Helical localized wave solutions of the scalar wave equation.
Overfelt, P L
2001-08-01
A right-handed helical nonorthogonal coordinate system is used to determine helical localized wave solutions of the homogeneous scalar wave equation. Introducing the characteristic variables in the helical system, i.e., u = zeta - ct and v = zeta + ct, where zeta is the coordinate along the helical axis, we can use the bidirectional traveling plane wave representation and obtain sets of elementary bidirectional helical solutions to the wave equation. Not only are these sets bidirectional, i.e., based on a product of plane waves, but they may also be broken up into right-handed and left-handed solutions. The elementary helical solutions may in turn be used to create general superpositions, both Fourier and bidirectional, from which new solutions to the wave equation may be synthesized. These new solutions, based on the helical bidirectional superposition, are members of the class of localized waves. Examples of these new solutions are a helical fundamental Gaussian focus wave mode, a helical Bessel-Gauss pulse, and a helical acoustic directed energy pulse train. Some of these solutions have the interesting feature that their shape and localization properties depend not only on the wave number governing propagation along the longitudinal axis but also on the normalized helical pitch. PMID:11488494
Localized modulated wave solutions in diffusive glucose-insulin systems
NASA Astrophysics Data System (ADS)
Mvogo, Alain; Tambue, Antoine; Ben-Bolie, Germain H.; Kofané, Timoléon C.
2016-06-01
We investigate intercellular insulin dynamics in an array of diffusively coupled pancreatic islet β-cells. The cells are connected via gap junction coupling, where nearest neighbor interactions are included. Through the multiple scale expansion in the semi-discrete approximation, we show that the insulin dynamics can be governed by the complex Ginzburg-Landau equation. The localized solutions of this equation are reported. The results suggest from the biophysical point of view that the insulin propagates in pancreatic islet β-cells using both temporal and spatial dimensions in the form of localized modulated waves.
On exact traveling-wave solutions for local fractional Korteweg-de Vries equation
NASA Astrophysics Data System (ADS)
Yang, Xiao-Jun; Tenreiro Machado, J. A.; Baleanu, Dumitru; Cattani, Carlo
2016-08-01
This paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces.
On exact traveling-wave solutions for local fractional Korteweg-de Vries equation.
Yang, Xiao-Jun; Tenreiro Machado, J A; Baleanu, Dumitru; Cattani, Carlo
2016-08-01
This paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of non-differentiable type with the generalized functions defined on Cantor sets are analyzed. The results for the non-differentiable solutions when fractal dimension is 1 are also discussed. It is shown that the exact solutions for the local fractional Korteweg-de Vries equation characterize the fractal wave on shallow water surfaces. PMID:27586629
Genesis of Streamwise-Localized Solutions from Globally Periodic Traveling Waves in Pipe Flow
NASA Astrophysics Data System (ADS)
Chantry, M.; Willis, A. P.; Kerswell, R. R.
2014-04-01
The aim in the dynamical systems approach to transitional turbulence is to construct a scaffold in phase space for the dynamics using simple invariant sets (exact solutions) and their stable and unstable manifolds. In large (realistic) domains where turbulence can coexist with laminar flow, this requires identifying exact localized solutions. In wall-bounded shear flows, the first of these has recently been found in pipe flow, but questions remain as to how they are connected to the many known streamwise-periodic solutions. Here we demonstrate that the origin of the first localized solution is in a modulational symmetry-breaking Hopf bifurcation from a known global traveling wave that has twofold rotational symmetry about the pipe axis. Similar behavior is found for a global wave of threefold rotational symmetry, this time leading to two localized relative periodic orbits. The clear implication is that many global solutions should be expected to lead to more realistic localized counterparts through such bifurcations, which provides a constructive route for their generation.
Decay of solutions of the wave equation with arbitrary localized nonlinear damping
NASA Astrophysics Data System (ADS)
Bellassoued, Mourad
We study the problem of decay rate for the solutions of the initial-boundary value problem to the wave equation, governed by localized nonlinear dissipation and without any assumption on the dynamics (i.e., the control geometric condition is not satisfied). We treat separately the autonomous and the non-autonomous cases. Providing regular initial data, without any assumption on an observation subdomain, we prove that the energy decays at last, as fast as the logarithm of time. Our result is a generalization of Lebeau (in: A. Boutet de Monvel, V. Marchenko (Eds.), Algebraic and Geometric Methods in Mathematical Physics, Kluwer Academic Publishers, Dordrecht, the Netherlands, 1996, pp. 73) result in the autonomous case and Nakao (Adv. Math. Sci. Appl. 7 (1) (1997) 317) work in the non-autonomous case. In order to prove that result we use a new method based on the Fourier-Bross-Iaglintzer (FBI) transform.
NASA Astrophysics Data System (ADS)
Adams, R. J.; Wang, G.; Canning, F. X.; Davis, B. A.
2006-12-01
A procedure is outlined for determining compressed representations of the plane wave response matrix (P matrix) for transverse magnetic scattering with respect to the z axis from convex cylinders. The method is based on the determination of band-limited spectral modes that excite spatially localized solutions to the wave equation and satisfy global boundary conditions. Numerical examples indicate that the proposed method provides a representation of the P matrix with reduced computational complexity.
Various Boussinesq solitary wave solutions
Yates, G.T.
1995-12-31
The generalized Boussinesq (gB) equations have been used to model nonlinear wave evolution over variable topography and wave interactions with structures. Like the KdV equation, the gB equations support a solitary wave solution which propagates without changing shape, and this solitary wave is often used as a primary test case for numerical studies of nonlinear waves using either the gB or other model equations. Nine different approximate solutions of the generalized Boussinesq equations are presented with simple closed form expressions for the wave elevation and wave speed. Each approximates the free propagation of a single solitary wave, and eight of these solutions are newly obtained. The author compares these solutions with the well known KdV solution, Rayleigh`s solution, Laitone`s higher order solution, and ``exact`` numerical integration of the gB equations. Existing experimental data on solitary wave shape and wave speed are compared with these models.
Localized wave pulse experiments
Chambers, D L; Henderson, T L; Krueger, K L; Lewis, D K; Zilkowski, R N
1999-06-01
The Localized Wave project of the Strategic System Support Program has recently finished an experiment in cooperation with the Advanced SONAR group of the Applied Research Laboratory of the University of Texas at Austin. The purpose of the experiment was three-fold. They wanted to see if (1) the LW pulse could propagate over significant distances, to see if (2) a new type of array and drive system specifically designed for the pulse would increase efficiency over single frequency tone bursts, and to see if (3) the complexity of our 24 channel drivers resulted in better efficiency than a single equivalent pulse driving a piston. In the experiment, several LW pulses were launched from the Lake Travis facility and propagated over distances of either 100 feet or 600 feet, through a thermocline for the 600 foot measurements. The results show conclusively that the Localized Wave will propagate past the near field distance. The LW pulses resulted in extremely broad frequency band width pulses with narrow spatial beam patterns and unmeasurable side lobes. Their array gain was better than most tone bursts and further, were better than their equivalent piston pulses. This marks the first test of several Low Diffraction beams against their equivalent piston pulses, as well as the first propagation of LW pulses over appreciable distances. The LW pulse is now proven a useful tool in open water, rather than a laboratory curiosity. The experimental system and array were built by ARL, and the experiments were conducted by ARL staff on their standard test range. The 600 feet measurements were made at the farthest extent of that range.
Localized wave pulses in the keyport experiment
Chambers, D.H.; Lewis, D.K.
1998-02-17
Localized wave (LW) pulses were produced using a standard Navy array in the anechoic tank at Navy Underwater Weapons Center (NUWC) Keyport. The LW pulses used were the MPS pulse first derived by Ziolkowski, and a new type of pulse based on a superposition of Gaussian beam modes. This new type is motivated by a desire to make a comparison of the MPS pulse with another broad band pulse built from solutions to the wave equation. The superposed Gaussian pulse can be described by parameters which are analogous to those describing the MPS pulse. We compare the directivity patternsand the axial energy decay between the pulses. We find the behavior of the pulses to be similar so that the superposed Gaussian could be another candidate in the class of low diffractive pulses known as localized waves.
Invariant current approach to wave propagation in locally symmetric structures
NASA Astrophysics Data System (ADS)
Zampetakis, V. E.; Diakonou, M. K.; Morfonios, C. V.; Kalozoumis, P. A.; Diakonos, F. K.; Schmelcher, P.
2016-05-01
A theory for wave mechanical systems with local inversion and translation symmetries is developed employing the two-dimensional solution space of the stationary Schrödinger equation. The local symmetries of the potential are encoded into corresponding local basis vectors in terms of symmetry-induced two-point invariant currents which map the basis amplitudes between symmetry-related points. A universal wavefunction structure in locally symmetric potentials is revealed, independently of the physical boundary conditions, by using special local bases which are adapted to the existing local symmetries. The local symmetry bases enable efficient computation of spatially resolved wave amplitudes in systems with arbitrary combinations of local inversion and translation symmetries. The approach opens the perspective of a flexible analysis and control of wave localization in structurally complex systems.
NASA Astrophysics Data System (ADS)
Méndez-Fragoso, Ricardo; Cabrera-Trujillo, Remigio
2015-05-01
The determination of the maximum number of atoms and the density profile of an ultra-cold wave-packet, under confinement conditions by an attractive impurity near the de-localization threshold, have been an open problem in ultra-cold atom physics. In this work, we study the effect of a wave-guide impurity on an ultra-cold matter wave-packet at the threshold of de-localization. The impurity is modeled by a 1-D square well potential with depth V 0 and length 2 R 0. Coupling of the square well potential to a contact impurity of strength β at the center is also considered. The time-independent non-linear Schrödinger equation describing a Bose-Einstein condensate at the delocalization threshold is exactly solved. The density profile, maximum non-linear coupling constant, g max, and maximum number of atoms, N max, prompt to be localized by the defect potential in the ground and first excited states are also reported. It is shown that g max and the density profiles become only functions of the reduced impurity size ξ = √ V 0 R 0. It is also found that the first excited state at the threshold of de-localization exists only for ξ ≥ π/(2√2), always holding a lower number of atoms than the corresponding ground state for the same reduced impurity size. Also, the addition of a repulsive contact impurity leads to a non-linear coupling constant at the de-localization threshold lower than that of the square well potential. In spite of the non-linear character of the Gross-Pitaevskii equation, it is found that a general scaling-law holds for defects with the same ξ, related with the same g max, having the same reduced density profile in the quasi-free direction. We report the full width at half maximum for the wave-function and density profile, finding a large spread for small reduced confining conditions. Implications of these results for the determination of the wave-packet properties under confinement in atom chip and Bose-Einstein condensates are presented with the
Damping filter method for obtaining spatially localized solutions.
Teramura, Toshiki; Toh, Sadayoshi
2014-05-01
Spatially localized structures are key components of turbulence and other spatiotemporally chaotic systems. From a dynamical systems viewpoint, it is desirable to obtain corresponding exact solutions, though their existence is not guaranteed. A damping filter method is introduced to obtain variously localized solutions and adapted in two typical cases. This method introduces a spatially selective damping effect to make a good guess at the exact solution, and we can obtain an exact solution through a continuation with the damping amplitude. The first target is a steady solution to the Swift-Hohenberg equation, which is a representative of bistable systems in which localized solutions coexist and a model for spanwise-localized cases. Not only solutions belonging to the well-known snaking branches but also those belonging to isolated branches known as "isolas" are found with continuation paths between them in phase space extended with the damping amplitude. This indicates that this spatially selective excitation mechanism has an advantage in searching spatially localized solutions. The second target is a spatially localized traveling-wave solution to the Kuramoto-Sivashinsky equation, which is a model for streamwise-localized cases. Since the spatially selective damping effect breaks Galilean and translational invariances, the propagation velocity cannot be determined uniquely while the damping is active, and a singularity arises when these invariances are recovered. We demonstrate that this singularity can be avoided by imposing a simple condition, and a localized traveling-wave solution is obtained with a specific propagation speed. PMID:25353864
Magneto-atmospheric waves from a localized source
NASA Technical Reports Server (NTRS)
Adam, J. A.; Thomas, J. H.
1984-01-01
A technique developed by Lighthill (1960, 1965, and 1967) for finding the asymptotic solution of an inhomogeneous wave equation with constant coefficients is applied to the study of wave propagation in magneto-atmospheres. The geometry of the wavenumber surface plays an important role in determining the generation and propagation of various types of magneto-atmospheric waves from a localized forcing region. Examples of these wavenumber surfaces are exhibited for various magnetic-field strengths and wave frequencies. The asymptotic far field is tabulated for a time-harmonic spatially Gaussian localized forcing term.
NASA Technical Reports Server (NTRS)
Collins, William
1989-01-01
The dispersion equation of Barnes (1966) is used to study the dissipation of asymptotic wave packets generated by localized periodic sources. The solutions of the equation are linear waves, damped by Landau and transit-time processes, in a collisionless warm plasma. For the case of an ideal MHD system, most of the waves emitted from a source are shown to cancel asympotically through destructive interference. The modes transporting significant flux to asymptotic distances are found to be Alfven waves and fast waves with theta (the angle between the magnetic field and the characteristics of the far-field waves) of about 0 and about pi/2.
Testing local Lorentz invariance with gravitational waves
NASA Astrophysics Data System (ADS)
Kostelecký, V. Alan; Mewes, Matthew
2016-06-01
The effects of local Lorentz violation on dispersion and birefringence of gravitational waves are investigated. The covariant dispersion relation for gravitational waves involving gauge-invariant Lorentz-violating operators of arbitrary mass dimension is constructed. The chirp signal from the gravitational-wave event GW150914 is used to place numerous first constraints on gravitational Lorentz violation.
Numerical Solutions in 5d Standing Wave Braneworld
NASA Astrophysics Data System (ADS)
Gogberashvili, Merab; Sakhelashvili, Otari; Tukhashvili, Giorgi
2013-06-01
Within the 5D standing wave braneworld model numerical solutions of the equations for matter fields with various spins are found. It is shown that corresponding action integrals are factorizable and convergent over the extra coordinate, i.e. 4D fields are localized on the brane. We find that only left massless fermions are localized on the brane, while the right fermions are localized in the bulk. We demonstrate also quantization of Kaluza-Klein excited modes in our model.
Localized travelling waves in the asymptotic suction boundary layer
NASA Astrophysics Data System (ADS)
Kreilos, Tobias; Gibson, John F.; Schneider, Tobias M.
2016-05-01
We present two spanwise-localized travelling wave solutions in the asymptotic suction boundary layer, obtained by continuation of solutions of plane Couette flow. One of the solutions has the vortical structures located close to the wall, similar to spanwise-localized edge states previously found for this system. The vortical structures of the second solution are located in the free stream far above the laminar boundary layer and are supported by a secondary shear gradient that is created by a large-scale low-speed streak. The dynamically relevant eigenmodes of this solution are concentrated in the free stream, and the departure into turbulence from this solution evolves in the free stream towards the walls. For invariant solutions in free-stream turbulence, this solution thus shows that that the source of energy of the vortical structures can be a dynamical structure of the solution itself, instead of the laminar boundary layer.
Exciton-polariton localized wave packets in a microcavity
NASA Astrophysics Data System (ADS)
Voronych, Oksana; Buraczewski, Adam; Matuszewski, MichałÂ; Stobińska, Magdalena
2016-06-01
We investigate the possibility of creating X waves, or localized wave packets, in resonantly excited exciton-polariton superfluids. We demonstrate the existence of X-wave traveling solutions in the coupled exciton-photon system past the inflection point, where the effective mass of lower polaritons is negative in the direction perpendicular to the wave vector of the pumping beam. Contrary to the case of bright solitons, X waves do not require nonlinearity for sustaining their shape. Nevertheless, we show that nonlinearity is important for their dynamics, as it allows for their spontaneous formation from an initial Gaussian wave packet. Unique properties of exciton-polaritons may lead to applications of their X waves in long-distance signal propagation inside novel integrated optoelectronic circuits based on excitons.
Dark- and bright-rogue-wave solutions for media with long-wave-short-wave resonance.
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. PMID:24580164
Localization of Waves in Merged Lattices.
Alagappan, G; Png, C E
2016-01-01
This article describes a new two-dimensional physical topology-merged lattice, that allows dense number of wave localization states. Merged lattices are obtained as a result of merging two lattices of scatters of the same space group, but with slightly different spatial resonances. Such merging creates two-dimensional scattering "beats" which are perfectly periodic on the longer spatial scale. On the shorter spatial scale, the systematic breakage of the translational symmetry leads to strong wave scattering, and this causes the occurrences of wave localization states. Merged Lattices promises variety of localization states including tightly confined, and ring type annular modes. The longer scale perfect periodicity of the merged lattice, enables complete prediction and full control over the density of the localization states and its' quality factors. In addition, the longer scale periodicity, also allows design of integrated slow wave components. Merged lattices, thus, can be engineered easily to create technologically beneficial applications. PMID:27535096
Localization of Waves in Merged Lattices
Alagappan, G.; Png, C. E.
2016-01-01
This article describes a new two–dimensional physical topology–merged lattice, that allows dense number of wave localization states. Merged lattices are obtained as a result of merging two lattices of scatters of the same space group, but with slightly different spatial resonances. Such merging creates two–dimensional scattering “beats” which are perfectly periodic on the longer spatial scale. On the shorter spatial scale, the systematic breakage of the translational symmetry leads to strong wave scattering, and this causes the occurrences of wave localization states. Merged Lattices promises variety of localization states including tightly confined, and ring type annular modes. The longer scale perfect periodicity of the merged lattice, enables complete prediction and full control over the density of the localization states and its’ quality factors. In addition, the longer scale periodicity, also allows design of integrated slow wave components. Merged lattices, thus, can be engineered easily to create technologically beneficial applications. PMID:27535096
Localization of flexural waves in a disordered periodic piezoelectric beam
NASA Astrophysics Data System (ADS)
Chen, A.-Li; Li, Feng-Ming; Wang, Yue-Sheng
2007-07-01
Localization of bending waves in a disordered periodic piezoelectric beam is studied in this paper. The equation of the wave motion for a piezoelectric beam is derived on the assumption of an Euler-Bernoulli beam, and the harmonic solution is presented. The transfer matrix between two consecutive unit cells in the structures is obtained by using the continuity conditions. The expression of the localization factor is given by Wolf's algorithm. Numerical examples are presented and the effects of several disordered parameters on the localization factor are analyzed. The results show that piezoelectricity has obvious effects on the passbands and stopbands of the periodic piezoelectric beam. The behavior of wave propagation and localization in disordered periodic piezoelectric beams can be altered by tuning different structural parameters.
Manipulating localized matter waves in multicomponent Bose-Einstein condensates.
Manikandan, K; Muruganandam, P; Senthilvelan, M; Lakshmanan, M
2016-03-01
We analyze vector localized solutions of two-component Bose-Einstein condensates (BECs) with variable nonlinearity parameters and external trap potentials through a similarity transformation technique which transforms the two coupled Gross-Pitaevskii equations into a pair of coupled nonlinear Schrödinger equations with constant coefficients under a specific integrability condition. In this analysis we consider three different types of external trap potentials: a time-independent trap, a time-dependent monotonic trap, and a time-dependent periodic trap. We point out the existence of different interesting localized structures; namely, rogue waves, dark- and bright-soliton rogue waves, and rogue-wave breatherlike structures for the above three cases of trap potentials. We show how the vector localized density profiles in a constant background get deformed when we tune the strength of the trap parameter. Furthermore, we investigate the nature of the trajectories of the nonautonomous rogue waves. We also construct the dark-dark rogue wave solution for the repulsive-repulsive interaction of two-component BECs and analyze the associated characteristics for the three different kinds of traps. We then deduce single-, two-, and three-composite rogue waves for three-component BECs and discuss the correlated characteristics when we tune the strength of the trap parameter for different trap potentials. PMID:27078349
Manipulating localized matter waves in multicomponent Bose-Einstein condensates
NASA Astrophysics Data System (ADS)
Manikandan, K.; Muruganandam, P.; Senthilvelan, M.; Lakshmanan, M.
2016-03-01
We analyze vector localized solutions of two-component Bose-Einstein condensates (BECs) with variable nonlinearity parameters and external trap potentials through a similarity transformation technique which transforms the two coupled Gross-Pitaevskii equations into a pair of coupled nonlinear Schrödinger equations with constant coefficients under a specific integrability condition. In this analysis we consider three different types of external trap potentials: a time-independent trap, a time-dependent monotonic trap, and a time-dependent periodic trap. We point out the existence of different interesting localized structures; namely, rogue waves, dark- and bright-soliton rogue waves, and rogue-wave breatherlike structures for the above three cases of trap potentials. We show how the vector localized density profiles in a constant background get deformed when we tune the strength of the trap parameter. Furthermore, we investigate the nature of the trajectories of the nonautonomous rogue waves. We also construct the dark-dark rogue wave solution for the repulsive-repulsive interaction of two-component BECs and analyze the associated characteristics for the three different kinds of traps. We then deduce single-, two-, and three-composite rogue waves for three-component BECs and discuss the correlated characteristics when we tune the strength of the trap parameter for different trap potentials.
Traveling wave solutions of compressible fluid equations and orbital stability
NASA Astrophysics Data System (ADS)
Li, Xiang; Zhang, Weiguo; Li, Zhengming
2015-11-01
In this paper, we discuss the existence of traveling wave solutions for compressible fluid equations by applying the theory and method of planar dynamical system, and obtain explicit expressions for all bounded traveling wave solutions by undetermined coefficient method, including kink and bell profile traveling wave solutions, as well as periodic wave solutions. We prove the kink profile solitary wave solution, both sides of which asymptotic values are not zero, is orbitally stable by the theory of Grillakis-Shatah-Strauss orbital stability.
Research for Locally Relevant Solutions
ERIC Educational Resources Information Center
Association of Universities and Colleges of Canada, 2004
2004-01-01
In the CIDA-funded University Partnerships in Cooperation and Development program--where Canadian universities establish knowledge partnerships with Southern universities--projects with a well-developed research dimension have proven to be the strongest projects, with broader and deeper contributions to the local institutions and larger community.…
Solutions of barotropic trapped waves over topography
NASA Astrophysics Data System (ADS)
Zavala Sanson, Luis
2010-05-01
Solutions of free, barotropic waves over variable topography are derived. In particular, we examine two cases: waves around axisymmetric seamounts and waves along a sloping bottom. Even though these types of oscillations have been studied before, we revisit the problem because of two main reasons: (i) The linear, barotropic, shallow-water equations with a rigid lid are now solved with no further approximations, in contrast with previous studies. (ii) The solutions are applied to a wide family of seamounts and bottom slopes with profiles proportional to exp(rs) and ys, respectively, where r is the radial distance from the centre of the mountain, y is the direction perpendicular to the slope, and s is an arbitrary positive real number. Most of previous works on seamounts are restricted to the special case s = 2. By varying the shape parameter one can study trapped waves around flat-topped seamounts or guyots (s > 2) or sharp, cone-shaped topographies (s < 2). Similarly, most of previous studies on sloping bottoms report cases with s = 1 (linear slopes), whilst the present results are applied to more general bottom profiles. The resulting dispersion relation in both cases possess a remarkable simplicity that reveals a number of wave characteristics as a function of the topography shape.
Rayleigh waves, surface disorder, and phonon localization in nanostructures
NASA Astrophysics Data System (ADS)
Maurer, L. N.; Mei, S.; Knezevic, I.
2016-07-01
We introduce a technique to calculate thermal conductivity in disordered nanostructures: a finite-difference time-domain solution of the elastic-wave equation combined with the Green-Kubo formula. The technique captures phonon wave behavior and scales well to nanostructures that are too large or too surface disordered to simulate with many other techniques. We investigate the role of Rayleigh waves and surface disorder on thermal transport by studying graphenelike nanoribbons with free edges (allowing Rayleigh waves) and fixed edges (prohibiting Rayleigh waves). We find that free edges result in a significantly lower thermal conductivity than fixed ones. Free edges both introduce Rayleigh waves and cause all low-frequency modes (bulk and surface) to become more localized. Increasing surface disorder on free edges draws energy away from the center of the ribbon and toward the disordered edges, where it gets trapped in localized surface modes. These effects are not seen in ribbons with fixed boundary conditions and illustrate the importance of phonon-surface modes in nanostructures.
NASA Astrophysics Data System (ADS)
Zhang, Qingling
2016-03-01
This paper is devoted to studying the simplified nonlinear chromatography equations by introducing the change of state variables. The Riemann solutions containing delta shock waves are presented. In order to study wave interactions of delta shock waves with elementary waves, the global structure of solutions is constructed completely when the initial data are taken as three pieces of constants and the delta shock waves are included. In particular, the strength of delta shock wave is expressed explicitly and the delta contact discontinuity is discovered during the process of wave interactions. Moreover, by analyzing the limits of the solutions as the middle region vanishes, we observe that the Riemann solutions are stable for such a local small perturbation of the Riemann initial data.
Traveling waves and their tails in locally resonant granular systems
Xu, H.; Kevrekidis, P. G.; Stefanov, A.
2015-04-22
In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as mass-in-mass systems. We use three distinct approaches to identify relevant traveling waves. In addition, the first consists of a direct solution of the traveling wave problem. The second one consists of the solution of the Fourier tranformed variant of the problem, or, more precisely, of its convolution reformulation (upon an inverse Fourier transform) in real space. Finally, our third approach will restrict considerations to a finite domain, utilizing the notion of Fourier series for important technical reasons, namely themore » avoidance of resonances, which will be discussed in detail. All three approaches can be utilized in either the displacement or the strain formulation. Typical resulting computations in finite domains result in the solitary waves bearing symmetric non-vanishing tails at both ends of the computational domain. Importantly, however, a countably infinite set of anti-resonance conditions is identified for which solutions with genuinely rapidly decaying tails arise.« less
Traveling waves and their tails in locally resonant granular systems
Xu, H.; Kevrekidis, P. G.; Stefanov, A.
2015-04-22
In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as mass-in-mass systems. We use three distinct approaches to identify relevant traveling waves. In addition, the first consists of a direct solution of the traveling wave problem. The second one consists of the solution of the Fourier tranformed variant of the problem, or, more precisely, of its convolution reformulation (upon an inverse Fourier transform) in real space. Finally, our third approach will restrict considerations to a finite domain, utilizing the notion of Fourier series for important technical reasons, namely the avoidance of resonances, which will be discussed in detail. All three approaches can be utilized in either the displacement or the strain formulation. Typical resulting computations in finite domains result in the solitary waves bearing symmetric non-vanishing tails at both ends of the computational domain. Importantly, however, a countably infinite set of anti-resonance conditions is identified for which solutions with genuinely rapidly decaying tails arise.
Bifurcations of traveling wave solutions for an integrable equation
Li Jibin; Qiao Zhijun
2010-04-15
This paper deals with the following equation m{sub t}=(1/2)(1/m{sup k}){sub xxx}-(1/2)(1/m{sup k}){sub x}, which is proposed by Z. J. Qiao [J. Math. Phys. 48, 082701 (2007)] and Qiao and Liu [Chaos, Solitons Fractals 41, 587 (2009)]. By adopting the phase analysis method of planar dynamical systems and the theory of the singular traveling wave systems to the traveling wave solutions of the equation, it is shown that for different k, the equation may have infinitely many solitary wave solutions, periodic wave solutions, kink/antikink wave solutions, cusped solitary wave solutions, and breaking loop solutions. We discuss in a detail the cases of k=-2,-(1/2),(1/2),2, and parametric representations of all possible bounded traveling wave solutions are given in the different (c,g)-parameter regions.
Local properties of three-body atomic wave functions
Krivec, R.; Mandelzweig, V. B.; Varga, K.
2000-06-01
The local properties and accuracy of the positronium negative-ion (Ps{sup -}) ground-state wave functions obtained by the stochastic variational method (SVM) and by direct solution of the Schroedinger equation with the help of the correlation-function hyperspherical-harmonic method (CFHHM) are studied and compared. Though the energy, calculated by both methods, agrees to up to ten digits, the amplitudes of the values of the operator D=H{psi}/E{psi}-1, characterizing local deviation of the wave function from its true value, in all of the coordinate space in the SVM are consistently larger (by up to five orders of magnitude) than in the CFHHM, despite the fact that the SVM observables except <{delta}(r{sub k})> converge to significantly more digits than the CFHHM observables for their respective selected bases. (c) 2000 The American Physical Society.
McKenzie, J. F.; Doyle, T. B.; Rajah, S. S.
2012-11-15
The theory of fully nonlinear stationary electrostatic ion cyclotron waves is further developed. The existence of two fundamental constants of motion; namely, momentum flux density parallel to the background magnetic field and energy density, facilitates the reduction of the wave structure equation to a first order differential equation. For subsonic waves propagating sufficiently obliquely to the magnetic field, soliton solutions can be constructed. Importantly, analytic expressions for the amplitude of the soliton show that it increases with decreasing wave Mach number and with increasing obliquity to the magnetic field. In the subsonic, quasi-parallel case, periodic waves exist whose compressive and rarefactive amplitudes are asymmetric about the 'initial' point. A critical 'driver' field exists that gives rise to a soliton-like structure which corresponds to infinite wavelength. If the wave speed is supersonic, periodic waves may also be constructed. The aforementioned asymmetry in the waveform arises from the flow being driven towards the local sonic point in the compressive phase and away from it in the rarefactive phase. As the initial driver field approaches the critical value, the end point of the compressive phase becomes sonic and the waveform develops a wedge shape. This feature and the amplitudes of the compressive and rarefactive portions of the periodic waves are illustrated through new analytic expressions that follow from the equilibrium points of a wave structure equation which includes a driver field. These expressions are illustrated with figures that illuminate the nature of the solitons. The presently described wedge-shaped waveforms also occur in water waves, for similar 'transonic' reasons, when a Coriolis force is included.
Pair-tunneling induced localized waves in a vector nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Zhao, Li-Chen; Ling, Liming; Yang, Zhan-Ying; Liu, Jie
2015-06-01
We investigate localized waves of coupled two-mode nonlinear Schrödinger equations with a pair-tunneling term representing strongly interacting particles can tunnel between the modes as a fragmented pair. Facilitated by Darboux transformation, we have derived exact solution of nonlinear vector waves such as bright solitons, Kuznetsov-Ma soliton, Akhmediev breathers and rogue waves and demonstrated their interesting temporal-spatial structures. A phase diagram that demarcates the parameter ranges of the nonlinear waves is obtained. Possibilities to observe these localized waves are discussed in a two species Bose-Einstein condensate.
Local computational strategies for predicting wave propagation in nonlinear media
NASA Astrophysics Data System (ADS)
Leamy, Michael J.; Autrusson, Thibaut B.; Staszewski, Wieslaw J.; Uhl, Tadeusz; Packo, Pawel
2014-03-01
Two local computational strategies for modeling elastic wave propagation, namely the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE), are compared and contrasted in analyzing bulk waves in two-dimensional nonlinear media. Each strategy formulates the problem from the perspective of a cell and its local interactions with other cells, leading to robust treatments of anisotropy, heterogeneity, and nonlinearity. The local approach also enables straight-forward parallelization on high performance computing clusters. While the two share a common local perspective, they differ in two major respects. The first is that CAFE employs both rectangular and triangular cells, while LISA considers only rectangular. The second is that LISA appeared much earlier than CAFE (early 1990's versus late 2000's), and as such has been developed to a much greater degree with a multitude of material models, cell-to-cell interactions, loading possibilities, and boundary treatments. A hybrid approach which combines the two is of great interest since the non-uniform mesh capability of the CAFE triangular cell can be readily coupled to LISA's rectangular grids, taking advantage of the built-in LISA features on the uniform portion of the domain. For linear material domains, the hybrid implementation appears straight-forward since both methods have been shown to recover the same equations in the rectangular case. For nonlinear material domains, the formulations cannot be put into a one-to-one correspondence, and hybrid implementation may be more problematic. This paper addresses these differences by first presenting the underlying formulations, and then computing results for growth of a second harmonic in an introduced bulk pressure wave. Rectangular cells are used in both LISA and CAFE. Results from both approaches are compared to an approximate, analytical solution based on a two-scale field representation. Differences in the LISA and CAFE computed
Black Plane Solutions and Localized Gravitational Energy
Roberts, Jennifer
2015-01-01
We explore the issue of gravitational energy localization for static plane-symmetric solutions of the Einstein-Maxwell equations in 3+1 dimensions with asymptotic anti-de Sitter behavior. We apply three different energy-momentum complexes, the Einstein, Landau-Lifshitz, and Møller prescriptions, to the metric representing this category of solutions and determine the energy distribution for each. We find that the three prescriptions offer identical energy distributions, suggesting their utility for this type of model. PMID:27347499
Travelling wave solutions for higher-order wave equations of kdv type (iii).
Li, Jibin; Rui, Weigou; Long, Yao; He, Bin
2006-01-01
By using the theory of planar dynamical systems to the travelling wave equation of a higher order nonlinear wave equations of KdV type, the existence of smooth solitary wave, kink wave and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions are proved. In different regions of the parametric space, the sufficient conditions to guarantee the existence of the above solutions are given. In some conditions, exact explicit parametric representations of these waves are obtain. PMID:20361813
Waves on a vortex filament: exact solutions of dynamical equations
NASA Astrophysics Data System (ADS)
Brugarino, Tommaso; Mongiovi, Maria Stella; Sciacca, Michele
2015-06-01
In this paper, we take into account the dynamical equations of a vortex filament in superfluid helium at finite temperature (1 K < T < 2.17 K) and at very low temperature, which is called Biot-Savart law. The last equation is also valid for a vortex tube in a frictionless, unbounded, and incompressible fluid. Both the equations are approximated by the Local Induction Approximation (LIA) and Fukumoto's approximation. The obtained equations are then considered in the extrinsic frame of reference, where exact solutions (Kelvin waves) are shown. These waves are then compared one to each other in terms of their dispersion relations in the frictionless case. The same equations are then investigated for a quantized vortex line in superfluid helium at higher temperature, where friction terms are needed for a full description of the motion.
Killing spinors and exact plane-wave solutions of extended supergravity
NASA Astrophysics Data System (ADS)
Hull, C. M.
1984-07-01
Urrutia's ansatz for exact plane-wave solutions of simple supergravity is generalized to N=2 extended supergravity and conditions are given for the solutions to be nontrivial. Conditions are also given for the plane-wave background to be invariant under a local supersymmetry transformation generated by a Killing spinor. It is seen that even though a bosonic background can admit a spin-32 solution when it does not possess a Killing spinor, if it is supersymmetric it admits a more general gravitino solution. Comparison is made with the solutions of Aichelburg and Dereli.
Travelling-wave solutions bifurcating from relative periodic orbits in plane Poiseuille flow
NASA Astrophysics Data System (ADS)
Rawat, Subhandu; Cossu, Carlo; Rincon, François
2016-06-01
Travelling-wave solutions are shown to bifurcate from relative periodic orbits in plane Poiseuille flow at Re = 2000 in a saddle-node infinite-period bifurcation. These solutions consist in self-sustaining sinuous quasi-streamwise streaks and quasi-streamwise vortices located in the bulk of the flow. The lower branch travelling-wave solutions evolve into spanwise localized states when the spanwise size Lz of the domain in which they are computed is increased. On the contrary, the upper branch of travelling-wave solutions develops multiple streaks when Lz is increased. Upper-branch travelling-wave solutions can be continued into coherent solutions to the filtered equations used in large-eddy simulations where they represent turbulent coherent large-scale motions.
NASA Astrophysics Data System (ADS)
Starosvetsky, Yuli; Vakakis, Alexander F.
2010-08-01
We study a class of strongly nonlinear traveling waves and localized modes in one-dimensional homogeneous granular chains with no precompression. Until now the only traveling-wave solutions known for this class of systems were the single-hump solitary waves studied by Nesterenko in the continuum approximation limit. Instead, we directly study the discrete strongly nonlinear governing equations of motion of these media without resorting to continuum approximations or homogenization, which enables us to compute families of stable multihump traveling-wave solutions with arbitrary wavelengths. We develop systematic semianalytical approaches for computing different families of nonlinear traveling waves parametrized by spatial periodicity (wave number) and energy, and show that in a certain asymptotic limit, these wave families converge to the known single-hump solitary wave studied by Nesterenko. In addition, we demonstrate the existence of an additional class of stable strongly localized out-of-phase standing waves in perfectly homogeneous granular chains with no precompression or disorder. Until now such localized solutions were known to exist only in granular chains with strong precompression. Our findings indicate that homogeneous granular chains possess complex intrinsic nonlinear dynamics, including intrinsic nonlinear energy transfer and localization phenomena.
Asymptotic traveling wave solution for a credit rating migration problem
NASA Astrophysics Data System (ADS)
Liang, Jin; Wu, Yuan; Hu, Bei
2016-07-01
In this paper, an asymptotic traveling wave solution of a free boundary model for pricing a corporate bond with credit rating migration risk is studied. This is the first study to associate the asymptotic traveling wave solution to the credit rating migration problem. The pricing problem with credit rating migration risk is modeled by a free boundary problem. The existence, uniqueness and regularity of the solution are obtained. Under some condition, we proved that the solution of our credit rating problem is convergent to a traveling wave solution, which has an explicit form. Furthermore, numerical examples are presented.
Unsteady evolution of localized unidirectional deep-water wave groups
NASA Astrophysics Data System (ADS)
Cousins, Will; Sapsis, Themistoklis P.
2015-06-01
We study the evolution of localized wave groups in unidirectional water wave envelope equations [the nonlinear Schrödinger (NLSE) and the modified NLSE (MNLSE)]. These localizations of energy can lead to disastrous extreme responses (rogue waves). We analytically quantify the role of such spatial localization, introducing a technique to reduce the underlying partial differential equation dynamics to a simple ordinary differential equation for the wave packet amplitude. We use this reduced model to show how the scale-invariant symmetries of the NLSE break down when the additional terms in the MNLSE are included, inducing a critical scale for the occurrence of extreme waves.
Localization of Waves without Bistability: Worms in Nematic Electroconvection
Riecke, H.; Granzow, G.D.
1998-07-01
A general localization mechanism for waves in dissipative systems is identified that does not require the bistability of the basic state and the nonlinear plane-wave state. We conjecture that the mechanism explains the two-dimensional localized wave structures ({open_quotes}worms{close_quotes}) that recently have been observed in experiments on electroconvection in nematic liquid crystals where the transition to extended waves is supercritical. The mechanism accounts for the shape of the worms, their propagation direction, and certain aspects of their interaction. The dynamics of the localized waves can be steady or irregular. {copyright} {ital 1998} {ital The American Physical Society}
Rogue Waves and New Multi-wave Solutions of the (2+1)-Dimensional Ito Equation
NASA Astrophysics Data System (ADS)
Tian, Ying-hui; Dai, Zheng-de
2015-06-01
A three-soliton limit method (TSLM) for seeking rogue wave solutions to nonlinear evolution equation (NEE) is proposed. The (2+1)-dimensional Ito equation is used as an example to illustrate the effectiveness of the method. As a result, two rogue waves and a family of new multi-wave solutions are obtained. The result shows that rogue wave can be obtained not only from extreme form of breather solitary wave but also from extreme form of double-breather solitary wave. This is a new and interesting discovery.
Acousto-optical confirmation of the localized wave phenomena
Lewis, D.K.
1992-09-09
An acousto-optical measurement method is described which was used to conduct proof of principle experiments for a novel acoustic pulse system. The pulse theory, the Localized Wave pulse, is discussed and the system explained and described. The results of the experiments confirm the Localized Wave theory.
Family of electrovac colliding wave solutions of Einstein's equations
Li, W.; Ernst, F.J.
1989-03-01
Beginning with any colliding wave solution of the vacuum Einstein equations, a corresponding electrified colliding wave solution can be generated through the use of a transformation due to Harrison (J. Math. Phys. 9, 1744 (1968)). The method, long employed in the context of stationary axisymmetric fields, is equally applicable to colliding wave solutions. Here it is applied to a large family of vacuum metrics derived by applying a generalized Ehlers transformation to solutions published recently by Ernst, Garcia, and Hauser (EGH) (J. Math. Phys. 28, 2155, 2951 (1987); 29, 681 (1988)). Those EGH solutions were themselves a generalization of solutions first derived by Ferrari, Ibanez, and Bruni (Phys. Rev. D 36, 1053 (1987)). Among the electrovac solutions that are obtained is a charged version of the Nutku--Halil (Phys. Rev. Lett. 39, 1379 (1977)) metric that possesses an arbitrary complex charge parameter.
A family of electrovac colliding wave solutions of Einstein's equations
NASA Astrophysics Data System (ADS)
Li, Wei; Ernst, Frederick J.
1989-03-01
Beginning with any colliding wave solution of the vacuum Einstein equations, a corresponding electrified colliding wave solution can be generated through the use of a transformation due to Harrison [J. Math. Phys. 9, 1744 (1968)]. The method, long employed in the context of stationary axisymmetric fields, is equally applicable to colliding wave solutions. Here it is applied to a large family of vacuum metrics derived by applying a generalized Ehlers transformation to solutions published recently by Ernst, García, and Hauser (EGH) [J. Math. Phys. 28, 2155, 2951 (1987); 29, 681 (1988)]. Those EGH solutions were themselves a generalization of solutions first derived by Ferrari, Ibañez, and Bruni [Phys. Rev. D 36, 1053 (1987)]. Among the electrovac solutions that are obtained is a charged version of the Nutku-Halil [Phys. Rev. Lett. 39, 1379 (1977)] metric that possesses an arbitrary complex charge parameter.
Full wave solution for hydrodynamic behaviors of pile breakwater
NASA Astrophysics Data System (ADS)
Zhu, Da-tong
2013-06-01
Rayleigh expansion is used to study the water-wave interaction with a row of pile breakwater in finite water depth. Evanescent waves, the wave energy dissipated on the fluid resistance and the thickness of the breakwater are totally included in the model. The formulae of wave reflection and transmission coefficients are obtained. The accuracy of the present model is verified by a comparison with existing results. It is found that the predicted wave reflection and transmission coefficients for the zero order are all highly consistent with the experimental data (Hagiwara, 1984; Isaacson et al., 1998) and plane wave solutions (Zhu, 2011). The losses of the wave energy for the fluid passing through slits play an important role, which removes the phenomena of enhanced wave transmission.
Theoretical and experimental evidence of non-symmetric doubly localized rogue waves
He, Jingsong; Guo, Lijuan; Zhang, Yongshuai; Chabchoub, Amin
2014-01-01
We present determinant expressions for vector rogue wave (RW) solutions of the Manakov system, a two-component coupled nonlinear Schrödinger (NLS) equation. As a special case, we generate a family of exact and non-symmetric RW solutions of the NLS equation up to third order, localized in both space and time. The derived non-symmetric doubly localized second-order solution is generated experimentally in a water wave flume for deep-water conditions. Experimental results, confirming the characteristic non-symmetric pattern of the solution, are in very good agreement with theory as well as with numerical simulations, based on the modified NLS equation, known to model accurately the dynamics of weakly nonlinear wave packets in deep water. PMID:25383023
Nonperturbative quantum solutions to resonant four-wave mixing of two single-photon wave packets
Johnsson, Mattias; Fleischhauer, Michael
2003-08-01
We analyze both analytically and numerically the resonant four-wave mixing of two co-propagating single-photon wave packets. We present analytic expressions for the two-photon wave function, and show that quantum solutions exist which display a shape-preserving oscillatory exchange of excitations between the modes. Potential applications including quantum-information processing are discussed.
NASA Astrophysics Data System (ADS)
Hiruta, Yoshiki; Toh, Sadayoshi
2015-12-01
Two-dimensional Kolmogorov flow in wide periodic boxes is numerically investigated. It is shown that the total flow rate in the direction perpendicular to the force controls the characteristics of the flow, especially the existence of spatially localized solitary solutions such as traveling waves, periodic solutions, and chaotic solutions, which can behave as elementary components of the flow. We propose a procedure to construct approximate solutions consisting of solitary solutions. It is confirmed by direct numerical simulations that these solutions are stable and represent interactions between elementary components such as collisions, coexistence, and collapse of chaos.
Exact and explicit solitary wave solutions to some nonlinear equations
Jiefang Zhang
1996-08-01
Exact and explicit solitary wave solutions are obtained for some physically interesting nonlinear evolutions and wave equations in physics and other fields by using a special transformation. These equations include the KdV-Burgers equation, the MKdV-Burgers equation, the combined KdV-MKdV equation, the Newell-Whitehead equation, the dissipative {Phi}{sup 4}-model equation, the generalized Fisher equation, and the elastic-medium wave equation.
Propagation of radially localized helicon waves in longitudinally nonuniform plasmas
Arefiev, Alexey V.; Breizman, Boris N.
2006-06-15
A gradient in the plasma density across the guiding magnetic field can support a low-frequency radially localized helicon (RLH) wave in a plasma column. If the radial density gradient changes along the magnetic field, this wave can undergo reflection and also excite conventional whistlers. This paper presents calculations of the corresponding reflection coefficient, including the effect of whistler radiation. It is shown that a sharp longitudinal density drop causes a nearly complete reflection of the RLH wave. The longitudinal wavelength of the excited whistlers is much greater than that of the RLH wave, and, as a result, only a small fraction of the RLH wave energy is transferred to the whistlers.
Frank, Scott D; Collis, Jon M; Odom, Robert I
2015-06-01
Oceanic T-waves are earthquake signals that originate when elastic waves interact with the fluid-elastic interface at the ocean bottom and are converted to acoustic waves in the ocean. These waves propagate long distances in the Sound Fixing and Ranging (SOFAR) channel and tend to be the largest observed arrivals from seismic events. Thus, an understanding of their generation is important for event detection, localization, and source-type discrimination. Recently benchmarked seismic self-starting fields are used to generate elastic parabolic equation solutions that demonstrate generation and propagation of oceanic T-waves in range-dependent underwater acoustic environments. Both downward sloping and abyssal ocean range-dependent environments are considered, and results demonstrate conversion of elastic waves into water-borne oceanic T-waves. Examples demonstrating long-range broadband T-wave propagation in range-dependent environments are shown. These results confirm that elastic parabolic equation solutions are valuable for characterization of the relationships between T-wave propagation and variations in range-dependent bathymetry or elastic material parameters, as well as for modeling T-wave receptions at hydrophone arrays or coastal receiving stations. PMID:26093440
NASA Astrophysics Data System (ADS)
Peralta, J.; Imamura, T.; Read, P. L.; Luz, D.; Piccialli, A.; López-Valverde, M. A.
2014-07-01
This paper is the second in a two-part study devoted to developing tools for a systematic classification of the wide variety of atmospheric waves expected on slowly rotating planets with atmospheric superrotation. Starting with the primitive equations for a cyclostrophic regime, we have deduced the analytical solution for the possible waves, simultaneously including the effect of the metric terms for the centrifugal force and the meridional shear of the background wind. In those cases where the conditions for the method of the multiple scales in height are met, these wave solutions are also valid when vertical shear of the background wind is present. A total of six types of waves have been found and their properties were characterized in terms of the corresponding dispersion relations and wave structures. In this second part, we study the waves' solutions when several atmospheric approximations are applied: Lamb, surface, and centrifugal waves. Lamb and surface waves are found to be quite similar to those in a geostrophic regime. By contrast, centrifugal waves turn out to be a special case of Rossby waves that arise in atmospheres in cyclostrophic balance. Finally, we use our results to identify the nature of the waves behind atmospheric periodicities found in polar and lower latitudes of Venus's atmosphere.
Peralta, J.; López-Valverde, M. A.; Imamura, T.; Read, P. L.; Luz, D.; Piccialli, A.
2014-07-01
This paper is the second in a two-part study devoted to developing tools for a systematic classification of the wide variety of atmospheric waves expected on slowly rotating planets with atmospheric superrotation. Starting with the primitive equations for a cyclostrophic regime, we have deduced the analytical solution for the possible waves, simultaneously including the effect of the metric terms for the centrifugal force and the meridional shear of the background wind. In those cases where the conditions for the method of the multiple scales in height are met, these wave solutions are also valid when vertical shear of the background wind is present. A total of six types of waves have been found and their properties were characterized in terms of the corresponding dispersion relations and wave structures. In this second part, we study the waves' solutions when several atmospheric approximations are applied: Lamb, surface, and centrifugal waves. Lamb and surface waves are found to be quite similar to those in a geostrophic regime. By contrast, centrifugal waves turn out to be a special case of Rossby waves that arise in atmospheres in cyclostrophic balance. Finally, we use our results to identify the nature of the waves behind atmospheric periodicities found in polar and lower latitudes of Venus's atmosphere.
Nonlinear localized dust acoustic waves in a charge varying dusty plasma with nonthermal ions
Tribeche, Mouloud; Amour, Rabia
2007-10-15
A numerical investigation is presented to show the existence, formation, and possible realization of large-amplitude dust acoustic (DA) solitary waves in a charge varying dusty plasma with nonthermal ions. These nonlinear localized structures are self-consistent solutions of the collisionless Vlasov equation with a population of fast particles. The spatial patterns of the variable charge DA solitary wave are significantly modified by the nonthermal effects. The results complement and provide new insights into previously published results on this problem.
AdS waves as exact solutions to quadratic gravity
Guellue, Ibrahim; Sisman, Tahsin Cagri; Tekin, Bayram; Guerses, Metin
2011-04-15
We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane-fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity. A subset of the solutions change the asymptotic structure of the anti-de Sitter space due to their logarithmic behavior.
NASA Technical Reports Server (NTRS)
Xu, Jian-Jun
1989-01-01
The complicated dendritic structure of a growing needle crystal is studied on the basis of global interfacial wave theory. The local dispersion relation for normal modes is derived in a paraboloidal coordinate system using the multiple-variable-expansion method. It is shown that the global solution in a dendrite growth process incorporates the morphological instability factor and the traveling wave factor.
Nonlinear progressive acoustic-gravity waves: Exact solutions
NASA Astrophysics Data System (ADS)
Godin, Oleg
2013-04-01
We consider finite-amplitude mechanical waves in an inhomogeneous, compressible fluid in a uniform gravity field. The fluid is assumed to be inviscid, and wave motion is considered as an adiabatic thermodynamic process. The fluid either occupies an unbounded domain or has free and/or rigid boundaries. Wave motion is described by the momentum, continuity, and state equations in Lagrangian coordinates. We consider generic inhomogeneous fluids; no specific assumptions are made regarding the equation of state or spatial variations of the mass density or the sound speed in the absence of waves. The density and the sound speed are piece-wise continuous functions of position. The discontinuities represent fluid-fluid interfaces, such as the air-sea interface. Following a recent work on linear acoustic-gravity waves [O. A. Godin, Incompressible wave motion of compressible fluids, Phys. Rev. Lett., 108, 194501 (2012)], here we investigate a particular class of non-linear wave motions in fluids, in which pressure remains constant in each moving fluid parcel. Exact, analytic solutions of the non-linear hydrodynamics equations are obtained for two distinct scenarios. In the first scenario, the fluid is either unbounded or has a free surface. In the latter case, the exact analytic solution can be interpreted as a progressive surface wave. In the second scenario, the fluid has a free surface and a sloping, plane rigid boundary. Then the exact analytic solution represents an edge wave propagating horizontally along the rigid boundary. In both scenarios, the flow field associated with the finite-amplitude waves is rotational. When the sound speed tends to infinity, our results reduce to well-known finite-amplitude waves in incompressible fluids. In another limit, when the wave amplitude tends to zero, the exact solutions reduce to known results for linear waves in compressible fluids. The possibility of extending the theory to rotating fluids and fluids with a shearing background
NASA Astrophysics Data System (ADS)
Wang, Ying; Guo, Yunxi
2016-07-01
In this paper, we developed, for the first time, the exact expressions of several periodic travelling wave solutions and a solitary wave solution for a shallow water wave model of moderate amplitude. Then, we present the existence theorem of the global weak solutions. Finally, we prove the stability of solution in L1(R) space for the Cauchy problem of the equation.
Localization of wave packets in one-dimensional random potentials
NASA Astrophysics Data System (ADS)
Valdes, Juan Pablo Ramírez; Wellens, Thomas
2016-06-01
We study the expansion of an initially strongly confined wave packet in a one-dimensional weak random potential with short correlation length. At long times, the expansion of the wave packet comes to a halt due to destructive interferences leading to Anderson localization. We develop an analytical description for the disorder-averaged localized density profile. For this purpose, we employ the diagrammatic method of Berezinskii which we extend to the case of wave packets, present an analytical expression of the Lyapunov exponent which is valid for small as well as for high energies, and, finally, develop a self-consistent Born approximation in order to analytically calculate the energy distribution of our wave packet. By comparison with numerical simulations, we show that our theory describes well the complete localized density profile, not only in the tails but also in the center.
Full-Wave Solution Methods Using Gaussian Wavelet Basis
NASA Astrophysics Data System (ADS)
Smithe, David; Phillips, Cynthia K.; Pletzer, Alex
2004-11-01
We report on progress on work(1) toward practical use, in full-wave solution techniques, of Gaussian wavelet basis sets, in Gabor and Morlet wavelet expansions. Emphasis is on: a) tabulation of the difficult parallel-wave-number-part of the integration, including the cyclotron phase integral, and b) practical management of the complex Bessel function arguments of the perpendicular wave-number part. We also begin the process of optimizing the full-wave solution methods to take advantage of the greater matrix sparseness available in the each approach. (1)Wavelet and Gabor Transforms with Application to RF Heating Codes, A. Pletzer, C. K. Phillips, and D. N. Smithe, RF Power in Plasmas, 15th Topical Conference on Radio Frequency Power in Plasmas, May 19-21, 2003, [AIP, NY, 2003] pg. 503
Using time-reversal to generate generalized transversely localized transient waves (X-waves).
Walker, S C
2009-03-01
In the traditional approach to X-waves, the X-wave field is synthesized from a superposition of solutions to the homogenous wave equation (in three-dimensions) without regard to boundary conditions. As a consequence the synthesized solution is acausal. Here, it is shown that the solution to the inhomogenous scalar wave equation for the acoustic field from a supersonic source distribution consistent with the radiation condition, i.e., a Mach front, defines a causal X-wave. Using the connection between X-waves and a physical source, it is shown that an X-wave can be generated from a planar aperture using time-reversal. By appealing to the demonstrated self-adaptivity of time-reversal processes, the method should allow for the generation of X-waves in arbitrary (inhomogenous) media. Typically, the generation of approximate acoustic X-waves from a planar aperture is achieved using a complicated annular transducer arrangement. Here, the time-reversal method for the generation of approximate acoustic X-waves is experimentally proven using a line transducer array in two-dimensional geometry in free space. PMID:19275313
Spectral solution of acoustic wave-propagation problems
NASA Technical Reports Server (NTRS)
Kopriva, David A.
1990-01-01
The Chebyshev spectral collocation solution of acoustic wave propagation problems is considered. It is shown that the phase errors decay exponentially fast and that the number of points per wavelength is not sufficient to estimate the phase accuracy. Applications include linear propagation of a sinusoidal acoustic wavetrain in two space dimensions, and the interaction of a sound wave with the bow shock formed by placing a cylinder in a uniform Mach 4 supersonic free stream.
Peralta, J.; López-Valverde, M. A.; Imamura, T.; Read, P. L.; Luz, D.; Piccialli, A.
2014-07-01
This paper is the first of a two-part study devoted to developing tools for a systematic classification of the wide variety of atmospheric waves expected on slowly rotating planets with atmospheric superrotation. Starting with the primitive equations for a cyclostrophic regime, we have deduced the analytical solution for the possible waves, simultaneously including the effect of the metric terms for the centrifugal force and the meridional shear of the background wind. In those cases when the conditions for the method of the multiple scales in height are met, these wave solutions are also valid when vertical shear of the background wind is present. A total of six types of waves have been found and their properties were characterized in terms of the corresponding dispersion relations and wave structures. In this first part, only waves that are direct solutions of the generic dispersion relation are studied—acoustic and inertia-gravity waves. Concerning inertia-gravity waves, we found that in the cases of short horizontal wavelengths, null background wind, or propagation in the equatorial region, only pure gravity waves are possible, while for the limit of large horizontal wavelengths and/or null static stability, the waves are inertial. The correspondence between classical atmospheric approximations and wave filtering has been examined too, and we carried out a classification of the mesoscale waves found in the clouds of Venus at different vertical levels of its atmosphere. Finally, the classification of waves in exoplanets is discussed and we provide a list of possible candidates with cyclostrophic regimes.
Engineering wave localization in a fractal waveguide network
NASA Astrophysics Data System (ADS)
Pal, Biplab; Patra, Pinaki; Saha, Jyoti Prasad; Chakrabarti, Arunava
2013-02-01
We present an exact analytical method of engineering the localization of classical waves in a fractal waveguide network. It is shown that a countable infinity of localized eigenmodes with a multitude of localization lengths can exist in a Vicsek fractal geometry built with diamond-shaped monomode waveguides as the “unit cells.” The family of localized modes forms clusters of increasing size. The length scale at which the onset of localization for each mode takes place can be engineered at will, following a well-defined prescription developed within the framework of a real space renormalization group. The scheme leads to an exact evaluation of the wave vector for every such localized state, a task that is nontrivial, if not impossible for any random or deterministically disordered waveguide network.
Nonminimally coupled gravitational and electromagnetic fields: pp-wave solutions
Dereli, Tekin; Sert, Oezcan
2011-03-15
We give the Lagrangian formulation of a generic nonminimally extended Einstein-Maxwell theory with an action that is linear in the curvature and quadratic in the electromagnetic field. We derive the coupled field equations by a first-order variational principle using the method of Lagrange multipliers. We look for solutions describing plane-fronted Einstein-Maxwell waves with parallel rays. We give a family of exact pp-wave solutions associated with a partially massless spin-2 photon and a partially massive spin-2 graviton.
PML solution of longitudinal wave propagation in heterogeneous media
NASA Astrophysics Data System (ADS)
Farzanian, M.; Arbabi, Freydoon; Pak, Ronald
2016-06-01
This paper describes the development of a model for unbounded heterogeneous domains with radiation damping produced by an unphysical wave absorbing layer. The Perfectly Matched Layer (PML) approach is used along with a displacement-based finite element. The heterogeneous model is validated using the closed-form solution of a benchmark problem: a free rod with two-part modulus subjected to a specified time history. Both elastically supported and unsupported semi-infinite rods with different degrees of inhomogeneity and loading are considered. Numerical results illustrate the effects of inhomogeneity on the response and are compared with those for equivalent homogeneous domains. The effects of characteristic features of the inhomogeneous problem, presence of local maxima and cut-off frequency are determined. A degenerate case of a homogeneous semi-infinite rod on elastic foundations is produced by tending the magnitude of the foundation stiffness to zero. The response of the latter is compared with that of a free rod. The importance of proper selection of the PML parameters to highly accurate and efficient results is demonstrated by example problems.
Dynamical localization of matter waves in optomechanics
NASA Astrophysics Data System (ADS)
Ayub, Muhammad; Ammar Yasir, Kashif; Saif, Farhan
2014-11-01
We explain dynamical localization of Bose-Einstein condensate (BEC) in optomechanics both in position and in momentum space. The experimentally realizable optomechanical system is a Fabry-Pérot cavity with one moving end mirror driven by a single mode standing field. In our study we analyze variations in modulation strength and effective Planck’s constant. Keeping in mind present day experimental advancements, we suggest parameteric values to observe the phenomenon in the laboratory.
Spiral wave chimeras in locally coupled oscillator systems
NASA Astrophysics Data System (ADS)
Li, Bing-Wei; Dierckx, Hans
2016-02-01
The recently discovered chimera state involves the coexistence of synchronized and desynchronized states for a group of identical oscillators. In this work, we show the existence of (inwardly) rotating spiral wave chimeras in the three-component reaction-diffusion systems where each element is locally coupled by diffusion. A transition from spiral waves with the smooth core to spiral wave chimeras is found as we change the local dynamics of the system or as we gradually increase the diffusion coefficient of the activator. Our findings on the spiral wave chimera in the reaction-diffusion systems suggest that spiral chimera states may be found in chemical and biological systems that can be modeled by a large population of oscillators indirectly coupled via a diffusive environment.
Zabolotskii, A. A.
2009-11-15
An integrable Yajima-Oikawa system is solved in the case of a finite density, which corresponds to a slowly varying (long-wavelength) wave with finite amplitude at infinity and a localized fast-oscillating (short-wavelength) wave. Application of the results to spinor Bose-Einstein condensates and other physical systems is discussed.
Local interaction modeling for acousto-ultrasonic wave propagation
NASA Astrophysics Data System (ADS)
Lee, B. C.; Staszewski, Wieslaw J.
2002-07-01
Damage detection in metallic structures has been the subject of many investigations. Recent developments have shown applications of acousto-ultrasonic and Lamb wave testing. Lamb wave inspection is based on theory of longitudinal waves propagating in plates. In general, the principles of acousto-ultrasonic and Lamb wave inspection techniques are similar. Damage in a structure is identified by a change in the output signal. Previous studies show that even simple input signals can lead to complex output waves, which are difficult to interpret. It is clear that knowledge and understanding of wave propagation in analyzed structures can ease the interpretation of damage detection results. The paper reports an application of local interaction modeling of acousto-ultrasonic waves in metallic structures. The focus of the analysis is on one-dimensional interactions between different material boundaries. This includes modeling of acousto-ultrasonic waves in piezoceramic, adhesive glue and copper in an actuator/sensor configuration. The study also involves experimental validation of the simulation results. The method shows the potential for modeling of acousto-ultrasonic waves in complex media for damage detection applications.
Weak localization with nonlinear bosonic matter waves
Hartmann, Timo; Michl, Josef; Petitjean, Cyril; Wellens, Thomas; Urbina, Juan-Diego; Richter, Klaus; Schlagheck, Peter
2012-08-15
We investigate the coherent propagation of dilute atomic Bose-Einstein condensates through irregularly shaped billiard geometries that are attached to uniform incoming and outgoing waveguides. Using the mean-field description based on the nonlinear Gross-Pitaevskii equation, we develop a diagrammatic theory for the self-consistent stationary scattering state of the interacting condensate, which is combined with the semiclassical representation of the single-particle Green function in terms of chaotic classical trajectories within the billiard. This analytical approach predicts a universal dephasing of weak localization in the presence of a small interaction strength between the atoms, which is found to be in good agreement with the numerically computed reflection and transmission probabilities of the propagating condensate. The numerical simulation of this quasi-stationary scattering process indicates that this interaction-induced dephasing mechanism may give rise to a signature of weak antilocalization, which we attribute to the influence of non-universal short-path contributions. - Highlights: Black-Right-Pointing-Pointer Numerical simulation of scattering of Bose-Einstein condensate through billiards. Black-Right-Pointing-Pointer Novel analytical semiclassical theory for nonlinear coherent scattering. Black-Right-Pointing-Pointer Inversion of weak localization due to mean-field interaction within the condensate. Black-Right-Pointing-Pointer Relevance of non-universal short-path contributions.
Nonlinear Guided Wave Mixing for Localized Material State Characterization
NASA Astrophysics Data System (ADS)
Lissenden, Cliff J.; Liu, Yang; Chillara, Vamshi K.; Choi, Gloria; Cho, Hwanjeong
Material state characterization methods sensitive to incipient damage provide new opportunities for managing the life cycle of structures. Finite element simulations of ultrasonic guided waves show the potential of nonlinear wave mixing to detect localized degradation invisible to both linear elastic stress-strain response and the eye. Correlation of material degradation to the generation of higher harmonics or combinational harmonics makes estimation of remaining life possible from material state data early in the service life.
Localized finite-amplitude disturbances and selection of solitary waves
Kliakhandler; Porubov; Velarde
2000-10-01
It turns out that evolution of localized finite-amplitude disturbances in perturbed KdV equation is qualitatively different compared with conventional small-amplitude initial conditions. Namely, relatively fast solitary waves, with one and the same amplitude and velocity, are formed ahead of conventional chaotic-like irregular structures. The amplitude and velocity of the waves, obtained from the asymptotic theory, are in excellent agreement with numerics. PMID:11089043
NASA Astrophysics Data System (ADS)
Hoeke, Ron; Hemer, Mark; Contardo, Stephanie; Symonds, Graham; Mcinnes, Kathy
2016-04-01
As demonstrated by the Australian Wave Energy Atlas (AWavEA), the southern and western margins of the country possess considerable wave energy resources. The Australia Government has made notable investments in pre-commercial wave energy developments in these areas, however little is known about how this technology may impact local wave climate and subsequently affect neighbouring coastal environments, e.g. altering sediment transport, causing shoreline erosion or accretion. In this study, a network of in-situ wave measurement devices have been deployed surrounding the 3 wave energy converters of the Carnegie Wave Energy Limited's Perth Wave Energy Project. This data is being used to develop, calibrate and validate numerical simulations of the project site. Early stage results will be presented and potential simulation strategies for scaling-up the findings to larger arrays of wave energy converters will be discussed. The intended project outcomes are to establish zones of impact defined in terms of changes in local wave energy spectra and to initiate best practice guidelines for the establishment of wave energy conversion sites.
Spin-wave localization in tangentially magnetized films
NASA Astrophysics Data System (ADS)
Tartakovskaya, Elena V.; Pardavi-Horvath, Martha; McMichael, Robert D.
2016-06-01
We present an analytical description of localized spin-wave modes that form in a parabolic field minimum in a thin ferromagnetic film. Mode profiles proportional to Hermite functions are eigenfuctions of the applied field and exchange parts of the equations of motion, and also provide a basis for numerical approximation of magnetostatic interactions. We find that the spin-wave modes are roughly equally spaced in frequency and have roughly equal coupling to a uniform driving field. The calculated mode frequencies and corresponding profiles of localized spin-wave modes are in good agreement with micromagnetic modeling and previously published experimental results on multiple resonances from a series of localized modes detected by ferromagnetic resonance force microscopy.
Stokes waves revisited: Exact solutions in the asymptotic limit
NASA Astrophysics Data System (ADS)
Davies, Megan; Chattopadhyay, Amit K.
2016-03-01
The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic "secular variation" in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n -ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.
Arterial compliance probe for local blood pulse wave velocity measurement.
Nabeel, P M; Joseph, Jayaraj; Sivaprakasam, Mohanasankar
2015-08-01
Arterial compliance and vessel wall dynamics are significant in vascular diagnosis. We present the design of arterial compliance probes for measurement of local pulse wave velocity (PWV). Two designs of compliance probe are discussed, viz (a) a magnetic plethysmograph (MPG) based probe, and (b) a photoplethysmograph (PPG) based probe. The ability of the local PWV probes to consistently capture carotid blood pulse waves is verified by in-vivo trials on few volunteers. The probes could reliably perform repeatable measurements of local PWV from carotid artery along small artery sections less than 20 mm. Further, correlation between the measured values of local PWV using probes and various measures of blood pressure (BP) was also investigated. The study indicates that such arterial compliance probes have strong potential in cuff less BP monitoring. PMID:26737589
Impact Localization Using Lamb Wave and Spiral FSAT
NASA Astrophysics Data System (ADS)
Rimal, Nischal
Wear and tear exists in almost every physical infrastructure. Modern day science has something in its pocket to early detect such wear and tear known as Structural Health Monitoring (SHM). SHM features a key role in tracking a structural failure and could prevent loss of human lives and money. The size and prices of presently available defect detection devices make them not suitable for on-site SHM. The exploitation of directional transducers and Lamb wave propagation for SHM has been proposed. The basis of the project was to develop an accurate localization algorithm and implementation of Lamb waves to detect the crack present in the plate like structures. In regards, the use of Frequency Steerable Acoustic Transducer (FSAT) was studied. The theory governing the propagation of Lamb wave was reviewed. The derivation of the equations and dispersion curve of Lamb waves are included. FSAT was studied from both theoretical and application view of point. The experiments carried out give us better understanding of the FSAT excitation and Lamb wave generation and detection. The Lamb wave generation and crack localization algorithm was constructed and with the proposed algorithm, simulated impacts are detected.
Rational solitary wave and rogue wave solutions in coupled defocusing Hirota equation
NASA Astrophysics Data System (ADS)
Huang, Xin
2016-06-01
We derive and study a general rational solution of a coupled defocusing Hirota equation which can be used to describe evolution of light in a two-mode fiber with defocusing Kerr effect and some certain high-order effects. We find some new excitation patterns in the model, such as M-shaped soliton, W-shaped soliton, anti-eye-shaped rogue wave and four-petaled flower rogue wave. The results are compared with the solutions obtained in other coupled systems like vector nonlinear Schrödinger equation, coupled focusing Hirota and Sasa-Satsuma equations. We explain the new characters by modulational instability properties. This further indicates that rational solution does not necessarily correspond to rogue wave excitation dynamics and the quantitative relation between nonlinear excitations and modulational instability should exist.
Localization Problem in the 5d Standing Wave Braneworld
NASA Astrophysics Data System (ADS)
Gogberashvili, Merab; Midodashvili, Pavle; Midodashvili, Levan
2012-10-01
We investigate the problem of pure gravitational localization of matter fields within the 5D standing wave braneworld generated by gravity coupled to a phantom-like scalar field. We show that in the case of increasing warp factor there exist normalizable zero modes of spin-0, -1/2, -1 and -2 fields on the brane.
Evaluation of localized corrosion of zirconium in acidic chloride solutions
Fahey, J.; Holmes, D.; Yau, T.L.
1997-01-01
Zirconium is prone to localized corrosion in acidic chloride (Cl{sup {minus}}) solutions contaminated by oxidizing ions, such as ferric or cupric ions. This tendency can be reduced by ensuring that the zirconium surface is clean and smooth. The effect of surface condition on localized corrosion of zirconium in acidic chloride solutions was predicted using potentiodynamic polarization scans. Predictions were confirmed by mass-loss tests on various combinations of surface finish and acid concentrations. A real-time indication of localized corrosion was derived by monitoring electrochemical noise produced between two similar electrodes immersed in an acidic chloride solution. Electrochemical noise monitoring correlated well with predictions from the potentiodynamic polarization and mass-loss experiments. Electrochemical noise results showed a more anodic potential caused by ferric ion (Fe{sup 3+}) contamination might be necessary for localized corrosion but that it was not a sufficient condition. A clean zirconium surface reduced localized corrosion of zirconium.
Exact traveling wave solutions for system of nonlinear evolution equations.
Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H
2016-01-01
In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis. PMID:27347461
Comparison of gravitational wave detector network sky localization approximations
NASA Astrophysics Data System (ADS)
Grover, K.; Fairhurst, S.; Farr, B. F.; Mandel, I.; Rodriguez, C.; Sidery, T.; Vecchio, A.
2014-02-01
Gravitational waves emitted during compact binary coalescences are a promising source for gravitational-wave detector networks. The accuracy with which the location of the source on the sky can be inferred from gravitational-wave data is a limiting factor for several potential scientific goals of gravitational-wave astronomy, including multimessenger observations. Various methods have been used to estimate the ability of a proposed network to localize sources. Here we compare two techniques for predicting the uncertainty of sky localization—timing triangulation and the Fisher information matrix approximations—with Bayesian inference on the full, coherent data set. We find that timing triangulation alone tends to overestimate the uncertainty in sky localization by a median factor of 4 for a set of signals from nonspinning compact object binaries ranging up to a total mass of 20M⊙, and the overestimation increases with the mass of the system. We find that average predictions can be brought to better agreement by the inclusion of phase consistency information in timing-triangulation techniques. However, even after corrections, these techniques can yield significantly different results to the full analysis on specific mock signals. Thus, while the approximate techniques may be useful in providing rapid, large scale estimates of network localization capability, the fully coherent Bayesian analysis gives more robust results for individual signals, particularly in the presence of detector noise.
Mahillo-Isla, R; Gonźalez-Morales, M J; Dehesa-Martínez, C
2011-06-01
The slowly varying envelope approximation is applied to the radiation problems of the Helmholtz equation with a planar single-layer and dipolar sources. The analyses of such problems provide procedures to recover solutions of the Helmholtz equation based on the evaluation of solutions of the parabolic wave equation at a given plane. Furthermore, the conditions that must be fulfilled to apply each procedure are also discussed. The relations to previous work are given as well. PMID:21643384
Construction of rogue wave and lump solutions for nonlinear evolution equations
NASA Astrophysics Data System (ADS)
Lü, Zhuosheng; Chen, Yinnan
2015-07-01
Based on symbolic computation and an ansatz, we present a constructive algorithm to seek rogue wave and lump solutions for nonlinear evolution equations. As illustrative examples, we consider the potential-YTSF equation and a variable coefficient KP equation, and obtain nonsingular rational solutions of the two equations. The solutions can be rogue wave or lump solutions under different parameter conditions. We also present graphic illustration of some special solutions which would help better understand the evolution of solution waves.
ERIC Educational Resources Information Center
Collins, Mike
2013-01-01
The notion of localism and decentralization in national policy has come increasingly to the fore in recent years. The national succession planning strategy for headteachers in England introduced by the National College for School Leadership promoted "local solutions for a national challenge". This article deals with some aspects of the…
Accelerating Airy-Gauss-Kummer localized wave packets
NASA Astrophysics Data System (ADS)
Zhong, Wei-Ping; Belić, Milivoj; Zhang, Yiqi; Huang, Tingwen
2014-01-01
A general approach to generating three-dimensional nondiffracting spatiotemporal solutions of the linear Schrödinger equation with an Airy-beam time-dependence is reported. A class of accelerating optical pulses with the structure of Airy-Gauss-Kummer vortex beams is obtained. Our results demonstrate that the optical field contributions to the Airy-Gauss-Kummer accelerating optical wave packets of the cylindrical symmetry can be characterized by the radial and angular mode numbers.
Generalization of the Euler-type solution to the wave equation
NASA Astrophysics Data System (ADS)
Borisov, Victor V.
2001-08-01
Generalization of the Euler-type solution to the wave equation is given. Peculiarities of the space-time structure of obtained waves are considered. For some particular cases interpretation of these waves as `subliminal' and `superluminal' is discussed. The possibility of description of electromagnetic waves by means of the scalar solutions is shown.
NASA Astrophysics Data System (ADS)
Ali Akbar, M.; Norhashidah, Hj. Mohd. Ali; E. M. E., Zayed
2012-02-01
In this article, we construct abundant exact traveling wave solutions involving free parameters to the generalized Bretherton equation via the improved (G'/G)-expansion method. The traveling wave solutions are presented in terms of the trigonometric, the hyperbolic, and rational functions. When the parameters take special values, the solitary waves are derived from the traveling waves.
NASA Astrophysics Data System (ADS)
Li, Long-Xing; Liu, Jun; Dai, Zheng-De; Liu, Ren-Lang
2014-09-01
In this work, the rational homoclinic solution (rogue wave solution) can be obtained via the classical homoclinic solution for the nonlinear Schrödinger (NLS) equation and the coupled nonlinear Schrödinger (CNLS) equation, respectively. This is a new way for generating rogue wave comparing with direct constructing method and Darboux dressing technique
Solitary and periodic wave solutions of the Majda-Biello system
NASA Astrophysics Data System (ADS)
Adem, Abdullahi Rashid
2016-05-01
In this paper, we present the exact solutions of the Majda-Biello system. This system describes the nonlinear interaction of long-wavelength equatorial Rossby waves and barotropic Rossby waves with a substantial midlatitude projection, in the presence of suitable horizontally and vertically sheared zonal mean flows. The methods used to construct the exact solutions are the Kudryashov method and Jacobi elliptic function method. These two methods yield solitary wave solutions and periodic wave solutions.
Localized spin wave modes in parabolic field wells
NASA Astrophysics Data System (ADS)
McMichael, Robert; Tartakovskaya, Elena; Pardavi-Horvath, Martha
We describe spin wave modes trapped in parabolic-profile field wells. Trapped spin waves can be used as local probes of magnetic properties with resolution down to 100 nm in ferromagnetic resonance force microscopy. Localized modes have been shown to form around field minima from a number of sources, including stray fields from magnetic probe tips and inhomogeneous magnetostatic fields near film edges. Here, we address the most basic trap, which is a parabolic minimum in the applied field. The magnetic eigenmodes in this trap are tractable enough to serve as approximations in more realistic situations. For a parabolic field, we select basis mode profiles proportional to Hermite functions because they are eigenfuctions of the applied field and exchange parts of the equations of motion. Additionally, we find that these Hermite modes are approximate eigenfunctions of magnetostatic interactions, showing good agreement with micromagnetic calculations. More precise agreement is achieved by diagonalizing the equations of motion using only a few modes.
Plasmonic-based Imaging of Local Square Wave Voltammetry
Shan, Xiaonan; Wang, Shaopeng; Wang, Wei; Tao, Nongjian
2012-01-01
Square wave voltammetry (SWV) is widely used in electrochemical analysis and sensors because of its high sensitivity and efficient rejection of background current, but SWV by conventional electrochemical detection method does not provide spatial resolution. We report here a plasmonic method to image local SWV, which opens the door for analyzing heterogeneous electrochemical reactions and for high throughput detections of microarrays. We describe the basic principle, validate the principle by comparing the plasmonic-based SWV with those obtained with the conventional method, and demonstrate imaging capability for local electrochemical analysis. PMID:21793508
Localized wave generation with a standard underwater array
Lewis, D.K.; Chambers, D.H.; Mullin, C.S.; Ziolkowski, R.W.
1998-02-17
Recent work at the Navy Underwater Weapons Center Keyport test facility showed that existing Navy field equipment could generate Localized Waves. Results of angular scans show a narrowed beam pattern and lowered side lobes relative to standard beams. Results of axial range scans show evidence or an extended near field. Frequency analysis shows that the main beam is a decade wide while the surviving grating lobes are narrow band width, high frequency.
Numerical solutions of acoustic wave propagation problems using Euler computations
NASA Technical Reports Server (NTRS)
Hariharan, S. I.
1984-01-01
This paper reports solution procedures for problems arising from the study of engine inlet wave propagation. The first problem is the study of sound waves radiated from cylindrical inlets. The second one is a quasi-one-dimensional problem to study the effect of nonlinearities and the third one is the study of nonlinearities in two dimensions. In all three problems Euler computations are done with a fourth-order explicit scheme. For the first problem results are shown in agreement with experimental data and for the second problem comparisons are made with an existing asymptotic theory. The third problem is part of an ongoing work and preliminary results are presented for this case.
Nonlinear wave dynamics near phase transition in PT-symmetric localized potentials
NASA Astrophysics Data System (ADS)
Nixon, Sean; Yang, Jianke
2016-09-01
Nonlinear wave propagation in parity-time symmetric localized potentials is investigated analytically near a phase-transition point where a pair of real eigenvalues of the potential coalesce and bifurcate into the complex plane. Necessary conditions for a phase transition to occur are derived based on a generalization of the Krein signature. Using the multi-scale perturbation analysis, a reduced nonlinear ordinary differential equation (ODE) is derived for the amplitude of localized solutions near phase transition. Above the phase transition, this ODE predicts a family of stable solitons not bifurcating from linear (infinitesimal) modes under a certain sign of nonlinearity. In addition, it predicts periodically-oscillating nonlinear modes away from solitons. Under the opposite sign of nonlinearity, it predicts unbounded growth of solutions. Below the phase transition, solution dynamics is predicted as well. All analytical results are compared to direct computations of the full system and good agreement is observed.
Traveling wave solution of the Reggeon field theory
Peschanski, Robi
2009-05-15
We identify the nonlinear evolution equation in impact-parameter space for the 'Supercritical Pomeron' in Reggeon field theory as a two-dimensional stochastic Fisher-Kolmogorov-Petrovski-Piscounov equation. It exactly preserves unitarity and leads in its radial form to a high-energy traveling wave solution corresponding to a 'universal' behavior of the impact-parameter front profile of the elastic amplitude; its rapidity dependence and form depend only on one parameter, the noise strength, independently of the initial conditions and of the nonlinear terms restoring unitarity. Theoretical predictions are presented for the three typical distinct regimes corresponding to zero, weak, and strong noise.
Localization of gravitational wave sources with networks of advanced detectors
Klimenko, S.; Mitselmakher, G.; Pankow, C.; Vedovato, G.; Drago, M.; Prodi, G.; Mazzolo, G.; Salemi, F.; Re, V.; Yakushin, I.
2011-05-15
Coincident observations with gravitational wave (GW) detectors and other astronomical instruments are among the main objectives of the experiments with the network of LIGO, Virgo, and GEO detectors. They will become a necessary part of the future GW astronomy as the next generation of advanced detectors comes online. The success of such joint observations directly depends on the source localization capabilities of the GW detectors. In this paper we present studies of the sky localization of transient GW sources with the future advanced detector networks and describe their fundamental properties. By reconstructing sky coordinates of ad hoc signals injected into simulated detector noise, we study the accuracy of the source localization and its dependence on the strength of injected signals, waveforms, and network configurations.
NASA Astrophysics Data System (ADS)
Shen, Yanfeng; Cesnik, Carlos E. S.
2015-03-01
This paper presents a hybrid modeling technique for the efficient simulation of guided wave propagation and interaction with damage in composite structures. This hybrid approach uses a local finite element model (FEM) to compute the excitability of guided waves generated by piezoelectric transducers, while the global domain wave propagation, wave-damage interaction, and boundary reflections are modeled with the local interaction simulation approach (LISA). A small-size multi-physics FEM with non-reflective boundaries (NRB) was built to obtain the excitability information of guided waves generated by the transmitter. Frequency-domain harmonic analysis was carried out to obtain the solution for all the frequencies of interest. Fourier and inverse Fourier transform and frequency domain convolution techniques are used to obtain the time domain 3-D displacement field underneath the transmitter under an arbitrary excitation. This 3-D displacement field is then fed into the highly efficient time domain LISA simulation module to compute guided wave propagation, interaction with damage, and reflections at structural boundaries. The damping effect of composite materials was considered in the modified LISA formulation. The grids for complex structures were generated using commercial FEM preprocessors and converted to LISA connectivity format. Parallelization of the global LISA solution was achieved through Compute Unified Design Architecture (CUDA) running on Graphical Processing Unit (GPU). The multi-physics local FEM can reliably capture the detailed dimensions and local dynamics of the piezoelectric transducers. The global domain LISA can accurately solve the 3-D elastodynamic wave equations in a highly efficient manner. By combining the local FEM with global LISA, the efficient and accurate simulation of guided wave structural health monitoring procedure is achieved. Two numerical case studies are presented: (1) wave propagation in a unidirectional CFRP composite plate
A new class of solutions for interstellar magnetohydrodynamic shock waves
NASA Technical Reports Server (NTRS)
Roberge, W. G.; Draine, B. T.
1990-01-01
An analysis is presented of the equations of motion for steady MHD shock waves proopagating in interstellar clouds, for boundary conditions that preclude C shocks. In addition to J shocks, in which the neutral fluid component becomes subsonic at an adiabatic jump front, the equations admit a new class of solutions, called C-asterisk shocks, in which the transition to subsonic flow occurs continuously at a sonic point. Numerical methods are developed for computing the structure of J and C-asterisk shocks propagating in diffuse interstellar clouds. The effects of chemical, ionization, and recombination processes are included in this treatment. An alternative numerical method, which uses artificial viscosity to facilitate integration through sonic points, is analyzed and shown to be invalid. A set of exemplary solutions, computed for realistic shock parameters, shows that C-asterisk shocks occur for a broad range of conditions relevant to diffuse interstellar clouds.
A new class of solutions for interstellar magnetohydrodynamic shock waves
Roberge, W.G.; Draine, B.T. Princeton Univ. Observatory, NJ )
1990-02-01
An analysis is presented of the equations of motion for steady MHD shock waves propagating in interstellar clouds, for boundary conditions that preclude C shocks. In addition to J shocks, in which the neutral fluid component becomes subsonic at an adiabatic jump front, the equations admit a new class of solutions, called C-asterisk shocks, in which the transition to subsonic flow occurs continuously at a sonic point. Numerical methods are developed for computing the structure of J and C-asterisk shocks propagating in diffuse interstellar clouds. The effects of chemical, ionization, and recombination processes are included in this treatment. An alternative numerical method, which uses artificial viscosity to facilitate integration through sonic points, is analyzed and shown to be invalid. A set of exemplary solutions, computed for realistic shock parameters, shows that C-asterisk shocks occur for a broad range of conditions relevant to diffuse interstellar clouds. 27 refs.
Methods of localization of Lamb wave sources on thin plates
NASA Astrophysics Data System (ADS)
Turkaya, Semih; Toussaint, Renaud; Kvalheim Eriksen, Fredrik; Daniel, Guillaume; Grude Flekkøy, Eirik; Jørgen Måløy, Knut
2015-04-01
Signal localization techniques are ubiquitous in both industry and academic communities. We propose a new localization method on plates which is based on energy amplitude attenuation and inverted source amplitude comparison. This inversion is tested on synthetic data using Lamb wave propagation direct model and on experimental dataset (recorded with 4 Brüel & Kjær Type 4374 miniature piezoelectric shock accelerometers (1-26 kHz frequency range)). We compare the performance of the technique to the classical source localization algorithms, arrival time localization, time reversal localization, localization based on energy amplitude. Furthermore, we measure and compare the accuracy of these techniques as function of sampling rate, dynamic range, geometry, Signal to Noise Ratio, and we show that this very versatile technique works better than classical ones over the sampling rates 100kHz - 1MHz. Experimental phase consists of a glass plate having dimensions of 80cmx40cm with a thickness of 1cm. Generated signals due to a wooden hammer hit or a steel ball hit are captured by sensors placed on the plate on different locations with the mentioned sensors. Numerical simulations are done using dispersive far field approximation of plate waves. Signals are generated using a hertzian loading over the plate. Using imaginary sources outside the plate boundaries the effect of reflections is also included. This proposed method, can be modified to be implemented on 3d environments, monitor industrial activities (e.g boreholes drilling/production activities) or natural brittle systems (e.g earthquakes, volcanoes, avalanches).
WATER CONSERVATION: LOCAL SOLUTIONS TO A GLOBAL PROBLEM
Water conservation issues are discussed. Local solutions to a global problem include changing old habits relating to the usage and abuse of water resources. While the suggested behavioral changes may not solve the world's pending water crisis, they may ease the impact of the l...
An analytical solution to separate P-waves and S-waves in the VSP wavefield
Amano, Hiroshi
1994-12-31
An analytical solution to separate P-waves and S-waves in the VSP wavefield is derived with combinations of the formal solution of a forward VSP modeling. Some practical applications of this method to synthetic seismograms and field data are investigated and evaluated. Little wave distortion is recognized and the weak wavefield masked by dominant wave trains can be extracted with this method. The decomposed wavefield is expressed in frequency-depth (f-z) domain as a linear combination of up to the third order differential of traces, which is approximated by trace difference sin the practical separation process. In general, five traces with single-component data are required in this process, but the same process is implemented with only three traces in the acoustic case. Two-trace extrapolation is applied to each edge of data gather in order to enhance the accuracy of trace difference. Since the formulas are developed in f-z domain, the influence of anelasticity is taken into account with simplicity and the calculation is carried out fast enough with the benefit of fast Fourier transform (FFT).
Unstable spiral waves and local Euclidean symmetry in a model of cardiac tissue
Marcotte, Christopher D.; Grigoriev, Roman O.
2015-06-15
This paper investigates the properties of unstable single-spiral wave solutions arising in the Karma model of two-dimensional cardiac tissue. In particular, we discuss how such solutions can be computed numerically on domains of arbitrary shape and study how their stability, rotational frequency, and spatial drift depend on the size of the domain as well as the position of the spiral core with respect to the boundaries. We also discuss how the breaking of local Euclidean symmetry due to finite size effects as well as the spatial discretization of the model is reflected in the structure and dynamics of spiral waves. This analysis allows identification of a self-sustaining process responsible for maintaining the state of spiral chaos featuring multiple interacting spirals.
Streamwise-Localized Solutions with natural 1-fold symmetry
NASA Astrophysics Data System (ADS)
Altmeyer, Sebastian; Willis, Ashley; Hof, Björn
2014-11-01
It has been proposed in recent years that turbulence is organized around unstable invariant solutions, which provide the building blocks of the chaotic dynamics. In direct numerical simulations of pipe flow we show that when imposing a minimal symmetry constraint (reflection in an axial plane only) the formation of turbulence can indeed be explained by dynamical systems concepts. The hypersurface separating laminar from turbulent motion, the edge of turbulence, is spanned by the stable manifolds of an exact invariant solution, a periodic orbit of a spatially localized structure. The turbulent states themselves (turbulent puffs in this case) are shown to arise in a bifurcation sequence from a related localized solution (the upper branch orbit). The rather complex bifurcation sequence involves secondary Hopf bifurcations, frequency locking and a period doubling cascade until eventually turbulent puffs arise. In addition we report preliminary results of the transition sequence for pipe flow without symmetry constraints.
Is wave-particle objectivity compatible with determinism and locality?
NASA Astrophysics Data System (ADS)
Ionicioiu, Radu; Jennewein, Thomas; Mann, Robert B.; Terno, Daniel R.
2014-09-01
Wave-particle duality, superposition and entanglement are among the most counterintuitive features of quantum theory. Their clash with our classical expectations motivated hidden-variable (HV) theories. With the emergence of quantum technologies, we can test experimentally the predictions of quantum theory versus HV theories and put strong restrictions on their key assumptions. Here, we study an entanglement-assisted version of the quantum delayed-choice experiment and show that the extension of HV to the controlling devices only exacerbates the contradiction. We compare HV theories that satisfy the conditions of objectivity (a property of photons being either particles or waves, but not both), determinism and local independence of hidden variables with quantum mechanics. Any two of the above conditions are compatible with it. The conflict becomes manifest when all three conditions are imposed and persists for any non-zero value of entanglement. We propose an experiment to test our conclusions.
Is wave-particle objectivity compatible with determinism and locality?
Ionicioiu, Radu; Jennewein, Thomas; Mann, Robert B; Terno, Daniel R
2014-01-01
Wave-particle duality, superposition and entanglement are among the most counterintuitive features of quantum theory. Their clash with our classical expectations motivated hidden-variable (HV) theories. With the emergence of quantum technologies, we can test experimentally the predictions of quantum theory versus HV theories and put strong restrictions on their key assumptions. Here, we study an entanglement-assisted version of the quantum delayed-choice experiment and show that the extension of HV to the controlling devices only exacerbates the contradiction. We compare HV theories that satisfy the conditions of objectivity (a property of photons being either particles or waves, but not both), determinism and local independence of hidden variables with quantum mechanics. Any two of the above conditions are compatible with it. The conflict becomes manifest when all three conditions are imposed and persists for any non-zero value of entanglement. We propose an experiment to test our conclusions. PMID:25256419
Plane wave holonomies in quantum gravity. II. A sine wave solution
NASA Astrophysics Data System (ADS)
Neville, Donald E.
2015-08-01
This paper constructs an approximate sinusoidal wave packet solution to the equations of canonical gravity. The theory uses holonomy-flux variables with support on a lattice (LHF =lattice-holonomy flux ). There is an SU(2) holonomy on each edge of the LHF simplex, and the goal is to study the behavior of these holonomies under the influence of a passing gravitational wave. The equations are solved in a small sine approximation: holonomies are expanded in powers of sines and terms beyond sin2 are dropped; also, fields vary slowly from vertex to vertex. The wave is unidirectional and linearly polarized. The Hilbert space is spanned by a set of coherent states tailored to the symmetry of the plane wave case. Fixing the spatial diffeomorphisms is equivalent to fixing the spatial interval between vertices of the loop quantum gravity lattice. This spacing can be chosen such that the eigenvalues of the triad operators are large, as required in the small sine limit, even though the holonomies are not large. Appendices compute the energy of the wave, estimate the lifetime of the coherent state packet, discuss circular polarization and coarse-graining, and determine the behavior of the spinors used in the U(N) SHO realization of LQG.
Rozmus, W.; Casanova, M.; Pesme, D.; Heron, A.; Adam, J. )
1992-03-01
The effect of ion sound wave (ISW) nonlinearities on the stimulated Brillouin scattering (SBS) in long plasmas is investigated within the framework of the Korteweg--de Vries--Maxwell equations. The nonlinear evolution of the driven ISW results in the localization of the ion density on a scale shorter than the wavelength ({lambda}{sub {ital s}}) of the resonant ISW satisfying SBS three-wave matching conditions. Since the transverse wave amplitudes vary on a much longer scale, a local--global modeling of SBS is proposed in which this scale separation is exploited. The local part of the procedure includes a solution to the damped KdV equation with periodic boundary conditions and driven by a constant amplitude ponderomotive force. In the global part of the analysis approximate solutions for the transverse waves in long plasmas are constructed using the results from the local part. Particle-in-cell simulations have been performed in order to investigate the importance of kinetic effects for the local model. Numerical results obtained from the solutions to the KdV--Maxwell equations are well approximated by the local--global modeling. They are also compared with the results of a harmonic decomposition approximation.
Christov, C.I.; Maugin, G.A.
1995-01-01
We consider the nonlinear system of equations built up from a generalized Boussinesq equation coupled with a wave equation which is a model for the one-dimensional dynamics of phases in martensitic alloys. The strongly implicit scheme employing Newton`s quasilinearisation allows us to track the long time evolution of the localized solutions of the system. Two distinct classes of solutions are encountered for the pure Boussinesq equation. The first class consists of oscillatory pulses whose envelopes are localized waves. The second class consists of smoother solutions whose shapes are either heteroclinic (kinks) or homoclinic (bumps). The homoclinics decrease in amplitude with time while their support increases. An appropriate self-similar scaling is found analytically and confirmed by the direct numerical simulations to high accuracy. The rich phenomenology resulting from the coupling with the wave equation is also investigated. 11 refs., 12 figs., 2 tabs.
Localized corrosion of candidate container materials in ferric chloride solutions
Roy, A.K.; Fleming, D.L.; Lum, B.Y.
1999-07-01
Localized corrosion behavior of candidate inner- and outer-container materials of current nuclear waste package design was evaluated in aqueous solutions of various concentrations of ferric chloride (FeCl{sub 3}) at 30 C, 60 C and 90 C using the electrochemical cyclic potentiodynamic polarization (CPP) technique. Materials tested include A 516 carbon steel (UNS K01800), and high-performance UNS N08825, UNS N06985, UNS N06030, UNS N06455, UNS N06625, UNS N06022, and UNS R53400. A 516 steel suffered from severe general and localized attack including pitting and crevice corrosion. High-nickel UNS N08825 and N06985 also became susceptible to severe pitting and crevice corrosion. The extent of localized attack was less pronounced in UNS N06030 and N06455. UNS N06625 experienced severe surface degradation including general corrosion crevice corrosion and intergranular attack. In contrast, only slight crevice corrosion tendency was observed with nickel-base UNS N06022 in solutions containing higher concentrations of FeCl{sub 3} at 60 C and 90 C. UNS R53400 was immune to localized attack in all tested environments. The test solutions showed a significant amount of precipitated particles, especially at higher temperatures.
Localized corrosion of candidate container materials in ferric chloride solutions
Fleming, D L; Lum, B Y; Roy, A K
1998-10-01
Localized corrosion behavior of candidate inner and outer container materials of currently-designed nuclear waste package was evaluated in aqueous solutions of various concentrations of ferric chloride (FeCl{sub 3}) at 30 C, 60 C and 90 C using the electrochemical cyclic potentiodynamic polarization (CPP) technique. Materials tested include A 5 16 carbon steel and high-performance alloys 825, G-3, G-30, C-4, 625. C-22, and Ti Gr-12. A 516 steel suffered from severe general and localized attack including pitting and crevice corrosion. High-nickel alloys 825 and G-3 also became susceptible to severe pitting and crevice corrosion. The extent of localized attack was less pronounced in alloys G-30 and C-4. Alloy 625 experienced severe surface degradation including general corrosion, crevice corrosion and intergranular attack. In contrast, only a slight crevice corrosion tendency was observed with nickel-base alloy C-22 in solutions containing higher concentrations of FeCl{sub 3} at 60 C and 90 C. Ti Gr-12 was immune to localized attack in all tested environments. The test solutions showed significant amount of precipitated particles during and after testing especially at higher temperatures.
Rogue Waves: From Nonlinear Schrödinger Breather Solutions to Sea-Keeping Test
Onorato, Miguel; Proment, Davide; Clauss, Günther; Klein, Marco
2013-01-01
Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship. PMID:23405086
Explicit Solutions and Bifurcations for a Class of Generalized Boussinesq Wave Equation
NASA Astrophysics Data System (ADS)
Ma, Zhi-Min; Sun, Yu-Huai; Liu, Fu-Sheng
2013-03-01
In this paper, the generalized Boussinesq wave equation utt — uxx + a(um)xx + buxxxx = 0 is investigated by using the bifurcation theory and the method of phase portraits analysis. Under the different parameter conditions, the exact explicit parametric representations for solitary wave solutions and periodic wave solutions are obtained.
NASA Astrophysics Data System (ADS)
Wang, Chuanjian; Dai, Zhengde; Liu, Changfu
2014-07-01
In this paper, two types of multi-parameter breather homoclinic wave solutions—including breather homoclinic wave and rational homoclinic wave solutions—are obtained by using the Hirota technique and ansätz with complexity of parameter for the coupled Schrödinger-Boussinesq equation. Rogue waves in the form of the rational homoclinic solution are derived when the periods of breather homoclinic wave go to infinite. Some novel features of homoclinic wave solutions are discussed and presented. In contrast to the normal bright rogue wave structure, a structure like a four-petaled flower in temporal-spatial distribution is exhibited. Further with the change of the wave number of the plane wave, the bright and dark rogue wave structures may change into each other. The bright rogue wave structure results from the full merger of two nearby peaks, and the dark rogue wave structure results from the full merger of two nearby holes. The dark rogue wave for the uncoupled Boussinesq equation is finally obtained. Its structural properties show that it never takes on bright rogue wave features with the change of parameter. It is hoped that these results might provide us with useful information on the dynamics of the relevant fields in physics.
Wave propagation in granular chains with local resonances.
Bonanomi, Luca; Theocharis, Georgios; Daraio, Chiara
2015-03-01
We study wave propagation in a chain of spherical particles containing a local resonator. The resonant particles are made of an aluminum outer spherical shell and a steel inner mass connected by a polymeric plastic structure acting as a spring. We characterize the dynamic response of individual particles and the transmitted linear spectra of a chain of particles in contact. A wide band gap is observed both in theoretical and experimental results. We show the ability to tune the acoustic transmission by varying the contact interaction between particles. Higher driving amplitude leads to the generation of nonlinearities both in the response of a single particle and that of the whole chain. For a single resonant particle, we observe experimentally a resonant frequency downshift, which follows a complex nonlinear behavior. In the chain of particles, nonlinearity leads to the generation of nonlinear harmonics and the presence of localized modes inside the band gap. PMID:25871239
NASA Astrophysics Data System (ADS)
Lin, F.; Schmandt, B.; Tsai, V. C.
2012-12-01
The deployment of the EarthScope/USArray Transportable Array allows detailed empirical study of the surface-wave wavefield on a large scale. In this presentation, we show that three local properties of Rayleigh waves, i.e. phase velocity, ellipticity (or H/V ratio), and local amplification, can be determined across the array in the western US between 24 and 100 sec period based on teleseismic measurements. More than 900 earthquakes are analyzed where phase velocity and local amplification are determined based on empirical phase travel time and amplitude mapping. The three Rayleigh wave properties, which are all sensitive to the 1D structure beneath each location, have very distinct depth sensitivity to Vs, Vp/Vs ratio, and density. Joint inversion of these quantities therefore reduces the trade-off between the three different parameters at different depths. Including the H/V ratio, in particular, allows the uppermost (0-3 km) crustal velocity and density structure to be constrained, and our new results are in excellent agreement with known surface features. Pronounced low Vs, low density, and high Vp/Vs anomalies are imaged in the locations of several major sedimentary basins including the Williston, Powder River, Green River, Denver, and San Juan basins. Preliminary results on the inverted 3D Vs, Vp/Vs ratio, and density structure in the crust and upper mantle will also be discussed. (a)-(c) 30-sec Rayleigh-wave phase velocity, local amplification, and H/V ratio observed across USArray in the western US. The red lines denote the tectonic boundaries and the triangles in (b)-(c) shown the stations used. The thick black lines indicate 3-km sediment contours for several major sedimentary basins (WB: Williston Basin; PR: Powder River Basin; GR: Green River Basin; DB: Denver Basin). (d)-(f) The Vs, density, and Vp/Vs ratio in the uppermost crust (0-3 km) inverted by phase velocity and H/V ratio measurements.
Yao, Yu-Qin; Li, Ji; Han, Wei; Wang, Deng-Shan; Liu, Wu-Ming
2016-01-01
The intrinsic nonlinearity is the most remarkable characteristic of the Bose-Einstein condensates (BECs) systems. Many studies have been done on atomic BECs with time- and space- modulated nonlinearities, while there is few work considering the atomic-molecular BECs with space-modulated nonlinearities. Here, we obtain two kinds of Jacobi elliptic solutions and a family of rational solutions of the atomic-molecular BECs with trapping potential and space-modulated nonlinearity and consider the effect of three-body interaction on the localized matter wave solutions. The topological properties of the localized nonlinear matter wave for no coupling are analysed: the parity of nonlinear matter wave functions depends only on the principal quantum number n, and the numbers of the density packets for each quantum state depend on both the principal quantum number n and the secondary quantum number l. When the coupling is not zero, the localized nonlinear matter waves given by the rational function, their topological properties are independent of the principal quantum number n, only depend on the secondary quantum number l. The Raman detuning and the chemical potential can change the number and the shape of the density packets. The stability of the Jacobi elliptic solutions depends on the principal quantum number n, while the stability of the rational solutions depends on the chemical potential and Raman detuning. PMID:27403634
Yao, Yu-Qin; Li, Ji; Han, Wei; Wang, Deng-Shan; Liu, Wu-Ming
2016-01-01
The intrinsic nonlinearity is the most remarkable characteristic of the Bose-Einstein condensates (BECs) systems. Many studies have been done on atomic BECs with time- and space- modulated nonlinearities, while there is few work considering the atomic-molecular BECs with space-modulated nonlinearities. Here, we obtain two kinds of Jacobi elliptic solutions and a family of rational solutions of the atomic-molecular BECs with trapping potential and space-modulated nonlinearity and consider the effect of three-body interaction on the localized matter wave solutions. The topological properties of the localized nonlinear matter wave for no coupling are analysed: the parity of nonlinear matter wave functions depends only on the principal quantum number n, and the numbers of the density packets for each quantum state depend on both the principal quantum number n and the secondary quantum number l. When the coupling is not zero, the localized nonlinear matter waves given by the rational function, their topological properties are independent of the principal quantum number n, only depend on the secondary quantum number l. The Raman detuning and the chemical potential can change the number and the shape of the density packets. The stability of the Jacobi elliptic solutions depends on the principal quantum number n, while the stability of the rational solutions depends on the chemical potential and Raman detuning. PMID:27403634
Exciton localization in solution-processed organolead trihalide perovskites
He, Haiping; Yu, Qianqian; Li, Hui; Li, Jing; Si, Junjie; Jin, Yizheng; Wang, Nana; Wang, Jianpu; He, Jingwen; Wang, Xinke; Zhang, Yan; Ye, Zhizhen
2016-01-01
Organolead trihalide perovskites have attracted great attention due to the stunning advances in both photovoltaic and light-emitting devices. However, the photophysical properties, especially the recombination dynamics of photogenerated carriers, of this class of materials are controversial. Here we report that under an excitation level close to the working regime of solar cells, the recombination of photogenerated carriers in solution-processed methylammonium–lead–halide films is dominated by excitons weakly localized in band tail states. This scenario is evidenced by experiments of spectral-dependent luminescence decay, excitation density-dependent luminescence and frequency-dependent terahertz photoconductivity. The exciton localization effect is found to be general for several solution-processed hybrid perovskite films prepared by different methods. Our results provide insights into the charge transport and recombination mechanism in perovskite films and help to unravel their potential for high-performance optoelectronic devices. PMID:26996605
Exciton localization in solution-processed organolead trihalide perovskites
NASA Astrophysics Data System (ADS)
He, Haiping; Yu, Qianqian; Li, Hui; Li, Jing; Si, Junjie; Jin, Yizheng; Wang, Nana; Wang, Jianpu; He, Jingwen; Wang, Xinke; Zhang, Yan; Ye, Zhizhen
2016-03-01
Organolead trihalide perovskites have attracted great attention due to the stunning advances in both photovoltaic and light-emitting devices. However, the photophysical properties, especially the recombination dynamics of photogenerated carriers, of this class of materials are controversial. Here we report that under an excitation level close to the working regime of solar cells, the recombination of photogenerated carriers in solution-processed methylammonium-lead-halide films is dominated by excitons weakly localized in band tail states. This scenario is evidenced by experiments of spectral-dependent luminescence decay, excitation density-dependent luminescence and frequency-dependent terahertz photoconductivity. The exciton localization effect is found to be general for several solution-processed hybrid perovskite films prepared by different methods. Our results provide insights into the charge transport and recombination mechanism in perovskite films and help to unravel their potential for high-performance optoelectronic devices.
Plane wave based selfconsistent solution of the GW Dyson equation
NASA Astrophysics Data System (ADS)
Wang, Lin-Wang; Cao, Huawei
We have developed a selfconsistent procedure to calculate the full Dyson equation based on plane wave basis set. The whole formalism is based on the Greens function matrix of the plane wave G-vector. There is no truncation of the conduction band when the dielectric function is calculated. The Dyson equation is the variational minimum solution of the total energy in terms of the Greens function. The calculation uses the ''space-time'' method, with special algorithm for imaginary time integration and Fourier transformation. We have tested isolated molecules and periodic systems. The effects of selfconsistency compared to the G0W0 results will be presented. We will also discuss some special techniques used in the k-point summation for the periodic system. Massive parallelization is used to carry out such calculations. This work is supported by the Director, SC/BES/MSED of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, through the Material Theory program at Lawrence Berkeley National Laboratory.
Global, uniform, asymptotic wave-equation solutions for large wavenumbers
NASA Astrophysics Data System (ADS)
Klauder, John R.
1987-11-01
For each of a large class of linear wave equations-relevant, for example, to very general acoustical or optical propagation problems-we develop within a single expression a global, uniform, asymptotic solution for large wavenumbers (small wavelengths) based on coherentstate transformation techniques. Such techniques effectively separate the configuration-space field into its orientational components, and are thus analogous to a phase-space description of rays by their position and direction. The resultant coherent-state approximation offers distinct advantages over more traditional asymptotic approximations based on direct or Fourier transform techniques. In particular, coherent-state methods lead to an everywhere well-defined approximation independent of the complexity of the caustic structure, independent of whether there are a few or a vast number of relevant rays, or even in shadow regions where no conventional rays exist. For propagation in random media it is shown that coherent-state techniques also offer certain advantages. Approximations are developed for wave equations in an arbitrary number of space dimensions for single component fields as well as multicomponent fields that, for example, can account for backscattering. It is noteworthy that the coherentstate asymptotic approximation should lend itself to numerical studies as well.
Dudley, J. M.; Sarano, V.; Dias, F.
2013-01-01
The Hokusai woodcut entitled The great wave off Kanagawa has been interpreted as an unusually large storm wave, likely to be classed as a rogue wave, and possibly generated from nonlinear wave dynamics (J. H. E. Cartwright and H. Nakamura, Notes Rec. R. Soc. 63, 119–135 (2009)). In this paper, we present a complementary discussion of this hypothesis, discussing in particular how linear and nonlinear mechanisms can both contribute to the emergence of rogue wave events. By making reference to the Great wave's simultaneous transverse and longitudinal localization, we show that the purely linear mechanism of directional focusing also predicts characteristics consistent with those of the Great wave. In addition, we discuss the properties of a particular rogue wave photographed on the open ocean in sub-Antarctic waters, which shows two-dimensional localization and breaking dynamics remarkably similar to Hokusai's depiction in the woodcut. PMID:24687148
Crystallization of Local Anesthetics When Mixed With Corticosteroid Solutions
Hwang, Hyeoncheol; Park, Jihong; Lee, Won Kyung; Lee, Woo Hyung; Leigh, Ja-Ho; Lee, Jin Joo; Chung, Sun G.; Lim, Chaiyoung; Park, Sang Jun
2016-01-01
Objective To evaluate at which pH level various local anesthetics precipitate, and to confirm which combination of corticosteroid and local anesthetic crystallizes. Methods Each of ropivacaine-HCl, bupivacaine-HCl, and lidocaine-HCl was mixed with 4 different concentrations of NaOH solutions. Also, each of the three local anesthetics was mixed with the same volume of 3 corticosteroid solutions (triamcinolone acetonide, dexamethasone sodium phosphate, and betamethasone sodium phosphate). Precipitation of the local anesthetics (or not) was observed, by the naked eye and by microscope. The pH of each solution and the size of the precipitated crystal were measured. Results Alkalinized with NaOH to a certain value of pH, local anesthetics precipitated (ropivacaine pH 6.9, bupivacaine pH 7.7, and lidocaine pH 12.9). Precipitation was observed as a cloudy appearance by the naked eye and as the aggregation of small particles (<10 µm) by microscope. The amount of particles and aggregation increased with increased pH. Mixed with betamethasone sodium phosphate, ropivacaine was precipitated in the form of numerous large crystals (>300 µm, pH 7.5). Ropivacaine with dexamethasone sodium phosphate also precipitated, but it was only observable by microscope (a few crystals of 10–100 µm, pH 7.0). Bupivacaine with betamethasone sodium phosphate formed precipitates of non-aggregated smaller particles (<10 µm, pH 7.7). Lidocaine mixed with corticosteroids did not precipitate. Conclusion Ropivacaine and bupivacaine can precipitate by alkalinization at a physiological pH, and therefore also produce crystals at a physiological pH when they are mixed with betamethasone sodium phosphate. Thus, the potential risk should be noted for their use in interventions, such as epidural steroid injections. PMID:26949665
NASA Astrophysics Data System (ADS)
Shen, Chun; Sun, Meina
2013-08-01
This paper is devoted to studying the interactions of elementary waves for a model of a scalar conservation law with a flux function involving discontinuous coefficients. In order to cover all the situations completely, we take the initial data as three piecewise constant states and the middle region is regarded as the perturbed region with small distance. It is proved that the Riemann solutions are stable under the local small perturbations of the Riemann initial data by letting the perturbed parameter tend to zero. The proof is based on the detailed analysis of the interactions of stationary wave discontinuities with shock waves and rarefaction waves. Moreover, the global structures and large time asymptotic behaviors of the solutions are constructed and analyzed case by case.
A solution scheme for the Euler equations based on a multi-dimensional wave model
NASA Technical Reports Server (NTRS)
Powell, Kenneth G.; Barth, Timothy J.; Parpia, Ijaz H.
1993-01-01
A scheme for the solution of scalar advection on an unstructured mesh has been developed, tested, and extended to the Euler equations. The scheme preserves a linear function exactly, and yields nearly monotone results. The flux function associated with the Euler scheme is based on a discrete 'wave model' for the system of equations. The wave model decomposes the solution gradient at a location into shear waves, entropy waves and acoustic waves and calculates the speeds, strengths and directions associated with the waves. The approach differs from typical flux-difference splitting schemes in that the waves are not assumed to propagate normal to the faces of the control volumes; directions of propagation of the waves are instead computed from solution-gradient information. Results are shown for three test cases, and two different wave models. The results are compared to those from other approaches, including MUSCL and Galerkin least squares schemes.
Bifurcations and Exact Traveling Wave Solutions of a Modified Nonlinear Schrödinger Equation
NASA Astrophysics Data System (ADS)
Kou, Kitian; Li, Jibin
2016-06-01
In this paper, we consider two singular nonlinear planar dynamical systems created from the studies of one-dimensional bright and dark spatial solitons for one-dimensional beams in a nonlocal Kerr-like media. On the basis of the investigation of the dynamical behavior and bifurcations of solutions of the planar dynamical systems, we obtain all possible explicit exact parametric representations of solutions (including solitary wave solutions, periodic wave solutions, peakon and periodic peakons, compacton solutions, etc.) under different parameter conditions.
Monotone waves for non-monotone and non-local monostable reaction-diffusion equations
NASA Astrophysics Data System (ADS)
Trofimchuk, Elena; Pinto, Manuel; Trofimchuk, Sergei
2016-07-01
We propose a new approach for proving existence of monotone wavefronts in non-monotone and non-local monostable diffusive equations. This allows to extend recent results established for the particular case of equations with local delayed reaction. In addition, we demonstrate the uniqueness (modulo translations) of obtained monotone wavefront within the class of all monotone wavefronts (such a kind of conditional uniqueness was recently established for the non-local KPP-Fisher equation by Fang and Zhao). Moreover, we show that if delayed reaction is local then each monotone wavefront is unique (modulo translations) within the class of all non-constant traveling waves. Our approach is based on the construction of suitable fundamental solutions for linear integral-differential equations. We consider two alternative scenarios: in the first one, the fundamental solution is negative (typically holds for the Mackey-Glass diffusive equations) while in the second one, the fundamental solution is non-negative (typically holds for the KPP-Fisher diffusive equations).
Optical tracking of local surface wave for skin viscoelasticity.
Guan, Yubo; Lu, Mingzhu; Shen, Zhilong; Wan, Mingxi
2014-06-01
Rapid and effective determination of biomechanical properties is important in examining and diagnosing skin thermal injury. Among the methods used, viscoelasticity quantification is one of the most effective methods in determining such properties. This study aims to rapidly determine skin viscoelasticity by optically tracking the local surface wave. New elastic and viscous coefficients were proposed to indicate skin viscoelasticity based on a single impulse response of the skin. Experiments were performed using fresh porcine skin samples. Surface wave was generated in a single impulse using a vibrator with a ball-tipped device and was detected using a laser Doppler vibrometer. The motions along the depth direction were monitored using an ultrasound system. The ultrasound monitoring results indicated the multi-layered viscoelasticity of the epidermis and dermis. The viscoelastic coefficients from four healthy samples show a potential viscoelasticity variation of porcine skin. In one sample, the two coefficients were evidently higher than those in a healthy area if the skin was slightly burned. These results indicate that the proposed method is sensitive, effective, and quick in determining skin viscoelasticity. PMID:24674744
NASA Astrophysics Data System (ADS)
Shah, Rehan; Van Gorder, Robert A.
2016-03-01
We demonstrate the existence of localized structures along quantized vortex filaments in superfluid helium under the quantum form of the local induction approximation (LIA), which includes mutual friction and normal fluid effects. For small magnitude normal fluid velocities, the dynamics are dissipative under mutual friction. On the other hand, when normal fluid velocities are sufficiently large, we observe parametric amplification of the localized disturbances along quantized vortex filaments, akin to the Donnelly-Glaberson instability for regular Kelvin waves. As the waves amplify they will eventually cause breakdown of the LIA assumption (and perhaps the vortex filament itself), and we derive a characteristic time for which this breakdown occurs under our model. More complicated localized waves are shown to occur, and we study these asymptotically and through numerical simulations. Such solutions still exhibit parametric amplification for large enough normal fluid velocities, although this amplification may be less uniform than would be seen for more regular filaments such as those corresponding to helical curves. We find that large rotational velocities or large wave speeds of nonlinear waves along the filaments will result in more regular and stable structures, while small rotational velocities and wave speeds will permit far less regular dynamics.
Effect of wave localization on plasma instabilities. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Levedahl, William Kirk
1987-01-01
The Anderson model of wave localization in random media is involved to study the effect of solar wind density turbulence on plasma processes associated with the solar type III radio burst. ISEE-3 satellite data indicate that a possible model for the type III process is the parametric decay of Langmuir waves excited by solar flare electron streams into daughter electromagnetic and ion acoustic waves. The threshold for this instability, however, is much higher than observed Langmuir wave levels because of rapid wave convection of the transverse electromagnetic daughter wave in the case where the solar wind is assumed homogeneous. Langmuir and transverse waves near critical density satisfy the Ioffe-Reigel criteria for wave localization in the solar wind with observed density fluctuations -1 percent. Numerical simulations of wave propagation in random media confirm the localization length predictions of Escande and Souillard for stationary density fluctations. For mobile density fluctuations localized wave packets spread at the propagation velocity of the density fluctuations rather than the group velocity of the waves. Computer simulations using a linearized hybrid code show that an electron beam will excite localized Langmuir waves in a plasma with density turbulence. An action principle approach is used to develop a theory of non-linear wave processes when waves are localized. A theory of resonant particles diffusion by localized waves is developed to explain the saturation of the beam-plasma instability. It is argued that localization of electromagnetic waves will allow the instability threshold to be exceeded for the parametric decay discussed above.
NASA Astrophysics Data System (ADS)
Feng, Lian-Li; Tian, Shou-Fu; Yan, Hui; Wang, Li; Zhang, Tian-Tian
2016-07-01
In this paper, a lucid and systematic approach is proposed to systematically study the periodic-wave solutions and asymptotic behaviors of a (2 + 1) -dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt (gKDKK) equation, which can be used to describe certain situations from the fluid mechanics, ocean dynamics and plasma physics. Based on Bell's polynomials, the bilinear formalism and N -soliton solution of the gKDKK equation are derived, respectively. Furthermore, based on multidimensional Riemann theta functions, the periodic-wave solutions of the equation are also constructed. Finally, an asymptotic relation between the periodic-wave solutions and soliton solutions are strictly established under a limited procedure.
Existence and stability of traveling wave solutions for multilayer cellular neural networks
NASA Astrophysics Data System (ADS)
Hsu, Cheng-Hsiung; Lin, Jian-Jhong; Yang, Tzi-Sheng
2015-08-01
The purpose of this article is to investigate the existence and stability of traveling wave solutions for one-dimensional multilayer cellular neural networks. We first establish the existence of traveling wave solutions using the truncated technique. Then we study the asymptotic behaviors of solutions for the Cauchy problem of the neural model. Applying two kinds of comparison principles and the weighed energy method, we show that all solutions of the Cauchy problem converge exponentially to the traveling wave solutions provided that the initial data belong to a suitable weighted space.
Vassilev, V. M.; Djondjorov, P. A.; Hadzhilazova, M. Ts.; Mladenov, I. M.
2011-11-29
The Gardner equation is well-known in the mathematical literature since the late sixties of 20th century. Initially, it appeared in the context of the construction of local conservation laws admitted by the KdV equation. Later on, the Gardner equation was generalized and found to be applicable in various branches of physics (solid-state and plasma physics, fluid dynamics and quantum field theory). In this paper, we examine the travelling wave solutions of the Gardner equation and derive the full set of solutions to the corresponding reduced equation in terms of Weierstrass and Jacobi elliptic functions. Then, we use the travelling wave solutions of the focusing mKdV equation and obtain in explicit analytic form exact solutions of a special type of plane curve flow, known as the mKdV flow.
Existence of traveling wave solutions in a diffusive predator-prey model.
Huang, Jianhua; Lu, Gang; Ruan, Shigui
2003-02-01
We establish the existence of traveling front solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model with Holling type-II functional response. The traveling front solutions are equivalent to heteroclinic orbits in R(4) and the small amplitude traveling wave train solutions are equivalent to small amplitude periodic orbits in R(4). The methods used to prove the results are the shooting argument and the Hopf bifurcation theorem. PMID:12567231
Stimulated Brillouin scattering in the field of a two-dimensionally localized pumping wave
NASA Astrophysics Data System (ADS)
Solikhov, D. K.; Dvinin, S. A.
2016-06-01
Stimulated Brillouin scattering of electromagnetic waves in the field of a two-dimensionally localized pump wave at arbitrary scattering angles in the regime of forward scattering is analyzed. Spatial variations in the amplitudes of interacting waves are studied for different values of the pump field and different dimensions of the pump wave localization region. The intensity of scattered radiation is determined as a function of the scattering angle and the dimensions of the pump wave localization region. It is shown that the intensity increases with increasing scattering angle.
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
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
Inverse scattering transform analysis of rogue waves using local periodization procedure.
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
Local ventilation solution for large, warm emission sources.
Kulmala, Ilpo; Hynynen, Pasi; Welling, Irma; Säämänen, Arto
2007-01-01
In a foundry casting line, contaminants are released from a large area. Casting fumes include both volatile and particulate compounds. The volatile fraction contains hydrocarbons, whereas the particulate fraction mostly comprises a mixture of vaporized metal fumes. Casting fumes lower the air quality in foundries. The design of local ventilation for the casting area is a challenging task, because of the large casting area and convection plumes from warm moulds. A local ventilation solution for the mould casting area was designed and dimensioned with the aid of computational fluid dynamic (CFD) calculations. According to the calculations, the most efficient solution was a push-pull ventilation system. The prototype of the push-pull system was built and tested in actual operation at the foundry. The push flow was generated by a free plane jet that blew across the 10 m wide casting area towards an exhaust hood on the opposite side of the casting lines. The capture efficiency of the prototype was determined by the tracer gas method. The measured capture efficiencies with push jet varied between 40 and 80%, depending on the distance between the source and the exhaust. With the aid of the push flow, the average capture efficiency was increased from 40 (without jet) to 60%. PMID:16861238
Exact Travelling Wave Solutions of the Nonlinear Evolution Equations by Auxiliary Equation Method
NASA Astrophysics Data System (ADS)
Kaplan, Melike; Akbulut, Arzu; Bekir, Ahmet
2015-10-01
The auxiliary equation method presents wide applicability to handling nonlinear wave equations. In this article, we establish new exact travelling wave solutions of the nonlinear Zoomeron equation, coupled Higgs equation, and equal width wave equation. The travelling wave solutions are expressed by the hyperbolic functions, trigonometric functions, and rational functions. It is shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering. Throughout the article, all calculations are made with the aid of the Maple packet program.
Dynamic aspects of apparent attenuation and wave localization in layered media
Haney, M.M.; Van Wijk, K.
2008-01-01
We present a theory for multiply-scattered waves in layered media which takes into account wave interference. The inclusion of interference in the theory leads to a new description of the phenomenon of wave localization and its impact on the apparent attenuation of seismic waves. We use the theory to estimate the localization length at a CO2 sequestration site in New Mexico at sonic frequencies (2 kHz) by performing numerical simulations with a model taken from well logs. Near this frequency, we find a localization length of roughly 180 m, leading to a localization-induced quality factor Q of 360.
NASA Astrophysics Data System (ADS)
Shukla, K.; Wang, Y.; Jaiswal, P.
2014-12-01
In a porous medium the seismic energy not only propagates through matrix but also through pore-fluids. The differential movement between sediment grains of the matrix and interstitial fluid generates a diffusive wave which is commonly referred to as the slow P-wave. A combined system of equation which includes both elastic and diffusive phases is known as the poroelasticity. Analyzing seismic data through poroelastic modeling results in accurate interpretation of amplitude and separation of wave modes, leading to more accurate estimation of geomehanical properties of rocks. Despite its obvious multi-scale application, from sedimentary reservoir characterization to deep-earth fractured crust, poroelasticity remains under-developed primarily due to the complex nature of its constituent equations. We present a detail formulation of poroleastic wave equations for isotropic media by combining the Biot's and Newtonian mechanics. System of poroelastic wave equation constitutes for eight time dependent hyperbolic PDEs in 2D whereas in case of 3D number goes up to thirteen. Eigen decomposition of Jacobian of these systems confirms the presence of an additional slow-P wave phase with velocity lower than shear wave, posing stability issues on numerical scheme. To circumvent the issue, we derived a numerical scheme using nodal discontinuous Galerkin approach by adopting the triangular meshes in 2D which is extended to tetrahedral for 3D problems. In our nodal DG approach the basis function over a triangular element is interpolated using Legendre-Gauss-Lobatto (LGL) function leading to a more accurate local solutions than in the case of simple DG. We have tested the numerical scheme for poroelastic media in 1D and 2D case, and solution obtained for the systems offers high accuracy in results over other methods such as finite difference , finite volume and pseudo-spectral. The nodal nature of our approach makes it easy to convert the application into a multi-threaded algorithm
NASA Astrophysics Data System (ADS)
Hosseini, Vahid Reza; Shivanian, Elyas; Chen, Wen
2016-05-01
The purpose of the current investigation is to determine numerical solution of time-fractional diffusion-wave equation with damping for Caputo's fractional derivative of order α (1 < α ≤ 2). A meshless local radial point interpolation (MLRPI) scheme based on Galerkin weak form is analyzed. The reason of choosing MLRPI approach is that it does not require any background integrations cells, instead integrations are implemented over local quadrature domains which are further simplified for reducing the complication of computation using regular and simple shape. The unconditional stability and convergence with order O (τ 6 - 2 α) are proved, where τ is time stepping. Also, several numerical experiments are illustrated to verify theoretical analysis.
New Travelling Solitary Wave and Periodic Solutions of the Generalized Kawahara Equation
Chen Huaitang; Yin Huicheng
2007-09-06
A simple elliptic equation method is used for constructing exact trevelling wave solutions of nonlinear partial differential equations(PDEs) in a unified way. With the aid of Maple, more new travelling solitary wave and periodic solutions are obtained for the generalized Kawahara equation.
A Note on Exact Travelling Wave Solutions for the Klein-Gordon- Zakharov Equations
NASA Astrophysics Data System (ADS)
Zhang, Zai-Yun; Zhang, Ying-Hui; Gan, Xiang-Yang; Yu, De-Ming
2012-04-01
In this paper, we investigate the travelling wave solutions for the Klein-Gordon-Zakharov equations by using the modified trigonometric function series method benefited to the ideas of Z. Y. Zhang, Y. X. Li, Z. H. Liu, and X. J. Miao, Commun. Nonlin. Sci. Numer. Simul. , 3097 (2011). Exact travelling wave solutions are obtained
An Exact Solution for Geophysical Edge Waves in the {β}-Plane Approximation
NASA Astrophysics Data System (ADS)
Ionescu-Kruse, Delia
2015-12-01
By taking into account the {β}-plane effects, we provide an exact nonlinear solution to the geophysical edge-wave problem within the Lagrangian framework. This solution describes trapped waves propagating eastward or westward along a sloping beach with the shoreline parallel to the Equator.
Trapping and instability of directional gravity waves in localized water currents.
Eliasson, B; Haas, F
2014-06-01
The influence of localized water currents on the nonlinear dynamics and stability of large amplitude, statistically distributed gravity waves is investigated theoretically and numerically by means of an evolution equation for a Wigner function governing the spectrum of waves. It is shown that water waves propagating in the opposite direction of a localized current channel can be trapped in the channel, which can lead to the amplification of the wave intensity. Under certain conditions the wave intensity can be further localized due to a self-focusing (Benjamin-Feir) instability. The localized amplification of the wave intensity may increase the probability of extreme events in the form of freak waves, which have been observed in connection with ocean currents. PMID:25019886
Soliton solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics
NASA Astrophysics Data System (ADS)
Mirzazadeh, Mohammad; Ekici, Mehmet; Sonmezoglu, Abdullah; Ortakaya, Sami; Eslami, Mostafa; Biswas, Anjan
2016-05-01
This paper studies a few nonlinear evolution equations that appear with fractional temporal evolution and fractional spatial derivatives. These are Benjamin-Bona-Mahoney equation, dispersive long wave equation and Nizhnik-Novikov-Veselov equation. The extended Jacobi's elliptic function expansion method is implemented to obtain soliton and other periodic singular solutions to these equations. In the limiting case, when the modulus of ellipticity approaches zero or unity, these doubly periodic functions approach solitary waves or shock waves or periodic singular solutions emerge.
Steady-state solutions for relativistically strong electromagnetic waves in plasmas.
NASA Technical Reports Server (NTRS)
Max, C. E.
1973-01-01
New steady-state solutions are derived which describe electromagnetic waves strong enough to make plasma ions and electrons relativistic. A two-fluid model is used throughout. The following solutions are studied: (1) linearly polarized waves with phase velocity much greater than c; (2) arbitrarily polarized waves with phase velocity near c, in a cold uniform plasma; (3) circularly polarized waves in a uniform plasma characterized by a scalar pressure tensor. All of these waves are capable of propagating in normally overdense plasmas, due to nonlinearities introduced by relativistic effects. The propagation of relativistically strong waves in a density gradient is examined, for the example of a circularly polarized wave strong enough to make electrons but not ions relativistic. It is shown that such a wave propagates at constant energy flux despite the nonlinearity of the system.
NASA Astrophysics Data System (ADS)
Kuruoğlu, Zeki C.
2014-01-01
Recently there has been a growing interest in computational methods for quantum scattering equations that avoid the traditional decomposition of wave functions and scattering amplitudes into partial waves. The aim of the present work is to show that the weighted-residual approach in combination with local basis functions give rise to convenient computational schemes for the solution of the multi-variable integral equations without the partial wave expansion. The weighted-residual approach provides a unifying framework for various variational and degenerate-kernel methods for integral equations of scattering theory. Using a direct-product basis of localized quadratic interpolation polynomials, Galerkin, collocation and Schwinger variational realizations of the weighted-residual approach have been implemented for a model potential. It is demonstrated that, for a given expansion basis, Schwinger variational method exhibits better convergence with basis size than Galerkin and collocation methods. A novel hybrid-collocation method is implemented with promising results as well.
Travelling wave solutions for some two-component shallow water models
NASA Astrophysics Data System (ADS)
Dutykh, Denys; Ionescu-Kruse, Delia
2016-07-01
In the present study we perform a unified analysis of travelling wave solutions to three different two-component systems which appear in shallow water theory. Namely, we analyze the celebrated Green-Naghdi equations, the integrable two-component Camassa-Holm equations and a new two-component system of Green-Naghdi type. In particular, we are interested in solitary and cnoidal-type solutions, as two most important classes of travelling waves that we encounter in applications. We provide a complete phase-plane analysis of all possible travelling wave solutions which may arise in these models. In particular, we show the existence of new type of solutions.
Travelling waves and fold localization in hovercraft seals
NASA Astrophysics Data System (ADS)
Wiggins, Andrew; Zalek, Steve; Perlin, Marc; Ceccio, Steve
2013-11-01
The seal system on hovercraft consists of a series of open-ended fabric cylinders that contact the free surface and, when inflated, form a compliant pressure barrier. Due to a shortening constraint imposed by neighboring seals, bow seals operate in a post-buckled state. We present results from large-scale experiments on these structures. These experiment show the hydroelastic response of seals to be characterized by striking stable and unstable post-buckling behavior. Using detailed 3-d measurements of the deformed seal shape, dominant response regimes are identified. These indicate that mode number decreases with wetted length, and that the form of the buckling packet becomes localized with increased velocity and decreased bending stiffness. Eventually, at a critical pressure, travelling waves emerge. To interpret the wide range of observed behavior, a 2-d nonlinear post-buckling model is developed and compared with the experimental studies. The model shows the importance of seal shortening and the buckling length, which is driven by the balance of hydrodynamic and bending energies. Preliminary scaling laws for the fold amplitude and mode number are presented. The experiments may ultimately provide insight into the bedeviling problem of seal wear. Sponsored by the Office of Naval Research under grant N00014-10-1-0302, Ms. Kelly B. Cooper, program manager.
NASA Astrophysics Data System (ADS)
Xu, Mei-Juan; Tian, Shou-Fu; Tu, Jian-Min; Ma, Pan-Li; Zhang, Tian-Tian
2015-08-01
In this paper, the (2+1)-dimensional Saweda-Kotera-Kadomtsev-Petviashvili (SK-KP) equation is investigated, which can be used to describe certain situations from the fluid mechanics, ocean dynamics and plasma physics. With the aid of generalized Bell's polynomials, the Hirota's bilinear equation and N-soliton solution are explicitly constructed to the SK-KP equation, respectively. Based on the Riemann theta function, a direct and lucid way is presented to explicitly construct quasi-periodic wave solutions for the SK-KP equation. The two-periodic waves admit two independent spatial periods in two independent horizontal directions, which are a direct generalization of one-periodic waves. Finally, the relationships between soliton solutions and periodic wave solutions are strictly established, which implies the asymptotic behaviors of the periodic waves under a limited procedure.
Rod transduction parameters from the a wave of local receptor populations
NASA Astrophysics Data System (ADS)
Nusinowitz, Steven; Hood, Donald C.; Birch, David G.
1995-10-01
The analysis of electroretinogram a waves from locally stimulated populations of rods is complicated by the presence of scattered light within the eye. Scattered-light and cone contributions can be assessed after brief flashes of light designed to saturate only rods in the locally stimulated area. Subtracting the scattered-light and the cone responses from the local electroretinogram gives a pure rod a wave that can be fitted with models of photoreceptor activity. We demonstrate the feasibility of this technique by recording local rod a waves from a group of five normal subjects and by fitting the a waves with the rod model to derive transduction parameters. The local rod a waves are compared with expected responses derived from simulations in which the response of the entire retina to heterogeneous illumination is mimicked. electroretinography, rods, scattered light.
NASA Astrophysics Data System (ADS)
Fedorov, V. Yu.; Chanal, M.; Grojo, D.; Tzortzakis, S.
2016-07-01
Although tightly focused intense ultrashort laser pulses are used in many applications from nano-processing to warm dense matter physics, their nonparaxial propagation implies the use of numerical simulations with vectorial wave equations or exact Maxwell solvers that have serious limitations and thus have hindered progress in this important field up to now. Here we present an elegant and robust solution that allows one to map the problem on one that can be addressed by simple scalar wave equations. The solution is based on a transformation optics approach and its validity is demonstrated in both the linear and the nonlinear regime. Our solution allows accessing challenging problems of extreme spatiotemporal localization of high power laser radiation that remain almost unexplored theoretically until now.
Fedorov, V Yu; Chanal, M; Grojo, D; Tzortzakis, S
2016-07-22
Although tightly focused intense ultrashort laser pulses are used in many applications from nano-processing to warm dense matter physics, their nonparaxial propagation implies the use of numerical simulations with vectorial wave equations or exact Maxwell solvers that have serious limitations and thus have hindered progress in this important field up to now. Here we present an elegant and robust solution that allows one to map the problem on one that can be addressed by simple scalar wave equations. The solution is based on a transformation optics approach and its validity is demonstrated in both the linear and the nonlinear regime. Our solution allows accessing challenging problems of extreme spatiotemporal localization of high power laser radiation that remain almost unexplored theoretically until now. PMID:27494473
Wave Gradiometry and Helmholtz Equation Solutions Applied to USArray across the Contiguous U.S.
NASA Astrophysics Data System (ADS)
Liu, Y.; Holt, W. E.
2015-12-01
Wave gradiometry is an array processing technique utilizing the shape of seismic wavefields captured by USArray TA stations to determine fundamental wave propagation characteristics. We first explore a compatibility relation that links spatial gradients of the wavefield with the displacements and the time derivatives of displacements through two unknown coefficients Aand B, which are solved through iterative, damped least-square inversion, to provide estimates of phase velocity, back-azimuth, radiation pattern and geometrical spreading. We show that the A-coefficient corresponds to the gradient of logarithmic amplitude and the B-coefficient corresponds approximately to the local dynamic phase velocity. These vector fields are interpolated to explore a second compatibility relation through solutions to the Helmholtz equation. For most wavefields passing through the eastern U.S., we show that the A-coefficients are generally orthogonal to the B-coefficients. Where they are not completely orthogonal, there is a strong positive correlation between the gradients of B-coefficients and changes in geometrical spreading, which can be further linked with areas of strong energy focusing and defocusing. We then obtain isotropic phase velocity maps across the contiguous United States for 20 - 150 s Rayleigh wave by stacking results from 700 earthquakes. The strong velocity variations in the western U.S. correlate well with known geological features and the am- plitude correction terms from Helmholtz equation solutions generally improve the resolution of small-scale structures for all periods analyzed. We also observe a velocity change along the approximate boundary of the early Paleozoic continental margin in the eastern U.S and two significant low velocity anomalies within the central Appalachians, one centered where Eocene basaltic volcanism has occurred, and the other within the northeastern U.S., possibly associated with the Great Meteor Hotspot track.
Atom localization in a Doppler broadened medium via two standing-wave fields
NASA Astrophysics Data System (ADS)
Abd-Elnabi, Somia; Osman, Kariman I.
2016-01-01
The atom localization has been achieved in a four-level V-type atomic system interacting with two classical unidirectional standing-wave fields and weak probe field in a Doppler broadened medium under several conditions at very low temperature. The precision of the atom localization is compared with the system in the presence and absence of the Doppler broadened medium. The influence of some parameters such as the amplitude, wave vectors and the phase shift of the standing-wave fields on the atom localization is studied and has been found to obtain various atom localization patterns with symmetric shape.
Nonexistence of the solitary-wave solutions of the Sakuma-Nishiguchi equation
NASA Astrophysics Data System (ADS)
Lou, Sen-Yue
1992-10-01
Making a qualitative analysis, we prove that no nonsingular solitary-wave solution exists for the Sakuma-Nishiguchi equation utt-c2uxx-Muxxxx +N(u2xx)xx=0 [Phys. Rev. B 41, 12 117 (1990)], which describes surface acoustic waves in a semi-infinite layered medium with a free surface. From this, we conclude that the solitary-wave solutions obtained by Sakuma and Nishiguchi using the weak-nonlinearity approximation and by Huang using a function-series-solution approach [Phys. Rev. B 44, 3377 (1991)] do not pertain to this model equation.
Spherical wave propagation in a poroelastic medium with infinite permeability: time domain solution.
Ozyazicioglu, Mehmet
2014-01-01
Exact time domain solutions for displacement and porepressure are derived for waves emanating from a pressurized spherical cavity, in an infinitely permeable poroelastic medium with a permeable boundary. Cases for blast and exponentially decaying step pulse loadings are considered; letter case, in the limit as decay constant goes to zero, also covers the step (uniform) pressure. Solutions clearly show the propagation of the second (slow) p-wave. Furthermore, Biot modulus Q is shown to have a pronounced influence on wave propagation characteristics in poroelastic media. Results are compared with solutions in classical elasticity theory. PMID:24701190
Spherical Wave Propagation in a Poroelastic Medium with Infinite Permeability: Time Domain Solution
Ozyazicioglu, Mehmet
2014-01-01
Exact time domain solutions for displacement and porepressure are derived for waves emanating from a pressurized spherical cavity, in an infinitely permeable poroelastic medium with a permeable boundary. Cases for blast and exponentially decaying step pulse loadings are considered; letter case, in the limit as decay constant goes to zero, also covers the step (uniform) pressure. Solutions clearly show the propagation of the second (slow) p-wave. Furthermore, Biot modulus Q is shown to have a pronounced influence on wave propagation characteristics in poroelastic media. Results are compared with solutions in classical elasticity theory. PMID:24701190
Ivanov, J.; Miller, R.D.; Xia, J.; Steeples, D.; Park, C.B.
2006-01-01
We describe a possible solution to the inverse refraction-traveltime problem (IRTP) that reduces the range of possible solutions (nonuniqueness). This approach uses a reference model, derived from surface-wave shear-wave velocity estimates, as a constraint. The application of the joint analysis of refractions with surface waves (JARS) method provided a more realistic solution than the conventional refraction/tomography methods, which did not benefit from a reference model derived from real data. This confirmed our conclusion that the proposed method is an advancement in the IRTP analysis. The unique basic principles of the JARS method might be applicable to other inverse geophysical problems. ?? 2006 Society of Exploration Geophysicists.
NASA Astrophysics Data System (ADS)
Dong, Huan-He; Zhang, Yan-Feng
2015-04-01
With the aid of binary Bell polynomial and a general Riemann theta function, we introduce how to obtain the exact periodic wave solutions by applying the generalized Dp¯-operators in term of the Hirota direct method when the appropriate value of p¯ is determined. Furthermore, the resulting approach is applied to solve the extended (2+1)-dimensional Shallow Water Wave equation, and the periodic wave solution is obtained and reduced to soliton solution via asymptotic analysis. Supported by Shandong Provincial Key Laboratory of Marine Ecology and Environment & Disaster Prevention and Mitigation project under Grant No. 2012010, National Natural Science Foundation of China under Grant No. 11271007, Special Funds for Theoretical Physics of the National Natural Science Foundation of China under Grant No. 11447205, Shandong University of Science and Technology Research Fund under Grant No. 2012KYTD105
Teodorescu, Razvan; Lee, S - Y; Wiegmann, P
2008-01-01
We investigate the hydrodynamics of a Hele-Shaw flow as the free boundary evolves from smooth initial conditions into a generic cusp singularity (of local geometry type x{sup 3} {approx} y{sup 2}), and then into a density shock wave. This novel solution preserves the integrability of the dynamics and, unlike all the weak solutions proposed previously, is not underdetermined. The evolution of the shock is such that the net vorticity remains zero, as before the critical time, and the shock can be interpreted as a singular line distribution of fluid deficit.
Localization of ultra-low frequency waves in multi-ion plasmas of the planetary magnetosphere
Kim, Eun -Hwa; Johnson, Jay R.; Lee, Dong -Hun
2015-01-01
By adopting a 2D time-dependent wave code, we investigate how mode-converted waves at the Ion-Ion Hybrid (IIH) resonance and compressional waves propagate in 2D density structures with a wide range of field-aligned wavenumbers to background magnetic fields. The simulation results show that the mode-converted waves have continuous bands across the field line consistent with previous numerical studies. These waves also have harmonic structures in frequency domain and are localized in the field-aligned heavy ion density well. Lastly, our results thus emphasize the importance of a field-aligned heavy ion density structure for ultra-low frequency wave propagation, and suggest that IIH waves can be localized in different locations along the field line.
Orbital stability of periodic traveling-wave solutions for the regularized Schamel equation
NASA Astrophysics Data System (ADS)
de Andrade, Thiago Pinguello; Pastor, Ademir
2016-03-01
In this work we study the orbital stability of periodic traveling-wave solutions for dispersive models. The study of traveling waves started in the mid-18th century when John S. Russel established that the flow of water waves in a shallow channel has constant evolution. In recent years, the general strategy to obtain orbital stability consists in proving that the traveling wave in question minimizes a conserved functional restricted to a certain manifold. Although our method can be applied to other models, we deal with the regularized Schamel equation, which contains a fractional nonlinear term. We obtain a smooth curve of periodic traveling-wave solutions depending on the Jacobian elliptic functions and prove that such solutions are orbitally stable in the energy space. In our context, instead of minimizing the augmented Hamiltonian in the natural codimension two manifold, we minimize it in a "new" manifold, which is suitable to our purposes.
A more general model equation of nonlinear Rayleigh waves and their quasilinear solutions
NASA Astrophysics Data System (ADS)
Zhang, Shuzeng; Li, Xiongbing; Jeong, Hyunjo
2016-03-01
A more general two-dimensional wave motion equation with consideration of attenuation and nonlinearity is proposed to describe propagating nonlinear Rayleigh waves of finite amplitude. Based on the quasilinear theory, the numerical solutions for the sound beams of fundamental and second harmonic waves are constructed with Green’s function method. Compared with solutions from the parabolic approximate equation, results from the general equation have more accuracy in both the near distance of the propagation direction and the far distance of the transverse direction, as quasiplane waves are used and non-paraxial Green’s functions are obtained. It is more effective to obtain the nonlinear Rayleigh sound beam distributions accurately with the proposed general equation and solutions. Brief consideration is given to the measurement of nonlinear parameter using nonlinear Rayleigh waves.
Local measures of intermolecular free energies in solution.
Teng, Ching-Ling; Martini, Silvia; Bryant, Robert G
2004-11-24
Proton spin-lattice relaxation rate changes induced by freely diffusing oxygen in aqueous and mixed solvents are reported for representative amino acids and glucose. The local oxygen concentration at each spectrally resolved proton was deduced from the paramagnetic contribution to the relaxation rate. The measured relaxation increment is compared to that of the force-free diffusion relaxation model, and the differences are related to a free energy for the oxygen association with different portions of the solute molecules. The free energy differences are small, on the order of -800 to -2000 J/mol, but are uniformly negative for all proton positions measured on the amino acids in water and reflect the energetic benefit of weak association of hydrophobic cosolutes. For glucose, CH proton positions report negative free energies for oxygen association, the magnitude of which depends on the solvent; however, the hydroxyl positions report positive free energy differences relative to the force-free diffusion model, which is consistent with partial occupancy in the OH region by a solvent hydrogen bond. PMID:15548022
Solitary Surface Gravity Waves With Local Vortex Structure On Deep Water
NASA Astrophysics Data System (ADS)
Lukomsky, D. V.; Sedletsky, Y. V.; Lukomsky, V. P.; Gandzha, I. S.
We investigate flows with local vorticity in ideal heavy fluid with free surface in the framework of weakly non-linear theory in two-dimensional spatial representation. Steady flows with a singular structure of the velocity field in the vicinity of a free surface were found in [1] using a quadratic approximation. In the present work, we demonstrate new solutions by taking into account quadratic and cubic terms in the non-linear integro-differential equation with the kernel of Cauchy type for the limit- ing value W-(z) = lim W(z) of the complex potential W(z) y-0 i W(2)() + W(3)() + . . . - - - - (WR + WP )tt + i(WR - WP )x + d = 0, (1) - x + i0 - where z = x - t + iy, is the wave speed, WR(z) and WP (z) are the regular and singular parts of the complex potential, W(2)(z) and W(3)(z) are the quadratic and cubic terms in the expansion of W(z) at y = 0. Corresponding steady solutions of equation (1) M Nm Cnm W(z, t) = (z - t - zm)n m=1 n=1 represent singular solitary gravity waves with vortex filaments oriented across the mo- tion. Investigation of such localized steady flows is of high interest for modelling the optimal configuration of a body (M = 1) that moves without resistance with velocity and the depth of submergence given. This research has been supported by INTAS Grant 99-1637. [1] Lukomsky V.P., Sedletsky Y.V. 1994 JETP 79 761771.
NASA Astrophysics Data System (ADS)
Rai, Rajesh Kumar; Sharma, Swati; Gaur, Nidhi; Sharma, R. P.
2016-03-01
In this work, we have studied the trapping of obliquely propagating (with respect to the ambient magnetic field) weak whistler wave due to inhomogeneity created by 3D kinetic Alfvén wave (KAW) in a magnetized plasma (magnetotail region). The nonlinearity arises due to ponderomotive effects associated with 3D KAW, consequently, the background density gets modified. The weak whistler wave propagating in this modified density gets either trapped or localized. The study has been carried out numerically and semi-analytically. The semi-analytical analysis show that the typical scale size of localized 3D KAW is of the order of ion gyroradius and that of the trapped whistler is even less than that. The relevance of the results is also pointed out in the context of the recent CLUSTER observations in magnetized plasmas where whistler waves have been detected along with coherent ion-scale magnetic structures.
NASA Astrophysics Data System (ADS)
Fahlen, Jay Edward
The generation and propagation of nonlinear plasma waves is studied using particle-in-cell (PIC) simulations. We concentrate on regimes of interest to inertial fusion and space physics in which wave-particle interactions are important. Experiments soon to be performed at the National Ignition Facility require the understanding and control of stimulated Raman scattering (SRS) for their success. The SRS instability occurs when an incident laser decays into a backscattered light wave and an electron plasma wave. Recent computer simulations of SRS indicate that the daughter plasma waves have finite longitudinal and transverse extent and that they reach large amplitudes. The nonlinear behavior of such waves determines the growth, saturation, and recurrence of SRS. However, little attention has been paid to the behavior of plasma waves having these properties, and their study in SRS simulations is complicated by the large-amplitude light waves associated with the instability. Most theory and simulation work on SRS and its daughter plasma waves has been limited to infinite plane waves, often in the one-dimension limit. This thesis therefore studies isolated electron plasma waves over a wide range of parameters in one and multiple dimensions using PIC simulations. The simulations are performed with the goal of understanding the wave's behavior for parameters relevant to SRS, but the normalized parameters have general applicability to a range of densities and temperatures. Accordingly, an external ponderomotive driver generates traveling waves, driving them either continuously to study their peak amplitude and saturation mechanisms, or impulsively to study their propagation. Several novel effects are identified and characterized, including nonlinear resonance for driven waves, wave packet etching for finite-length waves, and localization and local damping for finite-width waves. Finite-length wave packets are found to erode away at a constant rate due to particle trapping
Traveling Wave Solutions for Epidemic Cholera Model with Disease-Related Death
Zhang, Tianran; Gou, Qingming
2014-01-01
Based on Codeço's cholera model (2001), an epidemic cholera model that incorporates the pathogen diffusion and disease-related death is proposed. The formula for minimal wave speed c∗ is given. To prove the existence of traveling wave solutions, an invariant cone is constructed by upper and lower solutions and Schauder's fixed point theorem is applied. The nonexistence of traveling wave solutions is proved by two-sided Laplace transform. However, to apply two-sided Laplace transform, the prior estimate of exponential decrease of traveling wave solutions is needed. For this aim, a new method is proposed, which can be applied to reaction-diffusion systems consisting of more than three equations. PMID:24883396
NASA Astrophysics Data System (ADS)
Seadawy, Aly R.
2015-12-01
The propagation of dust-ion-acoustic waves with high-energy electrons and positrons in three-dimensional is considered. The Zakharov-Kuznetsov-Burgers (ZKB) equations for the dust-ion-acoustic waves in dusty plasmas is obtained. The conservations laws and integrals of motion for the ZKB equation are deduced. In the present study, by applying the modified direct algebraic method, we found the electric field potential, electric field and quantum statistical pressure in form water wave solutions for three-dimensional ZKB equation. The solutions for the ZKB equation are obtained precisely and efficiency of the method can be demonstrated. The stability of the obtained solutions and the movement role of the waves by making the graphs of the exact solutions are discussed and analyzed.
Experimental signatures of localization in Langmuir wave turbulence
Rose, H.A.; DuBois, D.F.; Russell, D.; Bezzerides, B.
1988-01-01
Features in certain laser-plasma and ionospheric experiments are identified with the basic properties of Langmuir wave turbulence. Also, a model of caviton nucleation is presented which leads to certain novel scaling predictions. 12 refs., 19 figs.
On the Stability of Self-Similar Solutions to Nonlinear Wave Equations
NASA Astrophysics Data System (ADS)
Costin, Ovidiu; Donninger, Roland; Glogić, Irfan; Huang, Min
2016-04-01
We consider an explicit self-similar solution to an energy-supercritical Yang-Mills equation and prove its mode stability. Based on earlier work by one of the authors, we obtain a fully rigorous proof of the nonlinear stability of the self-similar blowup profile. This is a large-data result for a supercritical wave equation. Our method is broadly applicable and provides a general approach to stability problems related to self-similar solutions of nonlinear wave equations.
Are There Optical Solitary Wave Solutions in Linear Media with Group Velocity Dispersion?
NASA Technical Reports Server (NTRS)
Li, Zhonghao; Zhou, Guosheng
1996-01-01
A generalized exact optical bright solitary wave solution in a three dimensional dispersive linear medium is presented. The most interesting property of the solution is that it can exist in the normal group-velocity-dispersion (GVD) region. In addition, another peculiar feature is that it may achieve a condition of 'zero-dispersion' to the media so that a solitary wave of arbitrarily small amplitude may be propagated with no dependence on is pulse width.
Exact solution for a photoacoustic wave from a finite-length cylindrical source.
Zalev, Jason; Kolios, Michael C
2015-04-01
In wide-field pulsed photoacoustics, a nearly instantaneous source of electromagnetic energy is applied uniformly to an absorbing medium to create an acoustic wave. In this work, an exact solution is derived for the photoacoustic wave originating from a finite-length solid cylindrical source in terms of known analytic functions involving elliptic integrals of canonical form. The solution is compared with the output of a finite-element simulation. PMID:25920820
Nonlocal Symmetries, Explicit Solutions, and Wave Structures for the Korteweg-de Vries Equation
NASA Astrophysics Data System (ADS)
Ma, Zheng-Yi; Fei, Jin-Xi
2016-08-01
From the known Lax pair of the Korteweg-de Vries (KdV) equation, the Lie symmetry group method is successfully applied to find exact invariant solutions for the KdV equation with nonlocal symmetries by introducing two suitable auxiliary variables. Meanwhile, based on the prolonged system, the explicit analytic interaction solutions related to the hyperbolic and Jacobi elliptic functions are derived. Figures show the physical interaction between the cnoidal waves and a solitary wave.
NASA Astrophysics Data System (ADS)
Van Gorder, Robert A.
2015-09-01
In a recent paper, we give a study of the purely rotational motion of general stationary states in the two-dimensional local induction approximation (2D-LIA) governing superfluid turbulence in the low-temperature limit [B. Svistunov, "Superfluid turbulence in the low-temperature limit," Phys. Rev. B 52, 3647 (1995)]. Such results demonstrated that variety of stationary configurations are possible from vortex filaments exhibiting purely rotational motion in addition to commonly discussed configurations such as helical or planar states. However, the filaments (or, more properly, waves along these filaments) can also exhibit translational motion along the axis of orientation. In contrast to the study on vortex configurations for purely rotational stationary states, the present paper considers non-stationary states which exhibit a combination of rotation and translational motions. These solutions can essentially be described as waves or disturbances which ride along straight vortex filament lines. As expected from our previous work, there are a number of types of structures that can be obtained under the 2D-LIA. We focus on non-stationary states, as stationary states exhibiting translation will essentially take the form of solutions studied in [R. A. Van Gorder, "General rotating quantum vortex filaments in the low-temperature Svistunov model of the local induction approximation," Phys. Fluids 26, 065105 (2014)], with the difference being translation along the reference axis, so that qualitative appearance of the solution geometry will be the same (even if there are quantitative differences). We discuss a wide variety of general properties of these non-stationary solutions and derive cases in which they reduce to known stationary states. We obtain various routes to Kelvin waves along vortex filaments and demonstrate that if the phase and amplitude of a disturbance both propagate with the same wave speed, then Kelvin waves will result. We also consider the self
Van Gorder, Robert A.
2015-09-15
In a recent paper, we give a study of the purely rotational motion of general stationary states in the two-dimensional local induction approximation (2D-LIA) governing superfluid turbulence in the low-temperature limit [B. Svistunov, “Superfluid turbulence in the low-temperature limit,” Phys. Rev. B 52, 3647 (1995)]. Such results demonstrated that variety of stationary configurations are possible from vortex filaments exhibiting purely rotational motion in addition to commonly discussed configurations such as helical or planar states. However, the filaments (or, more properly, waves along these filaments) can also exhibit translational motion along the axis of orientation. In contrast to the study on vortex configurations for purely rotational stationary states, the present paper considers non-stationary states which exhibit a combination of rotation and translational motions. These solutions can essentially be described as waves or disturbances which ride along straight vortex filament lines. As expected from our previous work, there are a number of types of structures that can be obtained under the 2D-LIA. We focus on non-stationary states, as stationary states exhibiting translation will essentially take the form of solutions studied in [R. A. Van Gorder, “General rotating quantum vortex filaments in the low-temperature Svistunov model of the local induction approximation,” Phys. Fluids 26, 065105 (2014)], with the difference being translation along the reference axis, so that qualitative appearance of the solution geometry will be the same (even if there are quantitative differences). We discuss a wide variety of general properties of these non-stationary solutions and derive cases in which they reduce to known stationary states. We obtain various routes to Kelvin waves along vortex filaments and demonstrate that if the phase and amplitude of a disturbance both propagate with the same wave speed, then Kelvin waves will result. We also consider the self
Impedance of strip-traveling waves on an elastic half space - Asymptotic solution
NASA Technical Reports Server (NTRS)
Crandall, S. H.; Nigam, A. K.
1973-01-01
The dynamic normal-load distribution across a strip that is required to maintain a plane progressive wave along its length is studied for the case where the strip is of infinite length and lies on the surface of a homogeneous isotropic elastic half space. This configuration is proposed as a preliminary idealized model for analyzing the dynamic interaction between soils and flexible foundations. The surface load distribution across the strip and the motion of the strip are related by a pair of dual integral equations. An asymptotic solution is obtained for the limiting case of small wavelength. The nature of this solution depends importantly on the propagation velocity of the strip-traveling wave in comparison with the Rayleigh wave speed, the shear wave speed and the dilatational wave speed. When the strip-traveling wave propagates faster than the Rayleigh wave speed, a pattern of trailing Rayleigh waves is shed from the strip. The limiting amplitude of the trailing waves is provided by the asymptotic solution.
Two-state model based on the block-localized wave function method.
Mo, Yirong
2007-06-14
The block-localized wave function (BLW) method is a variant of ab initio valence bond method but retains the efficiency of molecular orbital methods. It can derive the wave function for a diabatic (resonance) state self-consistently and is available at the Hartree-Fock (HF) and density functional theory (DFT) levels. In this work we present a two-state model based on the BLW method. Although numerous empirical and semiempirical two-state models, such as the Marcus-Hush two-state model, have been proposed to describe a chemical reaction process, the advantage of this BLW-based two-state model is that no empirical parameter is required. Important quantities such as the electronic coupling energy, structural weights of two diabatic states, and excitation energy can be uniquely derived from the energies of two diabatic states and the adiabatic state at the same HF or DFT level. Two simple examples of formamide and thioformamide in the gas phase and aqueous solution were presented and discussed. The solvation of formamide and thioformamide was studied with the combined ab initio quantum mechanical and molecular mechanical Monte Carlo simulations, together with the BLW-DFT calculations and analyses. Due to the favorable solute-solvent electrostatic interaction, the contribution of the ionic resonance structure to the ground state of formamide and thioformamide significantly increases, and for thioformamide the ionic form is even more stable than the covalent form. Thus, thioformamide in aqueous solution is essentially ionic rather than covalent. Although our two-state model in general underestimates the electronic excitation energies, it can predict relative solvatochromic shifts well. For instance, the intense pi-->pi* transition for formamide upon solvation undergoes a redshift of 0.3 eV, compared with the experimental data (0.40-0.5 eV). PMID:17581041
NASA Astrophysics Data System (ADS)
Dornuf, Fabian; Dörr, Roland; Lämmle, David; Schlaak, Helmut F.; Krozer, Viktor
2016-03-01
We have studied several sensor concepts for biomedical applications operating in the millimeter wave and terahertz range. On one hand, rectangular waveguide structure were designed and extended with microfluidic channels. In this way a simple analysis of aqueous solutions at various waveguide bands is possible. In our case, we focused on the frequency range between 75 GHz and 110 GHz. On the other hand, planar sensor structures for aqueous solutions have been developed based on coplanar waveguides. With these planar sensors it is possible to concentrate the interaction volume on small sensor areas, which achieve a local exposure of the radiation to the sample. When equipping the sensor with microfluidic structures the sample volume could be reduced significantly and enabled a localized interaction with the sensor areas. The sensors are designed to exhibit a broadband behavior up to 300 GHz. Narrow-band operation can also be achieved for potentially increased sensitivity by using resonant structures. Several tests with Glucose dissolved in water show promising results for the distinction of different glucose levels at millimeter wave frequencies. The planar structures can also be used for the exposure of biological cells or cell model systems like liposomes with electromagnetic radiation. Several studies are planned to distinguish on one hand the influence of millimeter wave exposure on biological systems and also to have a spectroscopic method which enables the analysis of cell processes, like membrane transport processes, with millimeter wave and terahertz frequencies by focusing the electric field directly on the analyzing sample.
A Parabolic Equation Approach to Modeling Acousto-Gravity Waves for Local Helioseismology
NASA Astrophysics Data System (ADS)
Del Bene, Kevin; Lingevitch, Joseph; Doschek, George
2016-08-01
A wide-angle parabolic-wave-equation algorithm is developed and validated for local-helioseismic wave propagation. The parabolic equation is derived from a factorization of the linearized acousto-gravity wave equation. We apply the parabolic-wave equation to modeling acoustic propagation in a plane-parallel waveguide with physical properties derived from helioseismic data. The wavenumber power spectrum and wave-packet arrival-time structure for receivers in the photosphere with separation up to 30° is computed, and good agreement is demonstrated with measured values and a reference spectral model.
A Parabolic Equation Approach to Modeling Acousto-Gravity Waves for Local Helioseismology
NASA Astrophysics Data System (ADS)
Del Bene, Kevin; Lingevitch, Joseph; Doschek, George
2016-07-01
A wide-angle parabolic-wave-equation algorithm is developed and validated for local-helioseismic wave propagation. The parabolic equation is derived from a factorization of the linearized acousto-gravity wave equation. We apply the parabolic-wave equation to modeling acoustic propagation in a plane-parallel waveguide with physical properties derived from helioseismic data. The wavenumber power spectrum and wave-packet arrival-time structure for receivers in the photosphere with separation up to 30° is computed, and good agreement is demonstrated with measured values and a reference spectral model.
Lu, J Y; Greenleaf, J F
1992-01-01
The authors report families of generalized nondiffracting solutions of the free-space scalar wave equation, and specifically, a subset of these nondiffracting solutions, which are called X waves. These nondiffracting X waves can be almost exactly realized over a finite depth of field with finite apertures and by either broadband or bandlimited radiators. With a 25-mm diameter planar radiator, a zeroth-order broadband X wave will have about 2.5-mm lateral and 0.17-mm axial -6-dB beam widths with a -6-dB depth of field of about 171 mm. A zeroth-order bandlimited X wave was produced and measured in water by a 10 element, 50-mm diameter, 2.5-MHz PZT ceramic/polymer composite J (0) Bessel nondiffracting annular array transducer with -6-dB lateral and axial beam widths of about 4.7 mm and 0.65 mm, respectively, over a -6-dB depth of field of about 358 mm. Possible applications of X waves in acoustic imaging and electromagnetic energy transmission are discussed. PMID:18263114
Stability of a family of travelling wave solutions in a feedforward chain of phase oscillators
NASA Astrophysics Data System (ADS)
Lanford, O. E., III; Mintchev, S. M.
2015-01-01
Travelling waves are an important class of signal propagation phenomena in extended systems with a preferred direction of information flow. We study the generation of travelling waves in unidirectional chains of coupled oscillators communicating via a phase-dependent pulse-response interaction borrowed from mathematical neuroscience. Within the context of such systems, we develop a widely applicable, jointly numerical and analytical methodology for deducing existence and stability of periodic travelling waves. We provide careful numerical studies that support the existence of a periodic travelling wave solution as well as the asymptotic relaxation of a single oscillator to the wave when it is forced with the wave profile. Using this evidence as an assumption, we analytically prove global stability of waves in the infinite chain, with respect to initial perturbations of downstream sites. This rigorous stability result suggests that asymptotic relaxation to the travelling wave occurs even when the forcing is perturbed from the wave profile, a property of the motivating system that is supported by previous work as well as the convergence of the more sophisticated numerical algorithm that we propose in order to compute a high-precision approximation to the solution. We provide additional numerical studies that show that the wave is part of a one-parameter family, and we illustrate the structural robustness of this family with respect to changes in the coupling strength.
Scattering of acoustic evanescent waves by circular cylinders: Partial wave series solution
NASA Astrophysics Data System (ADS)
Marston, Philip L.
2002-05-01
Evanescent acoustical waves occur in a variety of situations such as when sound is incident on a fluid interface beyond the critical angle and when flexural waves on a plate are subsonic with respect to the surrounding fluid. The scattering by circular cylinders at normal incidence was calculated to give insight into the consequences on the scattering of the evanescence of the incident wave. To analyze the scattering, it is necessary to express the incident wave using a modified expansion involving cylindrical functions. For plane evanescent waves, the expansion becomes a double summation with products of modified and ordinary Bessel functions. The resulting modified series is found for the scattering by a fluid cylinder in an unbounded medium. The perfectly soft and rigid cases are also examined. Unlike the case of an ordinary incident wave, the counterpropagating partial waves of the same angular order have unequal magnitudes when the incident wave is evanescent. This is a consequence of the exponential dependence of the incident wave amplitude on the transverse coordinate. The associated exponential dependence of the scattering on the location of a scatterer was previously demonstrated [T. J. Matula and P. L. Marston, J. Acoust. Soc. Am. 93, 1192-1195 (1993)].
Rational solutions to the KPI equation and multi rogue waves
NASA Astrophysics Data System (ADS)
Gaillard, Pierre
2016-04-01
We construct here rational solutions to the Kadomtsev-Petviashvili equation (KPI) as a quotient of two polynomials in x, y and t depending on several real parameters. This method provides an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2 N(N + 1) in x, y and t depending on 2 N - 2 real parameters for each positive integer N. We give explicit expressions of the solutions in the simplest cases N = 1 and N = 2 and we study the patterns of their modulus in the (x , y) plane for different values of time t and parameters.
NASA Astrophysics Data System (ADS)
Semedo, Alvaro
2015-04-01
There are two types of waves at the ocean surface. During the generation and growing processes, they are designated as wind sea; as waves propagate away from their generation area, they are called swell. Swell waves travel long distances across the globe with little attenuation For this reason the wave field does not necessarily reflect the local wind field characteristics. Since swell propagates long distances, across entire ocean basins, in the open ocean the wave field is, most of the times, the result of contributions from waves with different frequencies and directions, reflecting different origins and ages. The qualitative analysis of ocean surface waves has been the focus of several recent studies, from the wave climate to the air-sea interaction community. The reason for this interest lies mostly in the fact that waves have an impact on the lower atmosphere, and that the air-sea coupling is different depending on the wave regime. Waves modulate the exchange of momentum, heat, and mass across the air-sea interface, and this modulation is different and dependent on the prevalence of one type of waves: wind sea or swell. For fully developed seas the coupling between the ocean-surface and the overlaying atmosphere can be seen as quasi-perfect, in a sense that the momentum transfer and energy dissipation at the ocean surface are in equilibrium. This can only occur in special areas of the Ocean, like marginal or enclosed seas, with limited fetch, or in Open Ocean, in areas with strong and persistent wind speed with little or no variation in direction. The wind pattern along eastern boundary currents, in the summer, is equator-ward and coast parallel, due to the presence of a semi-permanente high pressure system off-shore, in the ocean, and to a thermal low in-land. The resulting coast parallel winds are the geostrophically adjusted response to this synoptic pattern that drives upwelling along EBC, due to the Eknam transport offshore, sharpening the thermal and
Classification of homoclinic rogue wave solutions of the nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Osborne, A. R.
2014-01-01
Certain homoclinic solutions of the nonlinear Schrödinger (NLS) equation, with spatially periodic boundary conditions, are the most common unstable wave packets associated with the phenomenon of oceanic rogue waves. Indeed the homoclinic solutions due to Akhmediev, Peregrine and Kuznetsov-Ma are almost exclusively used in scientific and engineering applications. Herein I investigate an infinite number of other homoclinic solutions of NLS and show that they reduce to the above three classical homoclinic solutions for particular spectral values in the periodic inverse scattering transform. Furthermore, I discuss another infinity of solutions to the NLS equation that are not classifiable as homoclinic solutions. These latter are the genus-2N theta function solutions of the NLS equation: they are the most general unstable spectral solutions for periodic boundary conditions. I further describe how the homoclinic solutions of the NLS equation, for N = 1, can be derived directly from the theta functions in a particular limit. The solutions I address herein are actual spectral components in the nonlinear Fourier transform theory for the NLS equation: The periodic inverse scattering transform. The main purpose of this paper is to discuss a broader class of rogue wave packets1 for ship design, as defined in the Extreme Seas program. The spirit of this research came from D. Faulkner (2000) who many years ago suggested that ship design procedures, in order to take rogue waves into account, should progress beyond the use of simple sine waves. 1An overview of other work in the field of rogue waves is given elsewhere: Osborne 2010, 2012 and 2013. See the books by Olagnon and colleagues 2000, 2004 and 2008 for the Brest meetings. The books by Kharif et al. (2008) and Pelinovsky et al. (2010) are excellent references.
Singular boundary method using time-dependent fundamental solution for scalar wave equations
NASA Astrophysics Data System (ADS)
Chen, Wen; Li, Junpu; Fu, Zhuojia
2016-07-01
This study makes the first attempt to extend the meshless boundary-discretization singular boundary method (SBM) with time-dependent fundamental solution to two-dimensional and three-dimensional scalar wave equation upon Dirichlet boundary condition. The two empirical formulas are also proposed to determine the source intensity factors. In 2D problems, the fundamental solution integrating along with time is applied. In 3D problems, a time-successive evaluation approach without complicated mathematical transform is proposed. Numerical investigations show that the present SBM methodology produces the accurate results for 2D and 3D time-dependent wave problems with varied velocities c and wave numbers k.
NASA Technical Reports Server (NTRS)
Wang, Zhengzhi; Ulrich, Roger K.; Coroniti, Ferdinand V.
1995-01-01
The normal dispersion analysis for linear adiabatic wave propagation in stratified atmospheres adopts a real frequency and solves for the complex vertical wavenumber. We show that an exponentially stratified atmosphere does not have any spatially bounded normal modes for real frequencies. The usual treatment involves a representation where the imaginary part of the vertical wavenumber yields a rho(sup -1/2) dependence of the velocity amplitude which diverges as the absolute value of z approaches infinity. This solution includes a cutoff frequency below which acoustic modes cannot propagate. The standard dispersion analysis is a local representation of the wave behavior in both space and time but which is assumed to represent the motion throughout - infinity is less than t is less than infinity and 0 is less than infinity. However, any solution which has a purely sinusoidal time dependence extends through this full domain and is divergent due to the rho(sup -1/2) dependence. We show that a proper description is in terms of a near field of a boundary piston which is driven arbitrarily as a function of space and time. The atmosphere which responds to this piston is a semi-infinite layer which has an initially constant sound speed but which has the usual gravitational stratification. In a restricted domain of space and time above this boundary, the wavelike behavior of the medium may be described by frequencies and vertical wavenumbers which are both complex. When both parameters are allowed to have imaginary components, a new range of solutions is found for which there is virtually no cutoff frequency. We show that vertical energy propagation can take place through the solar atmosphere as a result of oscillations below the nominal cutoff frequency. Previously, the largest amplitude oscillations which generally have low frequencies were dropped from the calculation of energy flux becuase their frequencies are below the cutoff frequency. This new family of near
Localization of ultra-low frequency waves in multi-ion plasmas of the planetary magnetosphere
Kim, Eun -Hwa; Johnson, Jay R.; Lee, Dong -Hun
2015-01-01
By adopting a 2D time-dependent wave code, we investigate how mode-converted waves at the Ion-Ion Hybrid (IIH) resonance and compressional waves propagate in 2D density structures with a wide range of field-aligned wavenumbers to background magnetic fields. The simulation results show that the mode-converted waves have continuous bands across the field line consistent with previous numerical studies. These waves also have harmonic structures in frequency domain and are localized in the field-aligned heavy ion density well. Lastly, our results thus emphasize the importance of a field-aligned heavy ion density structure for ultra-low frequency wave propagation, and suggest that IIH wavesmore » can be localized in different locations along the field line.« less
A simple and direct method for generating travelling wave solutions for nonlinear equations
Bazeia, D. Das, Ashok; Silva, A.
2008-05-15
We propose a simple and direct method for generating travelling wave solutions for nonlinear integrable equations. We illustrate how nontrivial solutions for the KdV, the mKdV and the Boussinesq equations can be obtained from simple solutions of linear equations. We describe how using this method, a soliton solution of the KdV equation can yield soliton solutions for the mKdV as well as the Boussinesq equations. Similarly, starting with cnoidal solutions of the KdV equation, we can obtain the corresponding solutions for the mKdV as well as the Boussinesq equations. Simple solutions of linear equations can also lead to cnoidal solutions of nonlinear systems. Finally, we propose and solve some new families of KdV equations and show how soliton solutions are also obtained for the higher order equations of the KdV hierarchy using this method.
A noninvasive method to estimate pulse wave velocity in arteries locally by means of ultrasound.
Brands, P J; Willigers, J M; Ledoux, L A; Reneman, R S; Hoeks, A P
1998-11-01
Noninvasive evaluation of vessel wall properties in humans is hampered by the absence of methods to assess directly local distensibility, compliance, and Young's modulus. Contemporary ultrasound methods are capable of assessing end-diastolic artery diameter, the local change in artery diameter as a function of time, and local wall thickness. However, to assess vessel wall properties of the carotid artery, for example, the pulse pressure in the brachial artery still must be used as a substitute for local pulse pressure. The assessment of local pulse wave velocity as described in the present article provides a direct estimate of local vessel wall properties (distensibility, compliance, and Young's modulus) and, in combination with the relative change in artery cross-sectional area, an estimate of the local pulse pressure. The local pulse wave velocity is obtained by processing radio frequency ultrasound signals acquired simultaneously along two M-lines spaced at a known distance along the artery. A full derivation and mathematical description of the method to assess local pulse wave velocity, using the temporal and longitudinal gradients of the change in diameter, are presented. A performance evaluation of the method was carried out by means of experiments in an elastic tube under pulsatile pressure conditions. It is concluded that, in a phantom set-up, the assessed local pulse wave velocity provides reliable estimates for local distensibility. PMID:10385955
NASA Astrophysics Data System (ADS)
Manakov, S. V.; Santini, P. M.
2011-10-01
We study the (n + 1)-dimensional generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation, a universal equation describing the propagation of weakly nonlinear, quasi-one-dimensional waves in n + 1 dimensions, and arising in several physical contexts, such as acoustics, plasma physics and hydrodynamics. For n = 2, this equation is integrable, and has been recently shown to be a prototype model equation in the description of the two-dimensional wave breaking of localized initial data. We construct an exact solution of the (n + 1)-dimensional model containing an arbitrary function of one variable, corresponding to its parabolic invariance, describing waves, constant on their paraboloidal wave front, breaking simultaneously in all points of it. Then, we use such a solution to build a uniform approximation of the solution of the Cauchy problem, for small and localized initial data, showing that such a small and localized initial data evolving according to the (n + 1)-dimensional dKP equation break, in the long time regime, if and only if 1 ⩽ n ⩽ 3, i.e., in physical space. Such a wave breaking takes place, generically, in a point of the paraboloidal wave front, and the analytic aspects of it are given explicitly in terms of the small initial data.
Fast neural solution of a nonlinear wave equation
NASA Technical Reports Server (NTRS)
Toomarian, Nikzad; Barhen, Jacob
1992-01-01
A neural algorithm for rapidly simulating a certain class of nonlinear wave phenomena using analog VLSI neural hardware is presented and applied to the Korteweg-de Vries partial differential equation. The corresponding neural architecture is obtained from a pseudospectral representation of the spatial dependence, along with a leap-frog scheme for the temporal evolution. Numerical simulations demonstrated the robustness of the proposed approach.
Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators
NASA Astrophysics Data System (ADS)
Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.; Vainchtein, A.; Rubin, J. E.
2016-06-01
Motivated by earlier studies of artificial perceptions of light called phosphenes, we analyze traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators modeling this phenomenon. We examine the discrete model problem in its co-traveling frame and systematically obtain the corresponding traveling waves in one spatial dimension. Direct numerical simulations as well as linear stability analysis are employed to reveal the parameter regions where the traveling waves are stable, and these waves are, in turn, connected to the standing waves analyzed in earlier work. We also consider a two-dimensional extension of the model and demonstrate the robust evolution and stability of planar fronts. Our simulations also suggest the radial fronts tend to either annihilate or expand and flatten out, depending on the phase value inside and the parameter regime. Finally, we observe that solutions that initially feature two symmetric fronts with bulged centers evolve in qualitative agreement with experimental observations of phosphenes.
Self-Similar Wave Produced by Local Perturbation of the Kelvin-Helmholtz Shear-Layer Instability
NASA Astrophysics Data System (ADS)
Hoepffner, Jérôme; Blumenthal, Ralf; Zaleski, Stéphane
2011-03-01
We show that the Kelvin-Helmholtz instability excited by a localized perturbation yields a self-similar wave. The instability of the mixing layer was first conceived by Helmholtz as the inevitable growth of any localized irregularity into a spiral, but the search and uncovering of the resulting self-similar evolution was hindered by the technical success of Kelvin’s wavelike perturbation theory. The identification of a self-similar solution is useful since its specific structure is witness of a subtle nonlinear equilibrium among the forces involved. By simulating numerically the Navier-Stokes equations, we analyze the properties of the wave: growth rate, propagation speed and the dependency of its shape upon the density ratio of the two phases of the mixing layer.
Transient axial solution for plane and axisymmetric waves focused by a paraboloidal reflector.
Tsai, Yi-Te; Zhu, Jinying; Haberman, Michael R
2013-04-01
A time domain analytical solution is presented to calculate the pressure response along the axis of a paraboloidal reflector for a normally incident plane wave. This work is inspired by Hamilton's axial solution for an ellipsoidal mirror and the same methodology is employed in this paper. Behavior of the reflected waves along reflector axis is studied, and special interest is placed on focusing gain obtained at the focal point. This analytical solution indicates that the focusing gain is affected by reflector geometry and the time derivative of the input signal. In addition, focused pressure response in the focal zone given by various reflector geometries and input frequencies are also investigated. This information is useful for selecting appropriate reflector geometry in a specific working environment to achieve the best signal enhancement. Numerical simulation employing the finite element method is used to validate the analytical solution, and visualize the wave field to provide a better understanding of the propagation of reflected waves. This analytical solution can be modified to apply to non-planar incident waves with axisymmetric wavefront and non-uniform pressure distribution. An example of incident waves with conical-shaped wavefront is presented. PMID:23556573
Gravitational wave solutions in string and M-theory AdS backgrounds
Kumar, Alok; Kunduri, Hari K.
2004-11-15
In this paper, we present several gravitational wave solutions in AdS{sub 5}xS{sup 5} string backgrounds, as well as in AdS{sub 7}xS{sup 4} and AdS{sub 4}xS{sup 7} backgrounds in M theory, generalizing the results of Phys. Lett. B 594, 368 (2004).. In each case, we present the general form of such solutions and give explicit examples, preserving certain amount of supersymmetry, by taking limits on known Bogomol'nyi-Prasad-Sommerfield D3 and M2, M5-brane solutions in pp-wave backgrounds. A key feature of our examples is the possibility of a wider variety of wave profiles, than in pure gravity and string/M-theory examples known earlier, coming from the presence of various p-form field strengths appearing in the gravitational wave structure.
NASA Technical Reports Server (NTRS)
Mcgowan, David M.; Camarda, Charles J.; Scotti, Stephen J.
1992-01-01
Type IV shock wave interference heating on a blunt body causes extremely intense heating over a very localized region of the body. An analytical solution is presented to a heat transfer problem that approximates the shock wave interference heating of an engine cowl leading edge of the National Aero-Space Plane. The problem uses a simplified geometry to represent the leading edge. An analytical solution is developed that provides a means for approximating maximum temperature differences between the outer and inner surface temperatures of the leading edge. The solution is computationally efficient and, as a result, is well suited for conceptual and preliminary design or trade studies. Transient and steady state analyses are conducted, and results obtained from the analytical solution are compared with results of 2-D thermal finite element analyses over a wide range of design parameters. Isotropic materials as well as laminated composite materials are studied. Results of parametric studies are presented to indicate the effects of the thickness of the cowl leading edge and the width of the region heated by the shock wave interference on the thermal response of the leading edge.
NASA Astrophysics Data System (ADS)
Ling, Liming; Feng, Bao-Feng; Zhu, Zuonong
2016-07-01
In the present paper, we are concerned with the general analytic solutions to the complex short pulse (CSP) equation including soliton, breather and rogue wave solutions. With the aid of a generalized Darboux transformation, we construct the N-bright soliton solution in a compact determinant form, the N-breather solution including the Akhmediev breather and a general higher order rogue wave solution. The first and second order rogue wave solutions are given explicitly and analyzed. The asymptotic analysis is performed rigorously for both the N-soliton and the N-breather solutions. All three forms of the analytical solutions admit either smoothed-, cusped- or looped-type ones for the CSP equation depending on the parameters. It is noted that, due to the reciprocal (hodograph) transformation, the rogue wave solution to the CSP equation can be a smoothed, cusponed or a looped one, which is different from the rogue wave solution found so far.
NASA Astrophysics Data System (ADS)
Smyrnakis, J.; Magiropoulos, M.; Kavoulakis, G. M.; Jackson, A. D.
2013-01-01
We derive solitary-wave solutions within the mean-field approximation in quasi-one-dimensional binary mixtures of Bose-Einstein condensates under periodic boundary conditions, for the case of an effective repulsive interatomic interaction. The particular gray-bright solutions that give the global energy minima are determined. Their characteristics and the associated dispersion relation are derived.
A Defect Localization Procedure Based on Warped Lamb Waves
NASA Astrophysics Data System (ADS)
De Marchi, L.; Marzani, A.; Caporale, S.; Speciale, N.
Passive defect location procedures based on ultrasonic guided waves are widely used for structural health monitoring purposes of plate-like structures. Approaches based on the measured time-of-flight delay of propagating waves recorded at different locations are generally adopted. In these approaches, uncertainties are due to the fixed speed assumed for the incoming waves to convert their time delay in distances. These distances are next used to solve a triangulation scheme that leads to the defect location. In this paper, this inconvenient is avoided by processing the time transient measurements acquired at the different locations with a "Warped Frequency Transform" (WFT) that is capable to reveal the distance travelled by dispersive waves. In fact, by means of the WFT the recorded time waveform is converted into the incipient pulse at a distance from the origin which is proportional to the distance travelled by a mode within the signal, thus fully compensating its dispersive effect. Then, the processed time waveforms recorded from simple sensors can be used for locating defects by means of classical triangulation procedures.
Lu, T H; Lin, Y C; Liang, H C; Huang, Y J; Chen, Y F; Huang, K F
2010-02-01
We investigate the lasing modes in large-Fresnel-number laser systems with astigmatism effects. Experimental results reveal that numerous lasing modes are concentrated on exotic patterns corresponding to intriguing geometries. We theoretically use the quantum operator algebra to construct the wave representation for manifesting the origin of the localized wave patterns. PMID:20125716
Electromagnetic Waves with Frequencies Near the Local Proton Gryofrequency: ISEF-3 1 AU Observations
NASA Technical Reports Server (NTRS)
Tsurutani, B.
1993-01-01
Low Frequency electromagnetic waves with periods near the local proton gyrofrequency have been detected near 1 AU by the magnetometer onboard ISEE-3. For these 1 AU waves two physical processes are possible: solar wind pickup of nuetral (interstellar?) particles and generation by relativistic electron beams propagating from the Sun.
A new semi-analytical solution for inertial waves in a rectangular parallelepiped
NASA Astrophysics Data System (ADS)
Nurijanyan, S.; Bokhove, O.; Maas, L. R. M.
2013-12-01
A study of inertial gyroscopic waves in a rotating homogeneous fluid is undertaken both theoretically and numerically. A novel approach is presented to construct a semi-analytical solution of a linear three-dimensional fluid flow in a rotating rectangular parallelepiped bounded by solid walls. The three-dimensional solution is expanded in vertical modes to reduce the dynamics to the horizontal plane. On this horizontal plane, the two dimensional solution is constructed via superposition of "inertial" analogs of surface Poincaré and Kelvin waves reflecting from the walls. The infinite sum of inertial Poincaré waves has to cancel the normal flow of two inertial Kelvin waves near the boundaries. The wave system corresponding to every vertical mode results in an eigenvalue problem. Corresponding computations for rotationally modified surface gravity waves are in agreement with numerical values obtained by Taylor ["Tidal oscillations in gulfs and basins," Proc. London Math. Soc., Ser. 2 XX, 148-181 (1921)], Rao ["Free gravitational oscillations in rotating rectangular basins," J. Fluid Mech. 25, 523-555 (1966)] and also, for inertial waves, by Maas ["On the amphidromic structure of inertial waves in a rectangular parallelepiped," Fluid Dyn. Res. 33, 373-401 (2003)] upon truncation of an infinite matrix. The present approach enhances the currently available, structurally concise modal solution introduced by Maas. In contrast to Maas' approach, our solution does not have any convergence issues in the interior and does not suffer from Gibbs phenomenon at the boundaries. Additionally, an alternative finite element method is used to contrast these two semi-analytical solutions with a purely numerical one. The main differences are discussed for a particular example and one eigenfrequency.
A new model for algebraic Rossby solitary waves in rotation fluid and its solution
NASA Astrophysics Data System (ADS)
Chen, Yao-Deng; Yang, Hong-Wei; Gao, Yu-Fang; Yin, Bao-Shu; Feng, Xing-Ru
2015-09-01
A generalized Boussinesq equation that includes the dissipation effect is derived to describe a kind of algebraic Rossby solitary waves in a rotating fluid by employing perturbation expansions and stretching transformations of time and space. Using this equation, the conservation laws of algebraic Rossby solitary waves are discussed. It is found that the mass, the momentum, the energy, and the velocity of center of gravity of the algebraic solitary waves are conserved in the propagation process. Finally, the analytical solution of the equation is generated. Based on the analytical solution, the properties of the algebraic solitary waves and the dissipation effect are discussed. The results point out that, similar to classic solitary waves, the dissipation can cause the amplitude and the speed of solitary waves to decrease; however, unlike classic solitary waves, the algebraic solitary waves can split during propagation and the decrease of the detuning parameter can accelerate the occurrence of the solitary waves fission phenomenon. Project supported by the Shandong Provincial Key Laboratory of Marine Ecology and Environment and Disaster Prevention and Mitigation Project, China (Grant No. 2012010), the National Natural Science Foundation of China (Grant Nos. 41205082 and 41476019), the Special Funds for Theoretical Physics of the National Natural Science Foundation of China (Grant No. 11447205), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), China.
An exact solution for effects of topography on free Rayleigh waves
Savage, W.Z.
2004-01-01
An exact solution for the effects of topography on Rayleigh wave amplification is presented. The solution is obtained by incorporating conformal mapping into complex-variable stress functions developed for free Rayleigh wave propagation in an elastic half-space with a flat upper surface. Results are presented for free Rayleigh wave propagation across isolated symmetric ridges and valleys. It is found for wavelengths that are comparable to ridge widths that horizontal Rayleigh wave amplitudes are amplified at ridge crests and that vertical amplitudes are strongly reduced near ridge crests relative to horizontal and vertical amplitudes of free Rayleigh waves in the flat case. Horizontal amplitudes are strongly deamplified at valley bottoms relative to those for the flat case for Rayleigh wavelengths comparable to valley widths. Wave amplitudes in the symmetric ridges and valleys asymptotically approach those for the flat case with increased wavelengths, increased ridge and valley widths, and with horizontal distance from and depth below the isolated ridges and valleys. Also, prograde particle motion is predicted near crests of narrow ridges and near the bottoms of narrow valleys. Finally, application of the theory at two sites known for topographic wave amplification gives a predicted surface wave amplification ratio of 3.80 at the ridge center for a frequency of 1.0 Hz at Robinwood Ridge in northern California and a predicted surface wave amplification ratio of 1.67 at the ridge center for the same frequency at the Cedar Hill Nursery site at Tarzana in southern California.
Spin wave localization in one-dimensional magnonic microcavity comprising yttrium iron garnet
Kanazawa, Naoki; Goto, Taichi Inoue, Mitsuteru
2014-08-28
We demonstrate the localization of magnetostatic surface waves, i.e., spin waves, in a one-dimensional magnonic microcavity substantialized with periodical conductivity modulation. The narrow localized state is observed inside band gaps and is responsible for a sharp transmission peak. The experimental results strongly agree with the theoretical prediction made with the shape magnetic anisotropy of the propagating medium composed of yttrium iron garnet taken into account.
Nealy, Jennifer L; Collis, Jon M; Frank, Scott D
2016-04-01
Normal mode solutions to range-independent seismo-acoustic problems are benchmarked against elastic parabolic equation solutions and then used to benchmark the shear elastic parabolic equation self-starter [Frank, Odom, and Collis, J. Acoust. Soc. Am. 133, 1358-1367 (2013)]. The Pekeris waveguide with an elastic seafloor is considered for a point source located in the ocean emitting compressional waves, or in the seafloor, emitting both compressional and shear waves. Accurate solutions are obtained when the source is in the seafloor, and when the source is at the interface between the fluid and elastic layers. PMID:27106346
Weak solutions and blow-up for wave equations of p-Laplacian type with supercritical sources
NASA Astrophysics Data System (ADS)
Pei, Pei; Rammaha, Mohammad A.; Toundykov, Daniel
2015-08-01
This paper investigates a quasilinear wave equation with Kelvin-Voigt damping, utt - Δpu - Δut = f(u), in a bounded domain Ω ⊂ ℝ3 and subject to Dirichlét boundary conditions. The operator Δp, 2 < p < 3, denotes the classical p-Laplacian. The nonlinear term f(u) is a source feedback that is allowed to have a supercritical exponent, in the sense that the associated Nemytskii operator is not locally Lipschitz from W0 1 , p ( Ω ) into L2(Ω). Under suitable assumptions on the parameters, we prove existence of local weak solutions, which can be extended globally provided the damping term dominates the source in an appropriate sense. Moreover, a blow-up result is proved for solutions with negative initial total energy.
Exact traveling wave solutions of the van der Waals normal form for fluidized granular matter
NASA Astrophysics Data System (ADS)
Abourabia, A. M.; Morad, A. M.
2015-11-01
Analytical solutions of the van der Waals normal form for fluidized granular media have been done to study the phase separation phenomenon by using two different exact methods. The Painlevé analysis is discussed to illustrate the integrability of the model equation. An auto-Bäcklund transformation is presented via the truncated expansion and symbolic computation. The results show that the exact solutions of the model introduce solitary waves of different types. The solutions of the hydrodynamic model and the van der Waals equation exhibit a behavior similar to the one observed in molecular dynamic simulations such that two pairs of shock and rarefaction waves appear and move away, giving rise to the bubbles. The dispersion properties and the relation between group and phase velocities of the model equation are studied using the plane wave assumption. The diagrams are drawn to illustrate the physical properties of the exact solutions, and indicate their stability and bifurcation.
Analytical solution of boundary integral equations for 2-D steady linear wave problems
NASA Astrophysics Data System (ADS)
Chuang, J. M.
2005-10-01
Based on the Fourier transform, the analytical solution of boundary integral equations formulated for the complex velocity of a 2-D steady linear surface flow is derived. It has been found that before the radiation condition is imposed, free waves appear both far upstream and downstream. In order to cancel the free waves in far upstream regions, the eigensolution of a specific eigenvalue, which satisfies the homogeneous boundary integral equation, is found and superposed to the analytical solution. An example, a submerged vortex, is used to demonstrate the derived analytical solution. Furthermore, an analytical approach to imposing the radiation condition in the numerical solution of boundary integral equations for 2-D steady linear wave problems is proposed.
Water Wave Solutions of the Coupled System Zakharov-Kuznetsov and Generalized Coupled KdV Equations
Seadawy, A. R.; El-Rashidy, K.
2014-01-01
An analytic study was conducted on coupled partial differential equations. We formally derived new solitary wave solutions of generalized coupled system of Zakharov-Kuznetsov (ZK) and KdV equations by using modified extended tanh method. The traveling wave solutions for each generalized coupled system of ZK and KdV equations are shown in form of periodic, dark, and bright solitary wave solutions. The structures of the obtained solutions are distinct and stable. PMID:25374940
Water wave solutions of the coupled system Zakharov-Kuznetsov and generalized coupled KdV equations.
Seadawy, A R; El-Rashidy, K
2014-01-01
An analytic study was conducted on coupled partial differential equations. We formally derived new solitary wave solutions of generalized coupled system of Zakharov-Kuznetsov (ZK) and KdV equations by using modified extended tanh method. The traveling wave solutions for each generalized coupled system of ZK and KdV equations are shown in form of periodic, dark, and bright solitary wave solutions. The structures of the obtained solutions are distinct and stable. PMID:25374940
Local Analytic Solutions of a Functional Differential Equation
NASA Astrophysics Data System (ADS)
Liu, Lingxia
This paper is concerned with the existence of analytic solutions of an iterative functional differential equation. Employing the method of majorant series, we need to discuss the constant α given in Schröder transformation. we study analytic solutions of the equation in the case of α at resonance and the case of α near resonance under the Brjuno condition.
Examples of Heun and Mathieu functions as solutions of wave equations in curved spaces
NASA Astrophysics Data System (ADS)
Birkandan, T.; Hortaçsu, M.
2007-02-01
We give examples of where the Heun function exists as solutions of wave equations encountered in general relativity. As a new example we find that while the Dirac equation written in the background of Nutku helicoid metric yields Mathieu functions as its solutions in four spacetime dimensions, the trivial generalization to five dimensions results in the double confluent Heun function. We reduce this solution to the Mathieu function with some transformations.
Quasiperiodic driving of Anderson localized waves in one dimension
NASA Astrophysics Data System (ADS)
Hatami, H.; Danieli, C.; Bodyfelt, J. D.; Flach, S.
2016-06-01
We consider a quantum particle in a one-dimensional disordered lattice with Anderson localization in the presence of multifrequency perturbations of the onsite energies. Using the Floquet representation, we transform the eigenvalue problem into a Wannier-Stark basis. Each frequency component contributes either to a single channel or a multichannel connectivity along the lattice, depending on the control parameters. The single-channel regime is essentially equivalent to the undriven case. The multichannel driving increases substantially the localization length for slow driving, showing two different scaling regimes of weak and strong driving, yet the localization length stays finite for a finite number of frequency components.
NASA Astrophysics Data System (ADS)
Zhao, Zhonglong; Han, Bo
2016-05-01
In this paper, we focus on a (2+1)-dimensional generalized breaking soliton equation, which describes the (2+1)-dimensional interaction of a Riemann wave propagating along the y -direction with a long wave along the x-direction. Based on a multidimensional Riemann theta function, the quasiperiodic wave solutions of a (2+1)-dimensional generalized breaking soliton equation are investigated by means of the bilinear Bäcklund transformation. The relations between the quasiperiodic wave solutions and the soliton solutions are rigorously established by a limiting procedure. The dynamical behaviors of the quasiperiodic wave solutions are discussed by presenting the numerical figures.
Discrimination of Mixed Taste Solutions using Ultrasonic Wave and Soft Computing
NASA Astrophysics Data System (ADS)
Kojima, Yohichiro; Kimura, Futoshi; Mikami, Tsuyoshi; Kitama, Masataka
In this study, ultrasonic wave acoustic properties of mixed taste solutions were investigated, and the possibility of taste sensing based on the acoustical properties obtained was examined. In previous studies, properties of solutions were discriminated based on sound velocity, amplitude and frequency characteristics of ultrasonic waves propagating through the five basic taste solutions and marketed beverages. However, to make this method applicable to beverages that contain many taste substances, further studies are required. In this paper, the waveform of an ultrasonic wave with frequency of approximately 5 MHz propagating through mixed solutions composed of sweet and salty substance was measured. As a result, differences among solutions were clearly observed as differences in their properties. Furthermore, these mixed solutions were discriminated by a self-organizing neural network. The ratio of volume in their mixed solutions was estimated by a distance-type fuzzy reasoning method. Therefore, the possibility of taste sensing was shown by using ultrasonic wave acoustic properties and the soft computing, such as the self-organizing neural network and the distance-type fuzzy reasoning method.
Localized Nonlinear Waves in Systems with Time- and Space-Modulated Nonlinearities
Belmonte-Beitia, Juan; Perez-Garcia, Victor M.; Vekslerchik, Vadym; Konotop, Vladimir V.
2008-04-25
Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schroedinger equations with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general theory and use it to calculate explicitly nontrivial solutions such as periodic (breathers), resonant, or quasiperiodically oscillating solitons. Some implications to the field of matter waves are also discussed.
NASA Astrophysics Data System (ADS)
Van Gorder, Robert A.
2016-05-01
Very recent experimental work has demonstrated the existence of Kelvin waves along quantized vortex filaments in superfluid helium. The possible configurations and motions of such filaments is of great physical interest, and Svistunov previously obtained a Hamiltonian formulation for the dynamics of quantum vortex filaments in the low-temperature limit under the assumption that the vortex filament is essentially aligned along one axis, resulting in a two-dimensional (2D) problem. It is standard to approximate the dynamics of thin filaments by employing the local induction approximation (LIA), and we show that by putting the two-dimensional LIA into correspondence with the first equation in the integrable Wadati-Konno-Ichikawa-Schimizu (WKIS) hierarchy, we immediately obtain solutions to the two-dimensional LIA, such as helix, planar, and self-similar solutions. These solutions are obtained in a rather direct manner from the WKIS equation and then mapped into the 2D-LIA framework. Furthermore, the approach can be coupled to existing inverse scattering transform results from the literature in order to obtain solitary wave solutions including the analog of the Hasimoto one-soliton for the 2D-LIA. One large benefit of the approach is that the correspondence between the 2D-LIA and the WKIS allows us to systematically obtain vortex filament solutions directly in the Cartesian coordinate frame without the need to solve back from curvature and torsion. Implications of the results for the physics of experimentally studied solitary waves, Kelvin waves, and postvortex reconnection events are mentioned.
Existence of Anderson localization of classical waves in a random two-component medium
Soukoulis, C.M.; Economou, E.N.; Grest, G.S.; Cohen, M.H.
1989-01-30
An exact mapping of the classical wave problem to that of electronic motion is utilized together with extensive numerical results to examine the question of the existence of genuine localization (i.e., one occurring when both components have real positive dielectric constants) of classical waves in random binary alloys A/sub 1-//sub x/B/sub x/. We find that scalar waves do exhibit localization. We have also developed a coherent potential approximation which for x<0.2 gives results not that much different from the numerical ones. This result can be easily generalized to electromagnetic fields as well.
Localized waves supported by the rotating waveguide array.
Zhang, Xiao; Ye, Fangwei; Kartashov, Yaroslav V; Vysloukh, Victor A; Chen, Xianfeng
2016-09-01
We show that truncated rotating square waveguide arrays support new types of localized modes that exist even in the linear case, in complete contrast to localized excitations in nonrotating arrays requiring nonlinearity for their existence and forming above the energy flow threshold. These new modes appear either around an array center, since the rotation leads to the emergence of the effective attractive potential with a minimum at the rotation axis, or in the array corners, in which case localization occurs due to competition between the centrifugal force and total internal reflection at the interface of the truncated array. The degree of localization of the central and corner modes mediated by the rotation increases with the rotation frequency. The stable rotating soliton families bifurcating from linear modes are analyzed in both focusing and defocusing media. PMID:27607984
Lin, Min-Kai
2012-07-20
Numerical calculations of the linear Rossby wave instability (RWI) in global three-dimensional (3D) disks are presented. The linearized fluid equations are solved for vertically stratified, radially structured disks with either a locally isothermal or polytropic equation of state, by decomposing the vertical dependence of the perturbed hydrodynamic quantities into Hermite and Gegenbauer polynomials, respectively. It is confirmed that the RWI operates in 3D. For perturbations with vertical dependence assumed above, there is little difference in growth rates between 3D and two-dimensional (2D) calculations. Comparison between 2D and 3D solutions of this type suggests the RWI is predominantly a 2D instability and that 3D effects, such as vertical motion, can be interpreted as a perturbative consequence of the dominant 2D flow. The vertical flow around corotation, where vortex formation is expected, is examined. In locally isothermal disks, the expected vortex center remains in approximate vertical hydrostatic equilibrium. For polytropic disks, the vortex center has positive vertical velocity, whose magnitude increases with decreasing polytropic index n.
Attenuation of transverse waves by using a metamaterial beam with lateral local resonators
NASA Astrophysics Data System (ADS)
Huang, Hsin-Haou; Lin, Chi-Kuang; Tan, Kwek-Tze
2016-08-01
This study numerically and experimentally investigated the wave propagation and vibrational behavior of a metamaterial beam with lateral local resonators. A two-dimensional simplified analytical model was proposed for feasibly and accurately capturing the in-plane dispersion behavior, which can be used for the initial design. The out-of-plane wave motions, however, required advanced three-dimensional (3D) modeling. Through experimental validations, 3D finite element simulations were demonstrated to be suitable for advanced design and analysis. This study provided a basis for designing metabeams for transverse wave mitigation. The proposed concept can be further extended to 3D metamaterial plates for wave and vibrational mitigation applications.
NASA Astrophysics Data System (ADS)
Lennart Kinscher, Jannes; Bernard, Pascal; Contrucci, Isabelle; Mangeney, Anne; Piguet, Jack Pierre; Bigarre, Pascal
2014-05-01
In order to improve our understanding of hazardous ground failures, caving processes, and collapses of large natural or man-made underground cavities, we studied microseismicity induced by the development and collapse of a salt solution mining cavity with a diameter of ~ 200 m at Cerville-Buissoncourt in Lorraine, France. Microseismicity was recorded as part of a large geophysical, multi-parameter monitoring research project (GISOS) by a local, high resolution, triggered 40 Hz geophone monitoring system consisting of five one-component and four three-component borehole stations located around and in the center of the cavity. The recorded microseismic events are very numerous (~ 50.000 recorded event files) where the major portion (~ 80 %) appear in unusual swarming sequences constituted by complex clusters of superimposed microseismic events. Body wave phase based routine tools for microseismic event detection and localization face strong limitations in the treatment of these signals. To overcome these shortcomings, we developed two probabilistic methods being able to assess the spatio-temporal characteristics in a semi-automatic manner. The first localization approach uses simple signal amplitude estimates on different frequency bands, and an attenuation model to constrain hypocenter source location. The second approach was designed to identify significantly polarized P wave energies and the associated polarization angles. Both approaches and its probabilistic conjunction were applied to the data of a two months lasting microseismic crisis occurring one year before the final collapse that was related to caving processes leading to a maximal growth of ~ 50 m of the cavity roof. The obtained epicenter locations show systematic spatio-temporal migration trends observed for different time scales. During three phases of major swarming activity, epicenter migration trends appear in the order of several seconds to minutes, are spatially constrained, and show partially a
Absence of localized acoustic waves in a scale-free correlated random system.
Costa, A E B; de Moura, F A B F
2011-02-16
We numerically study the propagation of acoustic waves in a one-dimensional medium with a scale-free long-range correlated elasticity distribution. The random elasticity distribution is assumed to have a power spectrum S(k) ∼ 1/k(α). By using a transfer-matrix method we solve the discrete version of the scalar wave equation and compute the localization length. In addition, we apply a second-order finite-difference method for both the time and spatial variables and study the nature of the waves that propagate in the chain. Our numerical data indicate the presence of extended acoustic waves for a high degree of correlations. In contrast with local correlations, we numerically demonstrate that scale-free correlations promote a stable phase of free acoustic waves in the thermodynamic limit. PMID:21406919
The Superposition of Eastward and Westward Rossby Waves in Response to Localized Forcing
NASA Astrophysics Data System (ADS)
Shaman, J. L.; Tziperman, E.
2015-12-01
Rossby waves are a principal form of atmospheric communication between disparate parts of the climate system. These planetary waves are typically excited by diabatic or orographic forcing and can be subject to considerable downstream modification. Due to differences in wave properties, including vertical structure, phase speed and group velocity, Rossby waves exhibit a wide range of behaviors. Here we demonstrate the combined effects of eastward propagating stationary barotropic Rossby waves and westward propagating very low zonal wavenumber stationary barotropic Rossby waves on the atmospheric response to wintertime El Niño convective forcing over the tropical Pacific. Experiments are conducted using the Community Atmospheric Model 4.0 in which both diabatic forcing over the Pacific and localized relaxation outside the forcing region are applied. The localized relaxation is used to dampen Rossby wave propagation to either the west or east of the forcing region and isolate the alternate direction signal. Wave responses match theoretical expectations and clarify that observed downstream stationary responses to diabatic forcing result from the superposition of planetary wave signals emanating in alternate directions.
Choudhury, Niharendu; Pettitt, Bernard M.
2005-05-15
We employ constant pressure molecular dynamics simulations to investigate the effects of solute size and solute-water dispersion interactions on the salvation behavior of nanoscopic hydrpophobic model solutes in water at normal temperature and pressure. The hydration behavior around a single planar atomic model solute as well as a pair of such solutes have been considered. The hydration water structure of a model nanoscopic solute with standard Lennard-Jones interaction is shown to be significantly different from that of their purely repulsive analogues. The density of water in the first salvation shell of a Lennard-Jones solute is much higher than that of bulk water and it remains almost unchanged with the increase of the solute dimensions from one to a few nanometers. On the other hand, for a purely repulsive analogue of the above model, solute hydration behavior shows a marked solute size dependence. The contact density of water in this case decreases with the increasing dimension of the solute. We also demonstrate the effect of solute-solvent attraction on the cavity formation in the inter solute region between two solutes with an inter solute separation of 6.8A, corresponding to the first solvent separated minimum in the free energy Profile as obtained in our earlier work.
Transient Localized Wave Patterns and Their Application to Migraine
2013-01-01
Abstract Transient dynamics is pervasive in the human brain and poses challenging problems both in mathematical tractability and clinical observability. We investigate statistical properties of transient cortical wave patterns with characteristic forms (shape, size, duration) in a canonical reaction-diffusion model with mean field inhibition. The patterns are formed by ghost behavior near a saddle-node bifurcation in which a stable traveling wave (node) collides with its critical nucleation mass (saddle). Similar patterns have been observed with fMRI in migraine. Our results support the controversial idea that waves of cortical spreading depression (SD) have a causal relationship with the headache phase in migraine and, therefore, occur not only in migraine with aura (MA), but also in migraine without aura (MO), i.e., in the two major migraine subtypes. We suggest a congruence between the prevalence of MO and MA with the statistical properties of the traveling waves’ forms according to which two predictions follow: (i) the activation of nociceptive mechanisms relevant for headache is dependent upon a sufficiently large instantaneous affected cortical area; and (ii) the incidence of MA is reflected in the distance to the saddle-node bifurcation. We also observed that the maximal instantaneous affected cortical area is anticorrelated to both SD duration and total affected cortical area, which can explain why the headache is less severe in MA than in MO. Furthermore, the contested notion of MO attacks with silent aura is resolved. We briefly discuss model-based control and means by which neuromodulation techniques may affect pathways of pain formation. PMID:23718283
Behavior of the formal solution to a mixed problem for the wave equation
NASA Astrophysics Data System (ADS)
Khromov, A. P.
2016-02-01
The behavior of the formal solution, obtained by the Fourier method, to a mixed problem for the wave equation with arbitrary two-point boundary conditions and the initial condition φ(x) (for zero initial velocity) with weaker requirements than those for the classical solution is analyzed. An approach based on the Cauchy-Poincare technique, consisting in the contour integration of the resolvent of the operator generated by the corresponding spectral problem, is used. Conditions giving the solution to the mixed problem when the wave equation is satisfied only almost everywhere are found. When φ(x) is an arbitrary function from L 2[0, 1], the formal solution converges almost everywhere and is a generalized solution to the mixed problem.
One Single Static Measurement Predicts Wave Localization in Complex Structures
NASA Astrophysics Data System (ADS)
Lefebvre, Gautier; Gondel, Alexane; Dubois, Marc; Atlan, Michael; Feppon, Florian; Labbé, Aimé; Gillot, Camille; Garelli, Alix; Ernoult, Maxence; Mayboroda, Svitlana; Filoche, Marcel; Sebbah, Patrick
2016-08-01
A recent theoretical breakthrough has brought a new tool, called the localization landscape, for predicting the localization regions of vibration modes in complex or disordered systems. Here, we report on the first experiment which measures the localization landscape and demonstrates its predictive power. Holographic measurement of the static deformation under uniform load of a thin plate with complex geometry provides direct access to the landscape function. When put in vibration, this system shows modes precisely confined within the subregions delineated by the landscape function. Also the maxima of this function match the measured eigenfrequencies, while the minima of the valley network gives the frequencies at which modes become extended. This approach fully characterizes the low frequency spectrum of a complex structure from a single static measurement. It paves the way for controlling and engineering eigenmodes in any vibratory system, especially where a structural or microscopic description is not accessible.
One Single Static Measurement Predicts Wave Localization in Complex Structures.
Lefebvre, Gautier; Gondel, Alexane; Dubois, Marc; Atlan, Michael; Feppon, Florian; Labbé, Aimé; Gillot, Camille; Garelli, Alix; Ernoult, Maxence; Mayboroda, Svitlana; Filoche, Marcel; Sebbah, Patrick
2016-08-12
A recent theoretical breakthrough has brought a new tool, called the localization landscape, for predicting the localization regions of vibration modes in complex or disordered systems. Here, we report on the first experiment which measures the localization landscape and demonstrates its predictive power. Holographic measurement of the static deformation under uniform load of a thin plate with complex geometry provides direct access to the landscape function. When put in vibration, this system shows modes precisely confined within the subregions delineated by the landscape function. Also the maxima of this function match the measured eigenfrequencies, while the minima of the valley network gives the frequencies at which modes become extended. This approach fully characterizes the low frequency spectrum of a complex structure from a single static measurement. It paves the way for controlling and engineering eigenmodes in any vibratory system, especially where a structural or microscopic description is not accessible. PMID:27563967
On waves below the local proton gyrofrequency in auroral acceleration regions
Gustafsson, G. ); Andre, M.; Matson, L. ); Koskinen, H. )
1990-05-01
The Viking wave electric field and density fluctuation measurements together with simultaneous particle observations are used to study waves at frequencies below the local proton gyrofrequency. Such waves were observed during about 20% of nightside auroral field line crossings by Viking at altitudes between 2,000 and 10,000 km. The observations are different from earlier spacecraft observations of similar waves in such a way that the center frequency in about one out of four of the observed events was below the gyrofrequency of singly charged helium, which has not been reported previously. The waves were well correlated with precipitating electrons of energies of a few keV and with VLF auroral hiss. Detailed investigations of simultaneously observed wave emissions, particles, and total densities strongly suggest that secondary peaks at keV energies in the distributions of downgoing electrons can cause the emissions.
A theory of non-local linear drift wave transport
Moradi, S.; Anderson, J.; Weyssow, B.
2011-06-15
Transport events in turbulent tokamak plasmas often exhibit non-local or non-diffusive action at a distance features that so far have eluded a conclusive theoretical description. In this paper a theory of non-local transport is investigated through a Fokker-Planck equation with fractional velocity derivatives. A dispersion relation for density gradient driven linear drift modes is derived including the effects of the fractional velocity derivative in the Fokker-Planck equation. It is found that a small deviation (a few percent) from the Maxwellian distribution function alters the dispersion relation such that the growth rates are substantially increased and thereby may cause enhanced levels of transport.
Van Gorder, Robert A
2015-05-01
The Hasimoto transformation between the classical LIA (local induction approximation, a model approximating the motion of a thin vortex filament) and the nonlinear Schrödinger equation (NLS) has proven very useful in the past, since it allows one to construct new solutions to the LIA once a solution to the NLS is known. In the present paper, the quantum form of the LIA (which includes mutual friction effects) is put into correspondence with a type of complex nonlinear dispersive partial differential equation (PDE) with cubic nonlinearity (similar in form to a Ginsburg-Landau equation, with additional nonlinear terms). Transforming the quantum LIA in such a way enables one to obtain quantum vortex filament solutions once solutions to this dispersive PDE are known. From our quantum Hasimoto transformation, we determine the form and behavior of Stokes waves, a standing one-soliton, traveling waves, and similarity solutions under normal and binormal friction effects. The quantum Hasimoto transformation is useful when normal fluid velocity is relatively weak, so for the case where the normal fluid velocity is dominant we resort to other approaches. We exhibit a number of solutions that exist only in the presence of the normal fluid velocity and mutual friction terms (which would therefore not exist in the limit taken to obtain the classical LIA, decaying into line filaments under such a limit), examples of which include normal fluid driven helices, stationary and propagating topological solitons, and a vortex ring whose radius varies inversely with the normal fluid magnitude. We show that, while chaos may not be impossible under the quantum LIA, it should not be expected to arise from traveling waves along quantum vortex filaments under the quantum LIA formulation. PMID:26066272
NASA Astrophysics Data System (ADS)
Van Gorder, Robert A.
2015-05-01
The Hasimoto transformation between the classical LIA (local induction approximation, a model approximating the motion of a thin vortex filament) and the nonlinear Schrödinger equation (NLS) has proven very useful in the past, since it allows one to construct new solutions to the LIA once a solution to the NLS is known. In the present paper, the quantum form of the LIA (which includes mutual friction effects) is put into correspondence with a type of complex nonlinear dispersive partial differential equation (PDE) with cubic nonlinearity (similar in form to a Ginsburg-Landau equation, with additional nonlinear terms). Transforming the quantum LIA in such a way enables one to obtain quantum vortex filament solutions once solutions to this dispersive PDE are known. From our quantum Hasimoto transformation, we determine the form and behavior of Stokes waves, a standing one-soliton, traveling waves, and similarity solutions under normal and binormal friction effects. The quantum Hasimoto transformation is useful when normal fluid velocity is relatively weak, so for the case where the normal fluid velocity is dominant we resort to other approaches. We exhibit a number of solutions that exist only in the presence of the normal fluid velocity and mutual friction terms (which would therefore not exist in the limit taken to obtain the classical LIA, decaying into line filaments under such a limit), examples of which include normal fluid driven helices, stationary and propagating topological solitons, and a vortex ring whose radius varies inversely with the normal fluid magnitude. We show that, while chaos may not be impossible under the quantum LIA, it should not be expected to arise from traveling waves along quantum vortex filaments under the quantum LIA formulation.