispersion.

Conversion of ultrashort laser pulses to wavelengths above 3 mm in tapered germanate fibres

NASA Astrophysics Data System (ADS)

Anashkina, E. A.; Andrianov, A. V.; Kim, A. V.

2015-05-01

Tapered germanate fibres are proposed for effective adiabatic conversion of Raman soliton pulses to the mid-IR region. A theoretical analysis demonstrates that, in fibres with anomalous group velocity dispersion decreasing along their length, wavelengths of up to 3.5 μm can be reached, which are unattainable in fibres with a constant core diameter at the same parameters of a 2-μm input signal. The analysis relies on a one-way wave equation that takes into account the combined effect of dispersion, Kerr and Raman nonlinearities, nonlinear dispersion and optical losses and the frequency dependence of the effective fundamental transverse mode size.

Hydrodynamic and kinetic models for spin-1/2 electron-positron quantum plasmas: Annihilation interaction, helicity conservation, and wave dispersion in magnetized plasmas

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

Andreev, Pavel A., E-mail: andreevpa@physics.msu.ru

2015-06-15

We discuss the complete theory of spin-1/2 electron-positron quantum plasmas, when electrons and positrons move with velocities mach smaller than the speed of light. We derive a set of two fluid quantum hydrodynamic equations consisting of the continuity, Euler, spin (magnetic moment) evolution equations for each species. We explicitly include the Coulomb, spin-spin, Darwin and annihilation interactions. The annihilation interaction is the main topic of the paper. We consider the contribution of the annihilation interaction in the quantum hydrodynamic equations and in the spectrum of waves in magnetized electron-positron plasmas. We consider the propagation of waves parallel and perpendicular tomore » an external magnetic field. We also consider the oblique propagation of longitudinal waves. We derive the set of quantum kinetic equations for electron-positron plasmas with the Darwin and annihilation interactions. We apply the kinetic theory to the linear wave behavior in absence of external fields. We calculate the contribution of the Darwin and annihilation interactions in the Landau damping of the Langmuir waves. We should mention that the annihilation interaction does not change number of particles in the system. It does not related to annihilation itself, but it exists as a result of interaction of an electron-positron pair via conversion of the pair into virtual photon. A pair of the non-linear Schrodinger equations for the electron-positron plasmas including the Darwin and annihilation interactions is derived. Existence of the conserving helicity in electron-positron quantum plasmas of spinning particles with the Darwin and annihilation interactions is demonstrated. We show that the annihilation interaction plays an important role in the quantum electron-positron plasmas giving the contribution of the same magnitude as the spin-spin interaction.« less

Gravity-Capillary Lumps

NASA Astrophysics Data System (ADS)

Akylas, Triantaphyllos R.; Kim, Boguk

2004-11-01

In dispersive wave systems, it is known that 1-D plane solitary waves can bifurcate from linear sinusoidal wavetrains at particular wave numbers k = k0 where the phase speed c(k) happens to be an extremum (dc/dk| _0=0) and equals the group speed c_g(k_0). Two distinct possibilities thus arise: either the extremum occurs in the long-wave limit (k_0=0) and, as in shallow water, the bifurcating solitary waves are of the KdV type; or k0 ne 0 and the solitary waves are in the form of packets, described by the NLS equation to leading order, as for gravity-capillary waves in deep water. Here it is pointed out that an entirely analogous scenario is valid for the genesis of 2-D solitary waves or `lumps'. Lumps also may bifurcate at extrema of the phase speed and do so when 1-D solitary waves happen to be unstable to transverse perturbations; moreover, they have algebraically decaying tails and are either of the KPI type (e.g. in shallow water in the presence of strong surface tension) or of the wave packet type (e.g. in deep water) and are described by an elliptic-elliptic Davey-Stewartson equation system to leading order. Examples of steady lump profiles are presented and their dynamics is discussed.

Solutions of the benchmark problems by the dispersion-relation-preserving scheme

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.; Shen, H.; Kurbatskii, K. A.; Auriault, L.

1995-01-01

The 7-point stencil Dispersion-Relation-Preserving scheme of Tam and Webb is used to solve all the six categories of the CAA benchmark problems. The purpose is to show that the scheme is capable of solving linear, as well as nonlinear aeroacoustics problems accurately. Nonlinearities, inevitably, lead to the generation of spurious short wave length numerical waves. Often, these spurious waves would overwhelm the entire numerical solution. In this work, the spurious waves are removed by the addition of artificial selective damping terms to the discretized equations. Category 3 problems are for testing radiation and outflow boundary conditions. In solving these problems, the radiation and outflow boundary conditions of Tam and Webb are used. These conditions are derived from the asymptotic solutions of the linearized Euler equations. Category 4 problems involved solid walls. Here, the wall boundary conditions for high-order schemes of Tam and Dong are employed. These conditions require the use of one ghost value per boundary point per physical boundary condition. In the second problem of this category, the governing equations, when written in cylindrical coordinates, are singular along the axis of the radial coordinate. The proper boundary conditions at the axis are derived by applying the limiting process of r approaches 0 to the governing equations. The Category 5 problem deals with the numerical noise issue. In the present approach, the time-independent mean flow solution is computed first. Once the residual drops to the machine noise level, the incident sound wave is turned on gradually. The solution is marched in time until a time-periodic state is reached. No exact solution is known for the Category 6 problem. Because of this, the problem is formulated in two totally different ways, first as a scattering problem then as a direct simulation problem. There is good agreement between the two numerical solutions. This offers confidence in the computed results. Both formulations are solved as initial value problems. As such, no Kutta condition is required at the trailing edge of the airfoil.

Dispersion of gravitational waves in cold spherical interstellar medium

NASA Astrophysics Data System (ADS)

Barta, Dániel; Vasúth, Mátyás

We investigate the propagation of locally plane, small-amplitude, monochromatic gravitational waves (GWs) through cold compressible interstellar gas in order to provide a more accurate picture of expected waveforms for direct detection. The quasi-isothermal gas is concentrated in a spherical symmetric cloud held together by self-gravitation. Gravitational waves can be treated as linearized perturbations on the background inner Schwarzschild spacetime. The perturbed quantities lead to the field equations governing the gas dynamics and describe the interaction of gravitational waves with matter. We have shown that the transport equation of these amplitudes provides numerical solutions for the frequency-alteration. The decrease in frequency is driven by the energy dissipating process of GW-matter interactions. The decrease is significantly smaller than the magnitude of the original frequency and too small to be detectable by present second-generation and planned third-generation detectors. It exhibits a power-law relationship between original and decreased frequencies. The frequency deviation was examined particularly for the transient signal GW150914.

A modified symplectic PRK scheme for seismic wave modeling

NASA Astrophysics Data System (ADS)

Liu, Shaolin; Yang, Dinghui; Ma, Jian

2017-02-01

A new scheme for the temporal discretization of the seismic wave equation is constructed based on symplectic geometric theory and a modified strategy. The ordinary differential equation in terms of time, which is obtained after spatial discretization via the spectral-element method, is transformed into a Hamiltonian system. A symplectic partitioned Runge-Kutta (PRK) scheme is used to solve the Hamiltonian system. A term related to the multiplication of the spatial discretization operator with the seismic wave velocity vector is added into the symplectic PRK scheme to create a modified symplectic PRK scheme. The symplectic coefficients of the new scheme are determined via Taylor series expansion. The positive coefficients of the scheme indicate that its long-term computational capability is more powerful than that of conventional symplectic schemes. An exhaustive theoretical analysis reveals that the new scheme is highly stable and has low numerical dispersion. The results of three numerical experiments demonstrate the high efficiency of this method for seismic wave modeling.

Inviscid dynamics of a wet foam drop with monodisperse bubble size distribution

NASA Astrophysics Data System (ADS)

McDaniel, J. Gregory; Akhatov, Iskander; Holt, R. Glynn

2002-06-01

Motivated by recent experiments involving the acoustic levitation of foam drops, we develop a model for nonlinear oscillations of a spherical drop composed of monodisperse aqueous foam with void fraction below 0.1. The model conceptually divides a foam drop into many cells, each cell consisting of a spherical volume of liquid with a bubble at its center. By treating the liquid as incompressible and inviscid, a nonlinear equation is obtained for bubble motion due to a pressure applied at the outer radius of the liquid sphere. Upon linearizing this equation and connecting the cells at their outer radii, a wave equation is obtained with a dispersion relation for the sound waves in a bubbly liquid. For the spherical drop, this equation is solved by a normal mode expansion that yields the natural frequencies as functions of standard foam parameters. Numerical examples illustrate how the analysis may be used to extract foam parameters, such as void fraction and bubble radius, from the experimentally measured natural frequencies of a foam drop.

Pancake Ice Thickness Mapping in the Beaufort Sea From Wave Dispersion Observed in SAR Imagery

NASA Astrophysics Data System (ADS)

Wadhams, P.; Aulicino, G.; Parmiggiani, F.; Persson, P. O. G.; Holt, B.

2018-03-01

The early autumn voyage of RV Sikuliaq to the southern Beaufort Sea in 2015 offered very favorable opportunities for observing the properties and thicknesses of frazil-pancake ice types. The operational region was overlaid by a dense network of retrieved satellite imagery, including synthetic aperture radar (SAR) imagery from Sentinel-1 and COSMO-SkyMed (CSK). This enabled us to fully test and apply the SAR-waves technique, first developed by Wadhams and Holt (1991), for deriving the thickness of frazil-pancake icefields from changed wave dispersion. A line of subimages from a main SAR image (usually CSK) is analyzed running into the ice along the main wave direction. Each subimage is spectrally analyzed to yield a wave number spectrum, and the change in the shape of the spectrum between open water and ice, or between two thicknesses of ice, is interpreted in terms of the viscous equations governing wave propagation in frazil-pancake ice. For each of the case studies considered here, there was good or acceptable agreement on thickness between the extensive in situ observations and the SAR-wave calculation. In addition, the SAR-wave analysis gave, parametrically, effective viscosities for the ice covering a consistent and narrow range of 0.03-0.05 m2 s-1.

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

Dechant, Lawrence J.

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

Rigorous coupled wave analysis of acousto-optics with relativistic considerations.

PubMed

Xia, Guoqiang; Zheng, Weijian; Lei, Zhenggang; Zhang, Ruolan

2015-09-01

A relativistic analysis of acousto-optics is presented, and a rigorous coupled wave analysis is generalized for the diffraction of the acousto-optical effect. An acoustic wave generates a grating with temporally and spatially modulated permittivity, hindering direct applications of the rigorous coupled wave analysis for the acousto-optical effect. In a reference frame which moves with the acoustic wave, the grating is static, the medium moves, and the coupled wave equations for the static grating may be derived. Floquet's theorem is then applied to cast these equations into an eigenproblem. Using a Lorentz transformation, the electromagnetic fields in the grating region are transformed to the lab frame where the medium is at rest, and relativistic Doppler frequency shifts are introduced into various diffraction orders. In the lab frame, the boundary conditions are considered and the diffraction efficiencies of various orders are determined. This method is rigorous and general, and the plane waves in the resulting expansion satisfy the dispersion relation of the medium and are propagation modes. Properties of various Bragg diffractions are results, rather than preconditions, of this method. Simulations of an acousto-optical tunable filter made by paratellurite, TeO(2), are given as examples.

Exploring the resonant vibration of thin plates: Reconstruction of Chladni patterns and determination of resonant wave numbers.

PubMed

Tuan, P H; Wen, C P; Chiang, P Y; Yu, Y T; Liang, H C; Huang, K F; Chen, Y F

2015-04-01

The Chladni nodal line patterns and resonant frequencies for a thin plate excited by an electronically controlled mechanical oscillator are experimentally measured. Experimental results reveal that the resonant frequencies can be fairly obtained by means of probing the variation of the effective impedance of the exciter with and without the thin plate. The influence of the extra mass from the central exciter is confirmed to be insignificant in measuring the resonant frequencies of the present system. In the theoretical aspect, the inhomogeneous Helmholtz equation is exploited to derive the response function as a function of the driving wave number for reconstructing experimental Chladni patterns. The resonant wave numbers are theoretically identified with the maximum coupling efficiency as well as the maximum entropy principle. Substituting the theoretical resonant wave numbers into the derived response function, all experimental Chladni patterns can be excellently reconstructed. More importantly, the dispersion relationship for the flexural wave of the vibrating plate can be determined with the experimental resonant frequencies and the theoretical resonant wave numbers. The determined dispersion relationship is confirmed to agree very well with the formula of the Kirchhoff-Love plate theory.

An arbitrary-order staggered time integrator for the linear acoustic wave equation

NASA Astrophysics Data System (ADS)

Lee, Jaejoon; Park, Hyunseo; Park, Yoonseo; Shin, Changsoo

2018-02-01

We suggest a staggered time integrator whose order of accuracy can arbitrarily be extended to solve the linear acoustic wave equation. A strategy to select the appropriate order of accuracy is also proposed based on the error analysis that quantitatively predicts the truncation error of the numerical solution. This strategy not only reduces the computational cost several times, but also allows us to flexibly set the modelling parameters such as the time step length, grid interval and P-wave speed. It is demonstrated that the proposed method can almost eliminate temporal dispersive errors during long term simulations regardless of the heterogeneity of the media and time step lengths. The method can also be successfully applied to the source problem with an absorbing boundary condition, which is frequently encountered in the practical usage for the imaging algorithms or the inverse problems.

Non-perturbative String Theory from Water Waves

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

Iyer, Ramakrishnan; Johnson, Clifford V.; /Southern California U.

2012-06-14

We use a combination of a 't Hooft limit and numerical methods to find non-perturbative solutions of exactly solvable string theories, showing that perturbative solutions in different asymptotic regimes are connected by smooth interpolating functions. Our earlier perturbative work showed that a large class of minimal string theories arise as special limits of a Painleve IV hierarchy of string equations that can be derived by a similarity reduction of the dispersive water wave hierarchy of differential equations. The hierarchy of string equations contains new perturbative solutions, some of which were conjectured to be the type IIA and IIB string theoriesmore » coupled to (4, 4k ? 2) superconformal minimal models of type (A, D). Our present paper shows that these new theories have smooth non-perturbative extensions. We also find evidence for putative new string theories that were not apparent in the perturbative analysis.« less

Utilizing a Coupled Nonlinear Schrödinger Model to Solve the Linear Modal Problem for Stratified Flows

NASA Astrophysics Data System (ADS)

Liu, Tianyang; Chan, Hiu Ning; Grimshaw, Roger; Chow, Kwok Wing

2017-11-01

The spatial structure of small disturbances in stratified flows without background shear, usually named the `Taylor-Goldstein equation', is studied by employing the Boussinesq approximation (variation in density ignored except in the buoyancy). Analytical solutions are derived for special wavenumbers when the Brunt-Väisälä frequency is quadratic in hyperbolic secant, by comparison with coupled systems of nonlinear Schrödinger equations intensively studied in the literature. Cases of coupled Schrödinger equations with four, five and six components are utilized as concrete examples. Dispersion curves for arbitrary wavenumbers are obtained numerically. The computations of the group velocity, second harmonic, induced mean flow, and the second derivative of the angular frequency can all be facilitated by these exact linear eigenfunctions of the Taylor-Goldstein equation in terms of hyperbolic function, leading to a cubic Schrödinger equation for the evolution of a wavepacket. The occurrence of internal rogue waves can be predicted if the dispersion and cubic nonlinearity terms of the Schrödinger equations are of the same sign. Partial financial support has been provided by the Research Grants Council contract HKU 17200815.

Soliton wave-speed management: Slowing, stopping, or reversing a solitary wave

NASA Astrophysics Data System (ADS)

Baines, Luke W. S.; Van Gorder, Robert A.

2018-06-01

While dispersion management is a well-known tool to control soliton properties such as shape or amplitude, far less effort has been directed toward the theoretical control of the soliton wave speed. However, recent experiments concerning the stopping or slowing of light demonstrate that the control of the soliton wave speed is of experimental interest. Motivated by these and other studies, we propose a management approach for modifying the wave speed of a soliton (or of other nonlinear wave solutions, such as periodic cnoidal waves) under the nonlinear Schrödinger equation. Making use of this approach, we are able to slow, stop, or even reverse a solitary wave, and we give several examples to bright solitons, dark solitons, and periodic wave trains, to demonstrate the method. An extension of the approach to spatially heterogeneous media, for which the wave may propagate differently at different spatial locations, is also discussed.

Wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes with surface and nonlocal effects

NASA Astrophysics Data System (ADS)

Zhen, Ya-Xin

2017-02-01

In this paper, the transverse wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes is investigated based on nonlocal elasticity theory with consideration of surface effect. The governing equation is formulated utilizing nonlocal Euler-Bernoulli beam theory and Kelvin-Voigt model. Explicit wave dispersion relation is developed and wave phase velocities and frequencies are obtained. The effect of the fluid flow velocity, structural damping, surface effect, small scale effects and tube diameter on the wave propagation properties are discussed with different wave numbers. The wave frequency increases with the increase of fluid flow velocity, but decreases with the increases of tube diameter and wave number. The effect of surface elasticity and residual surface tension is more significant for small wave number and tube diameter. For larger values of wave number and nonlocal parameters, the real part of frequency ratio raises.

Transport equations for linear surface waves with random underlying flows

NASA Astrophysics Data System (ADS)

Bal, Guillaume; Chou, Tom

1999-11-01

We define the Wigner distribution and use it to develop equations for linear surface capillary-gravity wave propagation in the transport regime. The energy density a(r, k) contained in waves propagating with wavevector k at field point r is given by dota(r,k) + nabla_k[U_⊥(r,z=0) \\cdotk + Ω(k)]\\cdotnabla_ra [13pt] \\: hspace1in - (nabla_r\\cdotU_⊥)a - nabla_r(k\\cdotU_⊥)\\cdotnabla_ka = Σ(δU^2) where U_⊥(r, z=0) is a slowly varying surface current, and Ω(k) = √(k^3+k)tanh kh is the free capillary-gravity dispersion relation. Note that nabla_r\\cdotU_⊥(r,z=0) neq 0, and that the surface currents exchange energy density with the propagating waves. When an additional weak random current √\\varepsilon δU(r/\\varepsilon) varying on the scale of k-1 is included, we find an additional scattering term Σ(δU^2) as a function of correlations in δU. Our results can be applied to the study of surface wave energy transport over a turbulent ocean.

Nonlinear Korteweg-de Vries-Burger equation for ion acoustic shock waves in a weakly relativistic electron-positron-ion plasma with thermal ions

NASA Astrophysics Data System (ADS)

Saeed, R.; Shah, Asif

2010-03-01

The nonlinear propagation of ion acoustic waves in electron-positron-ion plasma comprising of Boltzmannian electrons, positrons, and relativistic thermal ions has been examined. The Korteweg-de Vries-Burger equation has been derived by reductive perturbation technique, and its shock like solution is determined analytically through tangent hyperbolic method. The effect of various plasma parameters on strength and structure of shock wave is investigated. The pert graphical view of the results has been presented for illustration. It is observed that strength and steepness of the shock wave enervate with an increase in the ion temperature, relativistic streaming factor, positron concentrations, electron temperature and they accrue with an increase in coefficient of kinematic viscosity. The convective, dispersive, and dissipative properties of the plasma are also discussed. It is determined that the electron temperature has remarkable influence on the propagation and structure of nonlinear wave in such relativistic plasmas. The numerical analysis has been done based on the typical numerical data from a pulsar magnetosphere.

Scattering of a cross-polarized linear wave by a soliton at an optical event horizon in a birefringent nanophotonic waveguide.

PubMed

Ciret, Charles; Gorza, Simon-Pierre

2016-06-15

The scattering of a linear wave on an optical event horizon, induced by a cross-polarized soliton, is experimentally and numerically investigated in integrated structures. The experiments are performed in a dispersion-engineered birefringent silicon nanophotonic waveguide. In stark contrast with copolarized waves, the large difference between the group velocity of the two cross-polarized waves enables a frequency conversion almost independent of the soliton wavelength. It is shown that the generated idler is only shifted by 10 nm around 1550 nm over a pump tuning range of 350 nm. Simulations using two coupled full vectorial nonlinear Schrödinger equations fully support the experimental results.

Radiative corrections to the Coulomb law and model of dense quantum plasmas: Dispersion of longitudinal waves in magnetized quantum plasmas

NASA Astrophysics Data System (ADS)

Andreev, Pavel A.

2018-04-01

Two kinds of quantum electrodynamic radiative corrections to electromagnetic interactions and their influence on the properties of highly dense quantum plasmas are considered. Linear radiative correction to the Coulomb interaction is considered. Its contribution in the spectrum of the Langmuir waves is presented. The second kind of radiative corrections are related to the nonlinearity of the Maxwell equations for the strong electromagnetic field. Their contribution in the spectrum of transverse waves of magnetized plasmas is briefly discussed. At the consideration of the Langmuir wave spectrum, we included the effect of different distributions of the spin-up and spin-down electrons revealing in the Fermi pressure shift.

Observation of dust acoustic shock wave in a strongly coupled dusty plasma

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

Sharma, Sumita K., E-mail: sumita-sharma82@yahoo.com; Boruah, A.; Nakamura, Y.

2016-05-15

Dust acoustic shock wave is observed in a strongly coupled laboratory dusty plasma. A supersonic flow of charged microparticles is allowed to perturb a stationary dust fluid to excite dust acoustic shock wave. The evolution process beginning with steepening of initial wave front and then formation of a stable shock structure is similar to the numerical results of the Korteweg-de Vries-Burgers equation. The measured Mach number of the observed shock wave agrees with the theoretical results. Reduction of shock amplitude at large distances is also observed due to the dust neutral collision and viscosity effects. The dispersion relation and themore » spatial damping of a linear dust acoustic wave are also measured and compared with the relevant theory.« less

Optical Peregrine rogue waves of self-induced transparency in a resonant erbium-doped fiber.

PubMed

Chen, Shihua; Ye, Yanlin; Baronio, Fabio; Liu, Yi; Cai, Xian-Ming; Grelu, Philippe

2017-11-27

The resonant interaction of an optical field with two-level doping ions in a cryogenic optical fiber is investigated within the framework of nonlinear Schrödinger and Maxwell-Bloch equations. We present explicit fundamental rational rogue wave solutions in the context of self-induced transparency for the coupled optical and matter waves. It is exhibited that the optical wave component always features a typical Peregrine-like structure, while the matter waves involve more complicated yet spatiotemporally balanced amplitude distribution. The existence and stability of these rogue waves is then confirmed by numerical simulations, and they are shown to be excited amid the onset of modulation instability. These solutions can also be extended, using the same analytical framework, to include higher-order dispersive and nonlinear effects, highlighting their universality.

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves.

PubMed

Tsitoura, F; Gietz, U; Chabchoub, A; Hoffmann, N

2018-06-01

We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.

Phase Domain Walls in Weakly Nonlinear Deep Water Surface Gravity Waves

NASA Astrophysics Data System (ADS)

Tsitoura, F.; Gietz, U.; Chabchoub, A.; Hoffmann, N.

2018-06-01

We report a theoretical derivation, an experimental observation and a numerical validation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schrödinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wave vector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. Our present results demonstrate that nonlinear domain walls do exist in the weakly nonlinear regime of general systems exhibiting dispersive 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

Special discontinuities in nonlinearly elastic media

NASA Astrophysics Data System (ADS)

Chugainova, A. P.

2017-06-01

Solutions of a nonlinear hyperbolic system of equations describing weakly nonlinear quasitransverse waves in a weakly anisotropic elastic medium are studied. The influence of small-scale processes of dissipation and dispersion is investigated. The small-scale processes determine the structure of discontinuities (shocks) and a set of discontinuities with a stationary structure. Among the discontinuities with a stationary structure, there are special ones that, in addition to relations following from conservation laws, satisfy additional relations required for the existence of their structure. In the phase plane, the structure of such discontinuities is represented by an integral curve joining two saddles. Special discontinuities lead to nonunique self-similar solutions of the Riemann problem. Asymptotics of non-self-similar problems for equations with dissipation and dispersion are found numerically. These asymptotics correspond to self-similar solutions of the problems.

Optical rogue waves generation in a nonlinear metamaterial

NASA Astrophysics Data System (ADS)

Onana Essama, Bedel Giscard; Atangana, Jacques; Biya-Motto, Frederick; Mokhtari, Bouchra; Cherkaoui Eddeqaqi, Noureddine; Kofane, Timoleon Crepin

2014-11-01

We investigate the behavior of electromagnetic wave which propagates in a metamaterial for negative index regime. The optical pulse propagation is described by the nonlinear Schrödinger equation with cubic-quintic nonlinearities, second- and third-order dispersion effects. The behavior obtained for negative index regime is compared to that observed for positive index regime. The characterization of electromagnetic wave uses some pulse parameters obtained analytically and called collective coordinates such as amplitude, temporal position, width, chirp, frequency shift and phase. Six frequency ranges have been pointed out where a numerical evolution of collective coordinates and their stability are studied under a typical example to verify our analysis. It appears that a robust soliton due to a perfect compensation process between second-order dispersion and cubic-nonlinearity is presented at each frequency range for both negative and positive index regimes. Thereafter, the stability of the soliton pulse and physical conditions leading to optical rogue waves generation are discussed at each frequency range for both regimes, when third-order dispersion and quintic-nonlinearity come into play. We have demonstrated that collective coordinates give much useful information on external and internal behavior of rogue events. Firstly, we determine at what distance begins the internal excitation leading to rogue waves. Secondly, what kind of internal modification and how it modifies the system in order to build-up rogue events. These results lead to a best comprehension of the mechanism of rogue waves generation. So, it clearly appears that the rogue wave behavior strongly depends on nonlinearity strength of distortion, frequency and regime considered.

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

Peralta, J.; López-Valverde, M. A.; Imamura, T.

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

Ion acoustic solitary wave with weakly transverse perturbations in quantum electron-positron-ion plasma

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

Mushtaq, A.; Khan, S. A.; Department of Physics, COMSATS Institute of Information Technology, Islamabad

2007-05-15

The characteristics and stability of ion acoustic solitary wave with transverse perturbations are examined in ultracold quantum magnetospheric plasma consisting of electrons, positrons, and ions. Using the quantum hydrodynamic model, a dispersion relation in the linear regime, and the Kadomtsev-Petviashvili equation in the nonlinear regime are derived. The quantum corrections are studied through quantum statistics and diffraction effects. It is found that compressive solitary wave can propagate in this system. The quantum effects are also studied graphically for both linear and nonlinear profiles of ion acoustic wave. Using energy consideration method, conditions for existence of stable solitary waves are obtained.more » It is found that stable solitary waves depend on quantum corrections, positron concentration, and direction cosine of the wave vector k along the x axis.« less

Impact of interfacial imperfection on transverse wave in a functionally graded piezoelectric material structure with corrugated boundaries

NASA Astrophysics Data System (ADS)

Kumar Singh, Abhishek; Kumar, Santan; Kumari, Richa

2018-03-01

The propagation behavior of Love-type wave in a corrugated functionally graded piezoelectric material layered structure has been taken into account. Concretely, the layered structure incorporates a corrugated functionally graded piezoelectric material layer imperfectly bonded to a functionally graded piezoelectric material half-space. An analytical treatment has been employed to determine the dispersion relation for both cases of electrically open condition and electrically short condition. The phase velocity of the Love-type wave has been computed numerically and its dependence on the wave number has been depicted graphically for a specific type of corrugated boundary surfaces for both said conditions. The crux of the study lies in the fact that the imperfect bonding of the interface, the corrugated boundaries present in the layer, and the material properties of the layer and the half-space strongly influence the phase velocity of the Love-type wave. It can be remarkably noted that the imperfect bonding of the interface reduces the phase velocity of the Love-type wave significantly. As a special case of the problem, it is noticed that the procured dispersion relation for both cases of electrically open and electrically short conditions is in accordance with the classical Love wave equation.

Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.; Kumar, Dipankar; Chakrabarty, Anuz Kumar

2018-05-01

The (2+1)-dimensional hyperbolic and cubic-quintic nonlinear Schrödinger equations describe the propagation of ultra-short pulses in optical fibers of nonlinear media. By using an extended sinh-Gordon equation expansion method, some new complex hyperbolic and trigonometric functions prototype solutions for two nonlinear Schrödinger equations were derived. The acquired new complex hyperbolic and trigonometric solutions are expressed by dark, bright, combined dark-bright, singular and combined singular solitons. The obtained results are more compatible than those of other applied methods. The extended sinh-Gordon equation expansion method is a more powerful and robust mathematical tool for generating new optical solitary wave solutions for many other nonlinear evolution equations arising in the propagation of optical pulses.

Quantum dust magnetosonic waves with spin and exchange correlation effects

NASA Astrophysics Data System (ADS)

Maroof, R.; Mushtaq, A.; Qamar, A.

2016-01-01

Dust magnetosonic waves are studied in degenerate dusty plasmas with spin and exchange correlation effects. Using the fluid equations of magnetoplasma with quantum corrections due to the Bohm potential, temperature degeneracy, spin magnetization energy, and exchange correlation, a generalized dispersion relation is derived. Spin effects are incorporated via spin force and macroscopic spin magnetization current. The exchange-correlation potentials are used, based on the adiabatic local-density approximation, and can be described as a function of the electron density. For three different values of angle, the dispersion relation is reduced to three different modes under the low frequency magnetohydrodynamic assumptions. It is found that the effects of quantum corrections in the presence of dust concentration significantly modify the dispersive properties of these modes. The results are useful for understanding numerous collective phenomena in quantum plasmas, such as those in compact astrophysical objects (e.g., the cores of white dwarf stars and giant planets) and in plasma-assisted nanotechnology (e.g., quantum diodes, quantum free-electron lasers, etc.).

Dusty Pair Plasma—Wave Propagation and Diffusive Transition of Oscillations

NASA Astrophysics Data System (ADS)

Atamaniuk, Barbara; Turski, Andrzej J.

2011-11-01

The crucial point of the paper is the relation between equilibrium distributions of plasma species and the type of propagation or diffusive transition of plasma response to a disturbance. The paper contains a unified treatment of disturbance propagation (transport) in the linearized Vlasov electron-positron and fullerene pair plasmas containing charged dust impurities, based on the space-time convolution integral equations. Electron-positron-dust/ion (e-p-d/i) plasmas are rather widespread in nature. Space-time responses of multi-component linearized Vlasov plasmas on the basis of multiple integral equations are invoked. An initial-value problem for Vlasov-Poisson/Ampère equations is reduced to the one multiple integral equation and the solution is expressed in terms of forcing function and its space-time convolution with the resolvent kernel. The forcing function is responsible for the initial disturbance and the resolvent is responsible for the equilibrium velocity distributions of plasma species. By use of resolvent equations, time-reversibility, space-reflexivity and the other symmetries are revealed. The symmetries carry on physical properties of Vlasov pair plasmas, e.g., conservation laws. Properly choosing equilibrium distributions for dusty pair plasmas, we can reduce the resolvent equation to: (i) the undamped dispersive wave equations, (ii) and diffusive transport equations of oscillations.

Wave propagation in magneto-electro-elastic multilayered plates with nonlocal effect

NASA Astrophysics Data System (ADS)

Chen, Jiangyi; Guo, Junhong; Pan, Ernian

2017-07-01

In this paper, analytical solutions for propagation of time-harmonic waves in three-dimensional, transversely isotropic, magnetoelectroelastic and multilayered plates with nonlocal effect are derived. We first convert the time-harmonic wave problem into a linear eigenvalue system, from which we obtain the general solutions of the extended displacements and stresses. The solutions are then employed to derive the propagator matrix which connects the field variables at the upper and lower interfaces of each layer. Making use of the continuity conditions of the physical quantities across the interface, the global propagator relation is assembled by propagating the solutions in each layer from the bottom to the top of the layered plate. From the global propagator matrix, the dispersion equation is obtained by imposing the traction-free boundary conditions on both the top and bottom surfaces of the layered plate. Dispersion curves and mode shapes in layered plates made of piezoelectric BaTiO3 and magnetostrictive CoFe2O4 materials are presented to show the influence of the nonlocal parameter, stacking sequence, as well as the orientation of incident wave on the time-harmonic field response.

Modeling of visible-extended supercontinuum generation from a tapered Ytterbium-doped fiber amplifier

NASA Astrophysics Data System (ADS)

Song, Rui; Lei, Chengmin; Han, Kai; Chen, Zilun; Pu, Dongsheng; Hou, Jing

2017-05-01

Supercontinuum generation directly from a nonlinear fiber amplifier, especially from a nonlinear ytterbium-doped fiber amplifier, attracts more and more attention due to its all-fiber structure, high optical to optical conversion efficiency, and high power output potential. However, the modeling of supercontinuum generation from a nonlinear fiber amplifier has been rarely reported. In this paper, the modeling of a tapered Ytterbium-doped fiber amplifier for visible extended to infrared supercontinuum generation is proposed based on the combination of the laser rate equations and the generalized nonlinear Schrödinger equation. Ytterbium-doped fiber amplifier generally can not generate visible extended supercontinuum due to its pumping wavelength and zero-dispersion wavelength. However, appropriate tapering and four-wave mixing makes the visible extended supercontinuum generation from an ytterbium-doped fiber amplifier possible. Tapering makes the zero-dispersion wavelength of the ytterbium-doped fiber shift to the short wavelength and minimizes the dispersion matching. Four-wave mixing plays an important role in the visible spectrum generation. The influence of pulse width and pump power on the supercontinuum generation is calculated and analyzed. The simulation results imply that it is promising and possible to fabricate a visible-to-infrared supercontinuum with low pump power and flat spectrum by using the tapered ytterbium-doped fiber amplifier scheme as long as the related parameters are well-selected.

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.

Free and Convectively Coupled Equatorial Waves Simulated by CMIP5 Climate Models

NASA Astrophysics Data System (ADS)

Marques, Carlos A. F.; Castanheira, José M.

2015-04-01

It is well known that precipitation in the equatorial belt does not occur randomly, but is often organized into synoptic to planetary-scale disturbances with time scales smaller than a season. Several studies have shown that a large fraction of the convection variability in such disturbances is associated with dynamical Equatorial Waves, such as the Kelvin, Equatorial Rossby, Mixed Rossby-Gravity, Eastward and Westward Inertio-Gravity waves (e.g. Kiladis et al., Rev. Geophys., 2009). The horizontal structures and dispersion characteristics of such Convectively Coupled Equatorial Waves (CCEWs) correspond to the solutions of the shallow water (SW) equations on an equatorial β-plane obtained by Matsuno (J. Meteor. Soc. Japan, 1966). CCEWs have broad impacts within the tropics, but their simulation in general circulation models is still problematic. Using space-time spectral analyses of a proxy field for tropical convection (e.g. outgoing long wave radiation (OLR)), it has been shown the existence of spectral peaks aligned along the dispersion curves of equatorially trapped wave modes of SW theory, which have been interpreted as the effect of equatorial wave processes (e.g. Takayabu, J. Meteor. Soc. Japan, 1994; Wheeler and Kiladis, JAS, 1999). However, different equatorial modes may not be well separated in the wavenumber-frequency domain due to a vertical variation of the horizontal basic flow, that may introduce Doppler shiftings and changes in the vertical heating profiles which may distort the theoretical dispersion curves (Yang et al., JAS, 2003). In this communication, we present a new methodology for the diagnosis of CCEWs, which is based on a pre-filtering of the geopotential and horizontal wind, via three-dimensional (3-D) normal mode functions of the adiabatic linearized equations of a resting atmosphere, followed by a space-time power and cross spectral analysis applied to the 3-D normal mode filtered fields and the OLR (or other fields that may be proxies of tropical convection) to identify the spectral regions of coherence. The advantage of such an approach is that the theoretical vertical as well as horizontal structure functions are taken into account in the projection method, and so the structures obtained are better defined with respect to the theoretical normal modes of a 3-D atmosphere compared to other approaches. The methodology has been applied to the (u,v,φ) and OLR fields simulated by various of the most recent climate models (CMIP5). The methodology has been also applied to the ERA-Interim geopotential and horizontal wind fields and to the interpolated OLR data produced by the National Oceanic and Atmospheric Administration, against which model simulations are evaluated. This new diagnosis method permits a direct detection of various types of equatorial waves, compares the dispersion characteristics of the coupled waves with the theoretical dispersion curves and allows an identification of which vertical modes are more involved in the convection. Moreover, it is able to show the existence of free dry waves and moist coupled waves with a common vertical structure, which is in conformity with the effect of convective heating/cooling on the effective static stability, as deduced from the gross moist stability concept (Kiladis et al., Rev. Geophys., 2009). The methodology is also sensitive to wave's interactions. Deficiencies found in the models' simulations should help the identification of which physical processes need to be improved in climate models.

Study on photonic angular momentum states in coaxial magneto-optical waveguides

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

Yang, Mu; Wu, Li-Ting; Guo, Tian-Jing

2014-10-21

By rigorously solving Maxwell's equations, we develop a full-wave electromagnetic theory for the study of photonic angular momentum states (PAMSs) in coaxial magneto-optical (MO) waveguides. Paying attention to a metal-MO-metal coaxial configuration, we show that the dispersion curves of the originally degenerated PAMSs experience a splitting, which are determined by the off-diagonal permittivity tensor element of the MO medium. We emphasize that this broken degeneracy in dispersion relation is accompanied by modified distributions of field component and transverse energy flux. A qualitative analysis about the connection between the split dispersion behavior and the field distribution is provided. Potential applications aremore » discussed.« less

Experimental and numerical investigations of temporally and spatially periodic modulated wave trains

NASA Astrophysics Data System (ADS)

Houtani, H.; Waseda, T.; Tanizawa, K.

2018-03-01

A number of studies on steep nonlinear waves were conducted experimentally with the temporally periodic and spatially evolving (TPSE) wave trains and numerically with the spatially periodic and temporally evolving (SPTE) ones. The present study revealed that, in the vicinity of their maximum crest height, the wave profiles of TPSE and SPTE modulated wave trains resemble each other. From the investigation of the Akhmediev-breather solution of the nonlinear Schrödinger equation (NLSE), it is revealed that the dispersion relation deviated from the quadratic dependence of frequency on wavenumber and became linearly dependent instead. Accordingly, the wave profiles of TPSE and SPTE breathers agree. The range of this agreement is within the order of one wave group of the maximum crest height and persists during the long-term evolution. The findings extend well beyond the NLSE regime and can be applied to modulated wave trains that are highly nonlinear and broad-banded. This was demonstrated from the numerical wave tank simulations with a fully nonlinear potential flow solver based on the boundary element method, in combination with the nonlinear wave generation method based on the prior simulation with the higher-order spectral model. The numerical wave tank results were confirmed experimentally in a physical wave tank. The findings of this study unravel the fundamental nature of the nonlinear wave evolution. The deviation of the dispersion relation of the modulated wave trains occurs because of the nonlinear phase variation due to quasi-resonant interaction, and consequently, the wave geometry of temporally and spatially periodic modulated wave trains coincides.

Relativistic Kinetic Theory

NASA Astrophysics Data System (ADS)

Vereshchagin, Gregory V.; Aksenov, Alexey G.

2017-02-01

Preface; Acknowledgements; Acronyms and definitions; Introduction; Part I. Theoretical Foundations: 1. Basic concepts; 2. Kinetic equation; 3. Averaging; 4. Conservation laws and equilibrium; 5. Relativistic BBGKY hierarchy; 6. Basic parameters in gases and plasmas; Part II. Numerical Methods: 7. The basics of computational physics; 8. Direct integration of Boltzmann equations; 9. Multidimensional hydrodynamics; Part III. Applications: 10. Wave dispersion in relativistic plasma; 11. Thermalization in relativistic plasma; 12. Kinetics of particles in strong fields; 13. Compton scattering in astrophysics and cosmology; 14. Self-gravitating systems; 15. Neutrinos, gravitational collapse and supernovae; Appendices; Bibliography; Index.

Parsimonious surface wave interferometry

NASA Astrophysics Data System (ADS)

Li, Jing; Hanafy, Sherif; Schuster, Gerard T.

2018-03-01

To decrease the recording time of a 2-D seismic survey from a few days to one hour or less, we present a parsimonious surface wave interferometry method. Interferometry allows for the creation of a large number of virtual shot gathers from just two reciprocal shot gathers by crosscoherence of trace pairs. Then, the virtual surface waves can be inverted for the S-wave velocity model by wave-equation dispersion inversion (WD). Synthetic and field data tests suggest that parsimonious WD (PWD) gives S-velocity tomograms that are comparable to those obtained from a conventional survey with a shot at each receiver. The limitation of PWD is that the virtual data lose some information so that the resolution of the S-velocity tomogram can be modestly lower than that of the S-velocity tomogram inverted from a conventional survey.

Solitonic properties for a forced generalized variable-coefficient Korteweg-de Vries equation for the atmospheric blocking phenomenon

NASA Astrophysics Data System (ADS)

Chai, Jun; Tian, Bo; Qu, Qi-Xing; Zhen, Hui-Ling; Chai, Han-Peng

2018-07-01

In this paper, investigation is given to a forced generalized variable-coefficient Korteweg-de Vries equation for the atmospheric blocking phenomenon. Based on the Lax pair, under certain variable-coefficient-dependent constraints, we present an infinite sequence of the conservation laws. Through the Riccati equations obtained from the Lax pair, a Wahlquist-Estabrook-type Bäcklund transformation (BT) is derived, based on which the nonlinear superposition formula as well as one- and two-soliton-like solutions are obtained. Via the truncated Painlevé expansion, we give a Painlevé BT, along with the one-soliton-like solutions. With the Painlevé BT, bilinear forms are constructed, and we get a bilinear BT as well as the corresponding one-soliton-like solutions. Bell-type bright and dark soliton-like waves and kink-type soliton-like waves are observed, respectively. Graphic analysis shows that (1) the velocities of the soliton-like waves are related to h(t), d(t), f(t) and R(t), while the soliton-like wave amplitudes just depend on f(t), and (2) with the nonzero f(t) and R(t), soliton-like waves propagate on the varying backgrounds, where h(t), d(t) and f(t) are the dispersive, dissipative and line-damping coefficients, respectively, R(t) is the external-force term, and t is the scaled time coordinate.

Continuous-wave to pulse regimes for a family of passively mode-locked lasers with saturable nonlinearity

NASA Astrophysics Data System (ADS)

Dikandé, Alain M.; Voma Titafan, J.; Essimbi, B. Z.

2017-10-01

The transition dynamics from continuous-wave to pulse regimes of operation for a generic model of passively mode-locked lasers with saturable absorbers, characterized by an active medium with non-Kerr nonlinearity, are investigated analytically and numerically. The system is described by a complex Ginzburg-Landau equation with a general m:n saturable nonlinearity (i.e {I}m/{(1+{{Γ }}I)}n, where I is the field intensity and m and n are two positive numbers), coupled to a two-level gain equation. An analysis of stability of continuous waves, following the modulational instability approach, provides a global picture of the self-starting dynamics in the system. The analysis reveals two distinct routes depending on values of the couple (m, n), and on the dispersion regime: in the normal dispersion regime, when m = 2 and n is arbitrary, the self-starting requires positive values of the fast saturable absorber and nonlinearity coefficients, but negative values of these two parameters for the family with m = 0. However, when the spectral filter is negative, the laser can self-start for certain values of the input field and the nonlinearity saturation coefficient Γ. The present work provides a general map for the self-starting mechanisms of rare-earth doped figure-eight fiber lasers, as well as Kerr-lens mode-locked solid-state lasers.

Observations of planetary mixed Rossby-gravity waves in the upper stratosphere

NASA Technical Reports Server (NTRS)

Randel, William J.; Boville, Byron A.; Gille, John C.

1990-01-01

Observational evidence is presented for planetary scale (zonal wave number 1-2) mixed Rossby-gravity (MRG) waves in the equatorial upper stratosphere (35-50 km). These waves are detected in LIMS measurements as coherently propagating temperature maxima of amplitude 0.1-0.3 K, which are antisymmetric (out of phase) about the equator, centered near 10-15 deg north and south latitude. These features have vertical wavelengths of order 10-15 km, periods near 2-3 days, and zonal phase velocities close to 200 m/s. Both eastward and westward propagating waves are found, and the observed vertical wavelengths and meridional structures are in good agreement with the MRG dispersion relation. Theoretical estimates of the zonal accelerations attributable to these waves suggest they do not contribute substantially to the zonal momentum balance in the middle atmosphere.

Dynamics of unstable sound waves in a non-equilibrium medium at the nonlinear stage

NASA Astrophysics Data System (ADS)

Khrapov, Sergey; Khoperskov, Alexander

2018-03-01

A new dispersion equation is obtained for a non-equilibrium medium with an exponential relaxation model of a vibrationally excited gas. We have researched the dependencies of the pump source and the heat removal on the medium thermodynamic parameters. The boundaries of sound waves stability regions in a non-equilibrium gas have been determined. The nonlinear stage of sound waves instability development in a vibrationally excited gas has been investigated within CSPH-TVD and MUSCL numerical schemes using parallel technologies OpenMP-CUDA. We have obtained a good agreement of numerical simulation results with the linear perturbations dynamics at the initial stage of the sound waves growth caused by instability. At the nonlinear stage, the sound waves amplitude reaches the maximum value that leads to the formation of shock waves system.

Lagrangian averaging, nonlinear waves, and shock regularization

NASA Astrophysics Data System (ADS)

Bhat, Harish S.

In this thesis, we explore various models for the flow of a compressible fluid as well as model equations for shock formation, one of the main features of compressible fluid flows. We begin by reviewing the variational structure of compressible fluid mechanics. We derive the barotropic compressible Euler equations from a variational principle in both material and spatial frames. Writing the resulting equations of motion requires certain Lie-algebraic calculations that we carry out in detail for expository purposes. Next, we extend the derivation of the Lagrangian averaged Euler (LAE-alpha) equations to the case of barotropic compressible flows. The derivation in this thesis involves averaging over a tube of trajectories etaepsilon centered around a given Lagrangian flow eta. With this tube framework, the LAE-alpha equations are derived by following a simple procedure: start with a given action, expand via Taylor series in terms of small-scale fluid fluctuations xi, truncate, average, and then model those terms that are nonlinear functions of xi. We then analyze a one-dimensional subcase of the general models derived above. We prove the existence of a large family of traveling wave solutions. Computing the dispersion relation for this model, we find it is nonlinear, implying that the equation is dispersive. We carry out numerical experiments that show that the model possesses smooth, bounded solutions that display interesting pattern formation. Finally, we examine a Hamiltonian partial differential equation (PDE) that regularizes the inviscid Burgers equation without the addition of standard viscosity. Here alpha is a small parameter that controls a nonlinear smoothing term that we have added to the inviscid Burgers equation. We show the existence of a large family of traveling front solutions. We analyze the initial-value problem and prove well-posedness for a certain class of initial data. We prove that in the zero-alpha limit, without any standard viscosity, solutions of the PDE converge strongly to weak solutions of the inviscid Burgers equation. We provide numerical evidence that this limit satisfies an entropy inequality for the inviscid Burgers equation. We demonstrate a Hamiltonian structure for the PDE.

Magnetosonic solitons in space plasmas: dark or bright solitons?

NASA Astrophysics Data System (ADS)

Pokhotelov, O. A.; Onishchenko, O. G.; Balikhin, M. A.; Stenflo, L.; Shukla, P. K.

2007-12-01

The nonlinear theory of large-amplitude magnetosonic (MS) waves in highβ space plasmas is revisited. It is shown that solitary waves can exist in the form of `bright' or `dark' solitons in which the magnetic field is increased or decreased relative to the background magnetic field. This depends on the shape of the equilibrium ion distribution function. The basic parameter that controls the nonlinear structure is the wave dispersion, which can be either positive or negative. A general dispersion relation for MS waves propagating perpendicularly to the external magnetic field in a plasma with an arbitrary velocity distribution function is derived.It takes into account general plasma equilibria, such as the Dory-Guest-Harris (DGH) or Kennel-Ashour-Abdalla (KA) loss-cone equilibria, as well as distributions with a power-law velocity dependence that can be modelled by κdistributions. It is shown that in a bi-Maxwellian plasma the dispersion is negative, i.e. the phase velocity decreases with an increase of the wavenumber. This means that the solitary solution in this case has the form of a `bright' soliton with the magnetic field increased. On the contrary, in some non-Maxwellian plasmas, such as those with ring-type ion distributions or DGH plasmas, the solitary solution may have the form of a magnetic hole. The results of similar investigations based on nonlinear Hall-MHD equations are reviewed. The relevance of our theoretical results to existing satellite wave observations is outlined.

Magnetosonic Solitons in Non-Maxwellian Space Plasmas

NASA Astrophysics Data System (ADS)

Pokhotelov, O. A.; Balikhin, M.; Onishchenko, O. G.

2006-12-01

The nonlinear theory of large-amplitude magnetosonic (MS) waves in high-beta space plasmas is developed. It is shown that solitary waves can exist in the form of magnetic humps and holes in which the magnetic field is increased or decreased relative to the background magnetic field. This depends on the shape of the equilibrium ion velocity distribution function. The basic parameter that controls the nonlinear structure is the wave dispersion which can be either positive or negative. A general dispersion relation for MS waves propagating perpendicularly to the external magnetic field in a plasma with an arbitrary velocity distribution function is derived. It takes into account general plasma equilibria such as the Dory-Guest-Harris or Kennel- Ashour-Abdalla loss cone equilibria, as well as distributions with a power law velocity dependence that can be modelled by kappa-distributions. It is shown that in Maxwellian and bi-Maxwellian plasmas the dispersion is negative, i.e. the phase velocity decreases with an increase of the wave number. This means that the solitary solution in this case has the form of a magnetic hump with the magnetic field increased. On the contrary, in some non-Maxwellian plasmas such as those with ring-type ion distributions or DGH plasmas, the solitary solution may have the form of a magnetic hole. The results of similar investigations based on nonlinear Hall-MHD equations are reviewed. The relevance of our theoretical results to experimental observations is outlined

The structure of ion-acoustic waves in a low-frequency three-component electron-ion space plasma with two-electron populations

NASA Astrophysics Data System (ADS)

Govender, G.; Moolla, S.

2018-07-01

Low-frequency ion-acoustic waves are analysed on the ion time-scale, in a three-component electron-ion space plasma. The solitary waves propagate in the positive x direction relative to an ambient magnetic field ěc {B}_0 which forms static background for a configuration consisting of cool fluid ions and both warm and hot Boltzmann-distributed electrons with temperatures T_{ic}, T_{ew} and T_{eh}, respectively. We derive linear dispersion relation for the waves by introducing first-order density, pressure and velocity perturbations into the ion fluid equations. Additionally, the variation in the nonlinear structure of the waves are investigated by carrying out a full parametric analysis utilising our numerical code. Our results reveal that ion-acoustic waves exhibit well-defined nonlinear spikes at speeds of M≥ 2.25 and an electric field amplitude of E_0=0.85. It is also shown that low wave speeds (M≤ 2), higher densities of the hot electrons, antiparallel drifting of the cool fluid ions, and increased ion temperatures all lead to significant dispersive effects. The ion-acoustic plasma waves featured in this paper have forms that are consistent with those classified as the type-A and type-B broadband electrostatic noise (BEN) observed in the data obtained from earlier satellite missions.

Evaluating crude oil chemical dispersion efficacy in a flow-through wave tank under regular non-breaking wave and breaking wave conditions.

PubMed

Li, Zhengkai; Lee, Kenneth; King, Thomas; Boufadel, Michel C; Venosa, Albert D

2009-05-01

Testing dispersant effectiveness under conditions similar to that of the open environment is required for improvements in operational procedures and the formulation of regulatory guidelines. To this end, a novel wave tank facility was fabricated to study the dispersion of crude oil under regular non-breaking and irregular breaking wave conditions. This wave tank facility was designed for operation in a flow-through mode to simulate both wave- and current-driven hydrodynamic conditions. We report here an evaluation of the effectiveness of chemical dispersants (Corexit EC9500A and SPC 1000) on two crude oils (Medium South American [MESA] and Alaska North Slope [ANS]) under two different wave conditions (regular non-breaking and plunging breaking waves) in this wave tank. The dispersant effectiveness was assessed by measuring the water column oil concentration and dispersed oil droplet size distribution. In the absence of dispersants, nearly 8-19% of the test crude oils were dispersed and diluted under regular wave and breaking wave conditions. In the presence of dispersants, about 21-36% of the crude oils were dispersed and diluted under regular waves, and 42-62% under breaking waves. Consistently, physical dispersion under regular waves produced large oil droplets (volumetric mean diameter or VMD > or = 300 microm), whereas chemical dispersion under breaking waves created small droplets (VMD < or = 50 microm). The data can provide useful information for developing better operational guidelines for dispersant use and improved predictive models on dispersant effectiveness in the field.

Twisted waves and instabilities in a permeating dusty plasma

NASA Astrophysics Data System (ADS)

Bukhari, S.; Ali, S.; Khan, S. A.; Mendonca, J. T.

2018-04-01

New features of the twisted dusty plasma modes and associated instabilities are investigated in permeating plasmas. Using the Vlasov-Poisson model equations, a generalized dispersion relation is obtained for a Maxwellian distributed plasma to analyse the dust-acoustic and dust-ion-acoustic waves with finite orbital angular momentum (OAM) states. Existence conditions for damping/growth rates are discussed and showed significant modifications in twisted dusty modes as compared to straight propagating dusty modes. Numerically, the instability growth rate, which depends on particle streaming and twist effects in the wave potential, is significantly modified due to the Laguerre-Gaussian profiles. Relevance of the study to wave excitations due to penetration of solar wind into cometary clouds or interstellar dusty plasmas is discussed.

Observables and dispersion relations in κ-Minkowski spacetime

NASA Astrophysics Data System (ADS)

Aschieri, Paolo; Borowiec, Andrzej; Pachoł, Anna

2017-10-01

We revisit the notion of quantum Lie algebra of symmetries of a noncommutative spacetime, its elements are shown to be the generators of infinitesimal transformations and are naturally identified with physical observables. Wave equations on noncommutative spaces are derived from a quantum Hodge star operator. This general noncommutative geometry construction is then exemplified in the case of κ-Minkowski spacetime. The corresponding quantum Poincaré-Weyl Lie algebra of in-finitesimal translations, rotations and dilatations is obtained. The d'Alembert wave operator coincides with the quadratic Casimir of quantum translations and it is deformed as in Deformed Special Relativity theories. Also momenta (infinitesimal quantum translations) are deformed, and correspondingly the Einstein-Planck relation and the de Broglie one. The energy-momentum relations (dispersion relations) are consequently deduced. These results complement those of the phenomenological literature on the subject.

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Smets, Ruben

2017-08-01

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

Derivation of nonlinear wave equations for ultrasound beam in nonuniform bubbly liquids

NASA Astrophysics Data System (ADS)

Kanagawa, Tetsuya; Yano, Takeru; Kawahara, Junya; Kobayashi, Kazumichi; Watanabe, Masao; Fujikawa, Shigeo

2012-09-01

Weakly nonlinear propagation of diffracted ultrasound beams in a nonuniform bubbly liquid is theoretically studied based on the method of multiple scales with the set of scaling relations of some physical parameters. It is assumed that the spatial distribution of the number density of bubbles in an initial state at rest is a slowly varying function of space coordinates and the amplitude of its variation is small compared with a mean number density. As a result, a Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation with dispersion and nonuniform effects for a low frequency case and a nonlinear Schrödinger (NLS) equation with dissipation, diffraction, and nonuniform effects for a high frequency case, are derived from the basic equations of bubbly flows.

Measurement of mechanical properties of homogeneous tissue with ultrasonically induced shear waves

NASA Astrophysics Data System (ADS)

Greenleaf, James F.; Chen, Shigao

2007-03-01

Fundamental mechanical properties of tissue are altered by many diseases. Regional and systemic diseases can cause changes in tissue properties. Liver stiffness is caused by cirrhosis and fibrosis. Vascular wall stiffness and tone are altered by smoking, diabetes and other diseases. Measurement of tissue mechanical properties has historically been done with palpation. However palpation is subjective, relative, and not quantitative or reproducible. Elastography in which strain is measured due to stress application gives a qualitative estimate of Young's modulus at low frequency. We have developed a method that takes advantage of the fact that the wave equation is local and shear wave propagation depends only on storage and loss moduli in addition to density, which does not vary much in soft tissues. Our method is called shearwave dispersion ultrasonic velocity measurement (SDUV). The method uses ultrasonic radiation force to produce repeated motion in tissue that induces shear waves to propagate. The shear wave propagation speed is measured with pulse echo ultrasound as a function of frequency of the shear wave. The resulting velocity dispersion curve is fit with a Voight model to determine the elastic and viscous moduli of the tissue. Results indicate accurate and precise measurements are possible using this "noninvasive biopsy" method. Measurements in beef along and across the fibers are consistent with the literature values.

Electromagnetic drift waves dispersion for arbitrarily collisional plasmas

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

Lee, Wonjae, E-mail: wol023@ucsd.edu; Krasheninnikov, Sergei I., E-mail: skrash@mae.ucsd.edu; Angus, J. R.

2015-07-15

The impacts of the electromagnetic effects on resistive and collisionless drift waves are studied. A local linear analysis on an electromagnetic drift-kinetic equation with Bhatnagar-Gross-Krook-like collision operator demonstrates that the model is valid for describing linear growth rates of drift wave instabilities in a wide range of plasma parameters showing convergence to reference models for limiting cases. The wave-particle interactions drive collisionless drift-Alfvén wave instability in low collisionality and high beta plasma regime. The Landau resonance effects not only excite collisionless drift wave modes but also suppress high frequency electron inertia modes observed from an electromagnetic fluid model in collisionlessmore » and low beta regime. Considering ion temperature effects, it is found that the impact of finite Larmor radius effects significantly reduces the growth rate of the drift-Alfvén wave instability with synergistic effects of high beta stabilization and Landau resonance.« less

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.

Material Characterization using Passive Multispectral Polarimetric Imagery

DTIC Science & Technology

2013-03-01

least intuitive RS technique is undoubtedly polarimetry . Polarization is a property of all TEM waves, so its applications are not limited to any...Shaw. “Review of passive imaging polarimetry for remote sensing applications”. Applied Optics, 45(22):5453–5469, 2006. [48] Vanderbilt, V.C. and...refractive index; polarimetry ; multispectral; polarization; polarisation; polarimetric imagery; dispersion; Drude model; Cauchy equation; remote

Fluid equations with nonlinear wave-particle resonances^

NASA Astrophysics Data System (ADS)

Mattor, Nathan

1997-11-01

We have derived fluid equations that include linear and nonlinear wave-particle resonance effects. This greatly extends previous ``Landau-fluid'' closures, which include linear Landau damping. (G.W. Hammett and F.W. Perkins, Phys. Rev. Lett. 64,) 3019 (1990).^, (Z. Chang and J. D. Callen, Phys. Fluids B 4,) 1167 (1992). The new fluid equations are derived with no approximation regarding nonlinear kinetic interaction, and so additionally include numerous nonlinear kinetic effects. The derivation starts with the electrostatic drift kinetic equation for simplicity, with a Maxwellian distribution function. Fluid closure is accomplished through a simple integration trick applied to the drift kinetic equation, using the property that the nth moment of Maxwellian distribution is related to the nth derivative. The result is a compact closure term appearing in the highest moment equation, a term which involves a plasma dispersion function of the electrostatic field and its derivatives. The new term reduces to the linear closures in appropriate limits, so both approaches retain linear Landau damping. But the nonlinearly closed equations have additional desirable properties. Unlike linear closures, the nonlinear closure retains the time-reversibility of the original kinetic equation. We have shown directly that the nonlinear closure retains at least two nonlinear resonance effects: wave-particle trapping and Compton scattering. Other nonlinear kinetic effects are currently under investigation. The new equations correct two previous discrepancies between kinetic and Landau-fluid predictions, including a propagator discrepancy (N. Mattor, Phys. Fluids B 4,) 3952 (1992). and a numerical discrepancy for the 3-mode shearless bounded slab ITG problem. (S. E. Parker et al.), Phys. Plasmas 1, 1461 (1994). ^* In collaboration with S. E. Parker, Department of Physics, University of Colorado, Boulder. ^ Work performed at LLNL under DoE contract No. W7405-ENG-48.

Thermodynamics of saline and fresh water mixing in estuaries

NASA Astrophysics Data System (ADS)

Zhang, Zhilin; Savenije, Hubert H. G.

2018-03-01

The mixing of saline and fresh water is a process of energy dissipation. The freshwater flow that enters an estuary from the river contains potential energy with respect to the saline ocean water. This potential energy is able to perform work. Looking from the ocean to the river, there is a gradual transition from saline to fresh water and an associated rise in the water level in accordance with the increase in potential energy. Alluvial estuaries are systems that are free to adjust dissipation processes to the energy sources that drive them, primarily the kinetic energy of the tide and the potential energy of the river flow and to a minor extent the energy in wind and waves. Mixing is the process that dissipates the potential energy of the fresh water. The maximum power (MP) concept assumes that this dissipation takes place at maximum power, whereby the different mixing mechanisms of the estuary jointly perform the work. In this paper, the power is maximized with respect to the dispersion coefficient that reflects the combined mixing processes. The resulting equation is an additional differential equation that can be solved in combination with the advection-dispersion equation, requiring only two boundary conditions for the salinity and the dispersion. The new equation has been confronted with 52 salinity distributions observed in 23 estuaries in different parts of the world and performs very well.

Dispersion relation and electron acceleration in the combined circular and elliptical metallic-dielectric waveguide filled by plasma

NASA Astrophysics Data System (ADS)

Abdoli-Arani, A.; Montazeri, M. M.

2018-04-01

Two special types of metallic waveguide having dielectric cladding and plasma core including the combined circular and elliptical structure are studied. Longitudinal and transverse field components in the different regions are obtained. Applying the boundary conditions, dispersion relations of the electromagnetic waves in the structures are obtained and then plotted. The acceleration of an injected external relativistic electron in the considered waveguides is studied. The obtained differential equations related to electron motion are solved by the fourth-order Runge-Kutta method. Numerical computations are made, and the results are graphically presented.

Observation of Dispersive Shock Waves, Solitons, and Their Interactions in Viscous Fluid Conduits.

PubMed

Maiden, Michelle D; Lowman, Nicholas K; Anderson, Dalton V; Schubert, Marika E; Hoefer, Mark A

2016-04-29

Dispersive shock waves and solitons are fundamental nonlinear excitations in dispersive media, but dispersive shock wave studies to date have been severely constrained. Here, we report on a novel dispersive hydrodynamic test bed: the effectively frictionless dynamics of interfacial waves between two high viscosity contrast, miscible, low Reynolds number Stokes fluids. This scenario is realized by injecting from below a lighter, viscous fluid into a column filled with high viscosity fluid. The injected fluid forms a deformable pipe whose diameter is proportional to the injection rate, enabling precise control over the generation of symmetric interfacial waves. Buoyancy drives nonlinear interfacial self-steepening, while normal stresses give rise to the dispersion of interfacial waves. Extremely slow mass diffusion and mass conservation imply that the interfacial waves are effectively dissipationless. This enables high fidelity observations of large amplitude dispersive shock waves in this spatially extended system, found to agree quantitatively with a nonlinear wave averaging theory. Furthermore, several highly coherent phenomena are investigated including dispersive shock wave backflow, the refraction or absorption of solitons by dispersive shock waves, and the multiphase merging of two dispersive shock waves. The complex, coherent, nonlinear mixing of dispersive shock waves and solitons observed here are universal features of dissipationless, dispersive hydrodynamic flows.

Multifluid Theory of Solitons

NASA Astrophysics Data System (ADS)

Verheest, Frank

2008-03-01

After introducing the basic multifluid model equations, this review discusses three different methods to describe nonlinear plasma waves, by giving a rather general overview of the relevant methodology, followed by a specific and recent application. First, reductive perturbation analysis is applicable to waves that are not too strongly nonlinear, if their linear counterparts have an acoustic-like dispersion at low frequencies. It is discussed for electrostatic modes, with a brief application to dusty plasma waves. The typical paradigm for such problems is the well known KdV equation and its siblings. Stationary waves with larger amplitudes can be treated, i.a., via the fluid-dynamic approach pioneered by McKenzie, which focuses on essential insights into the limitations that restrict the range of available solitary electrostatic solutions. As an illustration, novel electrostatic solutions have been found in plasmas with two-temperature electron species that are relevant in understanding certain magnetospheric plasma observations. The older cousin of the large-amplitude technique is the Sagdeev pseudopotential description, to which the newer fluid-dynamic approach is essentially equivalent. Because the Sagdeev analysis has mostly been applied to electrostatic waves, some recent results are given for electromagnetic modes in pair plasmas, to show its versatility.

Assessment of numerical methods for the solution of fluid dynamics equations for nonlinear resonance systems

NASA Technical Reports Server (NTRS)

Przekwas, A. J.; Yang, H. Q.

1989-01-01

The capability of accurate nonlinear flow analysis of resonance systems is essential in many problems, including combustion instability. Classical numerical schemes are either too diffusive or too dispersive especially for transient problems. In the last few years, significant progress has been made in the numerical methods for flows with shocks. The objective was to assess advanced shock capturing schemes on transient flows. Several numerical schemes were tested including TVD, MUSCL, ENO, FCT, and Riemann Solver Godunov type schemes. A systematic assessment was performed on scalar transport, Burgers' and gas dynamic problems. Several shock capturing schemes are compared on fast transient resonant pipe flow problems. A system of 1-D nonlinear hyperbolic gas dynamics equations is solved to predict propagation of finite amplitude waves, the wave steepening, formation, propagation, and reflection of shocks for several hundred wave cycles. It is shown that high accuracy schemes can be used for direct, exact nonlinear analysis of combustion instability problems, preserving high harmonic energy content for long periods of time.

New Experimental Capabilities and Theoretical Insights of High Pressure Compression Waves

NASA Astrophysics Data System (ADS)

Orlikowski, Daniel; Nguyen, Jeffrey H.; Patterson, J. Reed; Minich, Roger; Martin, L. Peter; Holmes, Neil C.

2007-12-01

Currently there are three platforms that offer quasi-isentropic compression or ramp-wave compression (RWC): light-gas gun, magnetic flux (Z-pinch), and laser. We focus here on the light-gas gun technique and on some current theoretical insights from experimental data. An impedance gradient through the length of the impactor provides the pressure pulse upon impact to the subject material. Applications and results are given concerning high-pressure strength and the liquid-to-solid, phase transition of water giving its first associated phase fraction history. We also introduce the Korteweg-deVries-Burgers equation as a means to understand the evolution of these RWC waves as they propagate through the thickness of the subject material. This model equation has the necessary competition between non-linear, dispersion, and dissipation processes, which is shown through observed structures that are manifested in the experimental particle velocity histories. Such methodology points towards a possibility of quantifying dissipation, through which RWC experiments may be analyzed.

An algorithm for modeling entrainment and naturally and chemically dispersed oil droplet size distribution under surface breaking wave conditions.

PubMed

Li, Zhengkai; Spaulding, Malcolm L; French-McCay, Deborah

2017-06-15

A surface oil entrainment model and droplet size model have been developed to estimate the flux of oil under surface breaking waves. Both equations are expressed in dimensionless Weber number (We) and Ohnesorge number (Oh, which explicitly accounts for the oil viscosity, density, and oil-water interfacial tension). Data from controlled lab studies, large-scale wave tank tests, and field observations have been used to calibrate the constants of the two independent equations. Predictions using the new algorithm compared well with the observed amount of oil removed from the surface and the sizes of the oil droplets entrained in the water column. Simulations with the new algorithm, implemented in a comprehensive spill model, show that entrainment rates increase more rapidly with wind speed than previously predicted based on the existing Delvigne and Sweeney's (1988) model, and a quasi-stable droplet size distribution (d<~50μm) is developed in the near surface water. Copyright © 2017 Elsevier Ltd. All rights reserved.

Combined effects of nonparaxiality, optical activity, and walk-off on rogue wave propagation in optical fibers filled with chiral materials.

PubMed

Temgoua, D D Estelle; Tchokonte, M B Tchoula; Kofane, T C

2018-04-01

The generalized nonparaxial nonlinear Schrödinger (NLS) equation in optical fibers filled with chiral materials is reduced to the higher-order integrable Hirota equation. Based on the modified Darboux transformation method, the nonparaxial chiral optical rogue waves are constructed from the scalar model with modulated coefficients. We show that the parameters of nonparaxiality, third-order dispersion, and differential gain or loss term are the main keys to control the amplitude, linear, and nonlinear effects in the model. Moreover, the influence of nonparaxiality, optical activity, and walk-off effect are also evidenced under the defocusing and focusing regimes of the vector nonparaxial NLS equations with constant and modulated coefficients. Through an algorithm scheme of wider applicability on nonparaxial beam propagation methods, the most influential effect and the simultaneous controllability of combined effects are underlined, showing their properties and their potential applications in optical fibers and in a variety of complex dynamical systems.

Combined effects of nonparaxiality, optical activity, and walk-off on rogue wave propagation in optical fibers filled with chiral materials

NASA Astrophysics Data System (ADS)

Temgoua, D. D. Estelle; Tchokonte, M. B. Tchoula; Kofane, T. C.

2018-04-01

The generalized nonparaxial nonlinear Schrödinger (NLS) equation in optical fibers filled with chiral materials is reduced to the higher-order integrable Hirota equation. Based on the modified Darboux transformation method, the nonparaxial chiral optical rogue waves are constructed from the scalar model with modulated coefficients. We show that the parameters of nonparaxiality, third-order dispersion, and differential gain or loss term are the main keys to control the amplitude, linear, and nonlinear effects in the model. Moreover, the influence of nonparaxiality, optical activity, and walk-off effect are also evidenced under the defocusing and focusing regimes of the vector nonparaxial NLS equations with constant and modulated coefficients. Through an algorithm scheme of wider applicability on nonparaxial beam propagation methods, the most influential effect and the simultaneous controllability of combined effects are underlined, showing their properties and their potential applications in optical fibers and in a variety of complex dynamical systems.

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.

Rotational dynamics of bases in the gene coding interferon alpha 17 (IFNA17).

PubMed

Krasnobaeva, L A; Yakushevich, L V

2015-02-01

In the present work, rotational oscillations of nitrogenous bases in the DNA with the sequence of the gene coding interferon alpha 17 (IFNA17), are investigated. As a mathematical model simulating oscillations of the bases, we use a system of two coupled nonlinear partial differential equations that takes into account effects of dissipation, action of external fields and dependence of the equation coefficients on the sequence of bases. We apply the methods of the theory of oscillations to solve the equations in the linear approach and to construct the dispersive curves determining the dependence of the frequency of the plane waves (ω) on the wave vector (q). In the nonlinear case, the solutions in the form of kink are considered, and the main characteristics of the kink: the rest energy (E0), the rest mass (m0), the size (d) and sound velocity (C0), are calculated. With the help of the energetic method, the kink velocity (υ), the path (S), and the lifetime (τ) are also obtained.

A family of wave equations with some remarkable properties.

PubMed

da Silva, Priscila Leal; Freire, Igor Leite; Sampaio, Júlio Cesar Santos

2018-02-01

We consider a family of homogeneous nonlinear dispersive equations with two arbitrary parameters. Conservation laws are established from the point symmetries and imply that the whole family admits square integrable solutions. Recursion operators are found for two members of the family investigated. For one of them, a Lax pair is also obtained, proving its complete integrability. From the Lax pair, we construct a Miura-type transformation relating the original equation to the Korteweg-de Vries (KdV) equation. This transformation, on the other hand, enables us to obtain solutions of the equation from the kernel of a Schrödinger operator with potential parametrized by the solutions of the KdV equation. In particular, this allows us to exhibit a kink solution to the completely integrable equation from the 1-soliton solution of the KdV equation. Finally, peakon-type solutions are also found for a certain choice of the parameters, although for this particular case the equation is reduced to a homogeneous second-order nonlinear evolution equation.

The effects of dissipation on topological mechanical systems

NASA Astrophysics Data System (ADS)

Xiong, Ye; Wang, Tianxiang; Tong, Peiqing

2016-09-01

We theoretically study the effects of isotropic dissipation in a topological mechanical system which is an analogue of Chern insulator in mechanical vibrational lattice. The global gauge invariance is still conserved in this system albeit it is destroyed by the dissipation in the quantum counterpart. The chiral edge states in this system are therefore robust against strong dissipation. The dissipation also causes a dispersion of damping for the eigenstates. It will modify the equation of motion of a wave packet by an extra effective force. After taking into account the Berry curvature in the wave vector space, the trace of a free wave packet in the real space should be curved, feinting to break the Newton’s first law.

Light Meets Water in Nonlocal Media: Surface Tension Analogue in Optics

NASA Astrophysics Data System (ADS)

Horikis, Theodoros P.; Frantzeskakis, Dimitrios J.

2017-06-01

Shallow water wave phenomena find their analogue in optics through a nonlocal nonlinear Schrödinger (NLS) model in 2 +1 dimensions. We identify an analogue of surface tension in optics, namely, a single parameter depending on the degree of nonlocality, which changes the sign of dispersion, much like surface tension does in the shallow water wave problem. Using multiscale expansions, we reduce the NLS model to a Kadomtsev-Petviashvili (KP) equation, which is of the KPII (KPI) type, for strong (weak) nonlocality. We demonstrate the emergence of robust optical antidark solitons forming Y -, X -, and H -shaped wave patterns, which are approximated by colliding KPII line solitons, similar to those observed in shallow waters.

Light Meets Water in Nonlocal Media: Surface Tension Analogue in Optics.

PubMed

Horikis, Theodoros P; Frantzeskakis, Dimitrios J

2017-06-16

Shallow water wave phenomena find their analogue in optics through a nonlocal nonlinear Schrödinger (NLS) model in 2+1 dimensions. We identify an analogue of surface tension in optics, namely, a single parameter depending on the degree of nonlocality, which changes the sign of dispersion, much like surface tension does in the shallow water wave problem. Using multiscale expansions, we reduce the NLS model to a Kadomtsev-Petviashvili (KP) equation, which is of the KPII (KPI) type, for strong (weak) nonlocality. We demonstrate the emergence of robust optical antidark solitons forming Y-, X-, and H-shaped wave patterns, which are approximated by colliding KPII line solitons, similar to those observed in shallow waters.

Effect of dust on tilted electrostatic resistive instability in a Hall thruster

NASA Astrophysics Data System (ADS)

Tyagi, Jasvendra; Singh, Sukhmander; Malik, Hitendra K.

2018-03-01

Effect of negatively charged dust on resistive instability corresponding to the electrostatic wave is investigated in a Hall thruster plasma when this purely azimuthal wave is tilted and strong axial component of wave vector is developed. Analytical calculations are done to obtain the relevant dispersion equation, which is solved numerically to investigate the growth rate of the instability. The magnitude of the growth rate in the plasma having dust particles is found to be much smaller than the case of pure plasma. However, the instability grows faster for the increasing dust density and the higher charge on the dust particles. The higher magnetic field is also found to support the instability.

Arbitrary electron acoustic waves in degenerate dense plasmas

NASA Astrophysics Data System (ADS)

Rahman, Ata-ur; Mushtaq, A.; Qamar, A.; Neelam, S.

2017-05-01

A theoretical investigation is carried out of the nonlinear dynamics of electron-acoustic waves in a collisionless and unmagnetized plasma whose constituents are non-degenerate cold electrons, ultra-relativistic degenerate electrons, and stationary ions. A dispersion relation is derived for linear EAWs. An energy integral equation involving the Sagdeev potential is derived, and basic properties of the large amplitude solitary structures are investigated in such a degenerate dense plasma. It is shown that only negative large amplitude EA solitary waves can exist in such a plasma system. The present analysis may be important to understand the collective interactions in degenerate dense plasmas, occurring in dense astrophysical environments as well as in laser-solid density plasma interaction experiments.

Breather Rogue Waves in Random Seas

NASA Astrophysics Data System (ADS)

Wang, J.; Ma, Q. W.; Yan, S.; Chabchoub, A.

2018-01-01

Rogue or freak waves are extreme wave events that have heights exceeding 8 times the standard deviation of surrounding waves and emerge, for instance, in the ocean as well as in other physical dispersive wave guides, such as in optical fibers. One effective and convenient way to model such an extreme dynamics in laboratory environments within a controlled framework as well as for short process time and length scales is provided through the breather formalism. Breathers are pulsating localized structures known to model extreme waves in several nonlinear dispersive media in which the initial underlying process is assumed to be narrow banded. On the other hand, several recent studies suggest that breathers can also persist in more complex environments, such as in random seas, beyond the attributed physical limitations. In this work, we study the robustness of the Peregrine breather (PB) embedded in Joint North Sea Wave Project (JONSWAP) configurations using fully nonlinear hydrodynamic numerical simulations in order to validate its practicalness for ocean engineering applications. We provide a specific range for both the spectral bandwidth of the dynamical process as well as the background wave steepness and, thus, quantify the applicability of the PB in modeling rogue waves in realistic oceanic conditions. Our results may motivate analogous studies in fields of physics such as optics and plasma to quantify the limitations of exact weakly nonlinear models, such as solitons and breathers, within the framework of the fully nonlinear governing equations of the corresponding medium.

Modulated heavy nucleus-acoustic waves and associated rogue waves in a degenerate relativistic quantum plasma system

NASA Astrophysics Data System (ADS)

Sultana, S.; Islam, S.; Mamun, A. A.; Schlickeiser, R.

2018-01-01

A theoretical and numerical investigation has been carried out on amplitude modulated heavy nucleus-acoustic envelope solitons (HNAESs) in a degenerate relativistic quantum plasma (DRQP) system containing relativistically degenerate electrons and light nuclei, and non-degenerate mobile heavy nuclei. The cubic nonlinear Schrödinger equation, describing the nonlinear dynamics of the heavy nucleus-acoustic waves (HNAWs), is derived by employing a multi-scale perturbation technique. The dispersion relation for the HNAWs is derived, and the criteria for the occurrence of modulational instability of the HNAESs are analyzed. The localized structures (viz., envelope solitons and associated rogue waves) are found to be formed in the DRQP system under consideration. The basic features of the amplitude modulated HNAESs and associated rogue waves formed in realistic DRQP systems are briefly discussed.

Spin waves in rings of classical magnetic dipoles

NASA Astrophysics Data System (ADS)

Schmidt, Heinz-Jürgen; Schröder, Christian; Luban, Marshall

2017-03-01

We theoretically and numerically investigate spin waves that occur in systems of classical magnetic dipoles that are arranged at the vertices of a regular polygon and interact solely via their magnetic fields. There are certain limiting cases that can be analyzed in detail. One case is that of spin waves as infinitesimal excitations from the system’s ground state, where the dispersion relation can be determined analytically. The frequencies of these infinitesimal spin waves are compared with the peaks of the Fourier transform of the thermal expectation value of the autocorrelation function calculated by Monte Carlo simulations. In the special case of vanishing wave number an exact solution of the equations of motion is possible describing synchronized oscillations with finite amplitudes. Finally, the limiting case of a dipole chain with N\\longrightarrow ∞ is investigated and completely solved.

Plasma Instabilities in Hall Thrusters

NASA Astrophysics Data System (ADS)

Litvak, Andrei A.; Fisch, Nathaniel J.

2000-10-01

We describe theoretically waves in the channel of a Hall thruster, propagating transversely to the accelerated ion flow. In slab geometry, a two-fluid hydrodynamic theory with collisional terms shows that azimuthal lower-hybrid and Alfven waves will be unstable due to electron collisions in the presence of ExB drift. In addition, plasma inhomogeneities can drive other instabilities that can be analyzed through a dispersion relation in the well-known form of the Rayleigh equation. An instability condition is derived for azimuthal electrostatic waves, synchronized with the electron drift flow. Propagation with nonzero wavenumber along the magnetic field is also studied. Thus, several different aspects of wave propagation during thruster operation are explored. These waves may be important to understand and possibly to control in view of the possible influence of thruster electromagnetic effects on communication signal propagation.

Rogue wave generation by inelastic quasi-soliton collisions in optical fibres

NASA Astrophysics Data System (ADS)

Eberhard, M.; Savojardo, A.; Maruta, A.; Römer, R. A.

2017-11-01

We demonstrate a simple cascade mechanism that drives the formation and emergence of rogue waves in the generalized non-linear Schr\\"{o}dinger equation with third-order dispersion. This conceptually novel generation mechanism is based on inelastic collisions of quasi-solitons and is well described by a resonant-like scattering behaviour for the energy transfer in pair-wise quasi-soliton collisions. Our results demonstrate a threshold for rogue wave emergence and the existence of a period of reduced amplitudes - a "calm before the storm" - preceding the arrival of a rogue wave event. Comparing with ultra-long time window simulations of $3.865\\times 10^{6}$ps we observe the statistics of rogue waves in optical fibres with an unprecedented level of detail and accuracy, unambiguously establishing the long-ranged character of the rogue wave power-distribution function over seven orders of magnitude.

Computational Aeroacoustics: An Overview

NASA Technical Reports Server (NTRS)

Tam, Christopher K. W.

2003-01-01

An overview of recent advances in computational aeroacoustics (CAA) is presented. CAA algorithms must not be dispersive and dissipative. It should propagate waves supported by the Euler equations with the correct group velocities. Computation domains are inevitably finite in size. To avoid the reflection of acoustic and other outgoing waves at the boundaries of the computation domain, it is required that special boundary conditions be imposed at the boundary region. These boundary conditions either absorb all the outgoing waves without reflection or allow the waves to exit smoothly. High-order schemes, invariably, supports spurious short waves. These spurious waves tend to pollute the numerical solution. They must be selectively damped or filtered out. All these issues and relevant computation methods are briefly reviewed. Jet screech tones are known to have caused structural fatigue in military combat aircrafts. Numerical simulation of the jet screech phenomenon is presented as an example of a successful application of CAA.

Emergent rogue wave structures and statistics in spontaneous modulation instability.

PubMed

Toenger, Shanti; Godin, Thomas; Billet, Cyril; Dias, Frédéric; Erkintalo, Miro; Genty, Goëry; Dudley, John M

2015-05-20

The nonlinear Schrödinger equation (NLSE) is a seminal equation of nonlinear physics describing wave packet evolution in weakly-nonlinear dispersive media. The NLSE is especially important in understanding how high amplitude "rogue waves" emerge from noise through the process of modulation instability (MI) whereby a perturbation on an initial plane wave can evolve into strongly-localised "breather" or "soliton on finite background (SFB)" structures. Although there has been much study of such structures excited under controlled conditions, there remains the open question of how closely the analytic solutions of the NLSE actually model localised structures emerging in noise-seeded MI. We address this question here using numerical simulations to compare the properties of a large ensemble of emergent peaks in noise-seeded MI with the known analytic solutions of the NLSE. Our results show that both elementary breather and higher-order SFB structures are observed in chaotic MI, with the characteristics of the noise-induced peaks clustering closely around analytic NLSE predictions. A significant conclusion of our work is to suggest that the widely-held view that the Peregrine soliton forms a rogue wave prototype must be revisited. Rather, we confirm earlier suggestions that NLSE rogue waves are most appropriately identified as collisions between elementary SFB solutions.

Baroclinic stationary waves in aquaplanet models

NASA Astrophysics Data System (ADS)

Lucarini, V.; Zappa, G.

2012-04-01

An aquaplanet model is used to study the nature of the highly persistent low frequency waves that have been observed in models forced by zonally symmetric boundary conditions. Using the Hayashi spectral analysis of the extratropical waves, we find that a quasi-stationary (QS) wave five belongs to a wave packet obeying a well defined dispersion relation with eastward group velocity. The components of the dispersion relation with k>5 baroclinically convert eddy available potential energy into eddy kinetic energy, while those with k<5 are baroclinically neutral. In agreement with the Green's model of baroclinic instability, the wave five is weakly unstable, and the inverse energy cascade, which had been previously proposed as a main forcing for this type of waves, only acts as a positive feedback on its predominantly baroclinic energetics. The QS wave is reinforced by a phase lock to an analogous pattern in the tropical convection, which provides further amplification to the wave. We also find that the Pedlosky bounds on the phase speed of unstable waves provide guidance in explaining the latitudinal structure of the energy conversion, which is shown to be more enhanced where the zonal westerly surface wind is weaker. The wave energy is then trapped in the wave guide created by the upper tropospheric jet stream. In agreement with Green's theory, as the equator to pole SST difference is reduced the stationary marginally stable component shifts toward higher wavenumbers, while the wave five becomes neutral and westward propagating. Some properties of the aquaplanet QS waves are found in interesting agreement with a low frequency wave observed by Salby (1982) in the southern hemisphere DJF, so that this perspective on low frequency variability might be, apart from its value in terms of basic geophysical fluid dynamics, of specific interest for studying the Earth's atmosphere.

Kinematic dust viscosity effect on linear and nonlinear dust-acoustic waves in space dusty plasmas with nonthermal ions

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

El-Hanbaly, A. M.; Sallah, M., E-mail: msallahd@mans.edu.eg; El-Shewy, E. K.

2015-10-15

Linear and nonlinear dust-acoustic (DA) waves are studied in a collisionless, unmagnetized and dissipative dusty plasma consisting of negatively charged dust grains, Boltzmann-distributed electrons, and nonthermal ions. The normal mode analysis is used to obtain a linear dispersion relation illustrating the dependence of the wave damping rate on the carrier wave number, the dust viscosity coefficient, the ratio of the ion temperature to the electron temperatures, and the nonthermal parameter. The plasma system is analyzed nonlinearly via the reductive perturbation method that gives the KdV-Burgers equation. Some interesting physical solutions are obtained to study the nonlinear waves. These solutions aremore » related to soliton, a combination between a shock and a soliton, and monotonic and oscillatory shock waves. Their behaviors are illustrated and shown graphically. The characteristics of the DA solitary and shock waves are significantly modified by the presence of nonthermal (fast) ions, the ratio of the ion temperature to the electron temperature, and the dust kinematic viscosity. The topology of the phase portrait and the potential diagram of the KdV-Burgers equation is illustrated, whose advantage is the ability to predict different classes of traveling wave solutions according to different phase orbits. The energy of the soliton wave and the electric field are calculated. The results in this paper can be generalized to analyze the nature of plasma waves in both space and laboratory plasma systems.« less

Shear waves in elastic medium with void pores welded between vertically inhomogeneous and anisotropic magnetoelastic semi-infinite media

NASA Astrophysics Data System (ADS)

Gupta, Shishir; Ahmed, Mostaid; Pramanik, Abhijit

2017-03-01

The paper intends to study the propagation of horizontally polarized shear waves in an elastic medium with void pores constrained between a vertically inhomogeneous and an anisotropic magnetoelastic semi-infinite media. Elasto-dynamical equations of elastic medium with void pores and magnetoelastic solid have been employed to investigate the shear wave propagation in the proposed three-layered earth model. Method of separation of variables has been incorporated to deduce the dispersion relation. All possible special cases have been envisaged and they fairly comply with the corresponding results for classical cases. The role of inhomogeneity parameter, thickness of layer, angle with which the wave crosses the magnetic field and anisotropic magnetoelastic coupling parameter for three different materials has been elucidated and represented by graphs using MATHEMATICA.

Joint body and surface wave tomography applied to the Toba caldera complex (Indonesia)

NASA Astrophysics Data System (ADS)

Jaxybulatov, Kairly; Koulakov, Ivan; Shapiro, Nikolai

2016-04-01

We developed a new algorithm for a joint body and surface wave tomography. The algorithm is a modification of the existing LOTOS code (Koulakov, 2009) developed for local earthquake tomography. The input data for the new method are travel times of P and S waves and dispersion curves of Rayleigh and Love waves. The main idea is that the two data types have complementary sensitivities. The body-wave data have good resolution at depth, where we have enough crossing rays between sources and receivers, whereas the surface waves have very good near-surface resolution. The surface wave dispersion curves can be retrieved from the correlations of the ambient seismic noise and in this case the sampled path distribution does not depend on the earthquake sources. The contributions of the two data types to the inversion are controlled by the weighting of the respective equations. One of the clearest cases where such approach may be useful are volcanic systems in subduction zones with their complex magmatic feeding systems that have deep roots in the mantle and intermediate magma chambers in the crust. In these areas, the joint inversion of different types of data helps us to build a comprehensive understanding of the entire system. We apply our algorithm to data collected in the region surrounding the Toba caldera complex (north Sumatra, Indonesia) during two temporary seismic experiments (IRIS, PASSCAL, 1995, GFZ, LAKE TOBA, 2008). We invert 6644 P and 5240 S wave arrivals and ~500 group velocity dispersion curves of Rayleigh and Love waves. We present a series of synthetic tests and real data inversions which show that joint inversion approach gives more reliable results than the separate inversion of two data types. Koulakov, I., LOTOS code for local earthquake tomographic inversion. Benchmarks for testing tomographic algorithms, Bull. seism. Soc. Am., 99(1), 194-214, 2009, doi:10.1785/0120080013

Unveiling Extreme Anisotropy in Elastic Structured Media

NASA Astrophysics Data System (ADS)

Lefebvre, G.; Antonakakis, T.; Achaoui, Y.; Craster, R. V.; Guenneau, S.; Sebbah, P.

2017-06-01

Periodic structures can be engineered to exhibit unique properties observed at symmetry points, such as zero group velocity, Dirac cones, and saddle points; identifying these and the nature of the associated modes from a direct reading of the dispersion surfaces is not straightforward, especially in three dimensions or at high frequencies when several dispersion surfaces fold back in the Brillouin zone. A recently proposed asymptotic high-frequency homogenization theory is applied to a challenging time-domain experiment with elastic waves in a pinned metallic plate. The prediction of a narrow high-frequency spectral region where the effective medium tensor dramatically switches from positive definite to indefinite is confirmed experimentally; a small frequency shift of the pulse carrier results in two distinct types of highly anisotropic modes. The underlying effective equation mirrors this behavior with a change in form from elliptic to hyperbolic exemplifying the high degree of wave control available and the importance of a simple and effective predictive model.

On the stability of self-gravitating magnetized dusty plasmas

NASA Astrophysics Data System (ADS)

Salimullah, M.; Shukla, P. K.

1999-03-01

The effects of a homogeneous magnetic field and the plasma nonuniformity on the dispersion relations of various electrostatic waves in self-gravitating magnetized dusty plasmas have been investigated. For this purpose, the kinetic dielectric response functions for the electrons and ions distributions have been used and the dielectric response function for the magnetized dust grains has been derived from the hydrodynamic equations that include the self-gravitational potential. Thus, extremely massive charged dust grains are subjected to both the electromagnetic and gravitational forces. Analytical studies of the dispersion relations in various frequency and wave number regimes reveal that both the magnetic fields and plasma inhomogeneities contribute to the stability of a self-gravitating dusty plasma system. The results of this investigation should be useful in understanding the stability of dusty proto-stars and dusty dark molecular clouds, which are held in strong magnetic fields and equilibrium density gradients.

Scattering General Analysis; ANALISIS GENERAL DE LA DISPERSION

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

Tixaire, A.G.

1962-01-01

A definition of scattering states is given. It is shown that such states must belong to the absolutely continuous part of the spectrum of the total hamiltonian whenever scattering systems are considered. Such embedding may be proper unless the quantum system is physically admissible. The Moller wave operators are analyzed using Abel- and Cesaro-limit theoretical arguments. Von Neumann s ergodic theorem is partially generalized. A rigorous derivation of the Gell-Mann and Goldberger and Lippmann and Schwinger equations is obtained by making use of results on spectral theory, wave function, and eigendifferential concepts contained. (auth)

On the stability of nongyrotropic ion populations - A first (analytic and simulation) assessment

NASA Technical Reports Server (NTRS)

Brinca, A. L.; Borda De Agua, L.; Winske, D.

1993-01-01

The wave and dispersion equations for perturbations propagating parallel to an ambient magnetic field in magnetoplasmas with nongyrotropic ion populations show, in general, the occurrence of coupling between the parallel (left- and right-hand circularly polarized electromagnetic and longitudinal electrostatic) eigenmodes of the associated gyrotropic medium. These interactions provide a means to driving linearly one mode with free-energy sources of other modes in homogeneous media. Different types of nongyrotropy bring about distinct classes of coupling. The stability of a hydrogen magnetoplasma with anisotropic, nongyrotropic protons that only couple the electromagnetic modes to each other is investigated analytically (via solution of the derived dispersion equation) and numerically (via simulation with a hybrid code). Nongyrotropy enhances growth and enlarges the unstable spectral range relative to the corresponding gyrotropic situation. The relevance of the properties of nongyrotropic populations to space plasma environments is also discussed.

Mate Finding, Sexual Spore Production, and the Spread of Fungal Plant Parasites.

PubMed

Hamelin, Frédéric M; Castella, François; Doli, Valentin; Marçais, Benoît; Ravigné, Virginie; Lewis, Mark A

2016-04-01

Sexual reproduction and dispersal are often coupled in organisms mixing sexual and asexual reproduction, such as fungi. The aim of this study is to evaluate the impact of mate limitation on the spreading speed of fungal plant parasites. Starting from a simple model with two coupled partial differential equations, we take advantage of the fact that we are interested in the dynamics over large spatial and temporal scales to reduce the model to a single equation. We obtain a simple expression for speed of spread, accounting for both sexual and asexual reproduction. Taking Black Sigatoka disease of banana plants as a case study, the model prediction is in close agreement with the actual spreading speed (100 km per year), whereas a similar model without mate limitation predicts a wave speed one order of magnitude greater. We discuss the implications of these results to control parasites in which sexual reproduction and dispersal are intrinsically coupled.

Modeling ultrashort electromagnetic pulses with a generalized Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Hofstrand, A.; Moloney, J. V.

2018-03-01

In this paper we derive a properly scaled model for the nonlinear propagation of intense, ultrashort, mid-infrared electromagnetic pulses (10-100 femtoseconds) through an arbitrary dispersive medium. The derivation results in a generalized Kadomtsev-Petviashvili (gKP) equation. In contrast to envelope-based models such as the Nonlinear Schrödinger (NLS) equation, the gKP equation describes the dynamics of the field's actual carrier wave. It is important to resolve these dynamics when modeling ultrashort pulses. We proceed by giving an original proof of sufficient conditions on the initial pulse for a singularity to form in the field after a finite propagation distance. The model is then numerically simulated in 2D using a spectral-solver with initial data and physical parameters highlighting our theoretical results.

AKNS hierarchy, Darboux transformation and conservation laws of the 1D nonautonomous nonlinear Schroedinger equations

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

Zhao Dun; Center for Interdisciplinary Studies, Lanzhou University, Lanzhou 730000; Zhang Yujuan

2011-04-15

By constructing nonisospectral Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy, we investigate the nonautonomous nonlinear Schroedinger (NLS) equations which have been used to describe the Feshbach resonance management in matter-wave solitons in Bose-Einstein condensate and the dispersion and nonlinearity managements for optical solitons. It is found that these equations are some special cases of a new integrable model of nonlocal nonautonomous NLS equations. Based on the Lax pairs, the Darboux transformation and conservation laws are explored. It is shown that the local external potentials would break down the classical infinite number of conservation laws. The result indicates that the integrability of the nonautonomous NLSmore » systems may be nontrivial in comparison to the conventional concept of integrability in the canonical case.« less

Fast and accurate modeling of nonlinear pulse propagation in graded-index multimode fibers.

PubMed

Conforti, Matteo; Mas Arabi, Carlos; Mussot, Arnaud; Kudlinski, Alexandre

2017-10-01

We develop a model for the description of nonlinear pulse propagation in multimode optical fibers with a parabolic refractive index profile. It consists of a 1+1D generalized nonlinear Schrödinger equation with a periodic nonlinear coefficient, which can be solved in an extremely fast and efficient way. The model is able to quantitatively reproduce recently observed phenomena like geometric parametric instability and broadband dispersive wave emission. We envisage that our equation will represent a valuable tool for the study of spatiotemporal nonlinear dynamics in the growing field of multimode fiber optics.

Dispersion Energy Analysis of Rayleigh and Love Waves in the Presence of Low-Velocity Layers in Near-Surface Seismic Surveys

NASA Astrophysics Data System (ADS)

Mi, Binbin; Xia, Jianghai; Shen, Chao; Wang, Limin

2018-03-01

High-frequency surface-wave analysis methods have been effectively and widely used to determine near-surface shear (S) wave velocity. To image the dispersion energy and identify different dispersive modes of surface waves accurately is one of key steps of using surface-wave methods. We analyzed the dispersion energy characteristics of Rayleigh and Love waves in near-surface layered models based on numerical simulations. It has been found that if there is a low-velocity layer (LVL) in the half-space, the dispersion energy of Rayleigh or Love waves is discontinuous and ``jumping'' appears from the fundamental mode to higher modes on dispersive images. We introduce the guided waves generated in an LVL (LVL-guided waves, a trapped wave mode) to clarify the complexity of the dispersion energy. We confirm the LVL-guided waves by analyzing the snapshots of SH and P-SV wavefield and comparing the dispersive energy with theoretical values of phase velocities. Results demonstrate that LVL-guided waves possess energy on dispersive images, which can interfere with the normal dispersion energy of Rayleigh or Love waves. Each mode of LVL-guided waves having lack of energy at the free surface in some high frequency range causes the discontinuity of dispersive energy on dispersive images, which is because shorter wavelengths (generally with lower phase velocities and higher frequencies) of LVL-guided waves cannot penetrate to the free surface. If the S wave velocity of the LVL is higher than that of the surface layer, the energy of LVL-guided waves only contaminates higher mode energy of surface waves and there is no interlacement with the fundamental mode of surface waves, while if the S wave velocity of the LVL is lower than that of the surface layer, the energy of LVL-guided waves may interlace with the fundamental mode of surface waves. Both of the interlacements with the fundamental mode or higher mode energy may cause misidentification for the dispersion curves of surface waves.

Investigation of dispersion-relation-preserving scheme and spectral analysis methods for acoustic waves

NASA Technical Reports Server (NTRS)

Vanel, Florence O.; Baysal, Oktay

1995-01-01

Important characteristics of the aeroacoustic wave propagation are mostly encoded in their dispersion relations. Hence, a computational aeroacoustic (CAA) algorithm, which reasonably preserves these relations, was investigated. It was derived using an optimization procedure to ensure, that the numerical derivatives preserved the wave number and angular frequency of the differential terms in the linearized, 2-D Euler equations. Then, simulations were performed to validate the scheme and a compatible set of discretized boundary conditions. The computational results were found to agree favorably with the exact solutions. The boundary conditions were transparent to the outgoing waves, except when the disturbance source was close to a boundary. The time-domain data generated by such CAA solutions were often intractable until their spectra was analyzed. Therefore, the relative merits of three different methods were included in the study. For simple, periodic waves, the periodogram method produced better estimates of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window was more effective when used with the weighted-overlapped-segment-averaging and Blackman-Tukey methods gave better results than the periodogram method. Finally, it was demonstrated that the representation of time domain-data was significantly dependent on the particular spectral analysis method employed.

Properties of Longitudinal Electromagnetic Oscillations in Metals and Their Excitation at Planar and Spherical Surfaces.

PubMed

Datsyuk, Vitaly V; Pavlyniuk, Oleg R

2017-12-01

The common definition of the spatially dispersive permittivity is revised. The response of the degenerate electron gas on an electric field satisfying the vector Helmholtz equation is found with a solution to the Boltzmann equation. The calculated longitudinal dielectric function coincides with that obtained by Klimontovich and Silin in 1952 and Lindhard in 1954. However, it depends on the square of the wavenumber, a parameter of the vector Helmholtz equation, but not the wave vector of a plane electromagnetic wave. This new concept simplifies simulation of the nonlocal effects, for example, with a generalized Lorents-Mie theory, since no Fourier transforms should be made. The Fresnel coefficients are generalized allowing for excitation of the longitudinal electromagnetic waves. To verify the theory, the extinction spectra for silver and gold nanometer-sized spheres are calculated. For these particles, the generalized Lorents-Mie theory gives the blue shift and broadening of the plasmon resonance which are in excellent agreement with experimental data. In addition, the nonlocal theory explains vanishing of the plasmon resonance observed for gold spheres with diameters less than or equal to 2 nm. The calculations using the Klimontovich-Silin-Lindhard and hydrodynamic dielectric functions for silver are found to give close results at photon energies from 3 to 4 eV. We show that the absolute values of the wavenumbers of the longitudinal waves in solids are much higher than those of the transverse waves.

Properties of Longitudinal Electromagnetic Oscillations in Metals and Their Excitation at Planar and Spherical Surfaces

NASA Astrophysics Data System (ADS)

Datsyuk, Vitaly V.; Pavlyniuk, Oleg R.

2017-08-01

The common definition of the spatially dispersive permittivity is revised. The response of the degenerate electron gas on an electric field satisfying the vector Helmholtz equation is found with a solution to the Boltzmann equation. The calculated longitudinal dielectric function coincides with that obtained by Klimontovich and Silin in 1952 and Lindhard in 1954. However, it depends on the square of the wavenumber, a parameter of the vector Helmholtz equation, but not the wave vector of a plane electromagnetic wave. This new concept simplifies simulation of the nonlocal effects, for example, with a generalized Lorents-Mie theory, since no Fourier transforms should be made. The Fresnel coefficients are generalized allowing for excitation of the longitudinal electromagnetic waves. To verify the theory, the extinction spectra for silver and gold nanometer-sized spheres are calculated. For these particles, the generalized Lorents-Mie theory gives the blue shift and broadening of the plasmon resonance which are in excellent agreement with experimental data. In addition, the nonlocal theory explains vanishing of the plasmon resonance observed for gold spheres with diameters less than or equal to 2 nm. The calculations using the Klimontovich-Silin-Lindhard and hydrodynamic dielectric functions for silver are found to give close results at photon energies from 3 to 4 eV. We show that the absolute values of the wavenumbers of the longitudinal waves in solids are much higher than those of the transverse waves.

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.

X-ray diffraction and surface acoustic wave analysis of BST/Pt/TiO{sub 2}/SiO{sub 2}/Si thin films

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

Mseddi, Souhir; Hedi Ben Ghozlen, Mohamed; Njeh, Anouar

2011-11-15

High dielectric constant and electrostriction property of (Ba, Sr)Ti0{sub 3} (BST) thin films result in an increasing interest for dielectric devices and microwave acoustic resonator. Barium strontium titanate (Ba{sub 0.645}Sr{sub 0.355}TiO{sub 3}) films of about 300 nm thickness are grown on Pt(111)/TiO{sub 2}/SiO{sub 2}/Si(001) substrates by rf magnetron sputtering deposition techniques. X-ray diffraction is applied for the microstructural characterization. The BST films exhibit a cubic perovskite structure with a dense and smooth surface. A laser acoustic waves (LA-waves) technique is used to generate surface acoustic waves (SAW) propagating in the BST films. Young's modulus E and the Poisson ratio {nu}more » of TiO{sub 2,} Pt and BST films in different propagation directions are derived from the measured dispersion curves. Estimation of BST elastics constants are served in SAW studies. Impact of stratification process on SAW, propagating along [100] and [110] directions of silicon substrate, has been interpreted on the basis of ordinary differential equation (ODE) and stiffness matrix method (SMM). A good agreement is observed between experimental and calculated dispersion curves. The performed calculations are strongly related to the implemented crystallographic data of each layer. Dispersion curves are found to be sensitive to the SAW propagation direction and the stratification process for the explored frequency ranges 50-250 MHz, even though it corresponds to a wave length clearly higher than the whole films thickness.« less

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.

On a generating mechanism for Yanai waves and the 25-day oscillation

NASA Technical Reports Server (NTRS)

Kelly, Brian G.; Meyers, Steven D.; O'Brien, James J.

1995-01-01

A spectral Chebyshev-collocation method applied to the linear, 1.5 layer reduced-gravity ocean model equations is used to study the dynamics of Yanai (or mixed Rossby-gravity) wave packets. These are of interest because of the observations of equatorial instability waves (which have the characteristics of Yanai waves) and their role in the momentum and heat budgets in the tropics. A series of experiments is performed to investigate the generation of the waves by simple cross-equatorial wind stress forcings in various configurations and the influence of a western boundary on the waves. They may be generated in the interior ocean as well as from a western boundary. The observations from all the oceans indicate that the waves have a preferential period and wavelength of around 25 days and 1000 km respectively. These properties are also seen in the model results and a plausible explanation is provided as being due to the dispersive properties of Yanai waves.

Twisted electron-acoustic waves in plasmas

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

Aman-ur-Rehman, E-mail: amansadiq@gmail.com; Department of Physics and Applied Mathematics; Ali, S.

2016-08-15

In the paraxial limit, a twisted electron-acoustic (EA) wave is studied in a collisionless unmagnetized plasma, whose constituents are the dynamical cold electrons and Boltzmannian hot electrons in the background of static positive ions. The analytical and numerical solutions of the plasma kinetic equation suggest that EA waves with finite amount of orbital angular momentum exhibit a twist in its behavior. The twisted wave particle resonance is also taken into consideration that has been appeared through the effective wave number q{sub eff} accounting for Laguerre-Gaussian mode profiles attributed to helical phase structures. Consequently, the dispersion relation and the damping ratemore » of the EA waves are significantly modified with the twisted parameter η, and for η → ∞, the results coincide with the straight propagating plane EA waves. Numerically, new features of twisted EA waves are identified by considering various regimes of wavelength and the results might be useful for transport and trapping of plasma particles in a two-electron component plasma.« less

A guided wave dispersion compensation method based on compressed sensing

NASA Astrophysics Data System (ADS)

Xu, Cai-bin; Yang, Zhi-bo; Chen, Xue-feng; Tian, Shao-hua; Xie, Yong

2018-03-01

The ultrasonic guided wave has emerged as a promising tool for structural health monitoring (SHM) and nondestructive testing (NDT) due to their capability to propagate over long distances with minimal loss and sensitivity to both surface and subsurface defects. The dispersion effect degrades the temporal and spatial resolution of guided waves. A novel ultrasonic guided wave processing method for both single mode and multi-mode guided waves dispersion compensation is proposed in this work based on compressed sensing, in which a dispersion signal dictionary is built by utilizing the dispersion curves of the guided wave modes in order to sparsely decompose the recorded dispersive guided waves. Dispersion-compensated guided waves are obtained by utilizing a non-dispersion signal dictionary and the results of sparse decomposition. Numerical simulations and experiments are implemented to verify the effectiveness of the developed method for both single mode and multi-mode guided waves.

Dust acoustic solitary and shock excitations in a Thomas-Fermi magnetoplasma

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

Rahim, Z.; Qamar, A.; National Center for Physics

The linear and nonlinear properties of dust-acoustic waves are investigated in a collisionless Thomas-Fermi magnetoplasma, whose constituents are electrons, ions, and negatively charged dust particles. At dust time scale, the electron and ion number densities follow the Thomas-Fermi distribution, whereas the dust component is described by the classical fluid equations. A linear dispersion relation is analyzed to show that the wave frequencies associated with the upper and lower modes are enhanced with the variation of dust concentration. The effect of the latter is seen more strongly on the upper mode as compared to the lower mode. For nonlinear analysis, wemore » obtain magnetized Korteweg-de Vries (KdV) and Zakharov-Kuznetsov (ZK) equations involving the dust-acoustic solitary waves in the framework of reductive perturbation technique. Furthermore, the shock wave excitations are also studied by allowing dissipation effects in the model, leading to the Korteweg-de Vries-Burgers (KdVB) and ZKB equations. The analysis reveals that the dust-acoustic solitary and shock excitations in a Thomas-Fermi plasma are strongly influenced by the plasma parameters, e.g., dust concentration, dust temperature, obliqueness, magnetic field strength, and dust fluid viscosity. The present results should be important for understanding the solitary and shock excitations in the environments of white dwarfs or supernova, where dust particles can exist.« less

Energy mode distribution: An analysis of the ratio of anti-Stokes to Stokes amplitudes generated by a pair of counterpropagating Langmuir waves

NASA Astrophysics Data System (ADS)

Simões Júnior, F. J. R.; Alves, M. V.; Rizzato, F. B.

2005-12-01

Results from plasma wave experiments in spacecrafts give support to nonlinear interactions involving Langmuir, electromagnetic, and ion-acoustic waves in association with type III solar radio bursts. Starting from a general form of Zakharov equation (Zakharov, V.E., 1985. Collapse and self-focusing of Langmuir waves. Hand-book of Plasma Physics Cap.2, 81 121) the equations for electric fields and density fluctuations (density gratings) induced by a pair of counterpropagating Langmuir waves are obtained. We consider the coupling of four triplets. Each two triplets have in common the Langmuir pump wave (forward or backward wave) and a pair of independent density gratings. We numerically solve the dispersion relation for the system, extending the work of (Alves, M.V., Chian, A.C.L., Moraes, M.A.E., Abalde, J.R., Rizzato, F.B., 2002. A theory of the fundamental plasma emission of type- III solar radio bursts. Astronomy and Astrophysics 390, 351 357). The ratio of anti-Stokes (AS) (ω0+ω) to Stokes (S) (ω0-ω) electromagnetic mode amplitudes is obtained as a function of the pump wave frequency, wave number, and energy. We notice that the simultaneous excitation of AS and S distinguishable modes, i.e., with Re{ω}=ω≠0, only occurs when the ratio between the pump wave amplitudes, r is ≠1 and the pump wave vector k0 is <(13)W01/2, W0 being the forward pump wave energy. We also observe that the S mode always receives more energy.

Negative refraction, surface modes, and superlensing effect via homogenization near resonances for a finite array of split-ring resonators.

PubMed

Farhat, M; Guenneau, S; Enoch, S; Movchan, A B

2009-10-01

We present a theoretical and numerical analysis of liquid surface waves (LSWs) localized at the boundary of a phononic crystal consisting of split-ring resonators (SRRs). We first derive the homogenized parameters of the fluid-filled structure using a three-scale asymptotic expansion in the linearized Navier-Stokes equations. In the limit when the wavelength of the LSW is much larger than the typical heterogeneity size of the phononic crystal, we show that it behaves as an artificial fluid with an anisotropic effective shear modulus and a dispersive effective-mass density. We then analyze dispersion diagrams associated with LSW propagating within an infinite array of SRR, for which eigensolutions are sought in the form of Floquet-Bloch waves. The main emphasis is given to the study of localized modes within such a periodic fluid-filled structure and to the control of low-frequency stop bands associated with resonances of SRRs. Considering a macrocell, we are able to compute the dispersion of LSW supported by a semi-infinite phononic crystal of SRRs. We find that the dispersion of this evanescent mode nearly sits within the first stop band of the doubly periodic structure. We further discover that it is linked to the frequency at which the effective-mass density of the homogenized phononic crystal becomes negative. We demonstrate that this surface mode displays the hallmarks of all-angle negative refraction and it leads to a superlensing effect. Last, we note that our homogenization results for the velocity potential can be applied mutatis mutandis to designs of electromagnetic and acoustic superlenses for transverse electric waves propagating in arrays of infinite conducting SRRs and antiplane shear waves in arrays of cracks shaped as SRRs.

Non-equilibrium magnetic colloidal dispersions at liquid-air interfaces: dynamic patterns, magnetic order and self-assembled swimmers.

PubMed

Snezhko, Alexey

2011-04-20

Colloidal dispersions of interacting particles subjected to an external periodic forcing often develop nontrivial self-assembled patterns and complex collective behavior. A fundamental issue is how collective ordering in such non-equilibrium systems arises from the dynamics of discrete interacting components. In addition, from a practical viewpoint, by working in regimes far from equilibrium new self-organized structures which are generally not available through equilibrium thermodynamics can be created. In this review spontaneous self-assembly phenomena in magnetic colloidal dispersions suspended at liquid-air interfaces and driven out of equilibrium by an alternating magnetic field are presented. Experiments reveal a new type of nontrivially ordered self-assembled structures emerging in such systems in a certain range of excitation parameters. These dynamic structures emerge as a result of the competition between magnetic and hydrodynamic forces and have complex unconventional magnetic ordering. Nontrivial self-induced hydrodynamic fields accompany each out-of-equilibrium pattern. Spontaneous symmetry breaking of the self-induced surface flows leading to a formation of self-propelled microstructures has been discovered. Some features of the self-localized structures can be understood in the framework of the amplitude equation (Ginzburg-Landau type equation) for parametric waves coupled to the conservation law equation describing the evolution of the magnetic particle density and the Navier-Stokes equation for hydrodynamic flows. To understand the fundamental microscopic mechanisms governing self-assembly processes in magnetic colloidal dispersions at liquid-air interfaces a first-principle model for a non-equilibrium self-assembly is presented. The latter model allows us to capture in detail the entire process of out-of-equilibrium self-assembly in the system and reproduces most of the observed phenomenology.

Analysis of THG modes for femtosecond laser pulse

NASA Astrophysics Data System (ADS)

Trofimov, Vyacheslav A.; Sidorov, Pavel S.

2017-05-01

THG is used nowadays in many practical applications such as a substance diagnostics, and biological objects imaging, and etc. With developing of new materials and technology (for example, photonic crystal) an attention to THG process analysis grow. Therefore, THG features understanding are a modern problem. Early we have developed new analytical approach based on using the problem invariant for analytical solution construction of the THG process. It should be stressed that we did not use a basic wave non-depletion approximation. Nevertheless, a long pulse duration approximation and plane wave approximation has applied. The analytical solution demonstrates, in particular, an optical bistability property (and may other regimes of frequency tripling) for the third harmonic generation process. But, obviously, this approach does not reflect an influence of a medium dispersion on the frequency tripling. Therefore, in this paper we analyze THG efficiency of a femtosecond laser pulse taking into account a second order dispersion affect as well as self- and crossmodulation of the interacting waves affect on the frequency conversion process. Analysis is made using a computer simulation on the base of Schrödinger equations describing the process under consideration.

Impact of inhomogeneity on SH-type wave propagation in an initially stressed composite structure

NASA Astrophysics Data System (ADS)

Saha, S.; Chattopadhyay, A.; Singh, A. K.

2018-02-01

The present analysis has been made on the influence of distinct form of inhomogeneity in a composite structure comprised of double superficial layers lying over a half-space, on the phase velocity of SH-type wave propagating through it. Propagation of SH-type wave in the said structure has been examined in four distinct cases of inhomogeneity viz. when inhomogeneity in double superficial layer is due to exponential variation in density only (Case I); when inhomogeneity in double superficial layers is due to exponential variation in rigidity only (Case II); when inhomogeneity in double superficial layer is due to exponential variation in rigidity, density and initial stress (Case III) and when inhomogeneity in double superficial layer is due to linear variation in rigidity, density and initial stress (Case IV). Closed-form expression of dispersion relation has been accomplished for all four aforementioned cases through extensive application of Debye asymptotic analysis. Deduced dispersion relations for all the cases are found in well-agreement to the classical Love-wave equation. Numerical computation has been carried out to graphically demonstrate the effect of inhomogeneity parameters, initial stress parameters as well as width ratio associated with double superficial layers in the composite structure for each of the four aforesaid cases on dispersion curve. Meticulous examination of distinct cases of inhomogeneity and initial stress in context of considered problem has been carried out with detailed analysis in a comparative approach.

Nonlinear dynamics of the 3D FMS and Alfven wave beams propagating in plasma of ionosphere and magnetosphere

NASA Astrophysics Data System (ADS)

Belashov, Vasily

We study the formation, structure, stability and dynamics of the multidimensional soliton-like beam structures forming on the low-frequency branch of oscillation in the ionospheric and magnetospheric plasma for cases when beta=4pinT/B(2) <<1 and beta>1. In first case with the conditions omega>{k_{yz}}(2,) v_{x}$<

Dispersion analysis of passive surface-wave noise generated during hydraulic-fracturing operations

USGS Publications Warehouse

Forghani-Arani, Farnoush; Willis, Mark; Snieder, Roel; Haines, Seth S.; Behura, Jyoti; Batzle, Mike; Davidson, Michael

2014-01-01

Surface-wave dispersion analysis is useful for estimating near-surface shear-wave velocity models, designing receiver arrays, and suppressing surface waves. Here, we analyze whether passive seismic noise generated during hydraulic-fracturing operations can be used to extract surface-wave dispersion characteristics. Applying seismic interferometry to noise measurements, we extract surface waves by cross-correlating several minutes of passive records; this approach is distinct from previous studies that used hours or days of passive records for cross-correlation. For comparison, we also perform dispersion analysis for an active-source array that has some receivers in common with the passive array. The active and passive data show good agreement in the dispersive character of the fundamental-mode surface-waves. For the higher mode surface waves, however, active and passive data resolve the dispersive properties at different frequency ranges. To demonstrate an application of dispersion analysis, we invert the observed surface-wave dispersion characteristics to determine the near-surface, one-dimensional shear-wave velocity.

Coupled modes in magnetized dense plasma with relativistic-degenerate electrons

NASA Astrophysics Data System (ADS)

Khan, S. A.

2012-01-01

Low frequency electrostatic and electromagnetic waves are investigated in ultra-dense quantum magnetoplasma with relativistic-degenerate electron and non-degenerate ion fluids. The dispersion relation is derived for mobile as well as immobile ions by employing hydrodynamic equations for such plasma under the influence of electromagnetic forces and pressure gradient of relativistic-degenerate Fermi gas of electrons. The result shows the coexistence of shear Alfven and ion modes with relativistically modified dispersive properties. The relevance of results to the dense degenerate plasmas of astrophysical origin (for instance, white dwarf stars) is pointed out with brief discussion on ultra-relativistic and non-relativistic limits.

Study of dispersive and nonlinear effects of coastal wave dynamics with a fully nonlinear potential flow model

NASA Astrophysics Data System (ADS)

Benoit, Michel; Yates, Marissa L.; Raoult, Cécile

2017-04-01

Efficient and accurate numerical models simulating wave propagation are required for a variety of engineering projects including the evaluation of coastal risks, the design of protective coastal structures, and the estimation of the potential for marine renewable energy devices. Nonlinear and dispersive effects are particularly significant in the coastal zone where waves interact with the bottom, the shoreline, and coastal structures. The main challenge in developing a numerical models is finding a compromise between computational efficiency and the required accuracy of the simulated wave field. Here, a potential approach is selected and the (fully nonlinear) water wave problem is formulated using the Euler-Zakharov equations (Zakharov, 1968) describing the temporal evolution of the free surface elevation and velocity potential. The proposed model (Yates and Benoit, 2015) uses a spectral approach in the vertical (i.e. the vertical variation of the potential is approximated by a linear combination of the first NT+1 Chebyshev polynomials, following the work of Tian and Sato (2008)). The Zakharov equations are integrated in time using a fourth-order Runge-Kutta scheme with a constant time step. At each sub-timestep, the Laplace Boundary Value Problem (BVP) is solved to estimate the free surface vertical velocity using the spectral approach, with typical values of NT between 5 to 8 for practical applications. The 1DH version of the code is validated with comparisons to the experimental data set of Becq-Girard et al. (1999), which studied the propagation of irregular waves over a beach profile with a submerged bar. The nonlinear and dispersive capacities of the model are verified with the correct representation of wave-wave interactions, in particular the transfer of energy between different harmonic components during wave propagation (analysis of the transformation of the variance spectrum along the channel). Evolution of wave skewness, asymmetry and kurtosis along the bathymetric profile also compare well with the measured values. The statistical distributions of the free surface elevation and wave height, calculated from the simulated time series, are compared to those of the measurements, with particular attention paid to the extreme waves. To use this model for realistic cases with complex bathymetric variations and multidirectional wave fields, the model has been extended to two horizontal dimensions (2DH). The spectral approach in the vertical dimension is retained, while the horizontal plane is discretized with scattered nodes to maintain the model's flexibility. The horizontal derivatives are estimated with finite-difference type formulas using Radial Basis Functions (Wright and Fornberg, 2006). The 2DH version of the code is applied to simulate the propagation of regular waves over a semi-circular step, which acts as a focusing lens. The simulation results are compared to the experimental data set of Whalin (1971). The evolution of the higher harmonic amplitudes in the shallow-water zone demonstrates the ability of the model to simulate wave propagation over complex 2DH coastal bathymetries. References: Becq-Girard F., Forget P., Benoit M. (1999) Non-linear propagation of unidirectional wave fields over varying topography. Coastal Eng., 38, 91-113. Tian Y., Sato S. (2008) A numerical model on the interaction between nearshore nonlinear waves and strong currents. Coast. Eng. Journal, 50(4), 369-395. Whalin R.W. (1971) The limit of applicability of linear wave refraction theory in a convergence zone. Technical report, DTIC Documents. Wright G.B., Fornberg B. (2006) Scattered node compact finite difference-type formulas generated from radial basis functions. J. Comp. Phys., 212, 99-123. Yates M.L., Benoit M. (2015) Accuracy and efficiency of two numerical methods of solving the potential flow problem for highly nonlinear and dispersive water waves. Int. J. Numer. Meth. Fluids, 77, 616-640. Zakharov V.E. (1968) Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys., 9(2), 190-194.

Experimental observation of different soliton types in a net-normal group-dispersion fiber laser.

PubMed

Feng, Zhongyao; Rong, Qiangzhou; Qiao, Xueguang; Shao, Zhihua; Su, Dan

2014-09-20

Different soliton types are observed in a net-normal group-dispersion fiber laser based on nonlinear polarization rotation for passive mode locking. The proposed laser can deliver a dispersion-managed soliton, typical dissipation solitons, and a quasi-harmonic mode-locked pulse, a soliton bundle, and especially a dark pulse by only appropriately adjusting the linear cavity phase delay bias using one polarization controller at the fixed pump power. These nonlinear waves show different features, including the spectral shapes and time traces. The experimental observations show that the five soliton types could exist in the same laser cavity, which implies that integrable systems, dissipative systems, and dark pulse regimes can transfer and be switched in a passively mode-locked laser. Our studies not only verify the numeral simulation of the different soliton-types formation in a net-normal group-dispersion operation but also provide insight into Ginzburg-Landau equation systems.

Viscoelastic representation of surface waves in patchy saturated poroelastic media

NASA Astrophysics Data System (ADS)

Zhang, Yu; Xu, Yixian; Xia, Jianghai; Ping, Ping; Zhang, Shuangxi

2014-08-01

Wave-induced flow is observed as the dominated factor for P wave propagation at seismic frequencies. This mechanism has a mesoscopic scale nature. The inhomogeneous unsaturated patches are regarded larger than the pore size, but smaller than the wavelength. Surface wave, e.g., Rayleigh wave, which propagates along the free surface, generated by the interfering of body waves is also affected by the mesoscopic loss mechanisms. Recent studies have reported that the effect of the wave-induced flow in wave propagation shows a relaxation behavior. Viscoelastic equivalent relaxation function associated with the wave mode can describe the kinetic nature of the attenuation. In this paper, the equivalent viscoelastic relaxation functions are extended to take into account the free surface for the Rayleigh surface wave propagation in patchy saturated poroelastic media. Numerical results for the frequency-dependent velocity and attenuation and the time-dependent dynamical responses for the equivalent Rayleigh surface wave propagation along an interface between vacuum and patchy saturated porous media are reported in the low-frequency range (0.1-1,000 Hz). The results show that the dispersion and attenuation and kinetic characteristics of the mesoscopic loss effect for the surface wave can be effectively represented in the equivalent viscoelastic media. The simulation of surface wave propagation within mesoscopic patches requires solving Biot's differential equations in very small grid spaces, involving the conversion of the fast P wave energy diffusion into the Biot slow wave. This procedure requires a very large amount of computer consumption. An efficient equivalent approach for this patchy saturated poroelastic media shows a more convenient way to solve the single phase viscoelastic differential equations.

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

Chaston, C. C.; Bonnell, J. W.; Reeves, Geoffrey D.

We show how dispersive Alfvén waves observed in the inner magnetosphere during geomagnetic storms can extract O + ions from the topside ionosphere and accelerate these ions to energies exceeding 50 keV in the equatorial plane. This occurs through wave trapping, a variant of “shock” surfing, and stochastic ion acceleration. These processes in combination with the mirror force drive field-aligned beams of outflowing ionospheric ions into the equatorial plane that evolve to provide energetic O + distributions trapped near the equator. These waves also accelerate preexisting/injected ion populations on the same field lines. We show that the action of dispersivemore » Alfvén waves over several minutes may drive order of magnitude increases in O + ion pressure to make substantial contributions to magnetospheric ion energy density. These wave accelerated ions will enhance the ring current and play a role in the storm time evolution of the magnetosphere.« less

Lagrangian description of warm plasmas

NASA Technical Reports Server (NTRS)

Kim, H.

1970-01-01

Efforts are described to extend the averaged Lagrangian method of describing small signal wave propagation and nonlinear wave interaction, developed by earlier workers for cold plasmas, to the more general conditions of warm collisionless plasmas, and to demonstrate particularly the effectiveness of the method in analyzing wave-wave interactions. The theory is developed for both the microscopic description and the hydrodynamic approximation to plasma behavior. First, a microscopic Lagrangian is formulated rigorously, and expanded in terms of perturbations about equilibrium. Two methods are then described for deriving a hydrodynamic Lagrangian. In the first of these, the Lagrangian is obtained by velocity integration of the exact microscopic Lagrangian. In the second, the expanded hydrodynamic Lagrangian is obtained directly from the expanded microscopic Lagrangian. As applications of the microscopic Lagrangian, the small-signal dispersion relations and the coupled mode equations are derived for all possible waves in a warm infinite, weakly inhomogeneous magnetoplasma, and their interactions are examined.

The effects of dissipation on topological mechanical systems

PubMed Central

Xiong, Ye; Wang, Tianxiang; Tong, Peiqing

2016-01-01

We theoretically study the effects of isotropic dissipation in a topological mechanical system which is an analogue of Chern insulator in mechanical vibrational lattice. The global gauge invariance is still conserved in this system albeit it is destroyed by the dissipation in the quantum counterpart. The chiral edge states in this system are therefore robust against strong dissipation. The dissipation also causes a dispersion of damping for the eigenstates. It will modify the equation of motion of a wave packet by an extra effective force. After taking into account the Berry curvature in the wave vector space, the trace of a free wave packet in the real space should be curved, feinting to break the Newton’s first law. PMID:27605247

Theory of cavitons in complex plasmas.

PubMed

Shukla, P K; Eliasson, B; Sandberg, I

2003-08-15

Nonlinear coupling between Langmuir waves with finite amplitude dispersive dust acoustic perturbations is considered. It is shown that the interaction is governed by a pair of coupled nonlinear differential equations. Numerical results reveal the formation of Langmuir envelope solitons composed of the dust density depression created by the ponderomotive force of bell-shaped Langmuir wave envelops. The associated ambipolar potential is positive. The present nonlinear theory should be able to account for the trapping of large amplitude Langmuir waves in finite amplitude dust density holes. This scenario may appear in Saturn's dense rings, and the Cassini spacecraft should be able to observe fully nonlinear cavitons, as presented herein. Furthermore, we propose that new electron-beam plasma experiments should be conducted to verify our theoretical prediction.

Growth of electron plasma waves above and below f(p) in the electron foreshock

NASA Technical Reports Server (NTRS)

Cairns, Iver H.; Fung, Shing F.

1988-01-01

This paper investigates the conditions required for electron beams to drive wave growth significantly above and below the electron plasma frequency, f(p), by numerically solving the linear dispersion equation. It is shown that kinetic growth well below f(p) may occur over a broad range of frequencies due to the beam instability, when the electron beam is slow, dilute, and relatively cold. Alternatively, a cold or sharp feature at low parallel velocities in the distribution function may drive kinetic growth significantly below f(p). Kinetic broadband growth significantly above f(p) is explained in terms of faster warmer beams. A unified qualitative theory for the narrow-band and broad-band waves is proposed.

Ion acoustic shock waves in plasmas with warm ions and kappa distributed electrons and positrons

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

Hussain, S.; Mahmood, S.; Hafeez Ur-Rehman

2013-06-15

The monotonic and oscillatory ion acoustic shock waves are investigated in electron-positron-ion plasmas (e-p-i) with warm ions (adiabatically heated) and nonthermal kappa distributed electrons and positrons. The dissipation effects are included in the model due to kinematic viscosity of the ions. Using reductive perturbation technique, the Kadomtsev-Petviashvili-Burgers (KPB) equation is derived containing dispersion, dissipation, and diffraction effects (due to perturbation in the transverse direction) in e-p-i plasmas. The analytical solution of KPB equation is obtained by employing tangent hyperbolic (Tanh) method. The analytical condition for the propagation of oscillatory and monotonic shock structures are also discussed in detail. The numericalmore » results of two dimensional monotonic shock structures are obtained for graphical representation. The dependence of shock structures on positron equilibrium density, ion temperature, nonthermal spectral index kappa, and the kinematic viscosity of ions are also discussed.« less

Kinetic treatment of nonlinear magnetized plasma motions - General geometry and parallel waves

NASA Technical Reports Server (NTRS)

Khabibrakhmanov, I. KH.; Galinskii, V. L.; Verheest, F.

1992-01-01

The expansion of kinetic equations in the limit of a strong magnetic field is presented. This gives a natural description of the motions of magnetized plasmas, which are slow compared to the particle gyroperiods and gyroradii. Although the approach is 3D, this very general result is used only to focus on the parallel propagation of nonlinear Alfven waves. The derivative nonlinear Schroedinger-like equation is obtained. Two new terms occur compared to earlier treatments, a nonlinear term proportional to the heat flux along the magnetic field line and a higher-order dispersive term. It is shown that kinetic description avoids the singularities occurring in magnetohydrodynamic or multifluid approaches, which correspond to the degenerate case of sound speeds equal to the Alfven speed, and that parallel heat fluxes cannot be neglected, not even in the case of low parallel plasma beta. A truly stationary soliton solution is derived.

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.

Guided waves dispersion equations for orthotropic multilayered pipes solved using standard finite elements code.

PubMed

Predoi, Mihai Valentin

2014-09-01

The dispersion curves for hollow multilayered cylinders are prerequisites in any practical guided waves application on such structures. The equations for homogeneous isotropic materials have been established more than 120 years ago. The difficulties in finding numerical solutions to analytic expressions remain considerable, especially if the materials are orthotropic visco-elastic as in the composites used for pipes in the last decades. Among other numerical techniques, the semi-analytical finite elements method has proven its capability of solving this problem. Two possibilities exist to model a finite elements eigenvalue problem: a two-dimensional cross-section model of the pipe or a radial segment model, intersecting the layers between the inner and the outer radius of the pipe. The last possibility is here adopted and distinct differential problems are deduced for longitudinal L(0,n), torsional T(0,n) and flexural F(m,n) modes. Eigenvalue problems are deduced for the three modes classes, offering explicit forms of each coefficient for the matrices used in an available general purpose finite elements code. Comparisons with existing solutions for pipes filled with non-linear viscoelastic fluid or visco-elastic coatings as well as for a fully orthotropic hollow cylinder are all proving the reliability and ease of use of this method. Copyright © 2014 Elsevier B.V. All rights reserved.

Alpha models for rotating Navier-Stokes equations in geophysics with nonlinear dispersive regularization

NASA Astrophysics Data System (ADS)

Kim, Bong-Sik

Three dimensional (3D) Navier-Stokes-alpha equations are considered for uniformly rotating geophysical fluid flows (large Coriolis parameter f = 2O). The Navier-Stokes-alpha equations are a nonlinear dispersive regularization of usual Navier-Stokes equations obtained by Lagrangian averaging. The focus is on the existence and global regularity of solutions of the 3D rotating Navier-Stokes-alpha equations and the uniform convergence of these solutions to those of the original 3D rotating Navier-Stokes equations for large Coriolis parameters f as alpha → 0. Methods are based on fast singular oscillating limits and results are obtained for periodic boundary conditions for all domain aspect ratios, including the case of three wave resonances which yields nonlinear "2½-dimensional" limit resonant equations for f → 0. The existence and global regularity of solutions of limit resonant equations is established, uniformly in alpha. Bootstrapping from global regularity of the limit equations, the existence of a regular solution of the full 3D rotating Navier-Stokes-alpha equations for large f for an infinite time is established. Then, the uniform convergence of a regular solution of the 3D rotating Navier-Stokes-alpha equations (alpha ≠ 0) to the one of the original 3D rotating NavierStokes equations (alpha = 0) for f large but fixed as alpha → 0 follows; this implies "shadowing" of trajectories of the limit dynamical systems by those of the perturbed alpha-dynamical systems. All the estimates are uniform in alpha, in contrast with previous estimates in the literature which blow up as alpha → 0. Finally, the existence of global attractors as well as exponential attractors is established for large f and the estimates are uniform in alpha.

Seismic wavefield modeling based on time-domain symplectic and Fourier finite-difference method

NASA Astrophysics Data System (ADS)

Fang, Gang; Ba, Jing; Liu, Xin-xin; Zhu, Kun; Liu, Guo-Chang

2017-06-01

Seismic wavefield modeling is important for improving seismic data processing and interpretation. Calculations of wavefield propagation are sometimes not stable when forward modeling of seismic wave uses large time steps for long times. Based on the Hamiltonian expression of the acoustic wave equation, we propose a structure-preserving method for seismic wavefield modeling by applying the symplectic finite-difference method on time grids and the Fourier finite-difference method on space grids to solve the acoustic wave equation. The proposed method is called the symplectic Fourier finite-difference (symplectic FFD) method, and offers high computational accuracy and improves the computational stability. Using acoustic approximation, we extend the method to anisotropic media. We discuss the calculations in the symplectic FFD method for seismic wavefield modeling of isotropic and anisotropic media, and use the BP salt model and BP TTI model to test the proposed method. The numerical examples suggest that the proposed method can be used in seismic modeling of strongly variable velocities, offering high computational accuracy and low numerical dispersion. The symplectic FFD method overcomes the residual qSV wave of seismic modeling in anisotropic media and maintains the stability of the wavefield propagation for large time steps.

The effect of shear stress on solitary waves in arteries.

PubMed

Demiray, H

1997-09-01

In the present work, we study the propagation of solitary waves in a prestressed thick walled elastic tube filled with an incompressible inviscid fluid. In order to include the geometric dispersion in the analysis the wall inertia and shear deformation effects are taken into account for the inner pressure-cross-sectional area relation. Using the reductive perturbation technique, the propagation of weakly non-linear waves in the long-wave approximation is examined. It is shown that, contrary to thin tube theories, the present approach makes it possible to have solitary waves even for a Mooney-Rivlin (M-R) material. Due to dependence of the coefficients of the governing Korteweg-deVries equation on initial deformation, the solution profile changes with inner pressure and the axial stretch. The variation of wave profiles for a class of elastic materials are depicted in graphic forms. As might be seen from these illustrations, with increasing thickness ratio, the profile of solitary wave is steepened for a M-R material but it is broadened for biological tissue.