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.
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
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.
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.
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.
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.
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
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.
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.
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
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.
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
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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
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...
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).
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
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.
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
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.
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.
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
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
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.
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
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.
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.
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
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)
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.
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.
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.
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
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.
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.
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)
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
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.
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.
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
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
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)].
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.
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
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.
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
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.
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.
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.
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.
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.
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.
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 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.
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.
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
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.
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.
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.
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.
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.
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
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.
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
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.
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.
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.
Analytical solutions and rogue waves in (3+1)-dimensional nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Ma, Zheng-Yi; Ma, Song-Hua
2012-03-01
Analytical solutions in terms of rational-like functions are presented for a (3+1)-dimensional nonlinear Schrödinger equation with time-varying coefficients and a harmonica potential using the similarity transformation and a direct ansatz. Several free functions of time t are involved to generate abundant wave structures. Three types of elementary functions are chosen to exhibit the corresponding nonlinear rogue wave propagations.
NASA Astrophysics Data System (ADS)
Liu, Jun; Dai, Zheng-De; Lin, Song-Qing
2010-05-01
Exact heteroclinic breather-wave solutions for Davey-Stewartson (DSI, DSII) system with periodic boundary condition are constructed using Hirota's bilinear form method and generalized ansatz method. The heteroclinic structure of wave is investigated.
Numerical study of solute transport in shallow beach aquifers subjected to waves and tides
NASA Astrophysics Data System (ADS)
Geng, Xiaolong; Boufadel, Michel C.
2015-02-01
A numerical study was conducted to investigate the fate of solute in a laboratory beach in response to waves and tides. A new temporal upscaling approach labeled "net inflow" was introduced to address impacts of waves on solute transport within beaches. Numerical simulations using a computational fluid dynamic model were used as boundary conditions for the two-dimensional variably saturated flow and solute transport model MARUN. The modeling approach was validated against experimental data of solute transport due to waves and tides. Exchange fluxes across the beach face and subsurface solute transport (e.g., trajectory, movement speed, and residence time) were quantified. Simulation results revealed that waves increased the exchange fluxes, and engendered a wider exchange flux zone along the beach surface. Compared to tide-only forcing, waves superimposed on tide caused the plume to be deeper into the beach, and to migrate more seaward. The infiltration into the beach was found to be directly proportional to the general hydraulic gradient in the beach and inversely proportional to the matrix retention (or capillary) capacity. The simulations showed that a higher inland water table would attenuate wave-caused seawater infiltration, which might impact beach geochemical processes (e.g., nutrient recycle and redox condition), especially at low tide zone. The concept of biochemical residence time maps (BRTM) was introduced to account for the net effect of limiting concentration of chemicals on biochemical reactions. It was found that waves shifted the BRTMs downward and seaward in the beach, and subsequently they engendered different biochemical conditions within the beach.
Computation of viscous blast wave solutions with an upwind finite volume method
NASA Technical Reports Server (NTRS)
Molvik, Gregory A.
1987-01-01
A fully conservative, viscous, implicit, upwind, finite-volume scheme for the thin-layer Navier-Stokes equations is described with application to blast wave flow fields. In this scheme, shocks are captured without the oscillations typical of central differencing techniques and wave speeds are accurately predicted. The finite volume philosophy ensures conservation and since boundary conditions are also treated conservatively, accurate reflections of waves from surfaces are assured. Viscous terms in the governing equations are treated in a manner consistent with the finite volume philosophy, resulting in very accurate prediction of boundary layer quantities. Numerical results are presented for four viscous problems: a steady boundary layer, a shock-induced boundary layer, a blast wave/cylinder interaction and a blast wave/supersonic missile interaction. Comparisons of the results with an established boundary layer code, similarity solution, and experimental data show excellent agreement.
NASA Astrophysics Data System (ADS)
Xie, Xi-Yang; Tian, Bo; Wang, Yu-Feng; Sun, Ya; Jiang, Yan
2015-11-01
In this paper, we investigate a generalized nonautonomous nonlinear equation which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions for the generalized nonautonomous nonlinear equation are obtained, under some variable-coefficient constraints. Properties of the first- and second-order rogue waves are graphically presented and analyzed: When the coefficients are all chosen as the constants, we can observe the some functions, the shapes of wave crests and troughs for the first- and second-order rogue waves change. Oscillating behaviors of the first- and second-order rogue waves are observed when the coefficients are the trigonometric functions.
NASA Astrophysics Data System (ADS)
Saha, Asit; Pal, Nikhil; Saha, Tapash; Ghorui, M. K.; Chatterjee, Prasanta
2016-06-01
Bifurcations and chaotic behaviors of dust acoustic traveling waves in magnetoplasmas with nonthermal ions featuring Cairns-Tsallis distribution is investigated on the framework of the further modified Kadomtsev-Petviashili (FMKP) equation. The FMKP equation is derived employing the reductive perturbation technique (RPT). Bifurcations of dust acoustic traveling waves of the FMKP equation is presented. Using the bifurcation theory of planar dynamical systems, two new analytical traveling wave solutions for solitary and periodic waves are derived depending on the parameters α , α _1, q, l and U. Considering an external periodic perturbation, the chaotic behavior of dust acoustic traveling waves is investigated through quasiperiodic route to chaos. The parameter q significantly affects the chaotic behavior of the perturbed FMKP equation.
Tang, Liguo; Wu, Zhaojun; Liu, Shengxing; Yang, Wuyi
2012-08-01
The objective of this study is to investigate the three-dimensional (3-D) analytical solution for transient guided wave propagation in liquid-filled pipe systems using the eigenfunction expansion method (EEM). The eigenfunctions corresponding to finite liquid-filled pipe systems with a traction-free lateral boundary and rigid smooth end boundaries are obtained. Additionally, the orthogonality of the eigenfunctions is proved in detail. Subsequently, the exact 3-D analytical transient response of finite liquid-filled pipe systems to external body forces is constructed using the EEM, based on which, the approximate 3-D analytical transient response of the systems to external surface forces is derived. Furthermore, the analytical solution for transient guided wave propagation in finite liquid-filled pipe systems is extended explicitly and concisely to infinite liquid-filled pipe systems. Several numerical examples are given to illustrate the analysis of the spatial and frequency distributions of the radial and axial displacement amplitudes of various guided wave modes; the numerical examples also simulate the transient displacement of the pipe wall and the transient pressure of the internal liquid from the present solution. The present solution can provide some theoretical guidelines for the guided wave nondestructive evaluation of liquid-filled pipes and the guided wave technique for downhole data transfer. PMID:22899122
NASA Astrophysics Data System (ADS)
Luppescu, Gregory C.; Dawson, Alexander J.; Michaels, Jennifer E.
2016-02-01
Although bulk waves have served as the industry standard in nondestructive evaluation for many years, guided waves (Lamb waves in plates) have become the focus of many current research efforts because they are able to interrogate larger areas of a structure in less time. Despite this advantage, guided waves also have characteristics that obfuscate data interpretation. The first property of guided waves that complicates analysis is their dispersive nature: their wave speed is a function of frequency. The second is that they are multimodal: they propagate as multiple symmetric and antisymmetric modes. Using pulse-compression techniques and a priori calculations of theoretical dispersion curves, the dispersive matched filter attempts to take advantage of these otherwise undesirable characteristics by maximizing the autocorrelation for only one mode, ideally increasing both the signal-to-noise ratio and time-resolution of ultrasonic guided wave measurements. In this research, the responses from broadband chirp excitations are recorded from a sparse transducer array after propagation through an aluminum plate containing no damage and simulated damage. Dispersive matched filtering is applied to the measurements and localization images are generated using the delay-and-sum method. Imaging results are compared to those obtained with narrowband tone burst excitations in terms of their ability to detect and localize the different scatterers. Results show that the dispersive matched filter notably improves the quality of the localization images.
The existence of traveling wave solutions for a bistable three-component lattice dynamical system
NASA Astrophysics Data System (ADS)
Guo, Jong-Shenq; Wu, Chin-Chin
2016-01-01
We study the traveling wave solutions for a three-component lattice dynamical system. This problem arises in the modeling of three species competing two food resources in an environment with migration in which the habitat is one-dimensional and is divided into countable niches. We are concerned with the case when two species have different preferences of food and the third species has both preferences of food. To understand which species win the competition under the bistable condition, the existence of a traveling wave solution for this lattice dynamical system is proven.
NASA Astrophysics Data System (ADS)
Xiao, Mufei
2000-03-01
We have found the rigorous solution of transient propagation of electronmagnetic waves through a medium. The rogorousness enables the solution to exhibit its apparent consistency with the Einstein causality. Thus, we confirm that faster-than-light or superluminal propagation of electromagnetic waves is not possible. Evanescent transmission gives rise to the diffraction in time, which is the actual reason for deformation of group propagation. Based on the principle of diffraction in time, superluminal group propagation can be understood. The findings are also instructive for understanding the time problem for particle tunneling.
High-accuracy deterministic solution of the Boltzmann equation for the shock wave structure
NASA Astrophysics Data System (ADS)
Malkov, E. A.; Bondar, Ye. A.; Kokhanchik, A. A.; Poleshkin, S. O.; Ivanov, M. S.
2015-07-01
A new deterministic method of solving the Boltzmann equation has been proposed. The method has been employed in numerical studies of the plane shock wave structure in a hard sphere gas. Results for Mach numbers and have been compared with predictions of the direct simulation Monte Carlo (DSMC) method, which has been used to obtain the reference solution. Particular attention in estimating the solution accuracy has been paid to a fine structural effect: the presence of a total temperature peak exceeding the temperature value further downstream. The results of solving the Boltzmann equation for the shock wave structure are in excellent agreement with the DSMC predictions.
New Exact Solutions of the CDGSK Equation Related to a Non-local Symmetry
NASA Astrophysics Data System (ADS)
Lou, Senyue; Ruan, Hangyu; Chen, Weizhong; Wang, Zhenli; Chen, Lili
1994-10-01
A non-local symmetry of the Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGSK) equation has been used for finding exact solution in two different ways. Firstly, using the standard prolongation approach, we obtain the finite Lie Bäcklund transformation and the single soliton solution. Secondly, combining some local symmetries and the nonlocal symmetry, we get the group invariant solution which is described by the Weierstrass elliptic function and is deduced to the so-called interacting soliton for a special parameter.
Testing spontaneous localization theories with matter-wave interferometry
Nimmrichter, Stefan; Haslinger, Philipp; Arndt, Markus; Hornberger, Klaus
2011-04-15
We propose to test the theory of continuous spontaneous localization (CSL) in an all-optical time-domain Talbot-Lau interferometer for clusters with masses exceeding 10{sup 6} amu. By assessing the relevant environmental decoherence mechanisms, as well as the growing size of the particles relative to the grating fringes, we argue that it will be feasible to test the quantum superposition principle in a mass range excluded by recent estimates of the CSL effect.
Initial Value Problem Solution of Nonlinear Shallow Water-Wave Equations
Kanoglu, Utku; Synolakis, Costas
2006-10-06
The initial value problem solution of the nonlinear shallow water-wave equations is developed under initial waveforms with and without velocity. We present a solution method based on a hodograph-type transformation to reduce the nonlinear shallow water-wave equations into a second-order linear partial differential equation and we solve its initial value problem. The proposed solution method overcomes earlier limitation of small waveheights when the initial velocity is nonzero, and the definition of the initial conditions in the physical and transform spaces is consistent. Our solution not only allows for evaluation of differences in predictions when specifying an exact initial velocity based on nonlinear theory and its linear approximation, which has been controversial in geophysical practice, but also helps clarify the differences in runup observed during the 2004 and 2005 Sumatran tsunamigenic earthquakes.
Exact solution to plane-wave scattering by an ideal "left-handed" wedge
NASA Astrophysics Data System (ADS)
Monzon, Cesar; Forester, Donald W.; Smith, Douglas; Loschialpo, Peter
2006-02-01
An exact analytical solution to the problem of plane-wave diffraction by a penetrable left-handed medium (LHM) epsilon=µ=-1 wedge of arbitrary angle (subject to valid physical constraints) is presented. Standard analysis involving discontinuous angular eigenfunctions and even/odd symmetry decomposition resulted in a discrete spectrum leading to a series solution resembling the traditional perfect electric conductor wedge solution but exhibiting the expected negative refraction phenomenology. Numerical results are presented, some of which seemed paradoxical but are explainable by classical means. A new type of illusory edge radiation is observed and explained. Also, a novel edge-launched interface standing wave is observed on the directly illuminated side. The exact analytical solution is verified by comparison with finite-difference time-domain simulation on causal LHM materials.
Solution of the stochastic generalized shallow-water wave equation using RVT technique
NASA Astrophysics Data System (ADS)
Hussein, Abdallah; Selim, Mustafa M.
2015-12-01
In this paper, some exact solutions of the stochastic generalized nonlinear shallow-water wave (SGNSWW) equation are obtained. This equation is an important equation in fluid mechanics field. Opposite to what is usually assumed in the literature, the coefficients of the nonlinear terms in this stochastic nonlinear partial differential equation (SNLPDE) are considered to be random quantities. The random variable transformation (RVT) technique is combined with the modified extended-tanh function method (METFM) to get the stochastic solutions represented by the probability density functions (PDFs) of the solution processes in terms of the PDFs of the random coefficients. These solutions are illustrated graphically along the spacial and time dimensions at a certain wave speed.
Analytical Solutions Involving Shock Waves for Testing Debris Avalanche Numerical Models
NASA Astrophysics Data System (ADS)
Mungkasi, Sudi; Roberts, Stephen Gwyn
2012-10-01
Analytical solutions to debris avalanche problems involving shock waves are derived. The debris avalanche problems are described in two different coordinate systems, namely, the standard Cartesian and topography-linked coordinate systems. The analytical solutions can then be used to test debris avalanche numerical models. In this article, finite volume methods are applied as the numerical models. We compare the performance of the finite volume method with reconstruction of the conserved quantities based on stage, height, and velocity to that of the conserved quantities based on stage, height, and momentum for solving the debris avalanche problems involving shock waves. The numerical solutions agree with the analytical solution. In addition, both reconstructions lead to similar numerical results. This article is an extension of the work of Mangeney et al. (Pure Appl Geophys 157(6-8):1081-1096, 2000).
Joint Inversion of Earthquake Source Parameters with local and teleseismic body waves
NASA Astrophysics Data System (ADS)
Chen, W.; Ni, S.; Wang, Z.
2011-12-01
In the classical source parameter inversion algorithm of CAP (Cut and Paste method, by Zhao and Helmberger), waveform data at near distances (typically less than 500km) are partitioned into Pnl and surface waves to account for uncertainties in the crustal models and different amplitude weight of body and surface waves. The classical CAP algorithms have proven effective for resolving source parameters (focal mechanisms, depth and moment) for earthquakes well recorded on relatively dense seismic network. However for regions covered with sparse stations, it is challenging to achieve precise source parameters . In this case, a moderate earthquake of ~M6 is usually recorded on only one or two local stations with epicentral distances less than 500 km. Fortunately, an earthquake of ~M6 can be well recorded on global seismic networks. Since the ray paths for teleseismic and local body waves sample different portions of the focal sphere, combination of teleseismic and local body wave data helps constrain source parameters better. Here we present a new CAP mothod (CAPjoint), which emploits both teleseismic body waveforms (P and SH waves) and local waveforms (Pnl, Rayleigh and Love waves) to determine source parameters. For an earthquake in Nevada that is well recorded with dense local network (USArray stations), we compare the results from CAPjoint with those from the traditional CAP method involving only of local waveforms , and explore the efficiency with bootstraping statistics to prove the results derived by CAPjoint are stable and reliable. Even with one local station included in joint inversion, accuracy of source parameters such as moment and strike can be much better improved.
Local error estimates for discontinuous solutions of nonlinear hyperbolic equations
NASA Technical Reports Server (NTRS)
Tadmor, Eitan
1989-01-01
Let u(x,t) be the possibly discontinuous entropy solution of a nonlinear scalar conservation law with smooth initial data. Suppose u sub epsilon(x,t) is the solution of an approximate viscosity regularization, where epsilon greater than 0 is the small viscosity amplitude. It is shown that by post-processing the small viscosity approximation u sub epsilon, pointwise values of u and its derivatives can be recovered with an error as close to epsilon as desired. The analysis relies on the adjoint problem of the forward error equation, which in this case amounts to a backward linear transport with discontinuous coefficients. The novelty of this approach is to use a (generalized) E-condition of the forward problem in order to deduce a W(exp 1,infinity) energy estimate for the discontinuous backward transport equation; this, in turn, leads one to an epsilon-uniform estimate on moments of the error u(sub epsilon) - u. This approach does not follow the characteristics and, therefore, applies mutatis mutandis to other approximate solutions such as E-difference schemes.
Numerical simulations of the local generation of internal solitary waves in the Bay of Biscay
NASA Astrophysics Data System (ADS)
Grisouard, N.; Staquet, C.
2010-10-01
Oceanic observations from the Bay of Biscay, Portugal, Mozambique Channel and Mascarene Ridge have provided evidence of the generation of internal solitary waves due to an internal tidal beam impinging on the thermocline from below - a process referred to as "local generation". Here we present two-dimensional numerical simulations with a fully nonlinear nonhydrostatic model of situations that are relevant for the Bay of Biscay in summer. We show that a beam impinging on a thermocline initially at rest can induce a displacement of the isopycnals, large enough for internal solitary waves to be generated. These internal solitary waves however differ from those observed in the Bay of Biscay through their amplitude and distance between wave trains. We then show that the latter feature is recovered when the background flow around the thermocline as found in the Bay of Biscay is included in the forcing, thereby yielding a more accurate view on the local generation mechanism.
The local structure factor near an interface; beyond extended capillary-wave models.
Parry, A O; Rascón, C; Evans, R
2016-06-22
We investigate the local structure factor S (z;q) at a free liquid-gas interface in systems with short-ranged intermolecular forces and determine the corrections to the leading-order, capillary-wave-like, Goldstone mode divergence of S (z;q) known to occur for parallel (i.e. measured along the interface) wavevectors [Formula: see text]. We show from explicit solution of the inhomogeneous Ornstein-Zernike equation that for distances z far from the interface, where the profile decays exponentially, S (z;q) splits unambiguously into bulk and interfacial contributions. On each side of the interface, the interfacial contributions can be characterised by distinct liquid and gas wavevector dependent surface tensions, [Formula: see text] and [Formula: see text], which are determined solely by the bulk two-body and three-body direct correlation functions. At high temperatures, the wavevector dependence simplifies and is determined almost entirely by the appropriate bulk structure factor, leading to positive rigidity coefficients. Our predictions are confirmed by explicit calculation of S (z;q) within square-gradient theory and the Sullivan model. The results for the latter predict a striking temperature dependence for [Formula: see text] and [Formula: see text], and have implications for fluctuation effects. Our results account quantitatively for the findings of a recent very extensive simulation study by Höfling and Dietrich of the total structure factor in the interfacial region, in a system with a cut-off Lennard-Jones potential, in sharp contrast to extended capillary-wave models which failed completely to describe the simulation results. PMID:27115774
The local structure factor near an interface; beyond extended capillary-wave models
NASA Astrophysics Data System (ADS)
Parry, A. O.; Rascón, C.; Evans, R.
2016-06-01
We investigate the local structure factor S (zq) at a free liquid–gas interface in systems with short-ranged intermolecular forces and determine the corrections to the leading-order, capillary-wave-like, Goldstone mode divergence of S (zq) known to occur for parallel (i.e. measured along the interface) wavevectors q\\to 0 . We show from explicit solution of the inhomogeneous Ornstein–Zernike equation that for distances z far from the interface, where the profile decays exponentially, S (zq) splits unambiguously into bulk and interfacial contributions. On each side of the interface, the interfacial contributions can be characterised by distinct liquid and gas wavevector dependent surface tensions, {σ l}(q) and {σg}(q) , which are determined solely by the bulk two-body and three-body direct correlation functions. At high temperatures, the wavevector dependence simplifies and is determined almost entirely by the appropriate bulk structure factor, leading to positive rigidity coefficients. Our predictions are confirmed by explicit calculation of S (zq) within square-gradient theory and the Sullivan model. The results for the latter predict a striking temperature dependence for {σ l}(q) and {σg}(q) , and have implications for fluctuation effects. Our results account quantitatively for the findings of a recent very extensive simulation study by Höfling and Dietrich of the total structure factor in the interfacial region, in a system with a cut-off Lennard-Jones potential, in sharp contrast to extended capillary-wave models which failed completely to describe the simulation results.
Travelling wave solutions of a coupled Korteweg-de Vries-Burgers system
NASA Astrophysics Data System (ADS)
Motsepa, Tanki; Khalique, Chaudry Masood
2016-02-01
In this paper we study a coupled Korteweg-de Vries-Burgers system which arises in mathematical physics and has a wide range of scientific applications. We obtain new travelling wave solutions of this system by employing the (G'/G)-expansion method. The solutions that will be obtained are going to be expressed in two different forms, viz., hyperbolic functions and trigonometric functions.
Global stability of travelling wave fronts for non-local diffusion equations with delay
NASA Astrophysics Data System (ADS)
Wang, X.; Lv, G.
2014-04-01
This paper is concerned with the global stability of travelling wave fronts for non-local diffusion equations with delay. We prove that the non-critical travelling wave fronts are globally exponentially stable under perturbations in some exponentially weighted L^\\infty-spaces. Moreover, we obtain the decay rates of \\sup_{x\\in{R}}\\vert u(x,t)-\\varphi(x+ct)\\vert using weighted energy estimates.
Families of quasi-rational solutions of the NLS equation and multi-rogue waves
NASA Astrophysics Data System (ADS)
Gaillard, Pierre
2011-10-01
We construct a multi-parametric family of the solutions of the focusing nonlinear Schrödinger equation (NLS) from the known results describing the multi-phase almost-periodic elementary solutions given in terms of Riemann theta functions. We give a new representation of their solutions in terms of Wronskians determinants of order 2N composed of elementary trigonometric functions. When we perform a special passage to the limit when all the periods tend to infinity, we obtain a family of quasi-rational solutions. This leads to efficient representations for the Peregrine breathers of orders N = 1, 2, 3 first constructed by Akhmediev and his co-workers and also allows us to obtain a simpler derivation of the generic formulas corresponding the three or six rogue-wave formation in the frame of the NLS model first explained by V B Matveev in 2010. Our formulation allows us to isolate easily the second- or third-order Peregrine breathers from ‘generic’ solutions and also to compute the Peregrine breathers of orders 2 and 3 easily with respect to other approaches. In the cases N = 2, 3, we obtain the comfortable formulas to study the deformation of a higher Peregrine breather of order 2 to the three rogue-wave or order 3 to the six rogue-wave solutions via the variation of the free parameters of our construction.
Fractal dimensions of wave functions and local spectral measures on the Fibonacci chain
NASA Astrophysics Data System (ADS)
Macé, Nicolas; Jagannathan, Anuradha; Piéchon, Frédéric
2016-05-01
We present a theoretical framework for understanding the wave functions and spectrum of an extensively studied paradigm for quasiperiodic systems, namely the Fibonacci chain. Our analytical results, which are obtained in the limit of strong modulation of the hopping amplitudes, are in good agreement with published numerical data. In the perturbative limit, we show a symmetry of wave functions under permutation of site and energy indices. We compute the wave-function renormalization factors and from them deduce analytical expressions for the fractal exponents corresponding to individual wave functions, as well as their global averages. The multifractality of wave functions is seen to appear at next-to-leading order in ρ . Exponents for the local spectral density are given, in extremely good accord with numerical calculations. Interestingly, our analytical results for exponents are observed to describe the system rather well even for values of ρ well outside the domain of applicability of perturbation theory.
NASA Astrophysics Data System (ADS)
Casanova, David; Krylov, Anna I.
2016-01-01
A new method for quantifying the contributions of local excitation, charge resonance, and multiexciton configurations in correlated wave functions of multichromophoric systems is presented. The approach relies on fragment-localized orbitals and employs spin correlators. Its utility is illustrated by calculations on model clusters of hydrogen, ethylene, and tetracene molecules using adiabatic restricted-active-space configuration interaction wave functions. In addition to the wave function analysis, this approach provides a basis for a simple state-specific energy correction accounting for insufficient description of electron correlation. The decomposition scheme also allows one to compute energies of the diabatic states of the local excitonic, charge-resonance, and multi-excitonic character. The new method provides insight into electronic structure of multichromophoric systems and delivers valuable reference data for validating excitonic models.
Identification and mitigation of T-S waves using localized dynamic surface modification
NASA Astrophysics Data System (ADS)
Amitay, Michael; Tuna, Burak A.; Dell'Orso, Haley
2016-06-01
The control of transition from a laminar to a turbulent flow over a flat plate using localized dynamic surface modifications was explored experimentally in Rensselaer Polytechnic Institute's subsonic wind tunnel. Dynamic surface modification, via a pair of Piezoelectrically Driven Oscillating Surface (PDOS) actuators, was used to excite and control the T-S wave over a flat plate. Creating an upstream, localized small disturbance at the most amplified frequency of fact = 250 Hz led to phase-locking the T-S wave. This enabled observation of the excited T-S wave using phase-locked stereoscopic particle image velocimetry. The growth of the T-S wave as it moved downstream was also measured using this technique (25% growth over four wavelengths of the excited wave). Activation of a downstream PDOS actuator (in addition to the upstream PDOS) at the appropriate amplitude and phase shift resulted in attenuation of the peak amplitude of the coherent velocity fluctuations (by up to 68%) and a substantial reduction of the degree of coherence of the T-S wave. Since the PDOS actuators used in this work were localized, the effect of the control strategy was confined to the region directly downstream of the PDOS actuator.
Chou, D.-Y.; Liang, Z.-C.; Yang, M.-H.; Zhao Hui; Sun, M.-T.
2009-05-01
The power of solar acoustic waves in magnetic regions is lower relative to the quiet Sun. Absorption, emissivity reduction, and local suppression of acoustic waves contribute to the observed power reduction in magnetic regions. We propose a model for the energy budget of acoustic waves propagating through a sunspot in terms of the coefficients of absorption, emissivity reduction, and local suppression of the sunspot. Using the property that the waves emitted along the wave path between two points have no correlation with the signal at the starting point, we can separate the effects of these three mechanisms. Applying this method to helioseismic data filtered with direction and phase-velocity filters, we measure the fraction of the contribution of each mechanism to the power deficit in the umbra of the leading sunspot of NOAA 9057. The contribution from absorption is 23.3 {+-} 1.3%, emissivity reduction 8.2 {+-} 1.4%, and local suppression 68.5 {+-} 1.5%, for a wave packet corresponding to a phase velocity of 6.98 x 10{sup -5} rad s{sup -1}.
GLOBAL AND LOCAL CUTOFF FREQUENCIES FOR TRANSVERSE WAVES PROPAGATING ALONG SOLAR MAGNETIC FLUX TUBES
Routh, S.; Musielak, Z. E.; Hammer, R. E-mail: zmusielak@uta.edu
2013-01-20
It is a well-established result that the propagation of linear transverse waves along a thin but isothermal magnetic flux tube is affected by the existence of the global cutoff frequency, which separates the propagating and non-propagating waves. In this paper, the wave propagation along a thin and non-isothermal flux tube is considered and a local cutoff frequency is derived. The effects of different temperature profiles on this local cutoff frequency are studied by considering different power-law temperature distributions, as well as the semi-empirical VAL C model of the solar atmosphere. The obtained results show that the conditions for wave propagation strongly depend on the temperature gradients. Moreover, the local cutoff frequency calculated for the VAL C model gives constraints on the range of wave frequencies that are propagating in different parts of the solar atmosphere. These theoretically predicted constraints are compared to observational data and are used to discuss the role played by transverse tube waves in the atmospheric heating and dynamics, and in the excitation of solar atmospheric oscillations.
Local probing of magnetic films by optical excitation of magnetostatic waves
NASA Astrophysics Data System (ADS)
Chernov, A. I.; Kozhaev, M. A.; Vetoshko, P. M.; Dodonov, D. V.; Prokopov, A. R.; Shumilov, A. G.; Shaposhnikov, A. N.; Berzhanskii, V. N.; Zvezdin, A. K.; Belotelov, V. I.
2016-06-01
Excitation of volume and surface magnetostatic spin waves in ferrite garnet films by circularly polarized laser pulses utilizing to the inverse magnetooptical Faraday effect has been studied experimentally. The region of excitation of the magnetostatic spin waves is determined by the diameter of the laser beam (˜10 μm). At the same time, the characteristic propagation length of the modes is 30 μm. A method of finding the local characteristics of a magnetic film, in particular, the cubic and uniaxial anisotropy constants, based on the analysis of the azimuthal-angle dependence of the spectrum of the magnetostatic spin waves has been proposed.
Hashemiyan, Z; Packo, P; Staszewski, W J; Uhl, T
2016-01-01
Properties of soft biological tissues are increasingly used in medical diagnosis to detect various abnormalities, for example, in liver fibrosis or breast tumors. It is well known that mechanical stiffness of human organs can be obtained from organ responses to shear stress waves through Magnetic Resonance Elastography. The Local Interaction Simulation Approach is proposed for effective modelling of shear wave propagation in soft tissues. The results are validated using experimental data from Magnetic Resonance Elastography. These results show the potential of the method for shear wave propagation modelling in soft tissues. The major advantage of the proposed approach is a significant reduction of computational effort. PMID:26884808
Packo, P.; Staszewski, W. J.; Uhl, T.
2016-01-01
Properties of soft biological tissues are increasingly used in medical diagnosis to detect various abnormalities, for example, in liver fibrosis or breast tumors. It is well known that mechanical stiffness of human organs can be obtained from organ responses to shear stress waves through Magnetic Resonance Elastography. The Local Interaction Simulation Approach is proposed for effective modelling of shear wave propagation in soft tissues. The results are validated using experimental data from Magnetic Resonance Elastography. These results show the potential of the method for shear wave propagation modelling in soft tissues. The major advantage of the proposed approach is a significant reduction of computational effort. PMID:26884808
Levi, Paul
2015-01-01
Remarkable biological examples of molecular robots are the proteins kinesin-1 and dynein, which move and transport cargo down microtubule “highways,” e.g., of the axon, to final nerve nodes or along dendrites. They convert the energy of ATP hydrolysis into mechanical forces and can thereby push them forwards or backwards step by step. Such mechano-chemical cycles that generate conformal changes are essential for transport on all different types of substrate lanes. The step length of an individual molecular robot is a matter of nanometers but the dynamics of each individual step cannot be predicted with certainty (as it is a random process). Hence, our proposal is to involve the methods of quantum field theory (QFT) to describe an overall reliable, multi–robot system that is composed of a huge set of unreliable, local elements. The methods of QFT deliver techniques that are also computationally demanding to synchronize the motion of these molecular robots on one substrate lane as well as across lanes. Three different challenging types of solutions are elaborated. The impact solution reflects the particle point of view; the two remaining solutions are wave based. The second solution outlines coherent robot motions on different lanes. The third solution describes running waves. Experimental investigations are needed to clarify under which biological conditions such different solutions occur. Moreover, such a nano-chemical system can be stimulated by external signals, and this opens a new, hybrid approach to analyze and control the combined system of robots and microtubules externally. Such a method offers the chance to detect mal-functions of the biological system. PMID:26005415
DETECTION, LOCALIZATION, AND CHARACTERIZATION OF GRAVITATIONAL WAVE BURSTS IN A PULSAR TIMING ARRAY
Finn, Lee Samuel; Lommen, Andrea N.
2010-08-01
Efforts to detect gravitational waves by timing an array of pulsars have traditionally focused on stationary gravitational waves, e.g., stochastic or periodic signals. Gravitational wave bursts-signals whose duration is much shorter than the observation period-will also arise in the pulsar timing array waveband. Sources that give rise to detectable bursts include the formation or coalescence of supermassive black holes (SMBHs), the periapsis passage of compact objects in highly elliptic or unbound orbits about an SMBH, or cusps on cosmic strings. Here, we describe how pulsar timing array data may be analyzed to detect and characterize these bursts. Our analysis addresses, in a mutually consistent manner, a hierarchy of three questions. (1) What are the odds that a data set includes the signal from a gravitational wave burst? (2) Assuming the presence of a burst, what is the direction to its source? (3) Assuming the burst propagation direction, what is the burst waveform's time dependence in each of its polarization states? Applying our analysis to synthetic data sets, we find that we can detect gravitational waves even when the radiation is too weak to either localize the source or infer the waveform, and detect and localize sources even when the radiation amplitude is too weak to permit the waveform to be determined. While the context of our discussion is gravitational wave detection via pulsar timing arrays, the analysis itself is directly applicable to gravitational wave detection using either ground- or space-based detector data.
NASA Astrophysics Data System (ADS)
Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M. R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R. X.; Adya, V. B.; Affeldt, C.; Agathos, M.; Agatsuma, K.; Aggarwal, N.; Aguiar, O. D.; Ain, A.; Ajith, P.; Allen, B.; Allocca, A.; Altin, P. A.; Amariutei, D. V.; Anderson, S. B.; Anderson, W. G.; Arai, K.; Araya, M. C.; Arceneaux, C. C.; Areeda, J. S.; Arnaud, N.; Arun, K. G.; Ashton, G.; Ast, M.; Aston, S. M.; Astone, P.; Aufmuth, P.; Aulbert, C.; Babak, S.; Baker, P. T.; Baldaccini, F.; Ballardin, G.; Ballmer, S. W.; Barayoga, J. C.; Barclay, S. E.; Barish, B. C.; Barker, D.; Barone, F.; Barr, B.; Barsotti, L.; Barsuglia, M.; Barta, D.; Bartlett, J.; Bartos, I.; Bassiri, R.; Basti, A.; Batch, J. C.; Baune, C.; Bavigadda, V.; Bazzan, M.; Behnke, B.; Bejger, M.; Belczynski, C.; Bell, A. S.; Bell, C. J.; Berger, B. K.; Bergman, J.; Bergmann, G.; Berry, C. P. L.; Bersanetti, D.; Bertolini, A.; Betzwieser, J.; Bhagwat, S.; Bhandare, R.; Bilenko, I. A.; Billingsley, G.; Birch, J.; Birney, R.; Biscans, S.; Bisht, A.; Bitossi, M.; Biwer, C.; Bizouard, M. A.; Blackburn, J. K.; Blair, C. D.; Blair, D.; Blair, R. M.; Bloemen, S.; Bock, O.; Bodiya, T. P.; Boer, M.; Bogaert, G.; Bogan, C.; Bohe, A.; Bojtos, P.; Bond, C.; Bondu, F.; Bonnand, R.; Bork, R.; Boschi, V.; Bose, S.; Bozzi, A.; Bradaschia, C.; Brady, P. R.; Braginsky, V. B.; Branchesi, M.; Brau, J. E.; Briant, T.; Brillet, A.; Brinkmann, M.; Brisson, V.; Brockill, P.; Brooks, A. F.; Brown, D. A.; Brown, D. D.; Brown, N. M.; Buchanan, C. C.; Buikema, A.; Bulik, T.; Bulten, H. J.; Buonanno, A.; Buskulic, D.; Buy, C.; Byer, R. L.; Cadonati, L.; Cagnoli, G.; Cahillane, C.; Calderón Bustillo, J.; Callister, T.; Calloni, E.; Camp, J. B.; Cannon, K. C.; Cao, J.; Capano, C. D.; Capocasa, E.; Carbognani, F.; Caride, S.; Casanueva Diaz, J.; Casentini, C.; Caudill, S.; Cavaglià, M.; Cavalier, F.; Cavalieri, R.; Cella, G.; Cepeda, C.; Cerboni Baiardi, L.; Cerretani, G.; Cesarini, E.; Chakraborty, R.; Chalermsongsak, T.; Chamberlin, S. J.; Chan, M.; Chao, S.; Charlton, P.; Chassande-Mottin, E.; Chen, H. Y.; Chen, Y.; Cheng, C.; Chincarini, A.; Chiummo, A.; Cho, H. S.; Cho, M.; Chow, J. H.; Christensen, N.; Chu, Q.; Chua, S.; Chung, S.; Ciani, G.; Clara, F.; Clark, J. A.; Cleva, F.; Coccia, E.; Cohadon, P.-F.; Colla, A.; Collette, C. G.; Constancio, M.; Conte, A.; Conti, L.; Cook, D.; Corbitt, T. R.; Cornish, N.; Corsi, A.; Cortese, S.; Costa, C. A.; Coughlin, M. W.; Coughlin, S. B.; Coulon, J.-P.; Countryman, S. T.; Couvares, P.; Coward, D. M.; Cowart, M. J.; Coyne, D. C.; Coyne, R.; Craig, K.; Creighton, J. D. E.; Cripe, J.; Crowder, S. G.; Cumming, A.; Cunningham, L.; Cuoco, E.; Dal Canton, T.; Danilishin, S. L.; D'Antonio, S.; Danzmann, K.; Darman, N. S.; Dattilo, V.; Dave, I.; Daveloza, H. P.; Davier, M.; Davies, G. S.; Daw, E. J.; Day, R.; DeBra, D.; Debreczeni, G.; Degallaix, J.; De Laurentis, M.; Deléglise, S.; Del Pozzo, W.; Denker, T.; Dent, T.; Dereli, H.; Dergachev, V.; DeRosa, R.; De Rosa, R.; DeSalvo, R.; Dhurandhar, S.; Díaz, M. C.; Di Fiore, L.; Di Giovanni, M.; Di Lieto, A.; Di Palma, I.; Di Virgilio, A.; Dojcinoski, G.; Dolique, V.; Donovan, F.; Dooley, K. L.; Doravari, S.; Douglas, R.; Downes, T. P.; Drago, M.; Drever, R. W. P.; Driggers, J. C.; Du, Z.; Ducrot, M.; Dwyer, S. E.; Edo, T. B.; Edwards, M. C.; Effler, A.; Eggenstein, H.-B.; Ehrens, P.; Eichholz, J. M.; Eikenberry, S. S.; Engels, W.; Essick, R. C.; Etzel, T.; Evans, M.; Evans, T. M.; Everett, R.; Factourovich, M.; Fafone, V.; Fair, H.; Fairhurst, S.; Fan, X.; Fang, Q.; Farinon, S.; Farr, B.; Farr, W. M.; Favata, M.; Fays, M.; Fehrmann, H.; Fejer, M. M.; Ferrante, I.; Ferreira, E. C.; Ferrini, F.; Fidecaro, F.; Fiori, I.; Fisher, R. P.; Flaminio, R.; Fletcher, M.; Fournier, J.-D.; Franco, S.; Frasca, S.; Frasconi, F.; Frei, Z.; Freise, A.; Frey, R.; Fricke, T. T.; Fritschel, P.; Frolov, V. V.; Fulda, P.; Fyffe, M.; Gabbard, H. A. G.; Gair, J. R.; Gammaitoni, L.; Gaonkar, S. G.; Garufi, F.; Gatto, A.; Gaur, G.; Gehrels, N.; Gemme, G.; Gendre, B.; Genin, E.; Gennai, A.; George, J.; Gergely, L.; Germain, V.; Ghosh, A.; Ghosh, S.; Giaime, J. A.; Giardina, K. D.; Giazotto, A.; Gill, K.; Glaefke, A.; Goetz, E.; Goetz, R.; Gondan, L.; González, G.; Gonzalez Castro, J. M.; Gopakumar, A.; Gordon, N. A.; Gorodetsky, M. L.; Gossan, S. E.; Gosselin, M.; Gouaty, R.; Graef, C.; Graff, P. B.; Granata, M.; Grant, A.; Gras, S.; Gray, C.; Greco, G.; Green, A. C.; Groot, P.; Grote, H.; Grunewald, S.; Guidi, G. M.; Guo, X.; Gupta, A.; Gupta, M. K.; Gushwa, K. E.; Gustafson, E. K.; Gustafson, R.; Hacker, J. J.; Hall, B. R.; Hall, E. D.; Hammond, G.; Haney, M.; Hanke, M. M.; Hanks, J.; Hanna, C.; Hannam, M. D.; Hanson, J.; Hardwick, T.; Harms, J.; Harry, G. M.; Harry, I. W.; Hart, M. J.
2016-02-01
We present a possible observing scenario for the Advanced LIGO and Advanced Virgo gravitational-wave detectors over the next decade, with the intention of providing information to the astronomy community to facilitate planning for multi-messenger astronomy with gravitational waves. We determine the expected sensitivity of the network to transient gravitational-wave signals, and study the capability of the network to determine the sky location of the source. We report our findings for gravitational-wave transients, with particular focus on gravitational-wave signals from the inspiral of binary neutron-star systems, which are considered the most promising for multi-messenger astronomy. The ability to localize the sources of the detected signals depends on the geographical distribution of the detectors and their relative sensitivity, and 90% credible regions can be as large as thousands of square degrees when only two sensitive detectors are operational. Determining the sky position of a significant fraction of detected signals to areas of 5 deg^2 to 20 deg^2 will require at least three detectors of sensitivity within a factor of ~2 of each other and with a broad frequency bandwidth. Should the third LIGO detector be relocated to India as expected, a significant fraction of gravitational-wave signals will be localized to a few square degrees by gravitational-wave observations alone.
A ``local observables'' method for wave mechanics applied to atomic hydrogen
NASA Astrophysics Data System (ADS)
Bowman, Peter J.
2008-12-01
An alternative method of deriving the values of the observables of atomic systems is presented. Rather than using operators and eigenvalues the local variables method uses the continuity equation together with current densities derived from wave functions that are solutions of the Dirac or Pauli equation. The method is applied to atomic hydrogen using the usual language of quantum mechanics rather than that of geometric algebra with which the method is often associated. The picture of the atom that emerges is one in which the electron density as a whole is rotating about a central axis. The results challenge some assumptions of conventional quantum mechanics. Electron spin is shown to be a property of the dynamical motion of the electron and not an intrinsic property of the electron, the ground state of hydrogen is shown to have an orbital angular momentum of ℏ, and excited states are shown to have angular momenta that are different from the eigenvalues of the usual quantum mechanical operators. The uncertainty relations are found not to be applicable to the orthogonal components of the angular momentum. No double electron spin gyromagnetic ratio is required to account for the observed magnetic moments, and the behavior of the atom in a magnetic field is described entirely in kinetic terms.
NASA Technical Reports Server (NTRS)
Hagstrom, Thomas; Hariharan, S. I.; Maccamy, R. C.
1993-01-01
We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds.
Stability of the solitary wave solutions to a coupled BBM system
NASA Astrophysics Data System (ADS)
Chen, Hongqiu; Wang, Xiaojun
2016-07-01
In this work, we present a stability criteria for the solitary wave solutions to a BBM system that contains coupled nonlinear terms. Using the idea by Bona, Chen and Karakashian [5] and exploiting the accurate point spectrum information of the associated Schrödinger operator, we improve the stability results previously gotten by Pereira [15].
Existence of travelling wave solutions for a Fisher-Kolmogorov system with biomedical applications
NASA Astrophysics Data System (ADS)
Belmonte-Beitia, Juan
2016-07-01
We consider a Fisher-Kolmogorov system with applications in oncology Pérez-García et al. (2015). Of interest is the question of the existence of travelling front solutions of the system. When the speed of the travelling wave is sufficiently large, existence of such fronts is shown using singular geometric perturbation theory.
Data-driven and calibration-free Lamb wave source localization with sparse sensor arrays.
Harley, Joel B; Moura, José M F
2015-08-01
Most Lamb wave localization techniques require that we know the wave's velocity characteristics; yet, in many practical scenarios, velocity estimates can be challenging to acquire, are unavailable, or are unreliable because of the complexity of Lamb waves. As a result, there is a significant need for new methods that can reduce a system's reliance on a priori velocity information. This paper addresses this challenge through two novel source localization methods designed for sparse sensor arrays in isotropic media. Both methods exploit the fundamental sparse structure of a Lamb wave's frequency-wavenumber representation. The first method uses sparse recovery techniques to extract velocities from calibration data. The second method uses kurtosis and the support earth mover's distance to measure the sparseness of a Lamb wave's approximate frequency-wavenumber representation. These measures are then used to locate acoustic sources with no prior calibration data. We experimentally study each method with a collection of acoustic emission data measured from a 1.22 m by 1.22 m isotropic aluminum plate. We show that both methods can achieve less than 1 cm localization error and have less systematic error than traditional time-of-arrival localization methods. PMID:26276960
The APOSTLE simulations: solutions to the Local Group's cosmic puzzles
NASA Astrophysics Data System (ADS)
Sawala, Till; Frenk, Carlos S.; Fattahi, Azadeh; Navarro, Julio F.; Bower, Richard G.; Crain, Robert A.; Dalla Vecchia, Claudio; Furlong, Michelle; Helly, John. C.; Jenkins, Adrian; Oman, Kyle A.; Schaller, Matthieu; Schaye, Joop; Theuns, Tom; Trayford, James; White, Simon D. M.
2016-04-01
The Local Group galaxies offer some of the most discriminating tests of models of cosmic structure formation. For example, observations of the Milky Way (MW) and Andromeda satellite populations appear to be in disagreement with N-body simulations of the `lambda cold dark matter' (ΛCDM) model: there are far fewer satellite galaxies than substructures in CDM haloes (the `missing satellites' problem); dwarf galaxies seem to avoid the most massive substructures (the `too-big-to-fail' problem); and the brightest satellites appear to orbit their host galaxies on a thin plane (the `planes of satellites' problem). Here we present results from APOSTLE (A Project Of Simulating The Local Environment), a suite of cosmological hydrodynamic simulations of 12 volumes selected to match the kinematics of the Local Group (LG) members. Applying the EAGLE code to the LG environment, we find that our simulations match the observed abundance of LG galaxies, including the satellite galaxies of the MW and Andromeda. Due to changes to the structure of haloes and the evolution in the LG environment, the simulations reproduce the observed relation between stellar mass and velocity dispersion of individual dwarf spheroidal galaxies without necessitating the formation of cores in their dark matter profiles. Satellite systems form with a range of spatial anisotropies, including one similar to the MWs, confirming that such a configuration is not unexpected in ΛCDM. Finally, based on the observed velocity dispersion, size, and stellar mass, we provide estimates of the maximum circular velocity for the haloes of nine MW dwarf spheroidals.
Cao, Yanpeng; Tisse, Christel-Loic
2014-02-01
In this Letter, we propose an efficient and accurate solution to remove temperature-dependent nonuniformity effects introduced by the imaging optics. This single-image-based approach computes optics-related fixed pattern noise (FPN) by fitting the derivatives of correction model to the gradient components, locally computed on an infrared image. A modified bilateral filtering algorithm is applied to local pixel output variations, so that the refined gradients are most likely caused by the nonuniformity associated with optics. The estimated bias field is subtracted from the raw infrared imagery to compensate the intensity variations caused by optics. The proposed method is fundamentally different from the existing nonuniformity correction (NUC) techniques developed for focal plane arrays (FPAs) and provides an essential image processing functionality to achieve completely shutterless NUC for uncooled long-wave infrared (LWIR) imaging systems. PMID:24487887
Chen, Ding; Li, Dian-yi; Zhang, Ying-zhe; Kang, Zhi-tao
2013-11-01
Magnesium ferrite, MgFe2O4 nanoparticles with high saturation magnetization were successfully synthesized using ultrasonic wave-assisted ball milling. In this study, the raw materials were 4MgCO3·Mg(OH)2·5H2O and Fe2O3 powders and the grinding media was stainless steel ball. The average particle diameter of the product MgFe2O4 powders was 20 nm and the saturation magnetization of them reached 54.8 emu/g. The different results of aqueous solution ball milling with and without ultrasonic wave revealed that it was the coupling effect of ultrasonic wave and mechanical force that played an important role during the synthesis of MgFe2O4. In addition, the effect of the frequency of the ultrasonic wave on the ball milling process was investigated. PMID:23622867
NASA Astrophysics Data System (ADS)
Li, X. D.; O'Leary, M. A.; Boas, D. A.; Chance, Britton; Yodh, A. G.
1996-07-01
We present analytic solutions for fluorescent diffuse photon density waves originating from fluorophores distributed in thick turbid media. Solutions are derived for a homogeneous turbid medium containing a uniform distribution of fluorophores and for a system that is homogeneous except for the presence of a single spherical inhomogeneity. Generally the inhomogeneity has fluorophore concentration, and lifetime and optical properties that differ from those of the background. The analytic solutions are verified by numerical calculations and are used to determine the fluorophore lifetime and concentration changes required for the accurate detection of inhomogeneities in biologically relevant systems. The relative sensitivities of absorption and fluorescence methods are compared.
Examples of Heun and Mathieu functions as solutions of wave equations in curved spaces
NASA Astrophysics Data System (ADS)
Birkandan, T.; Horta, M.
We give examples of where the Heun function exists as solutions of wave equations encountered in general relativity. 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. We must apply Atiyah-Patodi-Singer spectral boundary conditions to this system since the metric has a singularity at the origin.
Diffusive and localization behavior of electromagnetic waves in a two-dimensional random medium
NASA Astrophysics Data System (ADS)
Wang, Ken Kang-Hsin; Ye, Zhen
2003-10-01
In this paper, we discuss the transport phenomena of electromagnetic waves in a two-dimensional random system which is composed of arrays of electrical dipoles, following the model presented earlier by Erdogan et al. [J. Opt. Soc. Am. B 10, 391 (1993)]. A set of self-consistent equations is presented, accounting for the multiple scattering in the system, and is then solved numerically. A strong localization regime is discovered in the frequency domain. The transport properties within, near the edge of, and nearly outside the localization regime are investigated for different parameters such as filling factor and system size. The results show that within the localization regime, waves are trapped near the transmitting source. Meanwhile, the diffusive waves follow an intuitive but expected picture. That is, they increase with traveling path as more and more random scattering incurs, followed by a saturation, then start to decay exponentially when the travelling path is large enough, signifying the localization effect. For the cases where the frequencies are near the boundary of or outside the localization regime, the results of diffusive waves are compared with the diffusion approximation, showing less encouraging agreement as in other systems [Asatryan et al., Phys. Rev. E 67, 036605 (2003)].
3D WKB solution for fast magnetoacoustic wave behaviour around an X-line
NASA Astrophysics Data System (ADS)
McLaughlin, J. A.; Botha, G. J. J.; Régnier, S.; Spoors, D. L.
2016-06-01
Context. We study the propagation of a fast magnetoacoustic wave in a 3D magnetic field created from two magnetic dipoles. The magnetic topology contains an X-line. Aims: We aim to contribute to the overall understanding of MHD wave propagation within inhomogeneous media, specifically around X-lines. Methods: We investigate the linearised, 3D MHD equations under the assumptions of ideal and cold plasma. We utilise the WKB approximation and Charpit's method during our investigation. Results: It is found that the behaviour of the fast magnetoacoustic wave is entirely dictated by the local, inhomogeneous, equilibrium Alfvén speed profile. All parts of the wave experience refraction during propagation, where the magnitude of the refraction effect depends on the location of an individual wave element within the inhomogeneous magnetic field. The X-line, along which the Alfvén speed is identically zero, acts as a focus for the refraction effect. There are two main types of wave behaviour: part of the wave is either trapped by the X-line or escapes the system, and there exists a critical starting region around the X-line that divides these two types of behaviour. For the set-up investigated, it is found that 15.5% of the fast wave energy is trapped by the X-line. Conclusions: We conclude that linear, β = 0 fast magnetoacoustic waves can accumulate along X-lines and thus these will be specific locations of fast wave energy deposition and thus preferential heating. The work here highlights the importance of understanding the magnetic topology of a system. We also demonstrate how the 3D WKB technique described in this paper can be applied to other magnetic configurations.
A method to evaluate the generation area of local wave climate
NASA Astrophysics Data System (ADS)
Perez, Jorge; Mendez, Fernando; Menendez, Melisa
2013-04-01
The description of wave conditions at a local scale is of paramount importance for off-shore and coastal engineering applications (maritime works, ship design and route definition, offshore structures design, harbours operability). However, wave characteristics at a specific location cannot be fully understood studying only information of such location. They are the integrated result of the dynamics of the ocean surface over an area of influence. The goal of this work is to provide a methodology to easily characterize the area of influence of any particular ocean location in the world. The method is based on a global scale analysis using both geographic and oceanographic criteria. The geographic criterion relies on the realistic assumption that deep water waves travel along great circle paths, taking into account the spherical shape of the Earth. This allows limiting the study area by neglecting energy that cannot reach a target point, as its path is blocked by land. The oceanographic criterion is applied to global wave reanalysis data (Reguero et al., 2012), considering different spectral parameters such as mean direction, directional spread, wave energy period and energy flux, and taking into account in its specific location, the fraction of energy of the directional sector that travels towards the target point. A better understanding of the spatial generation and propagation area and an estimation of the time span the waves take to arrive to the target point is obtained. We have applied the methodology worldwide to obtain detailed maps of the relative importance of different oceanic areas to the climate of any location. Results show important spatial patterns that cannot be inferred from local parameters and validation with different climate analysis of other authors (Izaguirre et al., 2012; Alves et al., 2006) confirm the robustness of the method. This methodology facilitates enormously the study of wave generation area that induces local wave climate.
Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations.
Islam, S M Rayhanul; Khan, Kamruzzaman; Akbar, M Ali
2015-01-01
In this paper, we implement the exp(-Φ(ξ))-expansion method to construct the exact traveling wave solutions for nonlinear evolution equations (NLEEs). Here we consider two model equations, namely the Korteweg-de Vries (KdV) equation and the time regularized long wave (TRLW) equation. These equations play significant role in nonlinear sciences. We obtained four types of explicit function solutions, namely hyperbolic, trigonometric, exponential and rational function solutions of the variables in the considered equations. It has shown that the applied method is quite efficient and is practically well suited for the aforementioned problems and so for the other NLEEs those arise in mathematical physics and engineering fields. PACS numbers: 02.30.Jr, 02.70.Wz, 05.45.Yv, 94.05.Fq. PMID:25810953
Dual series solution to the scattering of plane waves from a binary conducting grating
NASA Astrophysics Data System (ADS)
Kok, Yon-Lin; Gallagher, Neal C., Jr.; Ziolkowski, Richard W.
1989-07-01
The problem of EM-wave scattering from a perfectly conducting grating with a periodic groove structure is considered. A system of dual series equations is derived by enforcing the EM boundary conditions; this leads to a boundary-value problem that is solved. The mathematics leading to the solution of the dual series system is derived from the equivalent Riemann-Hilbert problem in complex-variable theory and its solution. The solution converges absolutely and makes it possible to obtain analytical results, even where other numerical methods, such as the mode-matching method and spectral iteration methods, are numerically unstable. Consideration is also given to the relative phase values for the diffracted fields. The phase differences between the scattered fields resulting from two orthogonally polarized incident plane waves can be explicitly determined for any incidence angles and for any groove dimensions.
Study of influence of millimeter range electromagnetic waves on water-saline solutions of albumin
NASA Astrophysics Data System (ADS)
Shahinyan, Mariam A.; Antonyan, Ara P.; Mikaelyan, Marieta S.; Vardevanyan, Poghos O.
2015-01-01
In this work, the effect of electromagnetic waves of millimeter diapason (EMW MM) on both melting parameters of serum albumin from human blood and its solution density has been studied. It was shown that the irradiation of albumin solution results in protein denaturation at higher temperatures than in the case of nonirradiated samples, which indicates the increase of albumin packing degree. It was also shown that the enhancement of albumin solution density takes place which indicates the protein packing degree change as well. The obtained data show that the effect of EMW MM does not depend on frequency of these waves, because alterations are revealed at all studied frequencies — 41.8, 48 and 51.8GHz.
The small data solutions of general 3-D quasilinear wave equations. II
NASA Astrophysics Data System (ADS)
Ding, Bingbing; Witt, Ingo; Yin, Huicheng
2016-07-01
This paper is a continuation of the work in [8], where the authors established the global existence of smooth small data solutions to the general 3-D quasilinear wave equation ∑ i , j = 0 3 gij (u , ∂ u) ∂ij2 u = 0 when the weak null condition holds. In the present paper, we show that the smooth small data solutions of equation ∑ i , j = 0 3 gij (u , ∂ u) ∂ij2 u = 0 will blow up in finite time when the weak null condition does not hold and a generic nondegenerate condition on the initial data is satisfied, moreover, a precise blowup time is completely determined. Therefore, collecting the main results in this paper and [8], we have given a basically complete study on the blowup or global existence of small data solutions to the 3-D quasilinear wave equation ∑ i , j = 0 3 gij (u , ∂ u) ∂ij2 u = 0.
Adur, Rohan Du, Chunhui; Manuilov, Sergei A.; Wang, Hailong; Yang, Fengyuan; Pelekhov, Denis V.; Hammel, P. Chris
2015-05-07
The dipole field from a probe magnet can be used to localize a discrete spectrum of standing spin wave modes in a continuous ferromagnetic thin film without lithographic modification to the film. Obtaining the resonance field for a localized mode is not trivial due to the effect of the confined and inhomogeneous magnetization precession. We compare the results of micromagnetic and analytic methods to find the resonance field of localized modes in a ferromagnetic thin film, and investigate the accuracy of these methods by comparing with a numerical minimization technique that assumes Bessel function modes with pinned boundary conditions. We find that the micromagnetic technique, while computationally more intensive, reveals that the true magnetization profiles of localized modes are similar to Bessel functions with gradually decaying dynamic magnetization at the mode edges. We also find that an analytic solution, which is simple to implement and computationally much faster than other methods, accurately describes the resonance field of localized modes when exchange fields are negligible, and demonstrating the accessibility of localized mode analysis.
NASA Astrophysics Data System (ADS)
Horng, Jason; Balch, Halleh; Feng Wang Team
The spatio-temporal dynamics of local electric fields in ionic solutions plays a central role in various chemical and biological processes ranging from batteries technologies to neuron signaling. A non-invasive, precise detection scheme for measuring local electric fields dynamics has long been sought for. Here, we report a sensitive, high-speed, high spatial resolution optical imaging method for local electric fields based on the unique optoelectronic properties of graphene. With enhancement from a waveguide involving critical coupling concept, we show that our graphene optical sensor provides an ideal platform for studying dynamics of local electric field fluctuations in different nonequilibrium solutions.
The local dispersion relation for magneto-atmospheric waves. [in solar atmosphere
NASA Technical Reports Server (NTRS)
Thomas, J. H.
1982-01-01
The local dispersion relation for magneto-atmospheric waves is discussed in terms of the linearized theory of waves in a plane-stratified, inviscid, perfectly conducting atmosphere under uniform gravity. The normally used local dispersion relation is demonstrated to not be unique, depending instead on the order of derivation from the fundamental first-order perturbation equations of continuity, momentum, energy, and induction. Furthermore, it is shown that the local dispersion relation predicts that the cutoff frequency decreases with increasing magnetic field strength, while the WKB approximation method projects an increase in the cutoff frequency with increasing magnetic field strength. A new form of the local dispersion relation is developed, and consideration is given to the special case of a global dispersion relation in conditions of an isothermal atmosphere with a horizontal magnetic field.
Disorder in Quantum Vacuum: Casimir-Induced Localization of Matter Waves
Moreno, G. A.; Messina, R.; Dalvit, D. A. R.; Lambrecht, A.; Reynaud, S.; Maia Neto, P. A.
2010-11-19
Disordered geometrical boundaries such as rough surfaces induce important modifications to the mode spectrum of the electromagnetic quantum vacuum. In analogy to Anderson localization of waves induced by a random potential, here we show that the Casimir-Polder interaction between a cold atomic sample and a rough surface also produces localization phenomena. These effects, that represent a macroscopic manifestation of disorder in quantum vacuum, should be observable with Bose-Einstein condensates expanding in proximity of rough surfaces.
Schematic way to find solution of the outcoupled matter wave with a source term
Prayitno, T. B.
2013-09-09
We propose a schematic way to obtain solution of the outcoupled atom laser beam wave function in the presence of a source term where the beam is influenced by gravity. In this case, we only focus on the external potentials inside the region of Bose-Einstein condensate that are generated by electromagnetic source and gravity. Since the evolution of the atom laser beam can be portrayed through the ordinary Schrödinger equation with a source, we are allowed to express the general solution as the superposition of the homogeneous solution and particular solution. With the given external potentials and ansatz solutions, we attain that the obtained energy depends on the parameter constituting to the ratio between the longitudinal frequency and transverse frequency.
NASA Astrophysics Data System (ADS)
Zhang, Hai-Qiang; Yuan, Sha-Sha; Wang, Yue
2016-05-01
In this paper, the generalized Darboux transformation for the coherently-coupled nonlinear Schrödinger (CCNLS) system is constructed in terms of determinant representations. Based on the Nth-iterated formula, the vector bright soliton solution and vector rogue wave solution are systematically derived under the nonvanishing background. The general first-order vector rogue wave solution can admit many different fundamental patterns including eye-shaped and four-petaled rogue waves. It is believed that there are many more abundant patterns for high order vector rogue waves in CCNLS system.
Dynamic Sensing of Localized Corrosion at the Metal/Solution Interface
Li, Wei; Yuan, Boyu; Wang, Chao; Li, Liang; Chen, Shenhao
2012-01-01
A Mach-Zehnder interferometer is employed to detect localized corrosion at the metal/solution interface in the potentiodynamic sweep of the iron electrode in solutions. During the electrochemical reactions, local variations of the electrolyte's refractive index, which correlate with the concentration of dissolved species, change the optical path length (OPL) of the object beam when the beam passes through the electrolyte. The distribution of the OPL difference was obtained to present the concentration change of the metal ions visually, which enable direct evidence of corrosion processes. The OPL difference distribution shows localized and general corrosion during the anodic dissolution of the iron electrode in solutions with and without chloride ions, respectively. This method provides an approach for dynamic detection of localized corrosion at the metal/solution interface. PMID:22666070
Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators
Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.; Vainchtein, A.; Rubin, J. E.
2016-02-27
Artificial perceptions of light called phosphenes were motivated by earlier studies. 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 evolutionmore » and stability of planar fronts. Moreover, 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.« less
Essick, Reed; Vitale, Salvatore; Katsavounidis, Erik; Vedovato, Gabriele; Klimenko, Sergey
2015-02-20
The Laser Interferometer Gravitational wave Observatory (LIGO) and Virgo advanced ground-based gravitational-wave detectors will begin collecting science data in 2015. With first detections expected to follow, it is important to quantify how well generic gravitational-wave transients can be localized on the sky. This is crucial for correctly identifying electromagnetic counterparts as well as understanding gravitational-wave physics and source populations. We present a study of sky localization capabilities for two search and parameter estimation algorithms: coherent WaveBurst, a constrained likelihood algorithm operating in close to real-time, and LALInferenceBurst, a Markov chain Monte Carlo parameter estimation algorithm developed to recover generic transient signals with latency of a few hours. Furthermore, we focus on the first few years of the advanced detector era, when we expect to only have two (2015) and later three (2016) operational detectors, all below design sensitivity. These detector configurations can produce significantly different sky localizations, which we quantify in detail. We observe a clear improvement in localization of the average detected signal when progressing from two-detector to three-detector networks, as expected. Although localization depends on the waveform morphology, approximately 50% of detected signals would be imaged after observing 100-200 deg{sup 2} in 2015 and 60-110 deg{sup 2} in 2016, although knowledge of the waveform can reduce this to as little as 22 deg{sup 2}. This is the first comprehensive study on sky localization capabilities for generic transients of the early network of advanced LIGO and Virgo detectors, including the early LIGO-only two-detector configuration.
Control and monitoring of the localized corrosion of zirconium in acidic chloride solutions
Fahey, J.; Holmes, D.; Yau, T.L.
1995-09-01
Zirconium in acidic chloride solutions which are contaminated with ferric or cupric cations is prone to localized corrosion. This tendency can be reduced by ensuring that the zirconium surface is clean and smooth. In this paper, the effect of surface condition on the localized corrosion of zirconium in acidic chloride solutions is predicted with potentiodynamic scans. These predictions are confirmed by weight loss tests on various combinations of surface finish and acid concentrations. A real time indication of localized corrosion is seen by monitoring the electrochemical noise produced between two similar electrodes immersed in an acidic chloride solutions. Electrochemical noise monitoring correlates well with the predictions from potentiodynamic and weight loss experiments. The electrochemical noise results show that while an elevated (more anodic) potential caused by ferric ion contamination may be a necessary condition for localized corrosion, it is not a sufficient condition: A smooth, clean zirconium surface reduces the localized corrosion of zirconium.
Yu, Tianbao; Wang, Zhong; Liu, Wenxing; Wang, Tongbiao; Liu, Nianhua; Liao, Qinghua
2016-04-18
We report numerically large and complete photonic and phononic band gaps that simultaneously exist in eight-fold phoxonic quasicrystals (PhXQCs). PhXQCs can possess simultaneous photonic and phononic band gaps over a wide range of geometric parameters. Abundant localized modes can be achieved in defect-free PhXQCs for all photonic and phononic polarizations. These defect-free localized modes exhibit multiform spatial distributions and can confine simultaneously electromagnetic and elastic waves in a large area, thereby providing rich selectivity and enlarging the interaction space of optical and elastic waves. The simulated results based on finite element method show that quasiperiodic structures formed of both solid rods in air and holes in solid materials can simultaneously confine and tailor electromagnetic and elastic waves; these structures showed advantages over the periodic counterparts. PMID:27137236
NASA Astrophysics Data System (ADS)
Oh, Myunghyun; Zumbrun, Kevin
2010-04-01
Under natural spectral stability assumptions motivated by previous investigations of the associated spectral stability problem, we determine sharp L p estimates on the linearized solution operator about a multidimensional planar periodic wave of a system of conservation laws with viscosity, yielding linearized L 1 ∩ L p → L p stability for all {p ≥q 2} and dimensions {d ≥q 1} and nonlinear L 1 ∩ H s → L p ∩ H s stability and L 2-asymptotic behavior for {p≥q 2} and {d≥q 3} . The behavior can in general be rather complicated, involving both convective (that is, wave-like) and diffusive effects.
Over-reflection of slow magnetosonic waves by homogeneous shear flow: Analytical solution
Dimitrov, Z. D.; Maneva, Y. G.; Hristov, T. S.; Mishonov, T. M.
2011-08-15
We have analyzed the amplification of slow magnetosonic (or pseudo-Alfvenic) waves (SMW) in incompressible shear flow. As found here, the amplification depends on the component of the wave-vector perpendicular to the direction of the shear flow. Earlier numerical results are consistent with the general analytic solution for the linearized magnetohydrodynamic equations, derived here for the model case of pure homogeneous shear (without Coriolis force). An asymptotically exact analytical formula for the amplification coefficient is derived for the case when the amplification is sufficiently large.
A semi-analytic model for localized variable charge dust acoustic waves
Tribeche, Mouloud; Gougam, Leila Ait; Aoutou, Kamal
2006-09-15
A semi-analytic model for nonlinear variable charge dust acoustic waves is outlined. It is shown that rarefactive variable charge dust acoustic solitons involving cusped density humps can exist. The effects of dust dynamics as well as equilibrium dust charge on these nonlinear localized structures are briefly discussed.
Photonic nanojets as a versatile optical tool for wave super-localization
NASA Astrophysics Data System (ADS)
Geints, Yu. E.; Zemlyanov, A. A.; Panina, E. K.
2016-08-01
The dimensional parameters and intensity of localized light structures (area "photonic nanojet"—PNJ) formed in the near field scattering of the optical wave by dielectric micron particles are studied. The difference between the PNJ characteristics of homogeneous quartz microparticles of different spatial shape and orientation are shown.
Simultaneous Local and Teleseismic P-Wave Velocity Tomography in Western Mexico
NASA Astrophysics Data System (ADS)
Escudero, C. R.; Alarcon, E.; Ochoa, J.; Nuñez-Cornu, F. J.
2015-12-01
In western Mexico, the subduction of the Rivera and Cocos plates beneath the North America plate has deformed and fragmented the overriding plate, forming several structural rifts and crustal blocks. To improve the current tomographic images of the continental crust and uppermost mantle in this complex area, we used P-wave arrivals of local and teleseismic earthquakes along with the Fast Marching Method tomography technique. Our traveltime datasets include 2100 local earthquakes P-wave arrival times and 5,062 P-wave relative arrival time residuals of teleseismic earthquakes. The local earthquake phase picking was manually corrected and the relative arrival time residuals were estimated using the Multi-Channel Cross-Correlation method. All earthquakes occurred between 2006 and 2007 and were recorded by seismic stations deployed during the Mapping the Rivera Subduction Zone (MARS) experiment. The temporal seismic network consisted of 50 stations equipped with Streckeisen STS-2 and Quanterra Q330. We use an iterative nonlinear tomographic procedure and the fast marching method to map the residual patterns as P wave velocity anomalies. We followed an inversion scheme consisting of: (1) selection of a local and teleseismic earthquake, (2) estimation of improved 1-D reference velocity model, and (3) checkerboard testing to determine the optimum configuration of the velocity nodes, and inversion parameters, finally (4) perform final tomography and results analysis.
NASA Astrophysics Data System (ADS)
Mehdipoor, M.; Neirameh, A.
2012-01-01
The nonlinear propagation of ion acoustic waves in an ideal plasmas containing degenerate electrons is investigated. The Korteweg-de-Vries (K-dV) equation is derived for ion acoustic waves by using reductive perturbation method. The analytical traveling wave solutions of the K-dV equation investigated, through the ( G'/ G)-expansion method. These traveling wave solutions are expressed by hyperbolic function, trigonometric functions are rational functions. When the parameters are taken special values, the solitary waves are derived from the traveling waves. Also, numerically the effect different parameters on these solitary waves investigated and it is seen that exist only the compressive solitary waves in Thomas-Fermi plasmas.
Directional cloaking of flexural waves in a plate with a locally resonant metamaterial.
Colombi, Andrea; Roux, Philippe; Guenneau, Sebastien; Rupin, Matthieu
2015-04-01
This paper deals with the numerical design of a directional invisibility cloak for backward scattered elastic waves propagating in a thin plate (A0 Lamb waves). The directional cloak is based on a set of resonating beams that are attached perpendicular to the plate and are arranged at a sub-wavelength scale in ten concentric rings. The exotic effective properties of this locally resonant metamaterial ensure coexistence of bandgaps and directional cloaking for certain beam configurations over a large frequency band. The best directional cloaking was obtained when the resonators' length decreases from the central to the outermost ring. In this case, flexural waves experience a vanishing index of refraction when they cross the outer layers, leading to a frequency bandgap that protects the central part of the cloak. Numerical simulation shows that there is no back-scattering in these configurations. These results might have applications in the design of seismic-wave protection devices. PMID:25920831
Approximation of traveling wave solutions in wall-bounded flows using resolvent modes
NASA Astrophysics Data System (ADS)
McKeon, Beverley; Graham, Michael; Moarref, Rashad; Park, Jae Sung; Sharma, Ati; Willis, Ashley
2014-11-01
Significant recent attention has been devoted to computing and understanding exact traveling wave solutions of the Navier-Stokes equations. These solutions can be interpreted as the state-space skeleton of turbulence and are attractive benchmarks for studying low-order models of wall turbulence. Here, we project such solutions onto the velocity response (or resolvent) modes supplied by the gain-based resolvent analysis outlined by McKeon & Sharma (JFM, 2010). We demonstrate that in both pipe (Pringle et al., Phil. Trans. R. Soc. A, 2009) and channel (Waleffe, JFM, 2001) flows, the solutions can be well-described by a small number of resolvent modes. Analysis of the nonlinear forcing modes sustaining these solutions reveals the importance of small amplitude forcing, consistent with the large amplifications admitted by the resolvent operator. We investigate the use of resolvent modes as computationally cheap ``seeds'' for the identification of further traveling wave solutions. The support of AFOSR under Grants FA9550-09-1-0701, FA9550-12-1-0469, FA9550-11-1-0094 and FA9550-14-1-0042 (program managers Rengasamy Ponnappan, Doug Smith and Gregg Abate) is gratefully acknowledged.
Streamwise-Localized Solutions at the Onset of Turbulence in Pipe Flow
NASA Astrophysics Data System (ADS)
Avila, M.; Mellibovsky, F.; Roland, N.; Hof, B.
2013-05-01
Although the equations governing fluid flow are well known, there are no analytical expressions that describe the complexity of turbulent motion. A recent proposition is that in analogy to low dimensional chaotic systems, turbulence is organized around unstable solutions of the governing equations which provide the building blocks of the disordered dynamics. We report the discovery of periodic solutions which just like intermittent turbulence are spatially localized and show that turbulent transients arise from one such solution branch.
Some New Traveling Wave Exact Solutions of the (2+1)-Dimensional Boiti-Leon-Pempinelli Equations
Qi, Jian-ming; Zhang, Fu; Yuan, Wen-jun; Huang, Zi-feng
2014-01-01
We employ the complex method to obtain all meromorphic exact solutions of complex (2+1)-dimensional Boiti-Leon-Pempinelli equations (BLP system of equations). The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic traveling wave exact solutions of the equations (BLP) are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions ur,2(z) and simply periodic solutions us,2–6(z) which are not only new but also not degenerated successively by the elliptic function solutions. We believe that this method should play an important role for finding exact solutions in the mathematical physics. For these new traveling wave solutions, we give some computer simulations to illustrate our main results. PMID:24678276
Chou, D.-Y.; Yang, M.-H.; Zhao Hui; Liang Zhichao; Sun, M.-T.
2009-11-20
Observed acoustic power in magnetic regions is lower than the quiet Sun because of absorption, emissivity reduction, and local suppression of solar acoustic waves in magnetic regions. In the previous studies, we have developed a method to measure the coefficients of absorption, emissivity reduction, and local suppression of sunspots. In this study, we go one step further to measure the spatial distributions of three coefficients in two active regions, NOAA 9055 and 9057. The maps of absorption, emissivity reduction, and local suppression coefficients correlate with the magnetic map, including plage regions, except the emissivity reduction coefficient of NOAA 9055 where the emissivity reduction coefficient is too weak and lost among the noise.
Chang, T H; Chen, N C
2006-07-01
The gyrotron traveling-wave amplifier employing the distributed-loss scheme is capable of very high gain and effective in suppressing the global absolute instabilities. This study systematically characterizes the local absolute instabilities and their transitional behavior. The local absolute instabilities are analyzed using a model that incorporates the penetration of the field from the copper section into the lossy section. The axial modes were characterized from the perspective of beam-wave interaction and were found to share many characteristics with the global modes. The transition from global modes to local modes as the distributed loss increases was demonstrated. The electron transit angle in the copper section, which determines the feedback criterion, governs the survivability of an oscillation. In addition, the oscillation thresholds predicted using this model are more accurate than those obtained using a simplified model. PMID:16907193
NASA Technical Reports Server (NTRS)
Grosse, Ralf
1990-01-01
Propagation of sound through the turbulent atmosphere is a statistical problem. The randomness of the refractive index field causes sound pressure fluctuations. Although no general theory to predict sound pressure statistics from given refractive index statistics exists, there are several approximate solutions to the problem. The most common approximation is the parabolic equation method. Results obtained by this method are restricted to small refractive index fluctuations and to small wave lengths. While the first condition is generally met in the atmosphere, it is desirable to overcome the second. A generalization of the parabolic equation method with respect to the small wave length restriction is presented.
Time-lapse monitoring of localized changes within heterogeneous media with scattered waves
NASA Astrophysics Data System (ADS)
Chinaemerem, Kanu
Time-lapse monitoring of geological and mechanical media has been the focus of various studies over the past four decades because of the information that the inferred changes within the medium provides insight into the dynamic characteristics of the medium. Time-lapse changes within a medium can be used to characterize the temporal evolution of the medium, evaluate the forces driving the changes within the medium and make predictions on the future state of the monitored medium. The detectability of the changes within a material depends on the characteristics of the change to be imaged, the sensitivity of the monitoring data to the change, and the time-lapse monitoring parameters such as the monitoring source-receiver array and the spectral content of the monitoring waves. Various time-lapse monitoring tools have been used to monitor changes within media ranging from the earth's surface to tumors within the human body. These monitoring tools include the use of 4D active surveys were an imprint of the change within the medium is extracted from the time-lapse surveys and the use of interferometric techniques that use singly or multiply scattered waves. My major goal in this study is to image and localize changes present within a scattering medium using time-lapse multiply scattered waves generated within the monitored medium. The changes to be imaged are generally localized in space. This work is an extension of coda wave interferometry. Coda wave interferometry focuses on the identification and extraction of average velocity change occurring within a scattering medium. Due to the non-linear characteristics of multiply scattered waves and limited information of the origin of the multiply scattered waves, coda wave interferometry resolves the average velocity change within the scattering medium with no or limited indication of the location of the change. In this study, I demonstrate that time-lapse changes can be imaged and localized within scattering media using
NASA Technical Reports Server (NTRS)
Hanson, R. K.; Presley, L. L.; Williams, E. V.
1972-01-01
The method of characteristics for a chemically reacting gas is used in the construction of the time-dependent, one-dimensional flow field resulting from the normal reflection of an incident shock wave at the end wall of a shock tube. Nonequilibrium chemical reactions are allowed behind both the incident and reflected shock waves. All the solutions are evaluated for oxygen, but the results are generally representative of any inviscid, nonconducting, and nonradiating diatomic gas. The solutions clearly show that: (1) both the incident- and reflected-shock chemical relaxation times are important in governing the time to attain steady state thermodynamic properties; and (2) adjacent to the end wall, an excess-entropy layer develops wherein the steady state values of all the thermodynamic variables except pressure differ significantly from their corresponding Rankine-Hugoniot equilibrium values.
Electromagnetic waves with frequencies near the local proton gyrofrequency: ISEE-3 1 AU observations
NASA Technical Reports Server (NTRS)
Tsurutani, Bruce T.; Arballo, John K.; Mok, John; Smith, Edward J.; Mason, Glenn M.; Tan, Lun C.
1994-01-01
Low Frequency (LF) electromagnetic waves with periods near the local proton gyrofrequency have been detected in interplanetary space by the magnetometer onboard International-Sun-Earth-Explorer-3 (ISEE-3). Transverse peak-to-peak amplitudes as large as delta vector B/absolute value of B approximately 0.4 have been noted with compressional components (Delta absolute value of B/absolute value of B) typically less than or = 0.1. Generally, the waves have even smaller amplitudes, or are not detectable within the solar wind turbulence. The waves are elliptically/linearly polarized and are often, but not always, found to propagate nearly along vector B(sub zero). Both right- and left-hand polarizations in the spacecraft-frame have been detected. The waves are observed during all orientations of the interplanetary magnetic field, with the Parker spiral orientation being the most common case. Because the waves are detected at and near the local proton cyclotron frequency, the generation mechanism must almost certainly be solar wind pickup of freshly created hydrogen ions. Possible sources for the hydrogen are the Earth's atmosphere, coronal mass ejections from the Sun, comets and interstellar neutral atoms. At this time it is not obvious which potential source is the correct one. Statistical tests employing over one year of ISEE-3 data will be done in the near future to eliminate/confirm some of these possibilities.
Controllable Discrete Rogue Wave Solutions of the Ablowitz—Ladik Equation in Optics
NASA Astrophysics Data System (ADS)
Wen, Xiao-Yong
2016-07-01
With the aid of symbolic computation Maple, the discrete Ablowitz—Ladik equation is studied via an algebra method, some new rational solutions with four arbitrary parameters are constructed. By analyzing related parameters, the discrete rogue wave solutions with alterable positions and amplitude for the focusing Ablowitz—Ladik equations are derived. Some properties are discussed by graphical analysis, which might be helpful for understanding physical phenomena in optics. Supported by the Beijing Natural Science Foundation under Grant No. 1153004, and China Postdoctoral Science Foundation under Grant No. 2015M570161 and the Natural Science Foundation of China under Grant No. 61471406
Time Periodic Solutions to the One-Dimensional Nonlinear Wave Equation
NASA Astrophysics Data System (ADS)
Ji, Shuguan; Li, Yong
2011-02-01
This paper is concerned with the time periodic solutions to the one-dimensional nonlinear wave equation with either variable or constant coefficients. By adjusting the basis of L 2 function space, we can circumvent the difficulties caused by η u = 0 and obtain the existence of a weak periodic solution, which was posed as an open problem by Baubu and Pavel in (Trans Am Math Soc 349:2035-2048, 1997). Finally, an application to the forced Sine-Gordon equation is presented to illustrate the utility of this technique.
NASA Astrophysics Data System (ADS)
Vardevanyan, P. O.; Antonyan, A. P.; Shahinyan, M. A.; Mikaelyan, M. S.
2016-07-01
The effect of electromagnetic waves of the millimeter region on the conformation and fluorescence characteristics of human serum albumin was studied. It is shown that the irradiation of the albumin solution leads to an increase of the fluorescence intensity depending on the duration of irradiation. At an irradiation frequency of 48 GHz the fluorescence intensity of albumin hardly changes at all, while at 41.8 and 51.8 GHz it increases. It is also shown that when the irradiation frequency is 51.8 GHz, the intensity of the albumin solution fluorescence increases with increase of the irradiation time.
Kinetic vortex chain solution in the drift-wave plasma regime
Jovanovic; Pegoraro
2000-01-01
A fully nonlinear Bernstein-Greene-Kruskal stationary solution is found in the form of a quasi-three-dimensional chain of electron holes coupled to hydrodynamic vortices. This new coherent structure is enabled by the trapping and depletion of resonant particles, and the cyclotron dissipation of the singular current sheets. It is expected to play an important role in the collisionless magnetic field line reconnection in the drift-wave plasma regime, where it represents a plausible saturated state. PMID:11015843
Anti-de Sitter-wave solutions of higher derivative theories.
Gürses, Metin; Hervik, Sigbjørn; Şişman, Tahsin Çağrı; Tekin, Bayram
2013-09-01
We show that the recently found anti-de Sitter (AdS)-plane and AdS-spherical wave solutions of quadratic curvature gravity also solve the most general higher derivative theory in D dimensions. More generally, we show that the field equations of such theories reduce to an equation linear in the Ricci tensor for Kerr-Schild spacetimes having type-N Weyl and type-N traceless Ricci tensors. PMID:25166648
NASA Astrophysics Data System (ADS)
Chen, Jianyi; Zhang, Zhitao
2016-04-01
In this paper, we consider the periodic-Dirichlet problem for a forced nonlinear wave equation with resonance utt - Δu = μu + a (t , x)| u | p - 1 u in a n-dimensional ball. Under some suitable assumptions on μ, p and a (t , x), we prove the existence of infinitely many radially symmetric time-periodic solutions for the problem by variational methods.
Kim, S.
1994-12-31
Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.
NASA Astrophysics Data System (ADS)
Sharma, Vivek Kumar; Goyal, Amit
2016-05-01
We explore the modulational instability and existence of dark, bright solitary wave solutions in negative index-materials (NIMs) modeled by generalized nonlinear Schrödinger equation with competing cubic-quintic and higher-order nonlinearities with dispersive permittivity and permeability. Parameter domains are delineated in which these ultrashort pulses exist in NIMs. Unlike the ordinary materials, these novel excitations occur for different signs of dispersion, Kerr and non-Kerr nonlinearities.
Wang, Zhen; Yang, Yong; Yuan, Li-jun; Liu, Jie; Duan, Yun-you; Cao, Tie-sheng
2015-01-01
Objectives To evaluate the validity and reproducibility of a noninvasive dual pulse wave Doppler (DPWD) method, which involves simultaneous recording of flow velocity of two independent sample volumes with a measurable distance, for measuring the local arterial pulse wave velocity (PWV) through in vitro and in vivo studies. Methods The DPWD mode of Hitachi HI Vision Preirus ultrasound system with a 5–13MHz transducer was used. An in vitro model was designed to compare the PWV of a homogeneous rubber tubing with the local PWV of its middle part measured by DPWD method. In the in vivo study, local PWV of 45 hypertensive patients (25 male, 49.8±3.1 years) and 45 matched healthy subjects (25 male, 49.3±3.0 years) were investigated at the left common carotid artery (LCCA) by DPWD method. Results In the in vitro study, the local PWV measured by DPWP method and the PWV of the homogeneous rubber tubing did not show statistical difference (5.16 ± 0.28 m/s vs 5.03 ± 0.15 m/s, p = 0.075). The coefficient of variation (CV) of the intra- and inter- measurements for local PWV were 3.46% and 4.96%, for the PWV of the homogeneous rubber tubing were 0.99% and 1.98%. In the in vivo study, a significantly higher local PWV of LCCA was found in the hypertensive patients as compared to that in healthy subjects (6.29±1.04m/s vs. 5.31±0.72m/s, P = 0.019). The CV of the intra- and inter- measurements in hypertensive patients were 2.22% and 3.94%, in healthy subjects were 2.07% and 4.14%. Conclusions This study demonstrated the feasibility of the noninvasive DPWD method to determine the local PWV, which was accurate and reproducible not only in vitro but also in vivo studies. This noninvasive echocardiographic method may be illuminating to clinical use. PMID:25786124
Nonlinear simplified model to study localization of kinetic Alfvén wave
Sharma, R. P. Gaur, Nidhi
2014-04-15
We have presented the numerical simulation of the coupled equations governing the dynamics of kinetic Alfvén wave (KAW) and ion acoustic wave in the intermediate β plasma, where β is the ratio of thermal pressure to the background magnetic pressure. We have also developed a simplified model for this nonlinear interaction using the results obtained from the simulation to understand the physics of nonlinear evolution of KAW. Localization of magnetic field intensity of KAW has been studied by means of the simplified model.
Cosine-Gauss plasmon beam: a localized long-range nondiffracting surface wave.
Lin, Jiao; Dellinger, Jean; Genevet, Patrice; Cluzel, Benoit; de Fornel, Frederique; Capasso, Federico
2012-08-31
A new surface wave is introduced, the cosine-Gauss beam, which does not diffract while it propagates in a straight line and tightly bound to the metallic surface for distances up to 80 μm. The generation of this highly localized wave is shown to be straightforward and highly controllable, with varying degrees of transverse confinement and directionality, by fabricating a plasmon launcher consisting of intersecting metallic gratings. Cosine-Gauss beams have potential for applications in plasmonics, notably for efficient coupling to nanophotonic devices, opening up new design possibilities for next-generation optical interconnects. PMID:23002838
Damage localization in metallic plate structures using edge-reflected lamb waves
NASA Astrophysics Data System (ADS)
Ebrahimkhanlou, A.; Dubuc, B.; Salamone, S.
2016-08-01
This paper presents a model-based guided ultrasonic waves imaging algorithm, in which multiple ultrasonic echoes caused by reflections from the plate’s boundaries are leveraged to enhance imaging performance. An analytical model is proposed to estimate the envelope of scattered waves. Correlation between the estimated and experimental data is used to generate images. The proposed method is validated through experimental tests on an aluminum plate instrumented with three low profile piezoelectric transducers. Different damage conditions are simulated including through-thickness holes. Results are compared with two other imaging localization methods, that is, delay and sum and minimum variance.
Validating the solutions of the D-Wave quantum annealers through graph mirroring
NASA Astrophysics Data System (ADS)
Perera, Dilina; Hall, J. S.; Novotny, M. A.
D-Wave quantum annealers seek to find the ground states of Ising spin glasses. The problem Hamiltonian is formulated as an undirected graph that can be embedded into the device's native disordered Chimera graph structure. However, depending on the complexity of the problem and the specifications of the annealing schedule, the device may not necessarily find the global minimum during a given annealing process. We present a method, which we call answer checking, that enhances the expectation that the solution provided by the device is the true ground state of the problem. The underlying principle is to embed a mirrored graph G' of the original graph G, and connect the two graphs via ferromagnetic/antiferromagnetic couplers. This allows one to rule out solutions for the composite graph that do not comply with the underlying mirror symmetry inherent to the true ground state, which in turn, reduces the uncertainty associated with the solutions. Using the 1097 qubit D-Wave 2X, we test this approach by applying it to a range of problems, including random spanning trees and generally allowed graphs G. Supported in part by Pacific Northwest National Laboratory. D-Wave time provided by USRA.
Excitation of ship waves by a submerged object: New solution to the classical problem
NASA Astrophysics Data System (ADS)
Arzhannikov, A. V.; Kotelnikov, I. A.
2016-08-01
We have proposed a new method for solving the problem of ship waves excited on the surface of a nonviscous liquid by a submerged object that moves at a variable speed. As a first application of this method, we have obtained a new solution to the classic problem of ship waves generated by a submerged ball that moves rectilinearly with constant velocity parallel to the equilibrium surface of the liquid. For this example, we have derived asymptotic expressions describing the vertical displacement of the liquid surface in the limit of small and large values of the Froude number. The exact solution is presented in the form of two terms, each of which is reduced to one-dimensional integrals. One term describes the "Bernoulli hump" and another term the "Kelvin wedge." As a second example, we considered vertical oscillation of the submerged ball. In this case, the solution leads to the calculation of one-dimensional integral and describes surface waves propagating from the epicenter above the ball.
Wave-like solutions for Bianchi type I cosmologies in 5D
NASA Astrophysics Data System (ADS)
Ponce de Leon, J.
2008-10-01
We derive exact solutions to the vacuum Einstein field equations in 5D, under the assumption that (i) the line element in 5D possesses self-similar symmetry, in the classical understanding of Sedov, Taub and Zeldovich, and that (ii) the metric tensor is diagonal and independent of the coordinates for ordinary 3D space. These assumptions lead to three different types of self-similarity in 5D: homothetic, conformal and 'wave-like'. In this work we present the most general wave-like solutions to the 5D field equations. Using the standard technique based on Campbell's theorem, they generate a large number of anisotropic cosmological models of Bianchi type I, which can be applied to our universe after the big bang, when anisotropies could have played an important role. We present a complete review of all possible cases of self-similar anisotropic cosmologies in 5D. Our analysis extends a number of previous studies on wave-like solutions in 5D with spatial spherical symmetry.
Kinetic Alfvén wave turbulence and formation of localized structures
Sharma, R. P.; Modi, K. V.
2013-08-15
This work presents non-linear interaction of magnetosonic wave with kinetic Alfvén wave for intermediate β-plasma (m{sub e}/m{sub i}≪β≪1). A set of dimensionless equations have been developed for analysis by considering ponderomotive force due to pump kinetic Alfvén wave in the dynamics of magnetosonic wave. Stability analysis has been done to study modulational instability or linear growth rate. Further, numerical simulation has been carried out to study the nonlinear stage of instability and resulting power spectrum applicable to solar wind around 1 AU. Due to the nonlinearity, background density of magnetosonic wave gets modified which results in localization of kinetic Alfvén wave. From the obtained results, we observed that spectral index follows k{sup −3.0}, consistent with observation received by Cluster spacecraft for the solar wind around 1 AU. The result shows the steepening of power spectrum which may be responsible for heating and acceleration of plasma particles in solar wind.
WAVE1 regulates Bcl-2 localization and phosphorylation in leukemia cells
Rui, Kang; Daolin, Tang; Yan, Yu; Zhuo, Wang; Ting, Hu; Haichao, Wang; Lizhi, Cao
2010-01-01
Bcl-2 proteins are over-expressed in many tumors, and are critically important for cell survival. Their anti-apoptotic activities are determined by intracellular localization and post-translational modifications (such as phosphorylation). Here we showed that WAVE1, a member of the Wiskott-Aldrich syndrome protein family, was over-expressed in blood cancer cell lines, and functioned as a negative regulator of apoptosis. Further enhanced expression of WAVE1 by gene transfection rendered leukemia cells more resistant to anti-cancer drug-induced apoptosis; whereas suppression of WAVE1 expression by RNA interference restored leukemia cells' sensitivity to anti-drug-induced apoptosis. WAVE1 was found to be associated with mitochondrial Bcl-2, and its depletion led to mitochondrial release of Bcl-2, and phosphorylation of ASK1/JNK and Bcl-2. Furthermore, depletion of WAVE1 expression increased anti-cancer drug-induced production of reactive oxygen species in leukemia cells. Taken together, these results suggest WAVE1 as a novel regulator of apoptosis, and potential drug target for therapeutic intervention of leukemia. PMID:19890377
Kinetic Alfvén wave turbulence and formation of localized structures
NASA Astrophysics Data System (ADS)
Sharma, R. P.; Modi, K. V.
2013-08-01
This work presents non-linear interaction of magnetosonic wave with kinetic Alfvén wave for intermediate β-plasma (me/mi≪β ≪1). A set of dimensionless equations have been developed for analysis by considering ponderomotive force due to pump kinetic Alfvén wave in the dynamics of magnetosonic wave. Stability analysis has been done to study modulational instability or linear growth rate. Further, numerical simulation has been carried out to study the nonlinear stage of instability and resulting power spectrum applicable to solar wind around 1 AU. Due to the nonlinearity, background density of magnetosonic wave gets modified which results in localization of kinetic Alfvén wave. From the obtained results, we observed that spectral index follows k-3.0, consistent with observation received by Cluster spacecraft for the solar wind around 1 AU. The result shows the steepening of power spectrum which may be responsible for heating and acceleration of plasma particles in solar wind.
Millimetre-Wave Backhaul for 5G Networks: Challenges and Solutions
Feng, Wei; Li, Yong; Jin, Depeng; Su, Li; Chen, Sheng
2016-01-01
The trend for dense deployment in future 5G mobile communication networks makes current wired backhaul infeasible owing to the high cost. Millimetre-wave (mm-wave) communication, a promising technique with the capability of providing a multi-gigabit transmission rate, offers a flexible and cost-effective candidate for 5G backhauling. By exploiting highly directional antennas, it becomes practical to cope with explosive traffic demands and to deal with interference problems. Several advancements in physical layer technology, such as hybrid beamforming and full duplexing, bring new challenges and opportunities for mm-wave backhaul. This article introduces a design framework for 5G mm-wave backhaul, including routing, spatial reuse scheduling and physical layer techniques. The associated optimization model, open problems and potential solutions are discussed to fully exploit the throughput gain of the backhaul network. Extensive simulations are conducted to verify the potential benefits of the proposed method for the 5G mm-wave backhaul design. PMID:27322265
Millimetre-Wave Backhaul for 5G Networks: Challenges and Solutions.
Feng, Wei; Li, Yong; Jin, Depeng; Su, Li; Chen, Sheng
2016-01-01
The trend for dense deployment in future 5G mobile communication networks makes current wired backhaul infeasible owing to the high cost. Millimetre-wave (mm-wave) communication, a promising technique with the capability of providing a multi-gigabit transmission rate, offers a flexible and cost-effective candidate for 5G backhauling. By exploiting highly directional antennas, it becomes practical to cope with explosive traffic demands and to deal with interference problems. Several advancements in physical layer technology, such as hybrid beamforming and full duplexing, bring new challenges and opportunities for mm-wave backhaul. This article introduces a design framework for 5G mm-wave backhaul, including routing, spatial reuse scheduling and physical layer techniques. The associated optimization model, open problems and potential solutions are discussed to fully exploit the throughput gain of the backhaul network. Extensive simulations are conducted to verify the potential benefits of the proposed method for the 5G mm-wave backhaul design. PMID:27322265
Wang, Lei; Zhu, Yu-Jie; Qi, Feng-Hua; Li, Min; Guo, Rui
2015-06-01
In this paper, the nonautonomous Lenells-Fokas (LF) model is investigated. The modulational instability analysis of the solutions with variable coefficients in the presence of a small perturbation is studied. Higher-order soliton, breather, earthwormon, and rogue wave solutions of the nonautonomous LF model are derived via the n-fold variable-coefficient Darboux transformation. The solitons and earthwormons display the elastic collisions. It is found that the nonautonomous LF model admits the higher-order periodic rogue waves, composite rogue waves (rogue wave pair), and oscillating rogue waves, whose dynamics can be controlled by the inhomogeneous nonlinear parameters. Based on the second-order rogue wave, a diamond structure consisting of four first-order rogue waves is observed. In addition, the semirational solutions (the mixed rational-exponential solutions) of the nonautonomous LF model are obtained, which can be used to describe the interactions between the rogue waves and breathers. Our results could be helpful for the design of experiments in the optical fiber communications. PMID:26117105
Local wave particle resonant interaction causing energetic particle prompt loss in DIII-D plasmas
NASA Astrophysics Data System (ADS)
Zhang, R. B.; Fu, G. Y.; White, R. B.; Wang, X. G.
2015-11-01
A new wave particle resonance mechanism is found explaining the first-orbit prompt neutral beam-ion losses induced by shear Alfvén Eigenmodes (AEs) in the DIII-D tokamak. Because of the large banana width, a typical trapped beam ion can only interact locally with a core localised Alfvén Eigenmode for a fraction of its orbit, i.e. part of its inner leg of the banana orbit. These trapped beam ions can experience substantial radial kick within one bounce as long as the phases of the wave seen by the particles are nearly constant during this local interaction. A wave particle resonant condition is found based on the locally averaged particle orbit frequencies over the interaction part of the particle orbit. It is further found that the frequency width of the local resonance is quite large because the interaction time is short. This implies that particles over a considerable region of phase space can interact effectively with the localised AEs and experience large radial kicks within one bounce orbit. The radial kick size is found numerically and analytically to scale linearly in AE amplitude and is about 5 cm for typical experimental parameters. These results are consistent with experimental measurement.
NASA Astrophysics Data System (ADS)
Graf, S.; Craiem, D.; Barra, J. G.; Armentano, R. L.
2011-12-01
Increased arterial stiffness is associated with an increased risk of cardiovascular events. Estimation of arterial stiffness using local pulse wave velocity (PWV) promises to be very useful for noninvasive diagnosis of arteriosclerosis. In this work we estimated in an instrumented sheep, the local aortic pulse wave velocity using two sonomicrometry diameter sensors (separated 7.5 cm) according to the transit time method (PWVTT) with a sampling rate of 4 KHz. We simultaneously measured aortic pressure in order to determine from pressure-diameter loops (PWVPDLoop), the "true" local aortic pulse wave velocity. A pneumatic cuff occluder was implanted in the aorta in order to compare both methods under a wide range of pressure levels. Mean pressure values ranged from 47 to 101 mmHg and mean proximal diameter values from 12.5. to 15.2 mm. There were no significant differences between PWVTT and PWVPDLoop values (451±43 vs. 447±48 cm/s, p = ns, paired t-test). Both methods correlated significantly (R = 0.81, p<0.05). The mean difference between both methods was only -4±29 cm/s, whereas the range of the limits of agreement (mean ± 2 standard deviation) was -61 to +53 cm/s, showing no trend. In conclusion, the diameter waveforms transit time method was found to allow an accurate and precise estimation of the local aortic PWV.
Lloyd, Jeffrey T.; Clayton, John D.; Austin, Ryan A.; McDowell, David L.
2015-07-10
Background: The shock response of metallic single crystals can be captured using a micro-mechanical description of the thermoelastic-viscoplastic material response; however, using a such a description within the context of traditional numerical methods may introduce a physical artifacts. Advantages and disadvantages of complex material descriptions, in particular the viscoplastic response, must be framed within approximations introduced by numerical methods. Methods: Three methods of modeling the shock response of metallic single crystals are summarized: finite difference simulations, steady wave simulations, and algebraic solutions of the Rankine-Hugoniot jump conditions. For the former two numerical techniques, a dislocation density based framework describes themore » rate- and temperature-dependent shear strength on each slip system. For the latter analytical technique, a simple (two-parameter) rate- and temperature-independent linear hardening description is necessarily invoked to enable simultaneous solution of the governing equations. For all models, the same nonlinear thermoelastic energy potential incorporating elastic constants of up to order 3 is applied. Results: Solutions are compared for plate impact of highly symmetric orientations (all three methods) and low symmetry orientations (numerical methods only) of aluminum single crystals shocked to 5 GPa (weak shock regime) and 25 GPa (overdriven regime). Conclusions: For weak shocks, results of the two numerical methods are very similar, regardless of crystallographic orientation. For strong shocks, artificial viscosity affects the finite difference solution, and effects of transverse waves for the lower symmetry orientations not captured by the steady wave method become important. The analytical solution, which can only be applied to highly symmetric orientations, provides reasonable accuracy with regards to prediction of most variables in the final shocked state but, by construction, does not provide
Lloyd, Jeffrey T.; Clayton, John D.; Austin, Ryan A.; McDowell, David L.
2015-07-10
Background: The shock response of metallic single crystals can be captured using a micro-mechanical description of the thermoelastic-viscoplastic material response; however, using a such a description within the context of traditional numerical methods may introduce a physical artifacts. Advantages and disadvantages of complex material descriptions, in particular the viscoplastic response, must be framed within approximations introduced by numerical methods. Methods: Three methods of modeling the shock response of metallic single crystals are summarized: finite difference simulations, steady wave simulations, and algebraic solutions of the Rankine-Hugoniot jump conditions. For the former two numerical techniques, a dislocation density based framework describes the rate- and temperature-dependent shear strength on each slip system. For the latter analytical technique, a simple (two-parameter) rate- and temperature-independent linear hardening description is necessarily invoked to enable simultaneous solution of the governing equations. For all models, the same nonlinear thermoelastic energy potential incorporating elastic constants of up to order 3 is applied. Results: Solutions are compared for plate impact of highly symmetric orientations (all three methods) and low symmetry orientations (numerical methods only) of aluminum single crystals shocked to 5 GPa (weak shock regime) and 25 GPa (overdriven regime). Conclusions: For weak shocks, results of the two numerical methods are very similar, regardless of crystallographic orientation. For strong shocks, artificial viscosity affects the finite difference solution, and effects of transverse waves for the lower symmetry orientations not captured by the steady wave method become important. The analytical solution, which can only be applied to highly symmetric orientations, provides reasonable accuracy with regards to prediction of most variables in the final shocked state but, by construction, does not provide insight
Local wave particle resonant interaction causing energetic particle prompt loss in DIII-D plasmas
NASA Astrophysics Data System (ADS)
Zhang, Ruibin; Fu, Guoyong; White, Roscoe
2014-10-01
A new resonance mechanism is introduced to explain the observed first-orbit prompt beam ion losses induced by RSAE in the D3D tokamak. Because of large banana width and localized radial structure, some trapped beam ions can only interact with RSAE on the inner legs of their banana orbits. A beam ion can interact resonantly with the RSAE when the mode phase is nearly constant within the local interaction region. We identify this strong local wave particle interaction as local resonance. The local resonance condition is determined by the local poloidal and toroidal velocity of beam ions and can be written as < - m . θ + n . ϕ >gc - ω = 0 , where < > denotes local time average within the interaction region and gc stands for guiding center coordinates. A full orbit test particle code FOST confirms the local resonance theory. Both the linear scaling with the mode amplitude and the frequency of the loss signals detected by FILD on D3D as well as the measured fast ion radial kick size can be well explained by this local resonance theory and simulation.
Local Finite-Amplitude Wave Activity as an Objective Diagnostic of Midlatitude Extreme Weather
NASA Astrophysics Data System (ADS)
Chen, G.; Lu, J.; Burrows, D. A.; Leung, L. R.
2015-12-01
Midlatitude extreme weather events are responsible for a large part of climate-related damage, yet our understanding of these extreme events is limited, partly due to the lack of a theoretical basis for midlatitude extreme weather. In this work, the local finite-amplitude wave activity (LWA) of Huang and Nakamura (2015) is introduced as a diagnostic of the 500-hPa geopotential height (Z500) for characterizing midlatitude weather events. It is found that the LWA climatology and its variability associated with the Arctic Oscillation (AO) agree broadly with the previously reported blocking frequency in literature. There is a strong seasonal and spatial dependence in the trends of LWA in recent decades. While there is no observational evidence for a hemispheric-scale increase in wave amplitude, robust trends in wave activity can be identified at the regional scales, with important implications for regional climate change.
Local finite-amplitude wave activity as an objective diagnostic of midlatitude extreme weather
NASA Astrophysics Data System (ADS)
Chen, Gang; Lu, Jian; Burrows, D. Alex; Leung, L. Ruby
2015-12-01
Midlatitude extreme weather events are responsible for a large part of climate-related damage, yet our understanding of these extreme events is limited, partly due to the lack of a theoretical basis for midlatitude extreme weather. In this letter, the local finite-amplitude wave activity (LWA) of Huang and Nakamura (2015) is introduced as a diagnostic of the 500 hPa geopotential height for characterizing midlatitude weather events. It is found that the LWA climatology and its variability associated with the Arctic Oscillation agree broadly with the previously reported blocking frequency in the literature. There is a strong seasonal and spatial dependence in the trends of LWA in recent decades. While there is no observational evidence for a hemispheric-scale increase in wave amplitude, robust trends in wave activity can be identified at the regional scales, with important implications for regional climate change.
LIGO: Impacting science education through gravity-wave research in the local community and beyond
NASA Astrophysics Data System (ADS)
McGuire, Stephen
2012-02-01
We describe our integration of the science teacher pre-service and in-service education programs at Southern University (SUBR) with the Laser Interferometer Gravitational-wave Observatory (LIGO) Science Education Center (SEC). Inquiry-based interactive exhibits are employed wherein we emphasize classical physics concepts of oscillations, waves, wave propagation, interference, resonance, lasers, light and Newtonian gravity. An aggressive museum docent training program is providing a means for undergraduates to learn how to effectively communicate science concepts within informal learning environments. This local educational partnership will ultimately create a science education continuum of engagement, working at multiple levels and multiple audiences to strengthen science literacy within the targeted STEM African-American community. Following a brief overview of our program of LIGO-related optical materials research, we give a detailed presentation of our K-12 science teacher preparation program with results.
Local finite-amplitude wave activity as an objective diagnostic of midlatitude extreme weather
Chen, Gang; Lu, Jian; Burrows, Alex D.; Leung, Lai-Yung R.
2015-12-28
Midlatitude extreme weather events are responsible for a large part of climate related damage, yet our understanding of these extreme events is limited, partly due to the lack of a theoretical basis for midlatitude extreme weather. In this letter, the local finite-amplitude wave activity (LWA) of Huang and Nakamura [2015] is introduced as a diagnostic of the 500-hPa geopotential height (Z500) to characterizing midlatitude weather events. It is found that the LWA climatology and its variability associated with the Arctic Oscillation (AO) agree broadly with the previously reported blocking frequency in literature. There is a strong seasonal and spatial dependence in the trend13 s of LWA in recent decades. While there is no observational evidence for a hemispheric-scale increase in wave amplitude, robust trends in wave activity can be identified at the regional scales, with important implications for regional climate change.
Self adaptive solution strategies: Locally bound constrained Newton Raphson solution algorithms
NASA Technical Reports Server (NTRS)
Padovan, Joe
1991-01-01
A summary is given of strategies which enable the automatic adjustment of the constraint surfaces recently used to extend the range and numerical stability/efficiency of nonlinear finite element equation solvers. In addition to handling kinematic and material induced nonlinearity, both pre-and postbuckling behavior can be treated. The scheme employs localized bounds on various hierarchical partitions of the field variables. These are used to resize, shape, and orient the global constraint surface, thereby enabling essentially automatic load/deflection incrementation. Due to the generality of the approach taken, it can be implemented in conjunction with the constraints of an arbitrary functional type. To benchmark the method, several numerical experiments are presented. These include problems involving kinematic and material nonlinearity, as well as pre- and postbuckling characteristics. Also included is a list of papers published in the course of the work.
NASA Astrophysics Data System (ADS)
Cywiak, D.; Barreiro-Argüelles, M. D.; Cywiak, M.; Landa-Curiel, A.; Garcia-Segundo, C.; Gutierrez-Juárez, G.
2013-09-01
A study based on the general solution of the one-dimensional photoacoustic (PA) wave equation for an acoustic plane source is presented. This study relies on obtaining the impulse response of the PA system considering a heating function proportional to the Lambert-Beer law and spatially bounded by a rectangle function. The PA pressure is obtained by convoluting the impulse response with the temporal profile of the exciting pulse of light. With the obtained solution, it is possible to comprise, on a single expression, the PA pressure profile for optically thin samples (whose dimensions are smaller than the optical absorption length) and optically opaque samples (whose dimensions are larger than the optical absorption length). In the limit of weak absorption, the solution is in good agreement with the one for a uniform distribution of energy. Also, a study of the dependence of the acoustic pressure with the duration of the laser pulse is included.
Effect of local synaptic strengthening on global activity-wave growth in the hippocampus.
Koch, P; Leisman, G
2001-08-01
Analysis of a continuum model of the hippocampus shows that strengthening of the synaptic connections within localized regions can convert the global activity-wave properties from decay to growth. These growing waves can play a part in the implantation of long-term memory in the higher brain regions. The wavelength of the fastest-growing mode decreases with increasing local synaptic strength and can be modified by the chemical state as reflected by synaptic sensitivity to stimuli. The temporal period of the response is a constant, equal to twice the delay time exhibited by some of the hippocampal inhibitory neurons ("d-cells"). The value for the period obtained from this relationship and measurement of the delay time agrees with the hippocampal gamma rhythm. For normal hippocampal function the proportion of d-cells is limited to one-third the total number of inhibitory neurons. PMID:11328707
Local probing of propagating acoustic waves in a gigahertz echo chamber
NASA Astrophysics Data System (ADS)
Gustafsson, Martin V.; Santos, Paulo V.; Johansson, Göran; Delsing, Per
2012-04-01
In the same way that micro-mechanical resonators resemble guitar strings and drums, surface acoustic waves resemble the sound these instruments produce, but moving over a solid surface rather than through air. In contrast with oscillations in suspended resonators, such propagating mechanical waves have not before been studied near the quantum mechanical limits. Here, we demonstrate local probing of surface acoustic waves with a displacement sensitivity of 30amRMSHz-1/2 and detection sensitivity on the single-phonon level after averaging, at a frequency of 932MHz. Our probe is a piezoelectrically coupled single-electron transistor, which is sufficiently fast, non-destructive and localized to enable us to track pulses echoing back and forth in a long acoustic cavity, self-interfering and ringing the cavity up and down. We project that strong coupling to quantum circuits will enable new experiments, and hybrids using the unique features of surface acoustic waves. Prospects include quantum investigations of phonon-phonon interactions, and acoustic coupling to superconducting qubits for which we present favourable estimates.
NASA Astrophysics Data System (ADS)
Ba, Zhenning; Yin, Xiao
2016-06-01
A multidomain indirect boundary element method (IBEM) is proposed to study the wave scattering of plane SH waves by complex local site in a layered half-space. The new method, using both the full-space and layered half-space Green's functions as its fundamental solutions can also be regarded as a coupled method of the full-space IBEM and half-space IBEM. First, the whole model is decomposed into independent closed regions and an opened layered half-space region with all of the irregular interfaces; then, fictitious uniformly distributed loads are applied separately on the boundaries of each region, and scattered fields of the closed regions and the opened layered half-space region are constructed by calculating the full-space and layered half-space Green's functions, respectively; finally, all of the regions are assembled to establish the linear algebraic system that arises from discretization. The densities of the distributed loads are determined directly by solving the algebraic system. The accuracy and capability of the new approach are verified extensively by comparing its results with those of published approaches for a class of hills, valleys and embedded inclusions. And the capability of the new method is further displayed when it is used to investigate a hill-triple layered valley-hill coupled topography in a multilayered half-space. All of the numerical calculations presented in this paper demonstrate that the new method is very suitable for solving multidomain coupled multilayered wave scattering problems with the merits of high accuracy and representing the scattered fields in different kinds of regions more reasonably and flexibly.
Quantum mechanical manifestation of cantori: Wave-packet localization in stochastic regions
NASA Astrophysics Data System (ADS)
Brown, Robert C.; Wyatt, Robert E.
1986-07-01
Numerical calculations for a model anharmonic system interacting with a laser are used to analyze the quantum mechanical implications of classical structure in stochastic regions due to cantori (associated with the breakup of invariant Kolmogorov-Arnol'd-Moser surfaces). The numerical results show that a quantum wave packet may remain localized, even though classical orbits are strongly chaotic. Consequently, the quantum dynamics continues to exhibit ``tunnelinglike'' behavior even when diffusion is not classically forbidden.
Self-bound dipolar droplet: A localized matter wave in free space
NASA Astrophysics Data System (ADS)
Baillie, D.; Wilson, R. M.; Bisset, R. N.; Blakie, P. B.
2016-08-01
We demonstrate that a dipolar condensate can be prepared into a three-dimensional wave packet that remains localized when released in free space. Such self-bound states arise from the interplay of the two-body interactions and quantum fluctuations. We develop a phase diagram for the parameter regimes where these self-bound states are stable, examine their properties, and demonstrate how they can be produced in current experiments.
Experimental investigation of the local wave speed in a draft tube with cavitation vortex rope
NASA Astrophysics Data System (ADS)
Landry, C.; Favrel, A.; Müller, A.; Nicolet, C.; Yamamoto, K.; Avellan, F.
2014-03-01
Hydraulic machines operating in a wider range are subjected to cavitation developments inducing undesirable pressure pulsations which could lead to potential instability of the power plant. The occurrence of pulsating cavitation volumes in the runner and the draft tube is considered as a mass source of the system and is depending on the cavitation compliance. This dynamic parameter represents the cavitation volume variation with the respect to a variation of pressure and defines implicitly the local wave speed in the draft tube. This parameter is also decisive for an accurate prediction of system eigen frequencies. Therefore, the local wave speed in the draft tube is intrinsically linked to the eigen frequencies of the hydraulic system. Thus, if the natural frequency of a hydraulic system can be determined experimentally, it also becomes possible to estimate a local wave speed in the draft tube with a numerical model. In the present study, the reduced scale model of a Francis turbine (v=0.29) was investigated at off-design conditions. In order to measure the first eigenmode of the hydraulic test rig, an additional discharge was injected at the inlet of the hydraulic turbine at a variable frequency and amplitude to excite the system. Thus, with different pressure sensors installed on the test rig, the first eigenmode was determined. Then, a hydro-acoustic test rig model was developed with the In-house EPFL SIMSEN software and the local wave speed in the draft tube was adjusted to obtain the same first eigen frequency as that measured experimentally. Finally, this method was applied for different Thoma and Froude numbers at part load conditions.
Exact density functional and wave function embedding schemes based on orbital localization
NASA Astrophysics Data System (ADS)
Hégely, Bence; Nagy, Péter R.; Ferenczy, György G.; Kállay, Mihály
2016-08-01
Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.
NASA Astrophysics Data System (ADS)
Yang, Xiao-Feng; Deng, Zi-Chen; Li, Qing-Jun; Wei, Yi
2016-07-01
The homogeneous balance of undetermined coefficients method (HBUCM) is firstly proposed to construct not only the exact traveling wave solutions, three-wave solutions, homoclinic solutions, N-soliton solutions, but also multi-symplectic structures of some nonlinear partial differential equations (NLPDEs). By applying the proposed method to the variant Boussinesq equations (VBEs), the exact combined traveling wave solutions and a multi-symplectic structure of the VBEs are obtained directly. Then, the definition and a multi-symplectic structure of the variant Boussinesq-Whitham-Broer-Kaup type equations (VBWBKTEs) which can degenerate to the VBEs, the Whitham-Broer-Kaup equations (WBKEs) and the Broer-Kaup equations (BKEs) are given in the multi-symplectic sense. The HBUCM is also a standard and computable method, which can be generalized to obtain the exact solutions and multi-symplectic structures for some types of NLPDEs.
Forests as a natural seismic metamaterial: Rayleigh wave bandgaps induced by local resonances
NASA Astrophysics Data System (ADS)
Colombi, Andrea; Roux, Philippe; Guenneau, Sebastien; Gueguen, Philippe; Craster, Richard V.
2016-01-01
We explore the thesis that resonances in trees result in forests acting as locally resonant metamaterials for Rayleigh surface waves in the geophysics context. A geophysical experiment demonstrates that a Rayleigh wave, propagating in soft sedimentary soil at frequencies lower than 150 Hz, experiences strong attenuation, when interacting with a forest, over two separate large frequency bands. This experiment is interpreted using finite element simulations that demonstrate the observed attenuation is due to bandgaps when the trees are arranged at the sub-wavelength scale with respect to the incident Rayleigh wave. The repetitive bandgaps are generated by the coupling of the successive longitudinal resonances of trees with the vertical component of the Rayleigh wave. For wavelengths down to 5 meters, the resulting bandgaps are remarkably large and strongly attenuating when the acoustic impedance of the trees matches the impedance of the soil. Since longitudinal resonances of a vertical resonator are inversely proportional to its length, a man-made engineered array of resonators that attenuates Rayleigh waves at frequency ≤10 Hz could be designed starting from vertical pillars coupled to the ground with longitudinal resonance ≤10 Hz.
Forests as a natural seismic metamaterial: Rayleigh wave bandgaps induced by local resonances
Colombi, Andrea; Roux, Philippe; Guenneau, Sebastien; Gueguen, Philippe; Craster, Richard V.
2016-01-01
We explore the thesis that resonances in trees result in forests acting as locally resonant metamaterials for Rayleigh surface waves in the geophysics context. A geophysical experiment demonstrates that a Rayleigh wave, propagating in soft sedimentary soil at frequencies lower than 150 Hz, experiences strong attenuation, when interacting with a forest, over two separate large frequency bands. This experiment is interpreted using finite element simulations that demonstrate the observed attenuation is due to bandgaps when the trees are arranged at the sub-wavelength scale with respect to the incident Rayleigh wave. The repetitive bandgaps are generated by the coupling of the successive longitudinal resonances of trees with the vertical component of the Rayleigh wave. For wavelengths down to 5 meters, the resulting bandgaps are remarkably large and strongly attenuating when the acoustic impedance of the trees matches the impedance of the soil. Since longitudinal resonances of a vertical resonator are inversely proportional to its length, a man-made engineered array of resonators that attenuates Rayleigh waves at frequency ≤10 Hz could be designed starting from vertical pillars coupled to the ground with longitudinal resonance ≤10 Hz. PMID:26750489
Forests as a natural seismic metamaterial: Rayleigh wave bandgaps induced by local resonances.
Colombi, Andrea; Roux, Philippe; Guenneau, Sebastien; Gueguen, Philippe; Craster, Richard V
2016-01-01
We explore the thesis that resonances in trees result in forests acting as locally resonant metamaterials for Rayleigh surface waves in the geophysics context. A geophysical experiment demonstrates that a Rayleigh wave, propagating in soft sedimentary soil at frequencies lower than 150 Hz, experiences strong attenuation, when interacting with a forest, over two separate large frequency bands. This experiment is interpreted using finite element simulations that demonstrate the observed attenuation is due to bandgaps when the trees are arranged at the sub-wavelength scale with respect to the incident Rayleigh wave. The repetitive bandgaps are generated by the coupling of the successive longitudinal resonances of trees with the vertical component of the Rayleigh wave. For wavelengths down to 5 meters, the resulting bandgaps are remarkably large and strongly attenuating when the acoustic impedance of the trees matches the impedance of the soil. Since longitudinal resonances of a vertical resonator are inversely proportional to its length, a man-made engineered array of resonators that attenuates Rayleigh waves at frequency ≤10 Hz could be designed starting from vertical pillars coupled to the ground with longitudinal resonance ≤10 Hz. PMID:26750489
NASA Astrophysics Data System (ADS)
Mirshekari, Mostafa; Pan, Shijia; Zhang, Pei; Noh, Hae Young
2016-04-01
The objective of this paper is to characterize frequency-dependent wave propagation of footstep induced floor vibration to improve robustness of vibration-based occupant localization. Occupant localization is an essential part of many smart structure applications (e.g., energy management, patient/customer tracking, etc.). Exist- ing techniques include visual (e.g. cameras and IR sensors), acoustic, RF, and load-based approaches. These approaches have many deployment and operational requirements that limits their adaptation. To overcome these limitations, prior work has utilized footstep-induced vibrations to allow sparse sensor configuration and non-intrusive detection. However, frequency dependent propagation characteristics and low signal-to-noise ratio (SNR) of footstep-induced vibrations change the shape of the signal. Furthermore, estimating the wave propagation velocity for forming the multilateration equations and localizing the footsteps is a challenging task. They, in turn, lead to large errors of localization. In this paper, we present a structural vibration based indoor occupant localization technique using improved time-difference-of-arrival between multiple vibration sensors. In particular we overcome signal distortion by decomposing the signal into frequency components and focusing on high energy components for accurate indoor localization. Such decomposition leverages the frequency-specific propagation characteristics and reduces the effect of low SNR (by choosing the components of highest energy). Furthermore, we develop a velocity calibration method that finds the optimal velocity which minimizes the localization error. We validate our approach through field experiments in a building with human participants. We are able to achieve an average localization error of less than 0.21 meters, which corresponds to a 13X reduction in error when compared to the baseline method using raw data.
Manikandan, K; Senthilvelan, M
2016-07-01
We construct spatiotemporal localized envelope solutions of a (3 + 1)-dimensional nonlinear Schrödinger equation with varying coefficients such as dispersion, nonlinearity and gain parameters through similarity transformation technique. The obtained localized rational solutions can serve as prototypes of rogue waves in different branches of science. We investigate the characteristics of constructed localized solutions in detail when it propagates through six different dispersion profiles, namely, constant, linear, Gaussian, hyperbolic, logarithm, and exponential. We also obtain expressions for the hump and valleys of rogue wave intensity profiles for these six dispersion profiles and study the trajectory of it in each case. Further, we analyze how the intensity of another localized solution, namely, breather, changes when it propagates through the aforementioned six dispersion profiles. Our studies reveal that these localized solutions co-exist with the collapsing solutions which are already found in the (3 + 1)-dimensional nonlinear Schrödinger equation. The obtained results will help to understand the corresponding localized wave phenomena in related fields. PMID:27475076
Broadband Lamb Wave Trapping in Cellular Metamaterial Plates with Multiple Local Resonances
Zhao, De-Gang; Li, Yong; Zhu, Xue-Feng
2015-01-01
We have investigated the Lamb wave propagation in cellular metamaterial plates constructed by bending-dominated and stretch-dominated unit-cells with the stiffness differed by orders of magnitude at an ultralow density. The simulation results show that ultralight metamaterial plates with textured stubs deposited on the surface can support strong local resonances for both symmetric and anti-symmetric modes at low frequencies, where Lamb waves at the resonance frequencies are highly localized in the vibrating stubs. The resonance frequency is very sensitive to the geometry of textured stubs. By reasonable design of the geometry of resonant elements, we establish a simple loaded-bar model with the array of oscillators having a gradient relative density (or weight) that can support multiple local resonances, which permits the feasibility of a broadband Lamb wave trapping. Our study could be potentially significant in designing ingenious weight-efficient acoustic devices for practical applications, such as shock absorption, cushioning, and vibrations traffic, etc. PMID:25790858
NASA Astrophysics Data System (ADS)
Lilienthal, Friederike; Sacha, Petr; Jacobi, Christoph; Pisoft, Petr
2016-04-01
Internal gravity waves (GW) are one of the most dominant features in the middle atmosphere. They are a main contributor for energy and angular momentum transport and thus play an important role for atmospheric dynamics such as the Quasi Biennial Oscillation or the Brewer-Dobson circulation (BDC). GPS radio occultation measurements (e.g. Sacha et al., 2015) have shown that GW can appear in local hotspots, e.g. in the lower stratosphere of the Eastern Asia/North-western Pacific (EA/NP) region. Using these data as an input for the GW parameterization of a 3D primitive equation model for the middle and upper atmosphere (MUAM) we study the dynamical effects of such a localized breaking region. We further introduce an additional artificial GW drag in the lower stratosphere EA/NP region and show that a localized GW forcing is more efficient in creating planetary waves (PWs) than zonally uniform GW forcing. We observe PWs propagating both equatorward and poleward and upward along the edge of the polar vortex. Possible consequences for the polar vortex stability and stratosphere-troposphere exchange in the tropical region are discussed. Finally, applying 3D wave activity flux and 3D residual circulation diagnostics, we investigated the possible role of this area in the longitudinal variability of the BDC with a hypothesis of its enhanced downwelling branch in this region.
NASA Astrophysics Data System (ADS)
Shen, Yanfeng; Cesnik, Carlos E. S.
2016-09-01
This paper presents a new hybrid modeling technique for the efficient simulation of guided wave generation, propagation, and interaction with damage in complex composite structures. A local finite element model is deployed to capture the piezoelectric effects and actuation dynamics of the transmitter, while the global domain wave propagation and interaction with structural complexity (structure features and damage) are solved utilizing a local interaction simulation approach (LISA). This hybrid approach allows the accurate modeling of the local dynamics of the transducers and keeping the LISA formulation in an explicit format, which facilitates its readiness for parallel computing. The global LISA framework was extended through the 3D Kelvin–Voigt viscoelasticity theory to include anisotropic damping effects for composite structures, as an improvement over the existing LISA formulation. The global LISA framework was implemented using the compute unified device architecture running on graphic processing units. A commercial preprocessor is integrated seamlessly with the computational framework for grid generation and material property allocation to handle complex structures. The excitability and damping effects are successfully captured by this hybrid model, with experimental validation using the scanning laser doppler vibrometry. To demonstrate the capability of our hybrid approach for complex structures, guided wave propagation and interaction with a delamination in a composite panel with stiffeners is presented.
Full 3D dispersion curve solutions for guided waves in generally anisotropic media
NASA Astrophysics Data System (ADS)
Hernando Quintanilla, F.; Lowe, M. J. S.; Craster, R. V.
2016-02-01
Dispersion curves of guided waves provide valuable information about the physical and elastic properties of waves propagating within a given waveguide structure. Algorithms to accurately compute these curves are an essential tool for engineers working in non-destructive evaluation and for scientists studying wave phenomena. Dispersion curves are typically computed for low or zero attenuation and presented in two or three dimensional plots. The former do not always provide a clear and complete picture of the dispersion loci and the latter are very difficult to obtain when high values of attenuation are involved and arbitrary anisotropy is considered in single or multi-layered systems. As a consequence, drawing correct and reliable conclusions is a challenging task in the modern applications that often utilize multi-layered anisotropic viscoelastic materials. These challenges are overcome here by using a spectral collocation method (SCM) to robustly find dispersion curves in the most complicated cases of high attenuation and arbitrary anisotropy. Solutions are then plotted in three-dimensional frequency-complex wavenumber space, thus gaining much deeper insight into the nature of these problems. The cases studied range from classical examples, which validate this approach, to new ones involving materials up to the most general triclinic class for both flat and cylindrical geometry in multi-layered systems. The apparent crossing of modes within the same symmetry family in viscoelastic media is also explained and clarified by the results. Finally, the consequences of the centre of symmetry, present in every crystal class, on the solutions are discussed.
NASA Astrophysics Data System (ADS)
Xu, Ling; Cheng, Xuan; Dai, Chao-Qing
2015-12-01
Although the mapping method based on Riccati equation was proposed to obtain variable separation solutions many years ago, two important problems have not been studied: i) the equivalence of variable separation solutions by means of the mapping method based on Riccati equation with the radical sign combined ansatz; and ii) lack of physical meanings for some localized structures constructed by variable separation solutions. In this paper, we re-study the (2+1)-dimensional Boiti-Leon-Pempinelli equation via the mapping method based on Riccati equation and prove that nine types of variable separation solutions are actually equivalent to each other. Moreover, we also re-study localized structures constructed by variable separation solutions. Results indicate that some localized structures reported in the literature are lacking real values due to the appearance of the divergent and un-physical phenomenon for the initial field. Therefore, we must be careful with the initial field to avoid the appearance of some un-physical or even divergent structures in it when we construct localized structures for the potential field.
Wave force on double cylindrical piles: a comparison between exact and finite difference solutions
NASA Astrophysics Data System (ADS)
Ali, Lotfollahi-Yaghin Mohammad; Mehdi, Moosavi Sayyid; Amin, Lotfollahi-Yaghin
2011-03-01
The wave force exerted on vertical piles of offshore structures is the main criterion in designing them. In structures with more than one large pile, the influence of piles on each other is one of the most important issues being concerned in past researches. An efficient method for determining the interaction of piles is introduced in present research. First the wave force is calculated by the exact method using the diffraction theory, then in the finite difference numerical method the force is calculated by adding the velocity potentials of each pile and integration of pressure on their surface. The results showed that the ratio of the wave force on each of the double piles to a single pile has a damped oscillation around unity in which the amplitude of oscillation decreases with the increase in the spacing parameter. Also different wave incident directions and diffraction parameters were used and the results showed that the numerical solution has acceptable accuracy when the diffraction parameter is larger than unity.
Local problems, local solutions: improving tuberculosis control at the district level in Malawi.
Kelly, P. M.
2001-01-01
OBJECTIVE: To examine the causes of a low cure rate at the district level of a tuberculosis (TB) control programme and to formulate, implement, and evaluate an intervention to improve the situation. METHODS: The study setting was Mzuzu (population 60,000), where the annual smear-positive pulmonary TB incidence was 160 per 100,000 and the human immunodeficiency virus (HIV) seroprevalence was 67% among TB patients. There is one TB treatment unit, but several other organizations are involved with TB control. An examination of case-holding activities was carried out, potential areas for improvement were identified, and interventions performed. FINDINGS: In 1990-91, the cure rate was 24% among smear-positive cases (29% among survivors to end of treatment). Problems identified included a fragmented TB control programme; inadequate training and supervision; suboptimal recording of patients' addresses; and nonadherence to national TB control programme protocols. These problems were addressed, and in 1992-93 the cure rate rose to 68% (relative risk (RR) = 2.85 (95% confidence interval (CI) = 1.63, 4.96)) and to 92% among survivors to the end of treatment (RR = 3.12 (95% CI = 1.84, 5.29)). High cure rates are therefore achievable despite high HIV prevalence. CONCLUSIONS: Simple, inexpensive, local programmatic interventions can dramatically improve TB case holding. This study demonstrates the need for evaluation, training, and supervision at all levels of the programme. PMID:11242817
NASA Astrophysics Data System (ADS)
Babin, Anatoli; Figotin, Alexander
2013-09-01
Einstein's relation E = Mc 2 between the energy E and the mass M is the cornerstone of the relativity theory. This relation is often derived in a context of the relativistic theory for closed systems which do not accelerate. By contrast, the Newtonian approach to the mass is based on an accelerated motion. We study here a particular neoclassical field model of a particle governed by a nonlinear Klein-Gordon (KG) field equation. We prove that if a solution to the nonlinear KG equation and its energy density concentrate at a trajectory, then this trajectory and the energy must satisfy the relativistic version of Newton's law with the mass satisfying Einstein's relation. Therefore the internal energy of a localized wave affects its acceleration in an external field as the inertial mass does in Newtonian mechanics. We demonstrate that the "concentration" assumptions hold for a wide class of rectilinear accelerating motions.
NASA Astrophysics Data System (ADS)
Zhang, Lijun; Chen, Li-Qun; Zhang, Jianming
2013-10-01
Bifurcation and exact solutions of the modified nonlinearly dispersive mK (m,n,k) equation with nonlinear dispersion um-1ut+a(un)x+b(uk)xxx = 0,nk≠0 are investigated in this paper. As a result, under different parameter conditions, abundant compactons, peakons and solitary solutions including not only some known results but also some new ones are obtained. We also point out the original reason of the existence of the non-smooth traveling wave solutions. The approach we used here is also suitable for the study of traveling wave solutions of some other nonlinear equations.
MicroResearch--Finding sustainable solutions to local health challenges in East Africa.
Kollmann, Tobias R; Bortolussi, Robert; MacDonald, Noni E
2015-06-01
The urgent need in Africa for research capacity building has been recognized by African leaders and governments for many years. However, lack of large research funding opportunities has been seen as a major obstacle to improving research capacity in precisely those countries that need it the most. Microfinance has shown that a small infusion of capital can "prime the pump" to creative local economic productivity. In a similar way, MicroResearch has proven effective in promoting a similar bottom-up strategy to find sustainable solutions to local health challenges through local community focused research. Specifically, MicroResearch through hands-on didactic courses, mentoring and small-scale research funding promotes small research projects that improve research skills across the entire health-care provider spectrum to unleash a culture of inquiry. This in turn stimulates health care providers to identify the locally most relevant obstacles that need to be overcome and implement locally feasible and sustainable solutions. MicroResearch is a bottom-up strategy proven effective at finding sustainable solutions to local health challenges. PMID:25934328
Interfacial wave theory of dendrite growth - Global mode solution and quantum condition
NASA Technical Reports Server (NTRS)
Xu, Jian-Jun
1990-01-01
The signal feedback process at the edge of the dendrite tip is investigated, and the global instability mechanism of the system is derived. A mechanism is developed to describe a discrete set of unstable global modes for the system. Called WEASR, the method considers the wave emission at the turning point and signal reflections between the turning point and the front edge of the tip. It is shown that the method can obtain the asymptotic solutions for the unstable global modes and the quantum condition for the corresponding eigenvalues. A turning point called the pattern formation condition is shown to be crucial in the formation of dendritic structure and the choice of the final tip velocity. The wave emission process is outlined, and the importance of a signal feedback process at the edge of the dendrite tip is demonstrated. Parameters such as stability and surface tension can be analyzed in terms of their effects on WEASR modes.
Solution of the Bethe-Goldstone equation without partial wave decomposition
NASA Astrophysics Data System (ADS)
White, Larz
Nucleon-nucleon scattering is a most fundamental process in nuclear physics. From the theoretical standpoint, its description in momentum space involves the solution of an integral equation in three dimensions, which is typically accomplished with the help of a partial wave expansion of the scattering amplitude. It is the purpose of this work to present a method for solving the nucleon-nucleon scattering equation without the use of such expansion. After verifying the accuracy of our numerical tools by comparing with existing solutions of the nucleon-nucleon scattering amplitude in free space, we proceed to apply the method to the equation describing scattering of two nucleons in the nuclear medium, known as the Bethe-Goldstone equation. An important feature of this equation is the presence of the so-called "Pauli blocking operator", which prevents scattering of two fermions into occupied states, as required by the Pauli principle. In standard solution methods based on partial wave expansions, it is necessary to apply an approximation to this operator, which involves averaging over angular variables and is therefore known as the "spherical approximation". In our method, this approximation can be avoided. Thus, a focal point of this study is a comparison of Pauli blocking effects calculated in the (angle-dependent) three-dimensional formalism as compared to the usual spherical approximation. We present results for nucleon-nucleon amplitudes and observables and discuss their implications.
NASA Astrophysics Data System (ADS)
Ernst, F. J.
The author presents a derivation of the Nutku-Halil colliding wave solution from the isotropic Kasner metric using a double-Harrison (Bäcklund) transformation. The method when applied to other seed metrics is expected to supply useful candidates for new colliding wave solutions. All calculations were carried out using a symbolic evaluation program designed for manipulating differential forms on MS-DOS microcomputers.
Study of localized structures of kinetic Alfvén wave and generation of turbulence
Kumari, Anju Sharma, R. P. Yadav, Nitin
2015-06-15
Localization of kinetic Alfvén waves (KAW) due to ponderomotive nonlinearity can be regarded as an important mechanism for heating the space plasmas. The present paper investigates the effect of background density fluctuations on the formation of large amplitude localized structures and turbulent spectrum of KAW applicable to magnetopause. The dynamical equations are derived, taking into account the ponderomotive nonlinearity of the KAW as well as the background fluctuations which are in the form of ion acoustic waves. The system is studied numerically as well as semi-analytically. The results reveal that the presence of density fluctuations affects the formation of localized structures. These fluctuations affecting the localization of KAW may also affect heating and acceleration of plasma. Respective turbulent scaling for the different amplitude of background fluctuations has also been studied. The relevance of the numerical results has been discussed with the THEMIS observations near the magnetopause [C. Chaston et al., Geophys. Res. Lett. 35, L17S08 (2008)].
Low-frequency four-wave mixing spectroscopy of biomolecules in aqueous solutions
Bunkin, Aleksei F; Pershin, S M
2011-01-24
Four-wave mixing (FWM) spectroscopy is used to detect the rotational resonances of H{sub 2}O and H{sub 2}O{sub 2} molecules in DNA and denatured DNA aqueous solutions in the range {+-}10 cm{sup -1} with a spectral resolution of 3 GHz. It is found that the resonance contribution of the rotational transitions of these molecules increases significantly in solutions rather than in distilled water. This fact is interpreted as a manifestation of specific properties of a hydration layer at DNA-water and denatured DNA-water interfaces. Analysis of the FWM spectra shows that the concentration of H{sub 2}O{sub 2} molecules in the hydration layer of the DNA solution increases by a factor of 3 after denaturation. The FWM spectra of aqueous solutions of {alpha}-chymotrypsin protein are obtained in the range {+-}7cm{sup -1} at the protein concentrations between 0 and 20 mg cm{sup -3}. It is found that the hypersound velocity in the protein aqueous solution, measured by the shift of Brillouin components in the scattering spectrum, obeys a cubic dependence on the protein concentration and reaches a value of about 3000 m s{sup -1} at 20 mg cm{sup -3}. (application of lasers and laser-optical methods in life sciences)
An analytical solution of finite-amplitude solitary kinetic Alfven waves
Wu, D.; Wang, D.; Faelthammar, C.
1995-12-01
An analytical solution of finite-amplitude solitary kinetic Alfven waves (SKAWs) in a low-{beta} ({beta}{much_lt}{ital m}{sub {ital e}}/{ital m}{sub {ital i}}{much_lt}1) plasma is presented. This solution has been compared with the solution of the Korteweg--de Vries (KdV) equation in the small-amplitude limit. It is found that the KdV soliton solution is valid only for the maximum relative density perturbation {ital N}{sub {ital m}}{lt}0.1. For the larger {ital N}{sub {ital m}}, the exact analytical solution shows that the SKAWs have a much wider structure and much stronger perturbed fields than the KdV solitons with the same {ital N}{sub {ital m}}. Moreover, the relations between the width and the amplitude of SKAWs are also considerably different from that of the KdV solitons. In addition, the possibility for applying these results to some events observed from the Freja scientific satellite is discussed. (The Freja is a Swedish--German scientific project for the investigation of ionospheric and magnetospheric plasmas, and the Freja satellite was launched on a Long-March II rocket of China on October 6, 1992.) {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
On the Nutku-Halil solution for colliding impulsive gravitational waves
NASA Astrophysics Data System (ADS)
Chandrasekhar, S.; Ferrari, V.
1984-11-01
The equations appropriate for space-times with two space-like Killing-vectors are set up, ab initio, and explicit expressions for the components of the Riemann, the Ricci, and the Einstein tensors in a suitable tetrad-frame are written. The equations for the vacuum are reduced to a single equation of the Ernst type. It is then shown that the simplest linear solution of the Ernst equation leads directly to the Nutku-Halil solution for two colliding impulsive gravitational waves with uncorrelated polarizations. Thus, in some sense, the Nutku-Halil solution occupies the same place in space-times with two space-like Killing-vectors as the Kerr solution does in space-times with one time-like and one space-like Killing-vector. The Nutku-Halil solution is further described in a Newman-Penrose formalism; and the expressions for the Weyl scalars, in particular, make the development of curvature singularities manifest. Finally, a theorem analogous to Robinson's theorem (but much less strong) is proved for space-times with two space-like Killing-vectors.
Numerical solution of the nonlinear Schrödinger equation with wave operator on unbounded domains.
Li, Hongwei; Wu, Xiaonan; Zhang, Jiwei
2014-09-01
In this paper, we generalize the unified approach proposed in Zhang et al. [J. Zhang, Z. Xu, and X. Wu, Phys. Rev. E 78, 026709 (2008)] to design the nonlinear local absorbing boundary conditions (LABCs) for the nonlinear Schrödinger equation with wave operator on unbounded domains. In fact, based on the methodology underlying the unified approach, we first split the original equation into two parts-the linear equation and the nonlinear equation-then achieve a one-way operator to approximate the linear equation to make the wave outgoing, and finally combine the one-way operator with the nonlinear equation to achieve the nonlinear LABCs. The stability of the equation with the nonlinear LABCs is also analyzed by introducing some auxiliary variables, and some numerical examples are presented to verify the accuracy and effectiveness of our proposed method. PMID:25314566
Global asymptotics of solutions to the Cauchy problem for the damped wave equation with absorption
NASA Astrophysics Data System (ADS)
Ikehata, Ryo; Nishihara, Kenji; Zhao, Huijiang
We consider the Cauchy problem for the damped wave equation with absorption u-Δu+u+|u=0, (t,x)∈R×R. The behavior of u as t→∞ is expected to be same as that for the corresponding heat equation ϕ-Δϕ+|ϕ=0, (t,x)∈R×R. In the subcritical case 1<ρ<ρ(N):=1+2/N there exists a similarity solution w(t,x) with the form tf(x/√{t} ) depending on b=lim|f(|x|)⩾0. Our first aim is to show the decay rates (‖u(t)‖,‖u(t)‖,‖∇u(t)‖)=O(t,t,t) provided that the initial data without initial data size restriction spatially decays with reasonable polynomial order. The decay rates (∗∗) are sharp in the sense that they are same as those of the similarity solution. The second aim is to show that the Gauss kernel is the asymptotic profile in the supercritical case, which has been shown in case of one-dimensional space by Hayashi, Kaikina and Naumkin [N. Hayashi, E.I. Kaikina, P.I. Naumkin, Asymptotics for nonlinear damped wave equations with large initial data, preprint, 2004]. We show this assertion in two- and three-dimensional space. To prove our results, both the weighted L-energy method and the explicit formula of solutions will be employed. The weight is an improved one originally developed in [Y. Todorova, B. Yordanov, Critical exponent for a nonlinear wave equation with damping, J. Differential Equations 174 (2001) 464-489].
From plane waves to local Gaussians for the simulation of correlated periodic systems.
Booth, George H; Tsatsoulis, Theodoros; Chan, Garnet Kin-Lic; Grüneis, Andreas
2016-08-28
We present a simple, robust, and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on the representation of the Gaussians within a finite bandwidth by their underlying plane wave coefficients. The core region is handled within the projected augment wave framework, by pseudizing the Gaussian functions within a cutoff radius around each nucleus, smoothing the functions so that they are faithfully represented by a plane wave basis with only moderate kinetic energy cutoff. To mitigate the effects of the basis set superposition error and incompleteness at the mean-field level introduced by the Gaussian basis, we also propose a hybrid approach, whereby the complete occupied space is first converged within a large plane wave basis, and the Gaussian basis used to construct a complementary virtual space for the application of correlated methods. We demonstrate that these pseudized Gaussians yield compact and systematically improvable spaces with an accuracy comparable to their non-pseudized Gaussian counterparts. A key advantage of the described method is its ability to efficiently capture and describe electronic correlation effects of weakly bound and low-dimensional systems, where plane waves are not sufficiently compact or able to be truncated without unphysical artifacts. We investigate the accuracy of the pseudized Gaussians for the water dimer interaction, neon solid, and water adsorption on a LiH surface, at the level of second-order Møller-Plesset perturbation theory. PMID:27586908
Transport solutions of the Lamé equations and shock elastic waves
NASA Astrophysics Data System (ADS)
Alexeyeva, L. A.; Kaishybaeva, G. K.
2016-07-01
The Lamé system describing the dynamics of an isotropic elastic medium affected by a steady transport load moving at subsonic, transonic, or supersonic speed is considered. Its fundamental and generalized solutions in a moving frame of reference tied to the transport load are analyzed. Shock waves arising in the medium at supersonic speeds are studied. Conditions on the jump in the stress, displacement rate, and energy across the shock front are obtained using distribution theory. Numerical results concerning the dynamics of an elastic medium influenced by concentrated transport loads moving at sub-, tran- and supersonic speeds are presented.
NASA Astrophysics Data System (ADS)
Qin, Chun-Yan; Tian, Shou-Fu; Wang, Xiu-Bin; Zhang, Tian-Tian
2016-07-01
Under investigation in this paper is a fifth-order Korteweg-de Vries type (fKdV-type) equation with time-dependent coefficients, which can be used to describe many nonlinear phenomena in fluid mechanics, ocean dynamics and plasma physics. The binary Bell polynomials are employed to find its Hirota’s bilinear formalism with an extra auxiliary variable, based on which its N-soliton solutions can be also directly derived. Furthermore, by considering multi-dimensional Riemann theta function, a lucid and straightforward generalization of the Hirota-Riemann method is presented to explicitly construct the multiperiodic wave solutions of the equation. Finally, the asymptotic properties of these periodic wave solutions are strictly analyzed to reveal the relationships between periodic wave solutions and soliton solutions.
Two-Dimensional Classical Wave Localization in a Third Sound System
Luhman, D. R.; Herrmann, J. C.; Hallock, R. B.
2006-09-07
Patterned calcium fluoride deposited on glass creates an effective two-dimensional scatterer of third sound propagating on a thin 4He film. We have utilized a substrate with a periodic arrangement of scatterers and a substrate with a random arrangement of scatterers to investigate classical wave propagation and localization using third sound. We observe pass bands on the periodic substrate while only low frequency modes are observed in the disordered case. The presence of high frequency modes on the ordered substrate and the absence of high frequency modes on the disordered substrate indicates we are observing localization on the disordered substrate. We compare the disordered data to the two-dimensional localization theory of Cohen and Machta and find reasonable agreement.
Localized Ionospheric Particle Acceleration and Wave Acceleration of Auroral Ions: Amicist Data Set
NASA Technical Reports Server (NTRS)
Lynch, Kristina A.
1999-01-01
Research supported by this grant covered two main topics: auroral ion acceleration from ELF-band wave activity, and from VLF-spikelet (lower hybrid solitary structure) wave activity. Recent auroral sounding rocket data illustrate the relative significance of various mechanisms for initiating auroral ion outflow. Two nightside mechanisms are shown in detail. The first mechanism is ion acceleration within lower hybrid solitary wave events. The new data from this two payload mission show clearly that: (1) these individual events are spatially localized to scales approximately 100 m wide perpendicular to B, in agreement with previous investigations of these structures, and (2) that the probability of occurrence of the events is greatest at times of maximum VLF wave intensity. The second mechanism is ion acceleration by broadband, low frequency electrostatic waves, observed in a 30 km wide region at the poleward edge of the arc. The ion fluxes from the two mechanisms are compared and it is shown that while lower hybrid solitary structures do indeed accelerate ions in regions of intense VLF waves, the outflow from the electrostatic ion wave acceleration region is dominant for the aurora investigated by this sounding rocket, AMICIST. The fluxes are shown to be consistent with DE-1 and Freja outflow measurements, indicating that the AMICIST observations show the low altitude, microphysical signatures of nightside auroral outflow. In this paper, we present a review of sounding rocket observations of the ion acceleration seen nightside auroral zone lower hybrid solitary structures. Observations from Topaz3, Amicist, and Phaze2 are presented on various spatial scales, including the two-point measurements of the Amicist mission. From this collection of observations, we will demonstrate the following characteristics of transverse ion acceleration (TAI) in LHSS. The ion acceleration process is narrowly confined to 90 degrees pitch angle, in spatially confined regions of up to a
Traveling Wave Solutions for Nonlinear Differential-Difference Equations of Rational Types
NASA Astrophysics Data System (ADS)
İsmail, Aslan
2016-01-01
Differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous. Although a considerable amount of research has been carried out in the field of nonlinear differential-difference equations, the majority of the results deal with polynomial types. Limited research has been reported regarding such equations of rational type. In this paper we present an adaptation of the (G‧/G)-expansion method to solve nonlinear rational differential-difference equations. The procedure is demonstrated using two distinct equations. Our approach allows one to construct three types of exact traveling wave solutions (hyperbolic, trigonometric, and rational) by means of the simplified form of the auxiliary equation method with reduced parameters. Our analysis leads to analytic solutions in terms of topological solitons and singular periodic functions as well.
Horizon wave function for single localized particles: GUP and quantum black-hole decay
NASA Astrophysics Data System (ADS)
Casadio, Roberto; Scardigli, Fabio
2014-01-01
A localized particle in Quantum Mechanics is described by a wave packet in position space, regardless of its energy. However, from the point of view of General Relativity, if the particle's energy density exceeds a certain threshold, it should be a black hole. To combine these two pictures, we introduce a horizon wave function determined by the particle wave function in position space, which eventually yields the probability that the particle is a black hole. The existence of a minimum mass for black holes naturally follows, albeit not in the form of a sharp value around the Planck scale, but rather like a vanishing probability that a particle much lighter than the Planck mass may be a black hole. We also show that our construction entails an effective generalized uncertainty principle (GUP), simply obtained by adding the uncertainties coming from the two wave functions associated with a particle. Finally, the decay of microscopic (quantum) black holes is also described in agreement with what the GUP predicts.
Local magnetohydrodynamic instabilities and the wave-driven dynamo in accretion disks
NASA Technical Reports Server (NTRS)
Vishniac, Ethan T.; Diamond, Patrick
1992-01-01
We consider the consequences of magnetic buoyancy and the magnetic shearing instability (MSI) on the strength and organization of the magnetic field in a thin accretion disk. We discuss a model in which the wave-driven dynamo growth rate is balanced by the dissipative effects of the MSI. As in earlier work, the net helicity is due to small advective motions driven by nonlinear interactions between internal waves. Assuming a simple model of the internal wave spectrum generated from the primary m = 1 internal waves, we find that the magnetic energy density saturates at about (H/r) exp 4/3 times the local pressure (where H is the disk thickness and r is its radius). On very small scales the shearing instability will produce an isotropic fluctuating field. For a stationary disk this is equivalent to a dimensionless 'viscosity' of about (H/r) exp 4/3. The vertical and radial diffusion coefficients will be comparable to each other. Magnetic buoyancy will be largely suppressed by the turbulence due to the MSI. We present a rough estimate of its effects and find that it removes magnetic flux from the disk at a rate comparable to that caused by turbulent diffusion.
Initial-Boundary Value Problem Solution of the Nonlinear Shallow-water Wave Equations
NASA Astrophysics Data System (ADS)
Kanoglu, U.; Aydin, B.
2014-12-01
The hodograph transformation solutions of the one-dimensional nonlinear shallow-water wave (NSW) equations are usually obtained through integral transform techniques such as Fourier-Bessel transforms. However, the original formulation of Carrier and Greenspan (1958 J Fluid Mech) and its variant Carrier et al. (2003 J Fluid Mech) involve evaluation integrals. Since elliptic integrals are highly singular as discussed in Carrier et al. (2003), this solution methodology requires either approximation of the associated integrands by smooth functions or selection of regular initial/boundary data. It should be noted that Kanoglu (2004 J Fluid Mech) partly resolves this issue by simplifying the resulting integrals in closed form. Here, the hodograph transform approach is coupled with the classical eigenfunction expansion method rather than integral transform techniques and a new analytical model for nonlinear long wave propagation over a plane beach is derived. This approach is based on the solution methodology used in Aydın & Kanoglu (2007 CMES-Comp Model Eng) for wind set-down relaxation problem. In contrast to classical initial- or boundary-value problem solutions, here, the NSW equations are formulated to yield an initial-boundary value problem (IBVP) solution. In general, initial wave profile with nonzero initial velocity distribution is assumed and the flow variables are given in the form of Fourier-Bessel series. The results reveal that the developed method allows accurate estimation of the spatial and temporal variation of the flow quantities, i.e., free-surface height and depth-averaged velocity, with much less computational effort compared to the integral transform techniques such as Carrier et al. (2003), Kanoglu (2004), Tinti & Tonini (2005 J Fluid Mech), and Kanoglu & Synolakis (2006 Phys Rev Lett). Acknowledgments: This work is funded by project ASTARTE- Assessment, STrategy And Risk Reduction for Tsunamis in Europe. Grant 603839, 7th FP (ENV.2013.6.4-3 ENV
Shock wave synthesis of amino acids from solutions of ammonium formate and ammonium bicarbonate
NASA Astrophysics Data System (ADS)
Suzuki, Chizuka; Furukawa, Yoshihiro; Kobayashi, Takamichi; Sekine, Toshimori; Nakazawa, Hiromoto; Kakegawa, Takeshi
2015-07-01
The emergence of life's building blocks, such as amino acids and nucleobases, on the prebiotic Earth was a critical step for the beginning of life. Reduced species with low mass, such as ammonia, amines, or carboxylic acids, are potential precursors for these building blocks of life. These precursors may have been provided to the prebiotic ocean by carbonaceous chondrites and chemical reactions related to meteorite impacts on the early Earth. The impact of extraterrestrial objects on Earth occurred more frequently during this period than at present. Such impacts generated shock waves in the ocean, which have the potential to progress chemical reactions to form the building blocks of life from reduced species. To simulate shock-induced reactions in the prebiotic ocean, we conducted shock-recovery experiments on ammonium bicarbonate solution and ammonium formate solution at impact velocities ranging from 0.51 to 0.92 km/s. In the products from the ammonium formate solution, several amino acids (glycine, alanine, ß-alanine, and sarcosine) and aliphatic amines (methylamine, ethylamine, propylamine, and butylamine) were detected, although yields were less than 0.1 mol % of the formic acid reactant. From the ammonium bicarbonate solution, smaller amounts of glycine, methylamine, ethylamine, and propylamine were formed. The impact velocities used in this study represent minimum cases because natural meteorite impacts typically have higher velocities and longer durations. Our results therefore suggest that shock waves could have been involved in forming life's building blocks in the ocean of prebiotic Earth, and potentially in aquifers of other planets, satellites, and asteroids.
Continuous time random walks for non-local radial solute transport
NASA Astrophysics Data System (ADS)
Dentz, Marco; Kang, Peter K.; Le Borgne, Tanguy
2015-08-01
This study formulates and analyzes continuous time random walk (CTRW) models in radial flow geometries for the quantification of non-local solute transport induced by heterogeneous flow distributions and by mobile-immobile mass transfer processes. To this end we derive a general CTRW framework in radial coordinates starting from the random walk equations for radial particle positions and times. The particle density, or solute concentration is governed by a non-local radial advection-dispersion equation (ADE). Unlike in CTRWs for uniform flow scenarios, particle transition times here depend on the radial particle position, which renders the CTRW non-stationary. As a consequence, the memory kernel characterizing the non-local ADE, is radially dependent. Based on this general formulation, we derive radial CTRW implementations that (i) emulate non-local radial transport due to heterogeneous advection, (ii) model multirate mass transfer (MRMT) between mobile and immobile continua, and (iii) quantify both heterogeneous advection in a mobile region and mass transfer between mobile and immobile regions. The expected solute breakthrough behavior is studied using numerical random walk particle tracking simulations. This behavior is analyzed by explicit analytical expressions for the asymptotic solute breakthrough curves. We observe clear power-law tails of the solute breakthrough for broad (power-law) distributions of particle transit times (heterogeneous advection) and particle trapping times (MRMT model). The combined model displays two distinct time regimes. An intermediate regime, in which the solute breakthrough is dominated by the particle transit times in the mobile zones, and a late time regime that is governed by the distribution of particle trapping times in immobile zones. These radial CTRW formulations allow for the identification of heterogeneous advection and mobile-immobile processes as drivers of anomalous transport, under conditions relevant for field tracer
Effect of localized microstructural evolution on higher harmonic generation of guided wave modes
NASA Astrophysics Data System (ADS)
Choi, Gloria; Liu, Yang; Yao, Xiaochu; Lissenden, Cliff J.
2015-03-01
Higher harmonic generation of ultrasonic waves has the potential to be used to detect precursors to macroscale damage of phenomenon like fatigue due to microstructural evolution contributing to nonlinear material behavior. Aluminum plates having various plastic zone sizes were plastically deformed to different levels. The fundamental shear horizontal mode was then generated in the plate samples via a magnetostrictive transducer. After propagating through the plastic zone the primary wave mode (SH0) and its third harmonic (sh0) were received by a second transducer. Results of a parallel numerical study using the S1-s2 Lamb mode pair, where sensitivity to changes in third order elastic constants were investigated, are described within the context of the experimental results. Specimens used within both studies are geometrically similar and have double edge notches for dog bone samples that introduce localized plastic deformation. Through both studies, the size of the plastic zone with respect to the propagation distance and damage intensity influence the higher harmonics.
Wave Impact on a Wall: Comparison of Experiments with Similarity Solutions
NASA Astrophysics Data System (ADS)
Wang, A.; Duncan, J. H.; Lathrop, D. P.
2014-11-01
The impact of a steep water wave on a fixed partially submerged cube is studied with experiments and theory. The temporal evolution of the water surface profile upstream of the front face of the cube in its center plane is measured with a cinematic laser-induced fluorescence technique using frame rates up to 4,500 Hz. For a small range of cube positions, the surface profiles are found to form a nearly circular arc with upward curvature between the front face of the cube and a point just downstream of the wave crest. As the crest approaches the cube, the effective radius of this portion of the profile decreases rapidly. At the same time, the portion of the profile that is upstream of the crest approaches a straight line with a downward slope of about 15°. As the wave impact continues, the circular arc shrinks to zero radius with very high acceleration and a sudden transition to a high-speed vertical jet occurs. This flow singularity is modeled with a power-law scaling in time, which is used to create a time-independent system of equations of motion. The scaled governing equations are solved numerically and the similarly scaled measured free surface shapes, are favorably compared with the solutions. The support of the Office of Naval Research is gratefully acknowledged.
Soliton solutions and chaotic motions of the Zakharov equations for the Langmuir wave in the plasma
Zhen, Hui-Ling; Tian, Bo Wang, Yu-Feng; Liu, De-Yin
2015-03-15
For the interaction between the high-frequency Langmuir waves and low-frequency ion-acoustic waves in the plasma, the Zakharov equations are studied in this paper. Via the Hirota method, we obtain the soliton solutions, based on which the soliton propagation is presented. It is found that with λ increasing, the amplitude of u decreases, whereas that of v remains unchanged, where λ is the ion-acoustic speed, u is the slowly-varying envelope of the Langmuir wave, and v is the fluctuation of the equilibrium ion density. Both the head-on and bound-state interactions between the two solitons are displayed. We observe that with λ decreasing, the interaction period of u decreases, while that of v keeps unchanged. It is found that the Zakharov equations cannot admit any chaotic motions. With the external perturbations taken into consideration, the perturbed Zakharov equations are studied for us to see the associated chaotic motions. Both the weak and developed chaotic motions are investigated, and the difference between them roots in the relative magnitude of the nonlinearities and perturbations. The chaotic motions are weakened with λ increasing, or else, strengthened. Periodic motion appears when the nonlinear terms and external perturbations are balanced. With such a balance kept, one period increases with λ increasing.
Charge density waves and local states in quasi-one-dimensional mixed valence inorganic complexes
NASA Astrophysics Data System (ADS)
Conradson, S. D.; Stroud, M. A.; Zietlow, M. H.; Swanson, B. I.; Baeriswyl, D.; Bishop, A. R.
1988-02-01
The ground state structures and local states associated with chemical defects in quasi-one-dimensional halogen ( X) bridged transition metal ( M) mixed valence solids of MX and MMX type have been studied. An adiabatic Hartree-Fock theoretical framework is presented and representative members are classified. The MX materials provide a class whose strong electron-phonon coupling usually favors a charge-density-wave (CDW) ground state. However, the coupling strength can be chemically tuned (e.g., by extension to MMX systems) or altered by pressure, driving the ground state structures towards, e.g., a bond-order-wave (BOW) phase. Electron-phonon driven self-trapped states are expected in both the CDW or BOW regimes. Resonance Raman spectra of the MMX solid K 4[Pt 2(P 2O 5H 2) 4Cl]·H 2O show, in addition to the homogeneous ground state modes, sharp new features with excitation profiles shifted to the red of the intervalence-charge-transfer (IVCT) band. We attribute these new bands to a local polaron state formed by oxidation of the Pt 2Cl chain by a chemical defect. The observed spectral characteristics of this local state are in good agreement with theoretical predictions.
NASA Astrophysics Data System (ADS)
Miroshnikov, Victor
2015-11-01
The Navier-Stokes system of PDEs is reduced to a system of the vorticity, continuity, Helmholtz, and Lamb-Helmholtz PDEs. The periodic Dirichlet problems are formulated for conservative internal waves vanishing at infinity in upper and lower domains. Stationary kinematic Fourier (SKF) structures, stationary kinematic Euler-Fourier (SKEF) structures, stationary dynamic Euler-Fourier (SDEF) structures, and SKEF-SDEF structures of three spatial variables and time are constructed to consider kinematic and dynamic problems of the three-dimensional theory of the Newtonian flows with harmonic velocity. Exact solutions for propagation and interaction of N internal waves in the upper and lower domains are developed by the method of decomposition in invariant structures and implemented through experimental and theoretical programming in Maple. Main results are summarized in a global existence theorem for the strong solutions. The SKEF, SDEF, and SKEF-SDEF structures of the cumulative flows are visualized by two-parametric surface plots for six fluid-dynamic variables.
Fast solution of elliptic partial differential equations using linear combinations of plane waves.
Pérez-Jordá, José M
2016-02-01
Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations Ax=b, where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O(NlogN) memory and executing an iteration in O(Nlog(2)N) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps. PMID:26986436
Fully developed travelling wave solutions and bubble formation in fluidized beds
NASA Astrophysics Data System (ADS)
Glasser, B. J.; Kevrekidis, I. G.; Sundaresan, S.
1997-03-01
It is well known that most gas fluidized beds of particles bubble, while most liquid fluidized beds do not. It was shown by Anderson, Sundaresan & Jackson (1995), through direct numerical integration of the volume-averaged equations of motion for the fluid and particles, that this distinction is indeed accounted for by these equations, coupled with simple, physically credible closure relations for the stresses and interphase drag. The aim of the present study is to investigate how the model equations afford this distinction and deduce an approximate criterion for separating bubbling and non-bubbling systems. To this end, we have computed, making use of numerical continuation techniques as well as bifurcation theory, the one- and two-dimensional travelling wave solutions of the volume-averaged equations for a wide range of parameter values, and examined the evolution of these travelling wave solutions through direct numerical integration. It is demonstrated that whether bubbles form or not is dictated by the value of [Omega] = ([rho]sv3t/Ag) 1/2, where [rho]s is the density of particles, vt is the terminal settling velocity of an isolated particle, g is acceleration due to gravity and A is a measure of the particle phase viscosity. When [Omega] is large (> [similar] 30), bubbles develop easily. It is then suggested that a natural scale for A is [rho]svtdp so that [Omega]2 is simply a Froude number.
Fast solution of elliptic partial differential equations using linear combinations of plane waves
NASA Astrophysics Data System (ADS)
Pérez-Jordá, José M.
2016-02-01
Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations A x =b , where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O (N logN ) memory and executing an iteration in O (N log2N ) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.
Local structure of the halite-sylvine solid solution according to the computer simulation data
Urusov, V. S. Leonenko, E. V.
2008-09-15
The structural, elastic, and thermodynamic properties of halite NaCl and sylvine KCl and the miscibility properties of the NaCl-KCl solid solution found by computer simulation are in good agreement with the experimental data. Analysis of the relaxation of the solid solution structure suggests that both anion and cation sublattices are distorted; however, the anion sublattice is distorted much more strongly. Calculations of the local bond valence at all types of ions in the solid solution show opposite deviations from the balance at cations, whereas the general balance is retained. The values of the electrostatic potential in the ion positions reflect weakening of bonding in the solid solution with respect to its pure components. In addition, with an increase in the average interatomic distance in the first coordination sphere around cations, the modulus of the electrostatic potential at cations decreases.
Barberopoulou, A.; Qamar, A.; Pratt, T.L.; Creager, K.C.; Steele, W.P.
2004-01-01
The Mw7.9 Denali, Alaska earthquake of 3 November, 2002, caused minor damage to at least 20 houseboats in Seattle, Washington by initiating water waves in Lake Union. These water waves were likely initiated during the large amplitude seismic surface waves from this earthquake. Maps of spectral amplification recorded during the Denali earthquake on the Pacific Northwest Seismic Network (PNSN) strong-motion instruments show substantially increased shear and surface wave amplitudes coincident with the Seattle sedimentary basin. Because Lake Union is situated on the Seattle basin, the size of the water waves may have been increased by local amplification of the seismic waves by the basin. Complete hazard assessments require understanding the causes of these water waves during future earthquakes. Copyright 2004 by the American Geophysical Union.
Accelerating spectral-element simulations of seismic wave propagation using local time stepping
NASA Astrophysics Data System (ADS)
Peter, D. B.; Rietmann, M.; Galvez, P.; Nissen-Meyer, T.; Grote, M.; Schenk, O.
2013-12-01
Seismic tomography using full-waveform inversion requires accurate simulations of seismic wave propagation in complex 3D media. However, finite element meshing in complex media often leads to areas of local refinement, generating small elements that accurately capture e.g. strong topography and/or low-velocity sediment basins. For explicit time schemes, this dramatically reduces the global time-step for wave-propagation problems due to numerical stability conditions, ultimately making seismic inversions prohibitively expensive. To alleviate this problem, local time stepping (LTS) algorithms allow an explicit time-stepping scheme to adapt the time-step to the element size, allowing near-optimal time-steps everywhere in the mesh. Numerical simulations are thus liberated of global time-step constraints potentially speeding up simulation runtimes significantly. We present here a new, efficient multi-level LTS-Newmark scheme for general use with spectral-element methods (SEM) with applications in seismic wave propagation. We fit the implementation of our scheme onto the package SPECFEM3D_Cartesian, which is a widely used community code, simulating seismic and acoustic wave propagation in earth-science applications. Our new LTS scheme extends the 2nd-order accurate Newmark time-stepping scheme, and leads to an efficient implementation, producing real-world speedup of multi-resolution seismic applications. Furthermore, we generalize the method to utilize many refinement levels with a design specifically for continuous finite elements. We demonstrate performance speedup using a state-of-the-art dynamic earthquake rupture model for the Tohoku-Oki event, which is currently limited by small elements along the rupture fault. Utilizing our new algorithmic LTS implementation together with advances in exploiting graphic processing units (GPUs), numerical seismic wave propagation simulations in complex media will dramatically reduce computation times, empowering high
Plane-wave solutions to frequency-domain and time-domain scattering from magnetodielectric slabs.
Yaghjian, Arthur D; Hansen, Thorkild B
2006-04-01
Plane-wave representations are used to formulate the exact solutions to frequency-domain and time-domain sources illuminating a magnetodielectric slab with complex permittivity epsilon(omega) and permeability mu(omega). In the special case of a line source at z = 0 a distance d < L in front of an L-wide lossless double-negative (DNG) slab with kappa(omega 0) = epsilon(omega 0) / epsilon 0 = mu(omega 0) / mu 0 = (-1), the single-frequency (omega 0) solution exhibits not only "perfectly focused" fields for z > 2L but also divergent infinite fields in the region 2d < z < 2L. In contrast, the solution to the same lossless kappa(omega 0) = (-1) DNG slab illuminated by a sinusoidal wave that begins at some initial time t = 0 (and thus has a nonzero bandwidth, unlike the single-frequency excitation that begins at t = (-infinity) is proven to have imperfectly focused fields and convergent finite fields everywhere for all finite time t. The proof hinges on the variation of kappa(omega) about omega = omega 0 having a lower bound imposed by causality and energy conservation. The minimum time found to produce a given resolution is proportional to the estimate obtained by G. Gómez-Santos, [Phys. Rev. Lett. 90, 077401 (2003)]. Only as t --> infinity do the fields become perfectly focused in the region z > 2L and divergent in the region 2d < z < 2L. These theoretical results, which are confirmed by numerical examples, imply that divergent fields of the single-frequency solution are not caused by an inherent inconsistency in assuming an ideal lossless kappa(omega 0) = (-1) DNG material, but are the result of the continuous single-frequency wave (which contains infinite energy) building up infinite reactive fields during the infinite duration of time from t = (-infinity) to the present time t that the single-frequency excitation has been applied. An analogous situation occurs at the resonant frequencies of a lossless cavity. A single-frequency (zero-bandwidth) source inside the
A method for localized computation of Pulse Wave Velocity in carotid structure.
Patil, Ravindra B; Krishnamoorthy, P; Sethuraman, Shriram
2015-08-01
Pulse Wave Velocity (PWV) promises to be a useful clinical marker for noninvasive diagnosis of atherosclerosis. This work demonstrates the ability to perform localized carotid PWV measurements from the distention waveform derived from the Radio Frequency (RF) ultrasound signal using a carotid phantom setup. The proposed system consists of low cost custom-built ultrasound probe and algorithms for envelope detection, arterial wall identification, echo tracking, distension waveform computation and PWV estimation. The method is proposed on a phantom data acquired using custom-built prototype non-imaging probe. The proposed approach is non-image based and can be seamlessly integrated into existing clinical ultrasound scanners. PMID:26736653
NASA Astrophysics Data System (ADS)
Latifi, A.
2016-07-01
A special case of coupled integrable nonlinear equations with a singular dispersion law is derived in the context of the small amplitude limit of general wave equations in a fluid-type warm electrons/cold ions plasma irradiated by a continuous laser beam. This model accounts for a nonlinear mode coupling of the electrostatic wave with the ion sound wave and is shown to be highly unstable. Its instability is understood as a continuous secular transfer of energy from the electrostatic wave to the ion sound wave through the ponderomotive force. The exact asymptotic solution of the system is constructed and shows that the dynamics of the energy transfer results in a singular asymptotic behavior of the ion sound wave, which explains the low penetration of the incident laser beam.
Periodontal ligament injection in the dog primary dentition: spread of local anaesthetic solution.
Tagger, E; Tagger, M; Sarnat, H; Mass, E
1994-09-01
The spread of local anaesthetic solution administered with a pressure syringe has not been studied as extensively in young animals having primary or mixed dentitions as in adult animals. The purpose of this investigation was to study the distribution of local anaesthetic solution injected into the periodontal ligament of young dogs. India ink was added to carpules containing 2% lidocaine and 1:100,000 epinephrine, and the spread of solution was examined macroscopically and microscopically. Injections were made with a pressure syringe (Ligmaject) at 58 sites mesial and distal to primary teeth in five dogs aged 3-9 months. Three dogs were killed within 12 hours, the other two after 5 days. Spread of the ink was studied in non-decalcified slabs, in three-dimensional cleared specimens, and in histological sections. The solution usually reached the alveolar bone crest, seeped under the periosteum and alongside vascular channels into bone marrow, reaching natural cavities such as the crypts of tooth buds and the mandibular canal. The ink did not penetrate into the enamel organ or contact the permanent tooth buds. The solution appeared to spread along the path of least resistance, governed by the intricacies of anatomical structures and fascial planes. Therefore the risk of mechanical damage to permanent tooth germs appears to be minimal. PMID:7811670
Moll, Jochen
2016-09-01
This work is based on the experimental observation that the phase and group velocity of the fundamental antisymmetric wave mode in a composite structure with linearly varying thickness changes as it propagates along the nonuniform waveguide (Moll et al., 2015). This adiabatic wave motion leads to systematic damage localization errors of conventional algorithms because a constant wave velocity is assumed in the reconstruction process. This paper presents a generalized beamforming approach for composite structures with nonuniform cross section that eliminates this systematic error. Damage localization results will be presented and discussed in comparison to existing techniques. PMID:27317966
Many-body Localization Transition in Rokhsar-Kivelson-type wave functions
NASA Astrophysics Data System (ADS)
Chen, Xiao; Yu, Xiongjie; Cho, Gil Young; Clark, Bryan; Fradkin, Eduardo
We construct a family of many-body wave functions to study the many-body localization phase transition. The wave functions have a Rokhsar-Kivelson form, in which the weight for the configurations are chosen from the Gibbs weights of a classical spin glass model, known as the Random Energy Model, multiplied by a random sign structure to represent a highly excited state. These wave functions show a phase transition into an MBL phase. In addition, we see three regimes of entanglement scaling with subsystem size: scaling with entanglement corresponding to an infinite temperature thermal phase, constant scaling, and a sub-extensive scaling between these limits. Near the phase transition point, the fluctuations of the Renyi entropies are non-Gaussian. We find that Renyi entropies with different Renyi index transition into the MBL phase at different points and have different scaling behavior, suggesting a multifractal behavior. This work was supported in part by DMR-1064319 and DMR-1408713 (XC,GYC,EF) at the University of Illinois, PHY11-25915 at KITP (EF), DOE, SciDAC FG02-12ER46875 (BKC and XY), and the Brain Korea 21 PLUS Project of Korea Government (GYC).
Shear Wave Splitting from Local Earthquakes in the New Madrid Seismic Zone
NASA Astrophysics Data System (ADS)
Martin, P.; Arroucau, P.; Vlahovic, G.
2012-12-01
In this study we investigate crustal anisotropy in the New Madrid seismic zone (NMSZ), by analyzing shear wave splitting from local earthquake data. The NMSZ is centrally located in the United States, spanning portions of western Tennessee, northeastern Arkansas, and southeastern Missouri. The NMSZ is also the location in which three of the largest known earthquakes took place in North America, occurring in 1811-1812. Although many seismic studies have been performed in this region, there is no consensus about which driving mechanism could satisfy both the current observations, as well as the historically observed seismicity. Therefore, it is important to continue investigating the NMSZ, to gain a better understanding of its seismicity, and the possible mechanisms that drive it. The automated technique developed by Savage et al. (2010) is used to perform the shear wave splitting measurements at 120 seismic stations within the NMSZ. The Center for Earthquake Research and Information (CERI) at the University of Memphis provided data for 1151 earthquakes spanning the years 2003-2011. The initial event selection was reduced to 245 earthquakes ranging in magnitude from 2.0 to 4.6, which fell within the shear wave window of one or more of the stations. The results of this study provide information about orientation of microcracks in the upper portion of the crust; future work will include analysis for temporal and spatial variations in order to assess the state of stress in the region.
Stable standing waves for a NLS on star graphs as local minimizers of the constrained energy
NASA Astrophysics Data System (ADS)
Adami, Riccardo; Cacciapuoti, Claudio; Finco, Domenico; Noja, Diego
2016-05-01
On a star graph made of N ≥ 3 halflines (edges) we consider a Schrödinger equation with a subcritical power-type nonlinearity and an attractive delta interaction located at the vertex. From previous works it is known that there exists a family of standing waves, symmetric with respect to the exchange of edges, that can be parametrized by the mass (or L2-norm) of its elements. Furthermore, if the mass is small enough, then the corresponding symmetric standing wave is a ground state and, consequently, it is orbitally stable. On the other hand, if the mass is above a threshold value, then the system has no ground state. Here we prove that orbital stability holds for every value of the mass, even if the corresponding symmetric standing wave is not a ground state, since it is anyway a local minimizer of the energy among functions with the same mass. The proof is based on a new technique that allows to restrict the analysis to functions made of pieces of soliton, reducing the problem to a finite-dimensional one. In such a way, we do not need to use direct methods of Calculus of Variations, nor linearization procedures.
NASA Astrophysics Data System (ADS)
Shue, Jih-Hong; Hsieh, Yi-Kai; Tam, Sunny W. Y.; Wang, Kaiti; Fu, Hui Shan; Bortnik, Jacob; Tao, Xin; Hsieh, Wen-Chieh; Pi, Gilbert
2015-10-01
Whistler mode chorus waves generally occur outside the plasmapause in the magnetosphere. The most striking feature of the waves is their occurrence in discrete elements. One of the parameters that describe the discrete elements is the repetition period (Trp), the time between consecutive elements. The Trp has not been studied statistically before. We use high-resolution waveform data to derive distributions of Trp for different local times. We find that the average Trp for the nightside (0.56 s) and dawnside (0.53 s) are smaller than those for the dayside (0.81 s) and duskside (0.97 s). Through a comparison with the background plasma and magnetic fields, we also find that the total magnetic field and temperature are the main controlling factors that affect the variability of Trp. These results are important for understanding the generation mechanism of chorus and choosing parameters in simulations that model the acceleration and loss of electrons by wave-particle interactions.
A trade-off solution between model resolution and covariance in surface-wave inversion
Xia, J.; Xu, Y.; Miller, R.D.; Zeng, C.
2010-01-01
Regularization is necessary for inversion of ill-posed geophysical problems. Appraisal of inverse models is essential for meaningful interpretation of these models. Because uncertainties are associated with regularization parameters, extra conditions are usually required to determine proper parameters for assessing inverse models. Commonly used techniques for assessment of a geophysical inverse model derived (generally iteratively) from a linear system are based on calculating the model resolution and the model covariance matrices. Because the model resolution and the model covariance matrices of the regularized solutions are controlled by the regularization parameter, direct assessment of inverse models using only the covariance matrix may provide incorrect results. To assess an inverted model, we use the concept of a trade-off between model resolution and covariance to find a proper regularization parameter with singular values calculated in the last iteration. We plot the singular values from large to small to form a singular value plot. A proper regularization parameter is normally the first singular value that approaches zero in the plot. With this regularization parameter, we obtain a trade-off solution between model resolution and model covariance in the vicinity of a regularized solution. The unit covariance matrix can then be used to calculate error bars of the inverse model at a resolution level determined by the regularization parameter. We demonstrate this approach with both synthetic and real surface-wave data. ?? 2010 Birkh??user / Springer Basel AG.
Hu, Shilin; Qu, Hongpeng; Li, Jiquan; Kishimoto, Y.
2014-10-15
Resistive drift wave instability is investigated numerically in tokamak edge plasma confined by sheared slab magnetic field geometry with an embedded magnetic island. The focus is on the structural characteristics of eigenmode inside the island, where the density profile tends to be flattened. A transition of the dominant eigenmode occurs around a critical island width w{sub c}. For thin islands with a width below w{sub c}, two global long wavelength eigenmodes with approximately the same growth rate but different eigenfrequency are excited, which are stabilized by the magnetic island through two-dimensional mode coupling in both x and y (corresponding to radial and poloidal in tokamak) directions. On the other hand, a short wavelength eigenmode, which is destabilized by thick islands with a width above w{sub c}, dominates the edge fluctuation, showing a prominent structural localization in the region between the X-point and the O-point of the magnetic island. The main destabilization mechanism is identified as the mode coupling in the y direction, which is similar to the so-called toroidal coupling in tokamak plasmas. These three eigenmodes may coexist in the drift wave fluctuation for the island with a width around w{sub c}. It is demonstrated that the structural localization results mainly from the quasilinear flattening of density profile inside the magnetic island.
Hybrid Matter-Wave-Microwave Solitons Produced by the Local-Field Effect.
Qin, Jieli; Dong, Guangjiong; Malomed, Boris A
2015-07-10
It was recently found that the electric local-field effect (LFE) can lead to a strong coupling of atomic Bose-Einstein condensates (BECs) to off-resonant optical fields. We demonstrate that the magnetic LFE gives rise to a previously unexplored mechanism for coupling a (pseudo-) spinor BEC or fermion gas to microwaves (MWs). We present a theory for the magnetic LFE and find that it gives rise to a short-range attractive interaction between two components of the (pseudo) spinor, and a long-range interaction between them. The latter interaction, resulting from deformation of the magnetic field, is locally repulsive but globally attractive, in sharp contrast with its counterpart for the optical LFE, produced by phase modulation of the electric field. Our analytical results, confirmed by the numerical computations, show that the long-range interaction gives rise to modulational instability of the spatially uniform state, and it creates stable ground states in the form of hybrid matter-wave-microwave solitons (which seem like one-dimensional magnetic monopoles), with a size much smaller than the MW wavelength, even in the presence of arbitrarily strong contact intercomponent repulsion. The setting is somewhat similar to exciton-polaritonic condensates in semiconductor microcavities. The release of matter waves from the soliton may be used for the realization of an atom laser. The analysis also applies to molecular BECs with rotational states coupled by the electric MW field. PMID:26207469
Hybrid Matter-Wave-Microwave Solitons Produced by the Local-Field Effect
NASA Astrophysics Data System (ADS)
Qin, Jieli; Dong, Guangjiong; Malomed, Boris A.
2015-07-01
It was recently found that the electric local-field effect (LFE) can lead to a strong coupling of atomic Bose-Einstein condensates (BECs) to off-resonant optical fields. We demonstrate that the magnetic LFE gives rise to a previously unexplored mechanism for coupling a (pseudo-) spinor BEC or fermion gas to microwaves (MWs). We present a theory for the magnetic LFE and find that it gives rise to a short-range attractive interaction between two components of the (pseudo) spinor, and a long-range interaction between them. The latter interaction, resulting from deformation of the magnetic field, is locally repulsive but globally attractive, in sharp contrast with its counterpart for the optical LFE, produced by phase modulation of the electric field. Our analytical results, confirmed by the numerical computations, show that the long-range interaction gives rise to modulational instability of the spatially uniform state, and it creates stable ground states in the form of hybrid matter-wave-microwave solitons (which seem like one-dimensional magnetic monopoles), with a size much smaller than the MW wavelength, even in the presence of arbitrarily strong contact intercomponent repulsion. The setting is somewhat similar to exciton-polaritonic condensates in semiconductor microcavities. The release of matter waves from the soliton may be used for the realization of an atom laser. The analysis also applies to molecular BECs with rotational states coupled by the electric MW field.
Localization and broadband follow-up of the gravitational-wave transient GW150914
Abbott, B. P.
2016-07-20
A gravitational-wave (GW) transient was identified in data recorded by the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) detectors on 2015 September 14. The event, initially designated G184098 and later given the name GW150914, is described in detail elsewhere. By prior arrangement, preliminary estimates of the time, significance, and sky location of the event were shared with 63 teams of observers covering radio, optical, near-infrared, X-ray, and gamma-ray wavelengths with ground- and space-based facilities. In this Letter we describe the low-latency analysis of the GW data and present the sky localization of the first observed compact binary merger. We summarize themore » follow-up observations reported by 25 teams via private Gamma-ray Coordinates Network circulars, giving an overview of the participating facilities, the GW sky localization coverage, the timeline and depth of the observations. As this event turned out to be a binary black hole merger, there is little expectation of a detectable electromagnetic (EM) signature. Nevertheless, this first broadband campaign to search for a counterpart of an Advanced LIGO source represents a milestone and highlights the broad capabilities of the transient astronomy community and the observing strategies that have been developed to pursue neutron star binary merger events. Furthermore, detailed investigations of the EM data and results of the EM follow-up campaign are being disseminated in papers by the individual teams.« less
NASA Astrophysics Data System (ADS)
Zhu, X.-J.; Wen, L.; Xiong, J.; Xu, Y.; Wang, Y.; Mohanty, S. D.; Hobbs, G.; Manchester, R. N.
2016-09-01
A pulsar timing array is a Galactic-scale detector of nanohertz gravitational waves (GWs). Its target signals contain two components: the `Earth term' and the `pulsar term' corresponding to GWs incident on the Earth and pulsar, respectively. In this work we present a Frequentist method for the detection and localization of continuous waves that takes into account the pulsar term and is significantly faster than existing methods. We investigate the role of pulsar terms by comparing a full-signal search with an Earth-term-only search for non-evolving black hole binaries. By applying the method to synthetic data sets, we find that (i) a full-signal search can slightly improve the detection probability (by about five per cent); (ii) sky localization is biased if only Earth terms are searched for and the inclusion of pulsar terms is critical to remove such a bias; (iii) in the case of strong detections (with signal-to-noise ratio ≳30), it may be possible to improve pulsar distance estimation through GW measurements.
Localization and Broadband Follow-up of the Gravitational-wave Transient GW150914
NASA Astrophysics Data System (ADS)
Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M. R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R. X.; Adya, V. B.; Affeldt, C.; Agathos, M.; Agatsuma, K.; Aggarwal, N.; Aguiar, O. D.; Aiello, L.; Ain, A.; Ajith, P.; Allen, B.; Allocca, A.; Altin, P. A.; Anderson, S. B.; Anderson, W. G.; Arai, K.; Araya, M. C.; Arceneaux, C. C.; Areeda, J. S.; Arnaud, N.; Arun, K. G.; Ascenzi, S.; Ashton, G.; Ast, M.; Aston, S. M.; Astone, P.; Aufmuth, P.; Aulbert, C.; Babak, S.; Bacon, P.; Bader, M. K. M.; Baker, P. T.; Baldaccini, F.; Ballardin, G.; Ballmer, S. W.; Barayoga, J. C.; Barclay, S. E.; Barish, B. C.; Barker, D.; Barone, F.; Barr, B.; Barsotti, L.; Barsuglia, M.; Barta, D.; Barthelmy, S.; Bartlett, J.; Bartos, I.; Bassiri, R.; Basti, A.; Batch, J. C.; Baune, C.; Bavigadda, V.; Bazzan, M.; Behnke, B.; Bejger, M.; Bell, A. S.; Bell, C. J.; Berger, B. K.; Bergman, J.; Bergmann, G.; Berry, C. P. 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F.; Pérez del Pulgar, C.; Castillo-Carrión, S.; Castro Cerón, J. M.; Hudec, R.; Caballero-García, M. D.; Páta, P.; Vitek, S.; Adame, J. A.; Konig, S.; Rendón, F.; Mateo Sanguino, T. de J.; Fernández-Muñoz, R.; Yock, P. C.; Rattenbury, N.; Allen, W. H.; Querel, R.; Jeong, S.; Park, I. H.; Bai, J.; Cui, Ch.; Fan, Y.; Wang, Ch.; Hiriart, D.; Lee, W. H.; Claret, A.; Sánchez-Ramírez, R.; Pandey, S. B.; Mediavilla, T.; Sabau-Graziati, L.; BOOTES Collaboration; Abbott, T. M. C.; Abdalla, F. B.; Allam, S.; Annis, J.; Armstrong, R.; Benoit-Lévy, A.; Berger, E.; Bernstein, R. A.; Bertin, E.; Brout, D.; Buckley-Geer, E.; Burke, D. L.; Capozzi, D.; Carretero, J.; Castander, F. J.; Chornock, R.; Cowperthwaite, P. S.; Crocce, M.; Cunha, C. E.; D’Andrea, C. B.; da Costa, L. N.; Desai, S.; Diehl, H. T.; Dietrich, J. P.; Doctor, Z.; Drlica-Wagner, A.; Drout, M. R.; Eifler, T. F.; Estrada, J.; Evrard, A. E.; Fernandez, E.; Finley, D. A.; Flaugher, B.; Foley, R. J.; Fong, W.-F.; Fosalba, P.; Fox, D. B.; Frieman, J.; Fryer, C. L.; Gaztanaga, E.; Gerdes, D. W.; Goldstein, D. A.; Gruen, D.; Gruendl, R. A.; Gutierrez, G.; Herner, K.; Honscheid, K.; James, D. J.; Johnson, M. D.; Johnson, M. W. G.; Karliner, I.; Kasen, D.; Kent, S.; Kessler, R.; Kim, A. G.; Kind, M. C.; Kuehn, K.; Kuropatkin, N.; Lahav, O.; Li, T. S.; Lima, M.; Lin, H.; Maia, M. A. G.; Margutti, R.; Marriner, J.; Martini, P.; Matheson, T.; Melchior, P.; Metzger, B. D.; Miller, C. J.; Miquel, R.; Neilsen, E.; Nichol, R. C.; Nord, B.; Nugent, P.; Ogando, R.; Petravick, D.; Plazas, A. A.; Quataert, E.; Roe, N.; Romer, A. K.; Roodman, A.; Rosell, A. C.; Rykoff, E. S.; Sako, M.; Sanchez, E.; Scarpine, V.; Schindler, R.; Schubnell, M.; Scolnic, D.; Sevilla-Noarbe, I.; Sheldon, E.; Smith, N.; Smith, R. C.; Soares-Santos, M.; Sobreira, F.; Stebbins, A.; Suchyta, E.; Swanson, M. E. C.; Tarle, G.; Thaler, J.; Thomas, D.; Thomas, R. C.; Tucker, D. L.; Vikram, V.; Walker, A. R.; Wechsler, R. H.; Wester, W.; Yanny, B.; Zhang, Y.; Zuntz, J.; Dark Energy Survey; Dark Energy Camera GW-EM Collaboration; Connaughton, V.; Burns, E.; Goldstein, A.; Briggs, M. S.; Zhang, B.-B.; Hui, C. M.; Jenke, P.; Wilson-Hodge, C. A.; Bhat, P. N.; Bissaldi, E.; Cleveland, W.; Fitzpatrick, G.; Giles, M. M.; Gibby, M. H.; Greiner, J.; von Kienlin, A.; Kippen, R. M.; McBreen, S.; Mailyan, B.; Meegan, C. A.; Paciesas, W. S.; Preece, R. D.; Roberts, O.; Sparke, L.; Stanbro, M.; Toelge, K.; Veres, P.; Yu, H.-F.; Blackburn, L.; Fermi GBM Collaboration; Ackermann, M.; Ajello, M.; Albert, A.; Anderson, B.; Atwood, W. B.; Axelsson, M.; Baldini, L.; Barbiellini, G.; Bastieri, D.; Bellazzini, R.; Bissaldi, E.; Blandford, R. D.; Bloom, E. D.; Bonino, R.; Bottacini, E.; Brandt, T. J.; Bruel, P.; Buson, S.; Caliandro, G. A.; Cameron, R. A.; Caragiulo, M.; Caraveo, P. A.; Cavazzuti, E.; Charles, E.; Chekhtman, A.; Chiang, J.; Chiaro, G.; Ciprini, S.; Cohen-Tanugi, J.; Cominsky, L. R.; Costanza, F.; Cuoco, A.; D’Ammando, F.; de Palma, F.; Desiante, R.; Digel, S. W.; Di Lalla, N.; Di Mauro, M.; Di Venere, L.; Domínguez, A.; Drell, P. S.; Dubois, R.; Favuzzi, C.; Ferrara, E. C.; Franckowiak, A.; Fukazawa, Y.; Funk, S.; Fusco, P.; Gargano, F.; Gasparrini, D.; Giglietto, N.; Giommi, P.; Giordano, F.; Giroletti, M.; Glanzman, T.; Godfrey, G.; Gomez-Vargas, G. A.; Green, D.; Grenier, I. A.; Grove, J. E.; Guiriec, S.; Hadasch, D.; Harding, A. K.; Hays, E.; Hewitt, J. W.; Hill, A. B.; Horan, D.; Jogler, T.; Jóhannesson, G.; Johnson, A. S.; Kensei, S.; Kocevski, D.; Kuss, M.; La Mura, G.; Larsson, S.; Latronico, L.; Li, J.; Li, L.; Longo, F.; Loparco, F.; Lovellette, M. N.; Lubrano, P.; Magill, J.; Maldera, S.; Manfreda, A.; Marelli, M.; Mayer, M.; Mazziotta, M. N.; McEnery, J. E.; Meyer, M.; Michelson, P. F.; Mirabal, N.; Mizuno, T.; Moiseev, A. A.; Monzani, M. E.; Moretti, E.; Morselli, A.; Moskalenko, I. V.; Negro, M.; Nuss, E.; Ohsugi, T.; Omodei, N.; Orienti, M.; Orlando, E.; Ormes, J. F.; Paneque, D.; Perkins, J. S.; Pesce-Rollins, M.; Piron, F.; Pivato, G.; Porter, T. A.; Racusin, J. L.; Rainò, S.; Rando, R.; Razzaque, S.; Reimer, A.; Reimer, O.; Salvetti, D.; Saz Parkinson, P. M.; Sgrò, C.; Simone, D.; Siskind, E. J.; Spada, F.; Spandre, G.; Spinelli, P.; Suson, D. J.; Tajima, H.; Thayer, J. B.; Thompson, D. J.; Tibaldo, L.; Torres, D. F.; Troja, E.; Uchiyama, Y.; Venters, T. M.; Vianello, G.; Wood, K. S.; Wood, M.; Zhu, S.; Zimmer, S.; Fermi LAT Collaboration; Brocato, E.; Cappellaro, E.; Covino, S.; Grado, A.; Nicastro, L.; Palazzi, E.; Pian, E.; Amati, L.; Antonelli, L. A.; Capaccioli, M.; D’Avanzo, P.; D’Elia, V.; Getman, F.; Giuffrida, G.; Iannicola, G.; Limatola, L.; Lisi, M.; Marinoni, S.; Marrese, P.; Melandri, A.; Piranomonte, S.; Possenti, A.; Pulone, L.; Rossi, A.; Stamerra, A.; Stella, L.; Testa, V.; Tomasella, L.; Yang, S.; GRAvitational Wave Inaf TeAm (GRAWITA); Bazzano, A.; Bozzo, E.; Brandt, S.; Courvoisier, T. J.-L.; Ferrigno, C.; Hanlon, L.; Kuulkers, E.; Laurent, P.; Mereghetti, S.; Roques, J. P.; Savchenko, V.; Ubertini, P.; INTEGRAL Collaboration; Kasliwal, M. M.; Singer, L. P.; Cao, Y.; Duggan, G.; Kulkarni, S. R.; Bhalerao, V.; Miller, A. A.; Barlow, T.; Bellm, E.; Manulis, I.; Rana, J.; Laher, R.; Masci, F.; Surace, J.; Rebbapragada, U.; Cook, D.; Van Sistine, A.; Sesar, B.; Perley, D.; Ferreti, R.; Prince, T.; Kendrick, R.; Horesh, A.; Intermediate Palomar Transient Factory (iPTF) Collaboration; Hurley, K.; Golenetskii, S. V.; Aptekar, R. L.; Frederiks, D. D.; Svinkin, D. S.; Rau, A.; von Kienlin, A.; Zhang, X.; Smith, D. M.; Cline, T.; Krimm, H.; InterPlanetary Network; Abe, F.; Doi, M.; Fujisawa, K.; Kawabata, K. S.; Morokuma, T.; Motohara, K.; Tanaka, M.; Ohta, K.; Yanagisawa, K.; Yoshida, M.; J-GEM Collaboration; Baltay, C.; Rabinowitz, D.; Ellman, N.; Rostami, S.; La Silla–QUEST Survey; Bersier, D. F.; Bode, M. F.; Collins, C. A.; Copperwheat, C. M.; Darnley, M. J.; Galloway, D. K.; Gomboc, A.; Kobayashi, S.; Mazzali, P.; Mundell, C. G.; Piascik, A. S.; Pollacco, Don; Steele, I. A.; Ulaczyk, K.; Liverpool Telescope Collaboration; Broderick, J. W.; Fender, R. P.; Jonker, P. G.; Rowlinson, A.; Stappers, B. W.; Wijers, R. A. M. J.; Low Frequency Array (LOFAR) Collaboration; Lipunov, V.; Gorbovskoy, E.; Tyurina, N.; Kornilov, V.; Balanutsa, P.; Kuznetsov, A.; Buckley, D.; Rebolo, R.; Serra-Ricart, M.; Israelian, G.; Budnev, N. M.; Gress, O.; Ivanov, K.; Poleshuk, V.; Tlatov, A.; Yurkov, V.; MASTER Collaboration; Kawai, N.; Serino, M.; Negoro, H.; Nakahira, S.; Mihara, T.; Tomida, H.; Ueno, S.; Tsunemi, H.; Matsuoka, M.; MAXI Collaboration; Croft, S.; Feng, L.; Franzen, T. M. O.; Gaensler, B. M.; Johnston-Hollitt, M.; Kaplan, D. L.; Morales, M. F.; Tingay, S. J.; Wayth, R. B.; Williams, A.; Murchison Wide-field Array (MWA) Collaboration; Smartt, S. J.; Chambers, K. C.; Smith, K. W.; Huber, M. E.; Young, D. R.; Wright, D. E.; Schultz, A.; Denneau, L.; Flewelling, H.; Magnier, E. A.; Primak, N.; Rest, A.; Sherstyuk, A.; Stalder, B.; Stubbs, C. W.; Tonry, J.; Waters, C.; Willman, M.; Pan-STARRS Collaboration; Olivares E., F.; Campbell, H.; Kotak, R.; Sollerman, J.; Smith, M.; Dennefeld, M.; Anderson, J. P.; Botticella, M. T.; Chen, T.-W.; Valle, M. D.; Elias-Rosa, N.; Fraser, M.; Inserra, C.; Kankare, E.; Kupfer, T.; Harmanen, J.; Galbany, L.; Le Guillou, L.; Lyman, J. D.; Maguire, K.; Mitra, A.; Nicholl, M.; Razza, A.; Terreran, G.; Valenti, S.; Gal-Yam, A.; PESSTO Collaboration; Ćwiek, A.; Ćwiok, M.; Mankiewicz, L.; Opiela, R.; Zaremba, M.; Żarnecki, A. F.; Pi of the Sky Collaboration; Onken, C. A.; Scalzo, R. A.; Schmidt, B. P.; Wolf, C.; Yuan, F.; SkyMapper Collaboration; Evans, P. A.; Kennea, J. A.; Burrows, D. N.; Campana, S.; Cenko, S. B.; Giommi, P.; Marshall, F. E.; Nousek, J.; O’Brien, P.; Osborne, J. P.; Palmer, D.; Perri, M.; Siegel, M.; Tagliaferri, G.; Swift Collaboration; Klotz, A.; Turpin, D.; Laugier, R.; TAROT, Zadko, Algerian National Observatory, C2PU Collaboration; Beroiz, M.; Peñuela, T.; Macri, L. M.; Oelkers, R. J.; Lambas, D. G.; Vrech, R.; Cabral, J.; Colazo, C.; Dominguez, M.; Sanchez, B.; Gurovich, S.; Lares, M.; Marshall, J. L.; DePoy, D. L.; Padilla, N.; Pereyra, N. A.; Benacquista, M.; TOROS Collaboration; Tanvir, N. R.; Wiersema, K.; Levan, A. J.; Steeghs, D.; Hjorth, J.; Fynbo, J. P. U.; Malesani, D.; Milvang-Jensen, B.; Watson, D.; Irwin, M.; Fernandez, C. G.; McMahon, R. G.; Banerji, M.; Gonzalez-Solares, E.; Schulze, S.; de Ugarte Postigo, A.; Thoene, C. C.; Cano, Z.; Rosswog, S.; VISTA Collaboration
2016-07-01
A gravitational-wave (GW) transient was identified in data recorded by the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) detectors on 2015 September 14. The event, initially designated G184098 and later given the name GW150914, is described in detail elsewhere. By prior arrangement, preliminary estimates of the time, significance, and sky location of the event were shared with 63 teams of observers covering radio, optical, near-infrared, X-ray, and gamma-ray wavelengths with ground- and space-based facilities. In this Letter we describe the low-latency analysis of the GW data and present the sky localization of the first observed compact binary merger. We summarize the follow-up observations reported by 25 teams via private Gamma-ray Coordinates Network circulars, giving an overview of the participating facilities, the GW sky localization coverage, the timeline, and depth of the observations. As this event turned out to be a binary black hole merger, there is little expectation of a detectable electromagnetic (EM) signature. Nevertheless, this first broadband campaign to search for a counterpart of an Advanced LIGO source represents a milestone and highlights the broad capabilities of the transient astronomy community and the observing strategies that have been developed to pursue neutron star binary merger events. Detailed investigations of the EM data and results of the EM follow-up campaign are being disseminated in papers by the individual teams.
Seal, Katyayani; Bintachitt, Patamas; Jesse, Stephen; Morozovska, A. N.; Baddorf, Arthur P; Trolier-McKinstry, Susan; Kalinin, Sergei V
2008-01-01
The local polarization dynamics in chemical solution deposited PZT thin film capacitors were studied using spatially resolved spectroscopic measurements. 2D maps of switchable polarization as a function of bias window allow the voltage-dependence and spatial distribution of regions with reversible and irreversible wall motion to be mapped. Extension of the measurements to mapping the disorder potential controlling domain wall pinning enabling development of a spatially resolved Preisach model is discussed.
Localization of the SFT inspired nonlocal linear models and exact solutions
NASA Astrophysics Data System (ADS)
Vernov, S. Yu.
2011-05-01
A general class of gravitational models driven by a nonlocal scalar field with a linear or quadratic potential is considered. We study the action with an arbitrary analytic function ℱ(□ g ), which has both simple and double roots. The way of localization of nonlocal Einstein equations is generalized on models with linear potentials. Exact solutions in the Friedmann-Robertson-Walker and Bianchi I metrics are presented.
New insights into classical solutions of the local instability of the sandwich panels problem
NASA Astrophysics Data System (ADS)
Pozorska, Jolanta; Pozorski, Zbigniew
2016-06-01
The paper concerns the problem of local instability of thin facings of a sandwich panel. The classic analytical solutions are compared and examined. The Airy stress function is applied in the case of the state of plane stress and the state of plane strain. Wrinkling stress values are presented. The differences between the results obtained using the differential equations method and energy method are discussed. The relations between core strain energies are presented.
Rapid guided wave delamination detection and quantification in composites using global-local sensing
NASA Astrophysics Data System (ADS)
Tian, Zhenhua; Yu, Lingyu; Leckey, Cara
2016-08-01
This paper presents a rapid guided ultrasonic wave inspection approach through global inspection by phased array beamforming and local damage evaluation via wavenumber analysis. The global-local approach uses a hybrid system consisting of a PZT wafer and a non-contact laser vibrometer. The overall inspection is performed in two steps. First, a phased array configured by a small number of measurements performs beamforming and beamsteering over the entire plate in order to detect and locate the presence of the damage. A local area is identified as target damage area for the second step. Then a high density wavefield measurement is taken over the target damage area and a spatial wavenumber imaging is performed to quantitatively evaluate the damage. The two-step inspection has been applied to locate and quantify impact-induced delamination damage in a carbon fiber reinforced polymer composite plate. The detected delamination location, size and shape agree well with those of an ultrasonic C-scan. For the test case studied in this work the global-local approach reduced the total composite inspection (damage detection and characterization) time by ∼97% compared to using a full scan approach.
NASA Astrophysics Data System (ADS)
Kharlamov, S. M.; Guzanov, V. V.; Bobylev, A. V.; Alekseenko, S. V.; Markovich, D. M.
2015-11-01
This article presents the results of experimental investigations of the process of transition from two-dimensional (2D) to three-dimensional (3D) waves in liquid films falling down a vertical plate. The method of laser induced fluorescence was used to obtain instant shapes of three dimensional waves and to investigate the regularities of formation of 3D wave patterns arising due to transverse instability of 2D waves. The obtained results were compared to the results from the published literature on the modeling of 3D wave regimes of film flow. Although many details of 3D wave patterns correspond well, there are a few significant distinctions between our experiments and modeling. In particular, during 2D-3D wave transition, we observed a strong transverse redistribution of liquid leading to the formation of rivulets on the surface of isothermal liquid film, which is a phenomenon not described previously. Possible discrepancies between modeling and experiments, including applicability of boundary layer models and downstream periodic boundary conditions, are discussed. The authors hope that the results presented in the article are of interest not only for modeling of film flows but also for practical applications because at large distances from the film inlet due to 2D-3D wave transition the local flow rates can differ several times at the transverse distances of about 1 cm, which is an effect that cannot be neglected.
Local ties verification based on analysis of long-term SLR and GPS solutions
NASA Astrophysics Data System (ADS)
Szafranek, Karolina; Schillak, Stanislaw; Araszkiewicz, Andrzej; Figurski, Mariusz; Lehmann, Marek; Lejba, Pawel
2013-04-01
The ITRF is determined on the basis of long-term observations by the following four techniques: GNSS, SLR, DORIS and VLBI. Analysis of the data delivered by different techniques provides a stable reference frame. Improvement of further ITRS realizations requires the advancement in the geometry of co-location network and the increase of agreement between the local ties in co-location sites, while many significant disagreements between techniques are being noticed. Ground local ties measurements are usually made once over a period of time, whereas different factors can cause change of its real value (earthquakes, change of GNSS antennas or different method of their calibration which result in different coordinates values in ITRF), which lead to the idea of co-locations vectors monitoring for the purpose of its verification. The authors analyzed solutions from several distributed globally SLR-GNSS sites. The data gathered between 1996-2011 by these two techniques were processed using coherent strategies (the same models and parameters were used). Up to now, results of coordinates and velocities determination with exemplary times series were introduced. The presentation goal is to show the results of analysis of NEU time series of SLR and GPS solutions reduced to the SLR markers positions using local ties in order to verify their values. Agreement of both types of solutions proves the good quality and timeliness of ground measurements, while high discrepancies point out that there is a need for their repetition to improve next ITRS realizations (e.g. ITRF2013).
Waves on Thin Plates: A New (Energy Based) Method on Localization
NASA Astrophysics Data System (ADS)
Turkaya, Semih; Toussaint, Renaud; Kvalheim Eriksen, Fredrik; Lengliné, Olivier; Daniel, Guillaume; Grude Flekkøy, Eirik; Jørgen Måløy, Knut
2016-04-01
Noisy acoustic signal localization is a difficult problem having a wide range of application. We propose a new localization method applicable for thin plates which is based on energy amplitude attenuation and inversed source amplitude comparison. This inversion is tested on synthetic data using a direct model of Lamb wave propagation 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 this technique with classical source localization algorithms, arrival time localization, time reversal localization, localization based on energy amplitude. The experimental setup consist of a glass / plexiglass plate having dimensions of 80 cm x 40 cm x 1 cm equipped with four accelerometers and an acquisition card. Signals are generated using a steel, glass or polyamide ball (having different sizes) quasi perpendicular hit (from a height of 2-3 cm) on the plate. Signals are captured by sensors placed on the plate on different locations. We measure and compare the accuracy of these techniques as function of sampling rate, dynamic range, array geometry, signal to noise ratio and computational time. We show that this new technique, which is very versatile, works better than conventional techniques over a range of sampling rates 8 kHz - 1 MHz. It is possible to have a decent resolution (3cm mean error) using a very cheap equipment set. The numerical simulations allow us to track the contributions of different error sources in different methods. The effect of the reflections is also included in our simulation by using the imaginary sources outside the plate boundaries. This proposed method can easily be extended for applications in three dimensional environments, to monitor industrial activities (e.g boreholes drilling/production activities) or natural brittle systems (e.g earthquakes, volcanoes, avalanches).
Warped AdS 6 × S 2 in Type IIB supergravity I: local solutions
NASA Astrophysics Data System (ADS)
D'Hoker, Eric; Gutperle, Michael; Karch, Andreas; Uhlemann, Christoph F.
2016-08-01
We investigate the existence of solutions with 16 residual supersymmetries to Type IIB supergravity on a space-time of the formc AdS 6× S 2 warped over a two-dimensional Riemann surface Σ. The SO(2 , 5) × SO(3) isometry extends to invariance under the exceptional Lie superalgebra F (4). In the present paper, we construct the general Ansatz compatible with these symmetries, derive the corresponding reduced BPS equations, and obtain their complete local solution in terms of two locally holomorphic functions {A}_{± } on Σ, subject to certain positivity and regularity conditions. Globally, ( {A}+ , {A}- ) are allowed to be multiple-valued on Σ and be holomorphic sections of a holomorphic bundle over Σ with structure group contained in SU(1,1)× C . Globally regular solutions are expected to provide the near-horizon geometry of ( p, q) 5-brane and 7-brane webs which are holographic duals to five-dimensional conformal field theories. A preliminary analysis of the positivity and regularity conditions will be presented here, leaving the construction of globally regular solutions to a subsequent paper.
Highly nonlinear wave solutions in a dual to the chiral model
NASA Astrophysics Data System (ADS)
Rajeev, S. G.; Ranken, Evan
2016-05-01
We consider a two-dimensional scalar field theory with a nilpotent current algebra, which is dual to the Principal Chiral Model. The quantum theory is renormalizable and not asymptotically free; the theory is strongly coupled at short distances (encountering a Landau pole). We suggest it can serve as a toy model for λ ϕ4 theory in four dimensions, just as the principal chiral model is a useful toy model for Yang-Mills theory. We find some classical wave solutions that survive the strong coupling limit and quantize them by the collective variable method. They describe excitations with an unusual dispersion relation ω ∝|k |2/3 . Perhaps they are the "preons" at strong coupling, the bound states of which form massless particles over long distances.
NASA Technical Reports Server (NTRS)
Yarrow, Maurice; Vastano, John A.; Lomax, Harvard
1992-01-01
Generic shapes are subjected to pulsed plane waves of arbitrary shape. The resulting scattered electromagnetic fields are determined analytically. These fields are then computed efficiently at field locations for which numerically determined EM fields are required. Of particular interest are the pulsed waveform shapes typically utilized by radar systems. The results can be used to validate the accuracy of finite difference time domain Maxwell's equations solvers. A two-dimensional solver which is second- and fourth-order accurate in space and fourth-order accurate in time is examined. Dielectric media properties are modeled by a ramping technique which simplifies the associated gridding of body shapes. The attributes of the ramping technique are evaluated by comparison with the analytic solutions.
NASA Astrophysics Data System (ADS)
Underwood, Thomas; Loebner, Keith; Cappelli, Mark
2015-11-01
Detailed measurements of the thermodynamic and electrodynamic plasma state variables within the plume of a pulsed plasma accelerator are presented. A quadruple Langmuir probe operating in current-saturation mode is used to obtain time resolved measurements of the plasma density, temperature, potential, and velocity along the central axis of the accelerator. This data is used in conjunction with a fast-framing, intensified CCD camera to develop and validate a model predicting the existence of two distinct types of ionization waves corresponding to the upper and lower solution branches of the Hugoniot curve. A deviation of less than 8% is observed between the quasi-steady, one-dimensional theoretical model and the experimentally measured plume velocity. This work is supported by the U.S. Department of Energy Stewardship Science Academic Program in addition to the National Defense Science Engineering Graduate Fellowship.
Class of solitary wave solutions of the one-dimensional Gross-Pitaevskii equation
Atre, Rajneesh; Panigrahi, Prasanta K.; Agarwal, G. S.
2006-05-15
We present a large family of exact solitary wave solutions of the one-dimensional Gross-Pitaevskii equation, with time-varying scattering length and gain or loss, in both expulsive and regular parabolic confinement regimes. The consistency condition governing the soliton profiles is shown to map onto a linear Schroedinger eigenvalue problem, thereby enabling one to find analytically the effect of a wide variety of temporal variations in the control parameters, which are experimentally realizable. Corresponding to each solvable quantum mechanical system, one can identify a soliton configuration. These include soliton trains in close analogy to experimental observations of Strecker et al. [Nature (London) 417, 150 (2002)], spatiotemporal dynamics, solitons undergoing rapid amplification, collapse and revival of condensates, and analytical expression of two-soliton bound states, to name a few.
Class of solitary wave solutions of the one-dimensional Gross-Pitaevskii equation.
Atre, Rajneesh; Panigrahi, Prasanta K; Agarwal, G S
2006-05-01
We present a large family of exact solitary wave solutions of the one-dimensional Gross-Pitaevskii equation, with time-varying scattering length and gain or loss, in both expulsive and regular parabolic confinement regimes. The consistency condition governing the soliton profiles is shown to map onto a linear Schrödinger eigenvalue problem, thereby enabling one to find analytically the effect of a wide variety of temporal variations in the control parameters, which are experimentally realizable. Corresponding to each solvable quantum mechanical system, one can identify a soliton configuration. These include soliton trains in close analogy to experimental observations of Streckeret al. [Nature (London) 417, 150 (2002)], spatiotemporal dynamics, solitons undergoing rapid amplification, collapse and revival of condensates, and analytical expression of two-soliton bound states, to name a few. PMID:16803061
Global existence and exponential decay of the solution for a viscoelastic wave equation with a delay
NASA Astrophysics Data System (ADS)
Dai, Qiuyi; Yang, Zhifeng
2014-10-01
In this paper, we consider initial-boundary value problem of viscoelastic wave equation with a delay term in the interior feedback. Namely, we study the following equation together with initial-boundary conditions of Dirichlet type in Ω × (0, + ∞) and prove that for arbitrary real numbers μ 1 and μ 2, the above-mentioned problem has a unique global solution under suitable assumptions on the kernel g. This improve the results of the previous literature such as Nicaise and Pignotti (SIAM J. Control Optim 45:1561-1585, 2006) and Kirane and Said-Houari (Z. Angew. Math. Phys. 62:1065-1082, 2011) by removing the restriction imposed on μ 1 and μ 2. Furthermore, we also get an exponential decay results for the energy of the concerned problem in the case μ 1 = 0 which solves an open problem proposed by Kirane and Said-Houari (Z. Angew. Math. Phys. 62:1065-1082, 2011).
Fabris, Júlio C.; Pelinson, Ana M.; Salles, Filipe de O.; Shapiro, Ilya L. E-mail: ana.pelinson@gmail.com E-mail: shapiro@fisica.ufjf.br
2012-02-01
The dynamics of metric perturbations is explored in the gravity theory with anomaly-induced quantum corrections. Our first purpose is to derive the equation for gravitational waves in this theory on the general homogeneous and isotropic background, and then verify the stability of such background with respect to metric perturbations. The problem under consideration has several interesting applications. Our first purpose is to explore the stability of the classical cosmological solutions in the theory with quantum effects taken into account. There is an interesting literature about stability of Minkowski and de Sitter spaces and here we extend the consideration also to the radiation and matter dominated cosmologies. Furthermore, we analyze the behavior of metric perturbations during inflationary period, in the stable phase of the Modified Starobinsky inflation.
NASA Astrophysics Data System (ADS)
Cuperman, S.; Heristchi, D.
1992-08-01
The transcendental dispersion equation for electromagnetic waves propagating in the slow mode in sheared non-neutral relativistic cylindrical electron beams in strong applied magnetic fields is solved exactly. Thus, rather than truncated power series for the modified Bessel functions involved, use is made of modern algorithms able to compute such functions up to 18-digit accuracy. Consequently, new and significantly more important branches of the velocity shear instability are found. When the shear-factor and/or the geometrical parameter a/b (pipe-to-beam radius ratio) are increased, the unstable branches join, and the higher-frequency, larger-wavenumber modes are significantly enhanced. Since analytical solutions of the exact dispersion relation cannot be obtained, it is suggested that in all similar cases the methods proposed and demonstrated here should be used to carry out a rigorous stability analysis.
Numerical solution of wave equations for the stability of the inner cometo-sheath
NASA Technical Reports Server (NTRS)
Srivastava, Krishna M.; Tsurutani, Bruce T.; Goldstein, Bruce E.
1993-01-01
Numerical solution of the MHD wave equations for stability of the cometary sheath determined by the balance between the inward Lorentz body force and the outward ion-neutral drag force is obtained by using a two-point boundary value method. The eigenvalues and the eigenfunctions are obtained numerically by treating the cometary inner sheath as a layer of finite thickness, bounded by the contact surface, i.e., the diamagnetic cavity boundary. The magnetic field structure discovered in the ionosphere of Comets Halley and Giacobini-Zinner is found to be unstable. The effects of finite plasma pressure, dissociative recombination, and mass loading due to photoionization are found to be stabilizing but are unable to quench the instability completely. It is also found that the higher the neutral production rate the lesser is the growth rate for the instability.
Incompressible SPH method based on Rankine source solution for violent water wave simulation
NASA Astrophysics Data System (ADS)
Zheng, X.; Ma, Q. W.; Duan, W. Y.
2014-11-01
With wide applications, the smoothed particle hydrodynamics method (abbreviated as SPH) has become an important numerical tool for solving complex flows, in particular those with a rapidly moving free surface. For such problems, the incompressible Smoothed Particle Hydrodynamics (ISPH) has been shown to yield better and more stable pressure time histories than the traditional SPH by many papers in literature. However, the existing ISPH method directly approximates the second order derivatives of the functions to be solved by using the Poisson equation. The order of accuracy of the method becomes low, especially when particles are distributed in a disorderly manner, which generally happens for modelling violent water waves. This paper introduces a new formulation using the Rankine source solution. In the new approach to the ISPH, the Poisson equation is first transformed into another form that does not include any derivative of the functions to be solved, and as a result, does not need to numerically approximate derivatives. The advantage of the new approach without need of numerical approximation of derivatives is obvious, potentially leading to a more robust numerical method. The newly formulated method is tested by simulating various water waves, and its convergent behaviours are numerically studied in this paper. Its results are compared with experimental data in some cases and reasonably good agreement is achieved. More importantly, numerical results clearly show that the newly developed method does need less number of particles and so less computational costs to achieve the similar level of accuracy, or to produce more accurate results with the same number of particles compared with the traditional SPH and existing ISPH when it is applied to modelling water waves.
Analytical solutions for the seismic response of underground structures under SH wave propagation
Smerzini, C.; Aviles, J.; Sanchez-Sesma, F. J.
2008-07-08
A theoretical approach is presented to study the antiplane seismic response of underground structures subjected to the incidence of plane waves. The structure is assumed to be a circular inclusion embedded in a homogenous, isotropic and linear visco-elastic halfspace and its mathematical formulation is approached through the theory of multiple scattering and diffraction. The inclusion may consist either of a cavity, with or without a ring-shaped boundary, or it may be filled in with a linear-elastic material, without loss of generality. The seismic response of the inclusion and its influence on surface ground motions are analyzed in both frequency and time domains. The dependence of the transfer function amplitudes on several parameters, such as the angle of incident SH waves, the frequency content of the excitation, the impedance contrast between the inclusion and the surrounding medium and the position along the ground surface, is underlined. Considering the lack of analytical solutions for quantifying the modification of ground motions induced by subterranean inhomogeneities, the results of this study can be used, on one side, as benchmark for both geophysical investigations and numerical dynamic soil-structure interaction studies, and, on the other side, to support the formulation of simplified approaches and/or formulas for the seismic design and assessment of underground structures.
High accuracy solution of bi-directional wave propagation in continuum mechanics
NASA Astrophysics Data System (ADS)
Mulloth, Akhil; Sawant, Nilesh; Haider, Ijlal; Sharma, Nidhi; Sengupta, Tapan K.
2015-10-01
Solution of partial differential equations by numerical method is strongly affected due to numerical errors, which are caused mainly by deviation of numerical dispersion relation from the physical dispersion relation. To quantify and control such errors and obtain high accuracy solutions, we consider a class of problems which involve second derivative of unknowns with respect to time. Here, we analyse numerical metrics such as the numerical group velocity, numerical phase speed and the numerical amplification factor for different methods in solving the model bi-directional wave equation (BDWE). Such equations can be solved directly, for example, by Runge-Kutta-Nyström (RKN) method. Alternatively, the governing equation can be converted to a set of first order in time equations and then using four-stage fourth order Runge-Kutta (RK4) method for time integration. Spatial discretisation considered are the classical second and fourth order central difference schemes, along with Lele's central compact scheme for evaluating second derivatives. In another version, we have used Lele's scheme for evaluating first derivatives twice to obtain the second derivative. As BDWE represents non-dissipative, non-dispersive dynamics, we also consider the canonical problem of linearised rotating shallow water equation (LRSWE) in a new formulation involving second order derivative in time, which represents dispersive waves along with a stationary mode. The computations of LRSWE with RK4 and RKN methods for temporal discretisation and Lele's compact schemes for spatial discretisation are compared with computations performed with RK4 method for time discretisation and staggered compact scheme (SCS) for spatial discretisation by treating it as a set of three equations as reported in Rajpoot et al. (2012) [1].
NASA Astrophysics Data System (ADS)
Xu, Mei-Juan; Tian, Shou-Fu; Tu, Jian-Min; Ma, Pan-Li; Zhang, Tian-Tian
2016-01-01
In this paper, an extended Korteweg-de Vries (eKdV) equation is investigated, which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. With the aid of the generalized Bell’s polynomials, the Hirota’s bilinear equation to the eKdV equation is succinctly constructed. Based on that, its solition solutions are directly obtained. By virtue of the Riemann theta function, a straightforward way is presented to explicitly construct Riemann theta function periodic wave solutions of the eKdV equation. Finally, the asymptotic behaviors of the Riemann theta function periodic waves are presented, which yields a relationship between the periodic waves and solition solutions by considering a limiting procedure.
NASA Astrophysics Data System (ADS)
Harko, T.; Mak, M. K.
2015-11-01
We consider quasi-stationary (travelling wave type) solutions to a general nonlinear reaction-convection-diffusion equation with arbitrary, autonomous coefficients. The second order nonlinear equation describing one dimensional travelling waves can be reduced to a first kind first order Abel equation. By using two integrability conditions for the Abel equation (the Chiellini lemma and the Lemke transformation), several classes of exact travelling wave solutions of the general reaction-convection-diffusion equation are obtained, corresponding to different functional relations imposed between the diffusion, convection and reaction functions. In particular, we obtain travelling wave solutions for two non-linear second order partial differential equations, representing generalizations of the standard diffusion equation and of the classical Fisher-Kolmogorov equation, to which they reduce for some limiting values of the model parameters. The models correspond to some specific, power law type choices of the reaction and convection functions, respectively. The travelling wave solutions of these two classes of differential equation are investigated in detail by using both numerical and semi-analytical methods.
Lo, Kam W; Ferguson, Brian G
2012-11-01
The accurate localization of small arms fire using fixed acoustic sensors is considered. First, the conventional wavefront-curvature passive ranging method, which requires only differential time-of-arrival (DTOA) measurements of the muzzle blast wave to estimate the source position, is modified to account for sensor positions that are not strictly collinear (bowed array). Second, an existing single-sensor-node ballistic model-based localization method, which requires both DTOA and differential angle-of-arrival (DAOA) measurements of the muzzle blast wave and ballistic shock wave, is improved by replacing the basic external ballistics model (which describes the bullet's deceleration along its trajectory) with a more rigorous model and replacing the look-up table ranging procedure with a nonlinear (or polynomial) equation-based ranging procedure. Third, a new multiple-sensor-node ballistic model-based localization method, which requires only DTOA measurements of the ballistic shock wave to localize the point of fire, is formulated. The first method is applicable to situations when only the muzzle blast wave is received, whereas the third method applies when only the ballistic shock wave is received. The effectiveness of each of these methods is verified using an extensive set of real data recorded during a 7 day field experiment. PMID:23145587
NASA Astrophysics Data System (ADS)
Ayhan, Burcu; Özer, M. Naci; Bekir, Ahmet
2016-08-01
In this article, we applied the method of multiple scales for Korteweg-de Vries (KdV) type equations and we derived nonlinear Schrödinger (NLS) type equations. So we get a relation between KdV type equations and NLS type equations. In addition, exact solutions were found for KdV type equations. The ( G'} over G )-expansion methods and the ( {G'} over G, {1 over G}} )-expansion methods were proposed to establish new exact solutions for KdV type differential equations. We obtained periodic and hyperbolic function solutions for these equations. These methods are very effective for getting travelling wave solutions of nonlinear evolution equations (NEEs).
NASA Astrophysics Data System (ADS)
Rangwala, Abbas A.; Rao, Jyoti A.
1990-05-01
Using the Bargmann-Darboux method, the Bäcklund transformations, n-soliton solutions and corresponding wave functions of the Kaup-Newell and Wadati-Konno-Ichikawa systems are obtained. These results culminate in an algebraic recursive procedure for the determination of multisoliton solutions and their wave functions of the derivative and mixed derivative nonlinear Schrödinger equations iQt+Qxx∓iα(||Q||2Q)x ±β||Q||2Q=0, α>0, β≥0.
NASA Astrophysics Data System (ADS)
Nguyen, Ba Phi; Kim, Kihong
2014-06-01
We study theoretically the influence of nonlinear gain effects on the transmission and the Anderson localization of waves in both uniform and random one-dimensional amplifying media by using the discrete nonlinear Schrödinger equation. In uniform amplifying media with nonlinear gain, we find that the strong oscillatory behavior of the transmittance and the reflectance for odd and even values of the sample length disappears for large nonlinearities. The exponential decay rate of the transmittance in the asymptotic limit is found to be independent of nonlinear gain. In random amplifying media, we find that the maximum values of the disorder-averaged logarithmic transmittance and reflectance depend nonmonotonically on the strength of nonlinear gain. We also find that the localization length is independent of nonlinear gain. In other words, the Anderson localization is neither enhanced nor weakened due to nonlinear gain. In both the uniform and the random cases, the crossover length, which is the critical length for the amplification to be efficient, is strongly reduced by the nonlinear nature of the gain.
NASA Astrophysics Data System (ADS)
Abdel-Gawad, H. I.; Tantawy, M.; Abo Elkhair, R. E.
2016-07-01
Rogue waves are more precisely defined as waves whose height is more than twice the significant wave height. This remarkable height was measured (by Draupner in 1995). Thus, the need for constructing a mechanism for the rogue waves is of great utility. This motivated us to suggest a mechanism, in this work, that rogue waves may be constructed via nonlinear interactions of solitons and periodic waves. This suggestion is consolidated here, in an example, by studying the behavior of solutions of the complex (KdV). This is done here by the extending the solutions of its real version.
NASA Astrophysics Data System (ADS)
Stevens, D.; Power, H.; Meng, C. Y.; Howard, D.; Cliffe, K. A.
2013-12-01
This work proposes an alternative decomposition for local scalable meshless RBF collocation. The proposed method operates on a dataset of scattered nodes that are placed within the solution domain and on the solution boundary, forming a small RBF collocation system around each internal node. Unlike other meshless local RBF formulations that are based on a generalised finite difference (RBF-FD) principle, in the proposed "finite collocation" method the solution of the PDE is driven entirely by collocation of PDE governing and boundary operators within the local systems. A sparse global collocation system is obtained not by enforcing the PDE governing operator, but by assembling the value of the field variable in terms of the field value at neighbouring nodes. In analogy to full-domain RBF collocation systems, communication between stencils occurs only over the stencil periphery, allowing the PDE governing operator to be collocated in an uninterrupted manner within the stencil interior. The local collocation of the PDE governing operator allows the method to operate on centred stencils in the presence of strong convective fields; the reconstruction weights assigned to nodes in the stencils being automatically adjusted to represent the flow of information as dictated by the problem physics. This "implicit upwinding" effect mitigates the need for ad-hoc upwinding stencils in convective dominant problems. Boundary conditions are also enforced within the local collocation systems, allowing arbitrary boundary operators to be imposed naturally within the solution construction. The performance of the method is assessed using a large number of numerical examples with two steady PDEs; the convection-diffusion equation, and the Lamé-Navier equations for linear elasticity. The method exhibits high-order convergence in each case tested (greater than sixth order), and the use of centred stencils is demonstrated for convective-dominant problems. In the case of linear elasticity
Inverse solution technique of steady-state responses for local nonlinear structures
NASA Astrophysics Data System (ADS)
Wang, Xing; Guan, Xin; Zheng, Gangtie
2016-03-01
An inverse solution technique with the ability of obtaining complete steady-state primary harmonic responses of local nonlinear structures in the frequency domain is proposed in the present paper. In this method, the nonlinear dynamic equations of motion is first condensed from many to only one algebraic amplitude-frequency equation of relative motion. Then this equation is transformed into a polynomial form, and with its frequency as the unknown variable, the polynomial equation is solved by tracing all the solutions of frequency with the increase of amplitude. With this solution technique, some complicated dynamic behaviors such as sharp tuning, anomalous jumps, breaks in responses and detached resonance curves could be obtained. The proposed method is demonstrated and validated through a finite element beam under force excitations and a lumped parameter model with a local nonlinear element under base excitations. The phenomenon of detached resonance curves in the frequency response and its coupling effects with multiple linear modes in the latter example are observed.
Solution chemistry of Mo(III) and Mo(IV): Thermodynamic foundation for modeling localized corrosion.
Wang, P; Wilson, L; Wesolowski, David J
2010-05-01
To investigate the behavior of molybdenum dissolution products in systems that approximate localized corrosion environments, solubility of Mo(III) in equilibrium with solid MoO{sub 2} has been determined at 80 C as a function of solution acidity, chloride concentration and partial pressure of hydrogen. The measurements indicate a strong increase in solubility with acidity and chloride concentration and a weak effect of hydrogen partial pressure. The obtained results have been combined with literature data for systems containing Mo(III), Mo(IV), and Mo(VI) in solutions to develop a comprehensive thermodynamic model of aqueous molybdenum chemistry. The model is based on a previously developed framework for simulating the properties of electrolyte systems ranging from infinite dilution to solid saturation or fused salt limit. To reproduce the measurements, the model assumes the presence of a chloride complex of Mo(III) (i.e., MoCl{sup 2+}) and hydrolyzed species (MoOH{sup 2+}, Mo(OH){sup 2+}, and Mo(OH){sub 3}{sup 0}) in addition to the Mo{sup 3+} ion. The model generally reproduces the experimental data within experimental scattering and provides a tool for predicting the phase behavior and speciation in complex, concentrated aqueous solutions. Thus, it provides a foundation for simulating the behavior of molybdenum species in localized corrosion environments.
Local structure in the disordered solid solution of cis- and trans-perinones.
Teteruk, Jaroslav L; Glinnemann, Jürgen; Heyse, Winfried; Johansson, Kristoffer E; van de Streek, Jacco; Schmidt, Martin U
2016-06-01
The cis- and trans-isomers of the polycyclic aromatic compound perinone, C26H12N4O2, form a solid solution (Vat Red 14). This solid solution is isotypic to the crystal structures of cis-perinone (Pigment Red 194) and trans-perinone (Pigment Orange 34) and exhibits a combined positional and orientational disorder: In the crystal, each molecular position is occupied by either a cis- or trans-perinone molecule, both of which have two possible molecular orientations. The structure of cis-perinone exhibits a twofold orientational disorder, whereas the structure of trans-perinone is ordered. The crystal structure of the solid solution was determined by single-crystal X-ray analysis. Extensive lattice-energy minimizations with force-field and DFT-D methods were carried out on combinatorially complete sets of ordered models. For the disordered systems, local structures were calculated, including preferred local arrangements, ordering lengths, and probabilities for the arrangement of neighbouring molecules. The superposition of the atomic positions of all energetically favourable calculated models corresponds well with the experimentally determined crystal structures, explaining not only the atomic positions, but also the site occupancies and anisotropic displacement parameters. PMID:27240774
NASA Technical Reports Server (NTRS)
Robbins, J. W.
1985-01-01
An autonomous spaceborne gravity gradiometer mission is being considered as a post Geopotential Research Mission project. The introduction of satellite diometry data to geodesy is expected to improve solid earth gravity models. The possibility of utilizing gradiometer data for the determination of pertinent gravimetric quantities on a local basis is explored. The analytical technique of least squares collocation is investigated for its usefulness in local solutions of this type. It is assumed, in the error analysis, that the vertical gravity gradient component of the gradient tensor is used as the raw data signal from which the corresponding reference gradients are removed to create the centered observations required in the collocation solution. The reference gradients are computed from a high degree and order geopotential model. The solution can be made in terms of mean or point gravity anomalies, height anomalies, or other useful gravimetric quantities depending on the choice of covariance types. Selected for this study were 30 x 30 foot mean gravity and height anomalies. Existing software and new software are utilized to implement the collocation technique. It was determined that satellite gradiometry data at an altitude of 200 km can be used successfully for the determination of 30 x 30 foot mean gravity anomalies to an accuracy of 9.2 mgal from this algorithm. It is shown that the resulting accuracy estimates are sensitive to gravity model coefficient uncertainties, data reduction assumptions and satellite mission parameters.
Tunable compression of template banks for fast gravitational-wave detection and localization
NASA Astrophysics Data System (ADS)
Chua, Alvin J. K.; Gair, Jonathan R.
2016-06-01
One strategy for reducing the online computational cost of matched-filter searches for gravitational waves is to introduce a compressed basis for the waveform template bank in a grid-based search. In this paper, we propose and investigate several tunable compression schemes for a general template bank. Through offline compression, such schemes are shown to yield faster detection and localization of signals, along with moderately improved sensitivity and accuracy over coarsened banks at the same level of computational cost. This is potentially useful for any search involving template banks, and especially in the analysis of data from future space-based detectors such as eLISA, for which online grid searches are difficult due to the long-duration waveforms and large parameter spaces.
Broadband continuous wave source localization via pair-wise, cochleagram processing
NASA Astrophysics Data System (ADS)
Nosal, Eva-Marie; Frazer, L. Neil
2005-04-01
A pair-wise processor has been developed for the passive localization of broadband continuous-wave underwater sources. The algorithm uses sparse hydrophone arrays and does not require previous knowledge of the source signature. It is applicable in multiple source situations. A spectrogram/cochleagram version of the algorithm has been developed in order to utilize higher frequencies at longer ranges where signal incoherence, and limited computational resources, preclude the use of full waveforms. Simulations demonstrating the robustness of the algorithm with respect to noise and environmental mismatch will be presented, together with initial results from the analysis of humpback whale song recorded at the Pacific Missile Range Facility off Kauai. [Work supported by MHPCC and ONR.
Localized spin-wave excitation by the evanescent microwave scanning probe
Sakran, F.; Golosovsky, M.; Davidov, D.; Monod, P.
2006-02-15
We report a technique for the local contactless spin-wave excitation using the evanescent microwave scanning probe. Our probe is based on a dielectric resonator with the thin slit aperture. It operates at 8.8 GHz, has a spatial resolution of 10-100 {mu}m, and may be operated in the parallel and in the perpendicular magnetic field. The measurements can be performed in contact mode or by scanning the sample at constant probe-sample separation. Using 120-150 nm thick Permalloy films on a glass substrate as test samples, we show how our technique can be used for thickness measurements of thin magnetic films and for the mapping of their magnetic properties, such as magnetization and surface anisotropy.
On the Design of Passive Resonant Circuits to Measure Local Pulse Wave Velocity in a Stent.
Schächtele, Jonathan
2016-06-01
In-stent restenosis is a frequent complication after stent implantation. This article investigates the design of a passive sensor system to be integrated into a stent for the detection of an in-stent restenosis by measuring the local pulse wave velocity (PWV). The proposed system uses two resonant circuits consisting of a capacitive pressure sensor and a coil as transponders. The pressure sensors are located at the proximal and distal end of the stent. An alternating external magnetic field with a constant frequency is applied such that the resonance frequencies of the transponders cross the excitation frequency when the pulse wave passes. The time delay between the resonances at the transponders can be captured to obtain the PWV. A model for the measurement system and a correlation between transponder design parameters and minimal resolvable time delay are derived. This correlation is based on the criterion that the 3 dB bandwidth of the transponder resonances may not overlap in the measurement time interval. This correlation can be used to design and analyze a transponder system for the proposed measurement system. In an experiment, in which the pressure sensors have been emulated by varactor diodes, it could be shown that the model is valid and that the criterion is suitable. Finally, the relevant design parameters of the transponders have been identified and their limitations investigated. PMID:26800547
Numerical assessment of time-domain methods for the estimation of local arterial pulse wave speed.
Alastruey, Jordi
2011-03-15
A local estimation of pulse wave speed c, an important predictor of cardiovascular events, can be obtained at arterial locations where simultaneous measurements of blood pressure (P) and velocity (U), arterial diameter (D) and U, flow rate (Q) and cross-sectional area (A), or P and D are available, using the PU-loop, sum-of-squares (∑(2)), lnDU-loop, QA-loop or new D(2)P-loop methods. Here, these methods were applied to estimate c from numerically generated P, U, D, Q and A waveforms using a visco-elastic one-dimensional model of the 55 larger human systemic arteries in normal conditions. Theoretical c were calculated from the parameters of the model. Estimates of c given by the loop methods were closer to theoretical values and more uniform within each arterial segment than those obtained using the ∑(2). The smaller differences between estimates and theoretical values were obtained using the D(2)P-loop method, with root-mean-square errors (RMSE) smaller than 0.18 ms(-1), followed by averaging the two c given by the PU- and lnDU-loops (RMSE <2.99 ms(-1)). In general, the errors of the PU-, lnDU- and QA-loops decreased at locations where visco-elastic effects were small and nearby junctions were well-matched for forward-travelling waves. The ∑(2) performed better at proximal locations. PMID:21211799
NASA Technical Reports Server (NTRS)
Kharkovsky, S.; Case, J. T.; Abou-Khousa, M. A.; Zoughi, R.; Hepburn, F.
2006-01-01
The Space Shuttle Columbia's catastrophic accident emphasizes the growing need for developing and applying effective, robust and life-cycle oriented nondestructive testing (NDT) methods for inspecting the shuttle external fuel tank spray on foam insulation (SOFI). Millimeter wave NDT techniques were one of the methods chosen for evaluating their potential for inspecting these structures. Several panels with embedded anomalies (mainly voids) were produced and tested for this purpose. Near-field and far-field millimeter wave NDT methods were used for producing images of the anomalies in these panels. This paper presents the results of an investigation for the purpose of detecting localized anomalies in several SOFI panels. To this end, reflectometers at a relatively wide range of frequencies (Ka-band (26.5 - 40 GHz) to W-band (75 - 110 GHz)) and utilizing different types of radiators were employed. The resulting raw images revealed a significant amount of information about the interior of these panels. However, using simple image processing techniques the results were improved in particular as it relate s to detecting the smaller anomalies. This paper presents the results of this investigation and a discussion of these results.
Evans, J.R.; Foulger, G.R.; Julian, B.R.; Miller, A.D.
1996-01-01
The Hengill region in SW Iceland is an unstable ridge-ridge-transform triple junction between an active and a waning segment of the mid-Atlantic spreading center and a transform that is transgressing southward. The triple junction contains active and extinct spreading segments and a widespread geothermal area. We evaluated shear-wave birefringence for locally recorded upper-crustal earthquakes using an array of 30 three-component digital seismographs. Fast-polarization directions, ??, are mostly NE to NNE, subparallel to the spreading axis and probably caused by fissures and microcracks related to spreading. However, there is significant variability in ?? throughout the array. The lag from fast to slow S is not proportional to earthquake depth (ray length), being scattered at all depths. The average wave-speed difference between qS1 and qS2 in the upper 2-5 km of the crust is 2-5%. Our results suggest considerable heterogeneity or strong S scattering.
Ambrose, David M.; Wilkening, Jon
2008-12-11
We classify all bifurcations from traveling waves to non-trivial time-periodic solutions of the Benjamin-Ono equation that are predicted by linearization. We use a spectrally accurate numerical continuation method to study several paths of non-trivial solutions beyond the realm of linear theory. These paths are found to either re-connect with a different traveling wave or to blow up. In the latter case, as the bifurcation parameter approaches a critical value, the amplitude of the initial condition grows without bound and the period approaches zero. We propose a conjecture that gives the mapping from one bifurcation to its counterpart on the other side of the path of non-trivial solutions. By experimentation with data fitting, we identify the form of the exact solutions on the path connecting two traveling waves, which represents the Fourier coefficients of the solution as power sums of a finite number of particle positions whose elementary symmetric functions execute simple orbits in the complex plane (circles or epicycles). We then solve a system of algebraic equations to express the unknown constants in the new representation in terms of the mean, a spatial phase, a temporal phase, four integers (enumerating the bifurcation at each end of the path) and one additional bifurcation parameter. We also find examples of interior bifurcations from these paths of already non-trivial solutions, but we do not attempt to analyze their algebraic structure.
Global classical solutions of the Vlasov–Fokker–Planck equation with local alignment forces
NASA Astrophysics Data System (ADS)
Choi, Young-Pil
2016-07-01
In this paper, we are concerned with the global well-posedness and time-asymptotic decay of the Vlasov–Fokker–Planck equation with local alignment forces. The equation can be formally derived from an agent-based model for self-organized dynamics called the Motsch–Tadmor model with noises. We present the global existence and uniqueness of classical solutions to the equation around the global Maxwellian in the whole space. For the large-time behavior, we show the algebraic decay rate of solutions towards the equilibrium under suitable assumptions on the initial data. We also remark that the rate of convergence is exponential when the spatial domain is periodic. The main methods used in this paper are the classical energy estimates combined with hyperbolic–parabolic dissipation arguments.
Komoda, Yoshiyuki; Leal, L Gary; Squires, Todd M
2014-05-13
Oscillatory microdisk rheometry was applied to evaluate the evolution of the viscoelastic properties at the surface of a film of an aqueous solution of poly(vinyl alcohol) (PVA) during drying. The drying rate was measured concurrently, based upon measurements of the variation of film thickness. A fully hydrolyzed PVA solution shows a constant drying rate, while a less hydrolyzed PVA solution exhibits a decreased drying rate in the latter part of the drying process, which occurred at the same time as an increase of the elastic modulus. We suggest that this difference in behavior is a consequence of the fact that both the configuration of the PVA molecule and the strength of interaction with water depend on the degree to which the PVA is hydrolyzed. The polymer concentration at the film surface can be estimated from the measured viscosity at the surface for the fully hydrolyzed PVA solution, and this result then can be compared with two theoretical calculations: one in which the polymer concentration is assumed to remain uniform throughout the film, and the other in which the polymer concentration distribution is determined via a one-dimensional diffusion model. This comparison suggests that the polymer is first concentrated locally near the surface but later in the drying process the distribution of polymer becomes increasingly uniform, possibly due to a spontaneously generated convective flow inside the film. PMID:24725080
NASA Astrophysics Data System (ADS)
Zaslavsky, A.; Volokitin, A. S.; Krasnoselskikh, V. V.; Maksimovic, M.; Bale, S. D.
2010-08-01
It is known from in situ observations that large-amplitude spatially localized Langmuir waves are frequent in the solar wind, and usually correlated with the presence of suprathermal electron beams, during type III events or close to the electron foreshock. It seems that the influence of the solar wind density fluctuations on the propagation effects of the Langmuir waves play an important role in the formation of these wave packets. In this article, we focus on the mechanism of generation of localized wave packets by electron beams propagating in an inhomogeneous medium. To this purpose, we present a theoretical model based on the resolution of the high-frequency component of the Zakharov's equation in which a source term describing the electron beam has been introduced, and show that this model is able to reproduce classical results about beam plasma instability and wave trapping in density cavities. Then we present simulation results of the generation of Langmuir wave packets in typical solar wind conditions at 1 A.U., and discuss the origin and nature of their localization.
Towards a unified solution of localization failure with mixed finite elements
NASA Astrophysics Data System (ADS)
Benedetti, Lorenzo; Cervera, Miguel; Chiumenti, Michele; Zeidler, Antonia; Fischer, Jan-Thomas
2015-04-01
Notwithstanding computational scientists made significant steps in the numerical simulation of failure in last three decades, the strain localization problem is still an open question. Especially in a geotechnical setting, when dealing with stability analysis of slopes, it is necessary to provide correct distribution of displacements, to evaluate the stresses in the ground and, therefore, to be able to identify the slip lines that brings to progressive collapse of the slope. Finite elements are an attractive method of solution thanks to profound mathematical foundations and the possibility of describing generic geometries. In order to account for the onset of localization band, the smeared crack approach [1] is introduced, that is the strain localization is assumed to occur in a band of finite width where the displacements are continuous and the strains are discontinuous but bounded. It is well known that this kind of approach poses some challenges. The standard irreducible formulation of FEM is known to be heavily affected by spurious mesh dependence when softening behavior occurs and, consequently, slip lines evolution is biased by the orientation of the mesh. Moreover, in the case of isochoric behavior, unbounded pressure oscillations arise and the consequent locking of the stresses pollutes the numerical solution. Both problems can be shown not to be related to the mathematical statement of the continuous problem but instead to its discrete (FEM) counterpart. Mixed finite element formulations represent a suitable alternative to mitigate these drawbacks. As it has been shown in previous works by Cervera [2], a mixed formulation in terms of displacements and pressure not only provides a propitious solution to the problem of incompressibility, but also it was found to possess the needed robustness in case of strain concentration. This presentation introduces a (stabilized) mixed finite element formulation with continuous linear strain and displacement
Local Existence of Weak Solutions to Kinetic Models of Granular Media
NASA Astrophysics Data System (ADS)
Agueh, Martial
2016-08-01
We prove in any dimension {d ≥q 1} a local in time existence of weak solutions to the Cauchy problem for the kinetic equation of granular media, partial_t f+v\\cdot nabla_x f = {div}_v[f(nabla W *_v f)] when the initial data are nonnegative, integrable and bounded functions with compact support in velocity, and the interaction potential {W} is a {C^2({{R}}^d)} radially symmetric convex function. Our proof is constructive and relies on a splitting argument in position and velocity, where the spatially homogeneous equation is interpreted as the gradient flow of a convex interaction energy with respect to the quadratic Wasserstein distance. Our result generalizes the local existence result obtained by Benedetto et al. (RAIRO Modél Math Anal Numér 31(5):615-641, 1997) on the one-dimensional model of this equation for a cubic power-law interaction potential.
Probing of local dissolution of Al-alloys in chloride solutions by AFM and SECM
NASA Astrophysics Data System (ADS)
Davoodi, A.; Pan, J.; Leygraf, C.; Norgren, S.
2006-05-01
Local dissolution of Al alloys was probed in situ in chloride solutions by using atomic force microscopy (AFM) and scanning electrochemical microscopy (SECM). Preferential dissolution in the boundary region between some intermetallic particles (IMPs) and alloy matrix, and trench formation around large IMPs during free immersion and under electrochemical anodic polarization were observed, which indicate different dissolution behavior associated to different types of IMPs. Moreover, by using an integrated AFM/SECM system with a dual mode cantilever/microelectrode probe, simultaneous probing of electrochemical active sites and topographic changes over the same area was performed with sub-micron resolution. This allowed the ongoing localized corrosion processes related to the IMP to be revealed.
Local non-negative initial data scalar characterization of the Kerr solution
NASA Astrophysics Data System (ADS)
García-Parrado Gómez-Lobo, Alfonso
2015-12-01
For any vacuum initial data set, we define a local, non-negative scalar quantity that vanishes at every point of the data hypersurface if and only if the data are Kerr initial data. Our scalar quantity depends only on the quantities used to construct the vacuum initial data set that are the Riemannian metric defined on the initial data hypersurface and a symmetric tensor that plays the role of the second fundamental form of the embedded initial data hypersurface. The dependency is algorithmic in the sense that given the initial data one can compute the scalar quantity by algebraic and differential manipulations, being thus suitable for an implementation in a numerical code. The scalar could also be useful in studies of the nonlinear stability of the Kerr solution because it serves to measure the deviation of a vacuum initial data set from the Kerr initial data in a local and algorithmic way.
NASA Astrophysics Data System (ADS)
Kim, K.-H.; Shiokawa, K.; Mann, I. R.; Park, J.-S.; Kwon, H.-J.; Hyun, K.; Jin, H.; Connors, M.
2016-02-01
Long-lasting (> 20 h) electromagnetic ion cyclotron (EMIC) Pc1-Pc2 waves were observed by the Athabasca (L =˜ 4.6) induction magnetometer and Canadian Array for Realtime Investigations of Magnetic Activity (L =˜ 4-6) fluxgate magnetometers on 5 April 2007. These waves showed a systematic frequency change with local time, the minimum frequency near dusk, and the maximum frequency near dawn. Assuming the plasmapause as a potential source region of the waves, we estimated the plasmapause location from localized proton enhancement (LPE) events observed at NOAA-Polar Orbiting Environmental Satellites and METOP-2 satellites. We found that the longitudinal frequency variation of EMIC waves has a clear correlation with the estimated plasmapause location and that the waves are in the frequency band between the equatorial helium and oxygen gyrofrequencies at the estimated plasmapause. With our analysis results we suggest that the LPE events are caused by wave-particle interaction with the helium band EMIC waves generated near the plasmapause.
Li, Xing; Gao, Yaru; Jiang, Shuna; Ma, Li; Liu, Chunxiang; Cheng, Chuanfu
2015-02-01
Using an L-shaped metal nanoslit to generate waves of the pure photonic and plasmonic modes simultaneously, we perform an experimental solution for the scattered imaging of the interference of the two waves. From the fringe data of interference, the amplitudes and the wavevector components of the two waves are obtained. The initial phases of the two waves are obtained from the phase map reconstructed with the interference of the scattered image and the reference wave in the interferometer. The difference in the wavevector components gives rise to an additional phase delay. We introduce the scattering theory under Kirchhoff's approximation to metal slit regime and explain the wavevector difference reasonably. The solution of the quantities is a comprehensive reflection of excitation, scattering and interference of the two waves. By decomposing the polarized incident field with respect to the slit element, the scattered image produced by slit of arbitrary shape can be solved with the nanoscale Huygens-Fresnel principle. This is demonstrated by the experimental intensity pattern and phase map produced by a ring-slit and its consistency with the calculated results. PMID:25836205
Skaropoulos, N.C.; Ioannidou, M.P.; Chrissoulidis, D.P.
1996-10-01
Understanding the interaction of EM radiation with humans is essential in a number of contemporary applications. Special attention is paid to the absorption of EM energy by the human head, which exhibits a resonant behavior in the frequency band 0.1--3 GHz. The use of handheld transceivers for wireless communications, which operate in close proximity to the head, has raised safety-related questions and questions concerning the effect of the head on the performance of the mobile phone antenna. The induced electromagnetic (EM) field in a layered eccentric spheres structure is determined through a concise analytical formulation based on indirect mode-matching (IMM). The exact analytical solution is applied to a six-layer model of the head. This model allows for eccentricity between the inner and outer sets of concentric spherical layers which simulate brain and skull, respectively. Excitation is provided by a nearby localized source or by an incident plane wave. The numerical application provides information about the total absorbed power, the absorption in each layer, and the spatial distribution of the specific absorption rate (SAR) at frequencies used by cellular phones. The effects of excitation frequency, eccentricity, exposure configuration, and antenna-head separation are investigated.
Climate downscaling: Local mean sea-level rise, surge and wave modelling
NASA Astrophysics Data System (ADS)
Wolf, J.; Lowe, J.; Howard, T.
2012-04-01
The investigation of future climate impacts at the coast requires sufficiently detailed projections for the nearshore waves and sea levels in both the present day and a future climate scenario, to provide an offshore boundary condition. Here we discuss the future changes in surge and wave climate forced by winds and pressures from a version of the Met Office Hadley Centre Climate model, for various greenhouse gas emission scenarios and for various climate model parameter choices. The local spatial variation in mean sea level is also taken into account, incorporating deviations from global mean sea level change caused by regional variations in ocean density and circulation. Some parts of the UK are still subject to glacial isostatic readjustment after the last ice age, counter-acting sea level rise, although this will be overwhelmed by the projected effects of sea level rise due to global warming in the 21st century, for most future emission scenarios. Model downscaling from the global coupled atmosphere-ocean model using a regional climate model is needed to provide more realistic and detailed wind simulations over the NW European continental shelf. There is large uncertainty in projected changes in storminess for the NE Atlantic region, with different climate models providing conflicting results for the future. Results from this study show that large increases in mean sea level (even up to 5 metres) have very little effect on the dynamics of extreme surge events, the primary effect being on the speed of propagation of tide and surge (Howard et al., 2010). Increasing storminess is expected to increase surge heights but more direct effects can be attributed directly to increased mean sea level. Based on the wave model results, seasonal mean and annual maximum wave heights are generally expected to increase to the SW of the UK, reduce to the north of the UK and experience little change in the southern North Sea or eastern Irish Sea. This pattern is consistent with a
NASA Astrophysics Data System (ADS)
Masnadi, N.; Duncan, J. H.
2012-11-01
The non-linear response of a water free surface to a localized pressure distribution moving at constant speed just below the minimum phase speed (Cmin ~ 23 cm/s) of gravity-capillary waves is studied experimentally in a long tank. The pressure distribution is generated by blowing air onto the water surface via a vertically oriented 2-mm-ID tube that is mounted on an instrument carriage that is in turn set to move along the tank at constant speeds between 20 and 23 cm/s. A cinematic light refraction method is used to obtain quantitative measurements of the surface deformation pattern behind the air jet. At towing speeds just below Cmin, an unsteady V-shaped wave pattern appears behind the pressure source. From observations of the wave pattern evolution, it is found that localized depressions are generated near the pressure source and propagate in pairs along the two arms of the V-shaped pattern. These are eventually shed from the tips of the pattern and rapidly decay. Measurements of the evolution of the speed of these localized depression patterns are compared to existing measurements of the speeds of steady three-dimensional solitary gravity-capillary waves (lumps) that appear behind the pressure source at even lower towing speeds. Supported by the National Science Foundation Division of Ocean Sciences.
NASA Astrophysics Data System (ADS)
Zhang, Chi; Pu, Yong; Manuilov, Sergei A.; Pelekhov, Denis V.; Hammel, P. Chris
Maintaining efficient spin-Hall anti-damping torque in micron-scale devices is challenging near the critical current for auto-oscillation, likely due to spin wave mode degeneracies and nonlinear magnon scattering between them. Localized spin wave modes confined by the strongly inhomogeneous dipole magnetic field of a nearby micro-spherical magnet provides a potentially powerful tool to study these multi-mode interactions by allowing systematic tunability while avoiding potential spurious effects arising from imperfections in fabricating microscopic structures. We demonstrate electrical ST-FMR detection of well-resolved localized modes in a Py/Pt stripe. We find that magnon spectral engineering by means of a micromagnetic particle enables clear observation of damping control and significant reduction of linewidth by means of the anti-damping torque arising from an imposed DC current. The observed linewidth variation suggests that localized modes can be controlled as effectively as the uniform mode.
NASA Astrophysics Data System (ADS)
Bialynicki-Birula, Iwo
2004-05-01
New solutions in the classical and quantum theory of relativistic charged particles will be presented. They describe a beam of particles guided by an electromagnetic vortex. The beam stabilization is caused by the same mechanism that confines particles in the Paul trap and the Trojan wave packets of electrons in atoms.
NASA Astrophysics Data System (ADS)
Johnson, Mathew A.; Zumbrun, Kevin
Extending previous results of Oh-Zumbrun and Johnson-Zumbrun, we show that spectral stability implies linearized and nonlinear stability of spatially periodic traveling wave solutions of viscous systems of conservation laws for systems of generic type, removing a restrictive assumption that wave speed be constant to first order along the manifold of nearby periodic solutions. Key to our analysis is a nonlinear cancellation estimate observed by Johnson and Zumbrun, along with a detailed understanding of the Whitham averaged system. The latter motivates a careful analysis of the Bloch perturbation expansion near zero frequency and suggests factoring out an appropriate translational modulation of the underlying wave, allowing us to derive the sharpened low-frequency estimates needed to close the nonlinear iteration arguments.
NASA Astrophysics Data System (ADS)
Iwase, Ryoichi
2016-07-01
An in situ method of estimating the seismic wave velocity at the seafloor surface by observing the particle motion of a wave transmitted into the sediment is presented; this method uses a sound source whose location is known. Conversely, a sound source localization method using the obtained seismic velocities and involving particle motion observation is also presented. Although this method is applicable only when the sound source exists within the critical incidence angle range, it is expected to contribute to the tracing of vocalizing baleen whales, which are unknown around Japanese waters.
Louis, H; Tlidi, M; Louvergneaux, E
2016-07-11
We perform a statistical analysis of the optical solitary wave propagation in an ultra-slow stochastic non-local focusing Kerr medium such as liquid crystals. Our experimental results show that the localized beam trajectory presents a dynamical random walk whose beam position versus the propagation distance z depicts two different kind of evolutions A power law is found for the beam position standard deviation during the first stage of propagation. It obeys approximately z^{3}/^{2} up to ten times the power threshold for solitary wave generation. PMID:27410886
Louis, H; Tlidi, M; Louvergneaux, E
2016-07-11
We perform a statistical analysis of the optical solitary wave propagation in an ultra-slow stochastic non-local focusing Kerr medium such as liquid crystals. Our experimental results show that the localized beam trajectory presents a dynamical random walk whose beam position versus the propagation distance z depicts two different kind of evolutions A power law is found for the beam position standard deviation during the first stage of propagation. It obeys approximately z^{3}/^{2} up to ten times the power threshold for solitary wave generation. PMID:27410887
The local properties of ocean surface waves by the phase-time method
NASA Technical Reports Server (NTRS)
Huang, Norden E.; Long, Steven R.; Tung, Chi-Chao; Donelan, Mark A.; Yuan, Yeli; Lai, Ronald J.
1992-01-01
A new approach using phase information to view and study the properties of frequency modulation, wave group structures, and wave breaking is presented. The method is applied to ocean wave time series data and a new type of wave group (containing the large 'rogue' waves) is identified. The method also has the capability of broad applications in the analysis of time series data in general.
Local Field Potentials Encode Place Cell Ensemble Activation during Hippocampal Sharp Wave Ripples.
Taxidis, Jiannis; Anastassiou, Costas A; Diba, Kamran; Koch, Christof
2015-08-01
Whether the activation of spiking cell ensembles can be encoded in the local field potential (LFP) remains unclear. We address this question by combining in vivo electrophysiological recordings in the rat hippocampus with realistic biophysical modeling, and explore the LFP of place cell sequence spiking ("replays") during sharp wave ripples. We show that multi-site perisomatic LFP amplitudes, in the ∼150-200 Hz frequency band, reliably reflect spatial constellations of spiking cells, embedded within non-spiking populations, and encode activation of local place cell ensembles during in vivo replays. We find spatiotemporal patterns in the LFP, which remain consistent between sequence replays, in conjunction with the ordered activation of place cell ensembles. Clustering such patterns provides an efficient segregation of replay events from non-replay-associated ripples. This work demonstrates how spatiotemporal ensemble spiking is encoded extracellularly, providing a window for efficient, LFP-based detection and monitoring of structured population activity in vivo. PMID:26247865
NASA Technical Reports Server (NTRS)
Schlesinger, R. E.; Johnson, D. R.; Uccellini, L. W.
1983-01-01
In the present investigation, a one-dimensional linearized analysis is used to determine the effect of Asselin's (1972) time filter on both the computational stability and phase error of numerical solutions for the shallow water wave equations, in cases with diffusion but without rotation. An attempt has been made to establish the approximate optimal values of the filtering parameter nu for each of the 'lagged', Dufort-Frankel, and Crank-Nicholson diffusion schemes, suppressing the computational wave mode without materially altering the physical wave mode. It is determined that in the presence of diffusion, the optimum filter length depends on whether waves are undergoing significant propagation. When moderate propagation is present, with or without diffusion, the Asselin filter has little effect on the spatial phase lag of the physical mode for the leapfrog advection scheme of the three diffusion schemes considered.
Exact solutions of regular approximate relativistic wave equations for hydrogen-like atoms
NASA Astrophysics Data System (ADS)
van Leeuwen, R.; van Lenthe, E.; Baerends, E. J.; Snijders, J. G.
1994-07-01
Apart from relativistic effects originating from high kinetic energy of an electron in a flat potential, which are treated in first order by the Pauli Hamiltonian, there are relativistic effects even for low-energy electrons if they move in a strong Coulomb potential. The latter effects can be accurately treated already in the zeroth order of an expansion of the Foldy-Wouthuysen transformation, if the expansion is carefully chosen to be nondivergent for r→0 even for Coulomb potentials, as shown by Van Lenthe et al. [J. Chem. Phys. 99, 4597 (1993)] (cf. also Heully et al. [J. Phys. B 19, 2799 (1986)] and Chang et al. [Phys. Scr. 34, 394 (1986)]). In the present paper, it is shown that the solutions of the zeroth order of this two-component regular approximate (ZORA) equation for hydrogen-like atoms are simply scaled solutions of the large component of the Dirac wave function for this problem. The eigenvalues are related in a similar way. As a consequence, it is proven that under some restrictions, the ZORA Hamiltonian is bounded from below for Coulomb-like potentials. Also, an exact result for the first order regular approximate Hamiltonian is given. The method can also be used to obtain exact results for regular approximations of scalar relativistic equations, like the Klein-Gordon equation. The balance between relativistic effects originating from the Coulombic singularity in the potential (typically core penetrating s and p valence electrons in atoms and molecules) and from high kinetic energy (important for high-energy electrons in a flat potential and also for core-avoiding high angular momentum (d, f, and g states in atoms) are discussed.
ESTELA: a method for evaluating the source and travel time of the wave energy reaching a local area
NASA Astrophysics Data System (ADS)
Pérez, Jorge; Méndez, Fernando J.; Menéndez, Melisa; Losada, Inigo J.
2014-08-01
The description of wave climate at a local scale is of paramount importance for offshore and coastal engineering applications. Conditions influencing wave characteristics at a specific location cannot, however, be fully understood by studying only local information. It is necessary to take into account the dynamics of the ocean surface over a large `upstream' wave generation area. The goal of this work is to provide a methodology to easily characterize the area of influence of any particular ocean location worldwide. Moreover, the developed method is able to characterize the wave energy and travel time in that area. The method is based on a global scale analysis using both geographically and physically based criteria. The geographic criteria rely on the assumption that deep water waves travel along great circle paths. This limits the area of influence by neglecting energy that cannot reach a target point, as its path is blocked by land. The individual spectral partitions from a global wave reanalysis are used to reconstruct the spectral information and apply the physically based criteria. The criteria are based on the selection of the fraction of energy that travels towards the target point for each analysed grid point. The method has been tested on several locations worldwide. Results provide maps that inform about the relative importance of different oceanic areas to the local wave climate at any target point. This information cannot be inferred from local parameters and agrees with information from other approaches. The methodology may be useful in a number of applications, such as statistical downscaling, storm tracking and grid definition in numerical modelling.
NASA Astrophysics Data System (ADS)
Ji, S.; Yuan, X.
2016-06-01
A generic probabilistic model, under fundamental Bayes' rule and Markov assumption, is introduced to integrate the process of mobile platform localization with optical sensors. And based on it, three relative independent solutions, bundle adjustment, Kalman filtering and particle filtering are deduced under different and additional restrictions. We want to prove that first, Kalman filtering, may be a better initial-value supplier for bundle adjustment than traditional relative orientation in irregular strips and networks or failed tie-point extraction. Second, in high noisy conditions, particle filtering can act as a bridge for gap binding when a large number of gross errors fail a Kalman filtering or a bundle adjustment. Third, both filtering methods, which help reduce the error propagation and eliminate gross errors, guarantee a global and static bundle adjustment, who requires the strictest initial values and control conditions. The main innovation is about the integrated processing of stochastic errors and gross errors in sensor observations, and the integration of the three most used solutions, bundle adjustment, Kalman filtering and particle filtering into a generic probabilistic localization model. The tests in noisy and restricted situations are designed and examined to prove them.
Solutions to Kuessner's integral equation in unsteady flow using local basis functions
NASA Technical Reports Server (NTRS)
Fromme, J. A.; Halstead, D. W.
1975-01-01
The computational procedure and numerical results are presented for a new method to solve Kuessner's integral equation in the case of subsonic compressible flow about harmonically oscillating planar surfaces with controls. Kuessner's equation is a linear transformation from pressure to normalwash. The unknown pressure is expanded in terms of prescribed basis functions and the unknown basis function coefficients are determined in the usual manner by satisfying the given normalwash distribution either collocationally or in the complex least squares sense. The present method of solution differs from previous ones in that the basis functions are defined in a continuous fashion over a relatively small portion of the aerodynamic surface and are zero elsewhere. This method, termed the local basis function method, combines the smoothness and accuracy of distribution methods with the simplicity and versatility of panel methods. Predictions by the local basis function method for unsteady flow are shown to be in excellent agreement with other methods. Also, potential improvements to the present method and extensions to more general classes of solutions are discussed.
Localization and implication of oblique whistler wave in the magnetopause region
NASA Astrophysics Data System (ADS)
Nandal, P.; Yadav, N.; Sharma, R. P.
2016-04-01
Nonlinear interaction between highly oblique whistler wave and ion acoustic wave pertinent to magnetopause has been investigated. The density perturbation in whistler wave is supposed to be originated due to the presence of ion acoustic wave in the background. The ponderomotive force components arising due to the high amplitude pump wave, viz., whistler wave are constituted in the nonlinear dynamics of low frequency ion acoustic wave. The coupled nonlinear dynamical equations are then modelled in the form of modified nonlinear Schrödinger equation by considering adiabatic response of low frequency ion acoustic wave. The numerical simulation of this coupled nonlinear equation is performed to study the temporal evolution of nonlinear whistler wave. The obtained simulation results show that the temporal evolution also leads to the cascade of broadband turbulence spectrum at smaller wavelengths. The relevance of the obtained results with the observations of THEMIS spacecraft in the magnetopause region has been pointed out.
NASA Astrophysics Data System (ADS)
Cheng, Wen-Guang; Li, Biao; Chen, Yong
2015-05-01
In this paper, the truncated Painlevé analysis and the consistent tanh expansion (CTE) method are developed for the (2+1)-dimensional breaking soliton equation. As a result, the soliton-cnoidal wave interaction solution of the equation is explicitly given, which is difficult to be found by other traditional methods. When the value of the Jacobi elliptic function modulus m = 1, the soliton-cnoidal wave interaction solution reduces back to the two-soliton solution. The method can also be extended to other types of nonlinear evolution equations in mathematical physics. Supported by National Natural Science Foundation of China under Grant Nos. 11271211, 11275072, 11435005, and K.C. Wong Magna Fund in Ningbo University
Phase conjugation by degenerate four wave mixing in disodium fluorescein solution in methanol
NASA Technical Reports Server (NTRS)
Abdeldayem, Hossin; Sekhar, P. Chandra; Venkateswarlu, P.; Geroge, M. C.
1989-01-01
Organic dyes are known to show the resonant type of nonlinear optical properties, including phase conjugation. In the present work, disodium fluorescein in methanol is used as an organic nonlinear medium for degenerate four wave mixing at 532 nm to see the intensity dependence of the phase conjugate signal at different concentrations of the solution. It is observed that the maximum reflectivity of the signal occurs in a concentration range of 5 x 10(exp -3)/cu cm to 1.2 x 10(exp -2) g/cu cm. It is also observed that the intensity of the signal drops suddenly to less than half of its maximum outside the concentration range mentioned above. An investigation of the phase conjugate signal intensity by changing the delay time between probe signal and the forward pump is also examined. Briefly discussed is the possibility of population grating in dye liquids as a source of enhancing the third order susceptibility besides the other techniques mentioned in reference. The experiment is done by beam splitting the second harmonic (532 nm) of Nd:YAG laser, Q-switched at 20 pulses/sec (pulse width is approximately 8 and 200 mJ per pulse).