Science.gov

Sample records for localized wave solutions

  1. Helical localized wave solutions of the scalar wave equation.

    PubMed

    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.

  2. Control of coupled localized nonlinear wave solutions

    NASA Astrophysics Data System (ADS)

    Porubov, A. V.; Antonov, I. D.

    2017-01-01

    A method of forced localization of non-linear wave by a feedback control is developed for coupled equations accounting for non-linear dynamic processes in complex lattices. It is shown, that the control of the shape and velocity of the wave function of macro-strain allows to achieve localization of the shape of the function describing variations of defects in the lattice. Moreover, change of the sign of the amplitude of the last wave may be achieved by variation of the parameters of the control function but independent of the initial conditions.

  3. 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.

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

    NASA Astrophysics Data System (ADS)

    Kiselev, A. P.

    2007-04-01

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

  5. Nonlinear Localized Dissipative Structures for Long-Time Solution of Wave Equation

    DTIC Science & Technology

    2009-07-01

    Fatemi, E., Engquist, B., and Osher, S., " Numerical Solution of the High Frequency Asymptotic Expansion for the Scalar Wave Equation ", Journal of...FINAL REPORT Grant Title: Nonlinear Localized Dissipative Structures for Long-Time Solution of Wave Equation By Dr. John Steinhoff Grant number... numerical method, "Wave Confinement" (WC), is developed to efficiently solve the linear wave equation . This is similar to the originally developed

  6. On exact traveling-wave solutions for local fractional Korteweg-de Vries equation.

    PubMed

    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.

  7. 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.

  8. Fast decay of solutions for linear wave equations with dissipation localized near infinity in an exterior domain

    NASA Astrophysics Data System (ADS)

    Ryo, Ikehata

    Uniform energy and L2 decay of solutions for linear wave equations with localized dissipation will be given. In order to derive the L2-decay property of the solution, a useful device whose idea comes from Ikehata-Matsuyama (Sci. Math. Japon. 55 (2002) 33) is used. In fact, we shall show that the L2-norm and the total energy of solutions, respectively, decay like O(1/ t) and O(1/ t2) as t→+∞ for a kind of the weighted initial data.

  9. Local mean consistency on numerical solutions of stochastic wave equation with cubic nonlinearities on 2D rectangles

    NASA Astrophysics Data System (ADS)

    Hazaimeh, Haziem M.

    2017-06-01

    In this article we study that the linear-implicit Euler method of the solution of nonlinear stochastic wave equation in 2 dimensions has the non-exploding explicit representation and is mean consistent. In [15], we proved that the strong Fourier solution of the semi-linear wave equations exists and is unique on an appropriate Hilbert space. A linear-implicit Euler method is used to discretize the related Fourier coefficients and mean consistency is discussed.

  10. Various Boussinesq solitary wave solutions

    SciTech Connect

    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.

  11. Control methods for localization of nonlinear waves

    NASA Astrophysics Data System (ADS)

    Porubov, Alexey; Andrievsky, Boris

    2017-03-01

    A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions. This article is part of the themed issue 'Horizons of cybernetical physics'.

  12. Control methods for localization of nonlinear waves.

    PubMed

    Porubov, Alexey; Andrievsky, Boris

    2017-03-06

    A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions.This article is part of the themed issue 'Horizons of cybernetical physics'.

  13. Local One-Dimensional ICRF Full-Wave Solutions Valid to All Orders in k-Perpendicular-Rho

    SciTech Connect

    Batchelor, D.B.; Berry, L.A.; Jaeger, E.F.

    1999-04-12

    High harmonic ion cyclotron resonances are important for understanding future fast wave heating experiments on NSTX 1 as well as recent ICRF flow drive experiments on PBX-M2 and TFTR3. Unfortunately, many of our ICRF wave analysis codes are based on an expansion to second order in k-perpendicular-Rho where k-perpendicular is the perpendicular wave number, and Rho is the Larmor radius. Such codes are limited to cyclotron harmonics less than or equal to 2. Integral codes4,5 on the other hand, are valid to all orders in both k-perpendicular-Rho and Rho/LL where L is the equilibrium scale length. But velocity space integrals in these codes require long running times. Here we take a simpler approach which assumes a local plasma conductivity (Rho/L << 1), while still retaining all orders in k-perpendicular-Rho. This allows high harmonic fast wave and flow drive applications, while requiring less computing time than conventional integral codes.

  14. Localized wave pulse experiments

    SciTech Connect

    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.

  15. Locally homogeneous pp-waves

    NASA Astrophysics Data System (ADS)

    Globke, Wolfgang; Leistner, Thomas

    2016-10-01

    We show that every n-dimensional locally homogeneous pp-wave is a plane wave, provided it is indecomposable and its curvature operator, when acting on 2-forms, has rank greater than one. As a consequence we obtain that indecomposable, Ricci-flat locally homogeneous pp-waves are plane waves. This generalises a classical result by Jordan, Ehlers and Kundt in dimension 4. Several examples show that our assumptions on indecomposability and the rank of the curvature are essential.

  16. Localized coherence of freak waves

    NASA Astrophysics Data System (ADS)

    Latifah, Arnida L.; van Groesen, E.

    2016-09-01

    This paper investigates in detail a possible mechanism of energy convergence leading to freak waves. We give examples of a freak wave as a (weak) pseudo-maximal wave to illustrate the importance of phase coherence. Given a time signal at a certain position, we identify parts of the time signal with successive high amplitudes, so-called group events, that may lead to a freak wave using wavelet transform analysis. The local coherence of the critical group event is measured by its time spreading of the most energetic waves. Four types of signals have been investigated: dispersive focusing, normal sea condition, thunderstorm condition and an experimental irregular wave. In all cases presented in this paper, it is shown that a high correlation exists between the local coherence and the appearance of a freak wave. This makes it plausible that freak waves can be developed by local interactions of waves in a wave group and that the effect of waves that are not in the immediate vicinity is minimal. This indicates that a local coherence mechanism within a wave group can be one mechanism that leads to the appearance of a freak wave.

  17. Localized wave and vortical solutions to linear hyperbolic systems and their application to linear shallow water equations

    NASA Astrophysics Data System (ADS)

    Dobrokhotov, S. Yu.; Shafarevich, A. I.; Tirozzi, B.

    2008-06-01

    The result of this paper is that any fast-decaying function can be represented as an integral over the canonical Maslov operator, on a special Lagrangian manifold, acting on a specific function. This representation enables one to construct effective explicit formulas for asymptotic solutions of a vast class of linear hyperbolic systems with variable coefficients.

  18. Local fluctuations in solution mixtures

    PubMed Central

    Ploetz, Elizabeth A.; Smith, Paul E.

    2011-01-01

    An extension of the traditional Kirkwood-Buff (KB) theory of solutions is outlined which provides additional fluctuating quantities that can be used to characterize and probe the behavior of solution mixtures. Particle-energy and energy-energy fluctuations for local regions of any multicomponent solution are expressed in terms of experimentally obtainable quantities, thereby supplementing the usual particle-particle fluctuations provided by the established KB inversion approach. The expressions are then used to analyze experimental data for pure water over a range of temperatures and pressures, a variety of pure liquids, and three binary solution mixtures – methanol and water, benzene and methanol, and aqueous sodium chloride. In addition to providing information on local properties of solutions it is argued that the particle-energy and energy-energy fluctuations can also be used to test and refine solute and solvent force fields for use in computer simulation studies. PMID:21806137

  19. Weak localization of seismic waves.

    PubMed

    Larose, E; Margerin, L; Van Tiggelen, B A; Campillo, M

    2004-07-23

    We report the observation of weak localization of seismic waves in a natural environment. It emerges as a doubling of the seismic energy around the source within a spot of the width of a wavelength, which is several tens of meters in our case. The characteristic time for its onset is the scattering mean-free time that quantifies the internal heterogeneity. Copyright 2004 The American Physical Society

  20. Confinement effects on an ultra-cold matter wave-packet by a square well impurity near the de-localization threshold: analytic solutions, scaling, and width properties

    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

  1. Damping filter method for obtaining spatially localized solutions.

    PubMed

    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.

  2. Damping filter method for obtaining spatially localized solutions

    NASA Astrophysics Data System (ADS)

    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.

  3. Numerical procedure for planetary wave solution

    SciTech Connect

    Choi, Woo Kap; Wuebbles, D.J.

    1993-09-01

    The newly-developed LLNL two-dimensional chemical-radiative-transport model requires a knowledge of the EP flux divergence as an input momentum forcing. The major contributions for this forcing term come from the synoptic wave in the troposphere, the planetary wave in the stratosphere and mesosphere and the gravity wave in the upper mesosphere. The major source of the zonal momentum forcing in the middle atmosphere is the nonlinear planetary wave breaking. This planetary wave breaking also plays a significant role of mixing the chemical tracers. Garcia suggested a way of parameterizing the planetary wave breaking by using, linear damping of the primary wave. In this note we describe the procedure of obtaining the wave solution for the parameterization.

  4. Scattering and Depolarization of Electromagnetic Waves--Full Wave Solutions.

    DTIC Science & Technology

    1984-01-01

    Analysis," Proceedings of the International Union of Radio Science URSI Conference at Ciudad Universitaria , Madrid, August 1983, in press. . . 13...rough land and seat3 J. The full wave approach was also used to determine the scattering and depolarization of radio waves in irregular spheroidal struc...Full Wave Solutions," Radio Science, Vol. 17, No. 5, September-October 1982, pp. 1055-1066. 4. "Scattering and Depolarization by Rough Surfaces: Full

  5. Numerical solutions of nonlinear wave equations

    SciTech Connect

    Kouri, D.J.; Zhang, D.S.; Wei, G.W.; Konshak, T.; Hoffman, D.K.

    1999-01-01

    Accurate, stable numerical solutions of the (nonlinear) sine-Gordon equation are obtained with particular consideration of initial conditions that are exponentially close to the phase space homoclinic manifolds. Earlier local, grid-based numerical studies have encountered difficulties, including numerically induced chaos for such initial conditions. The present results are obtained using the recently reported distributed approximating functional method for calculating spatial derivatives to high accuracy and a simple, explicit method for the time evolution. The numerical solutions are chaos-free for the same conditions employed in previous work that encountered chaos. Moreover, stable results that are free of homoclinic-orbit crossing are obtained even when initial conditions are within 10{sup {minus}7} of the phase space separatrix value {pi}. It also is found that the present approach yields extremely accurate solutions for the Korteweg{endash}de Vries and nonlinear Schr{umlt o}dinger equations. Our results support Ablowitz and co-workers{close_quote} conjecture that ensuring high accuracy of spatial derivatives is more important than the use of symplectic time integration schemes for solving solitary wave equations. {copyright} {ital 1999} {ital The American Physical Society}

  6. Experimental study of spatiotemporally localized surface gravity water waves.

    PubMed

    Chabchoub, A; Akhmediev, N; Hoffmann, N P

    2012-07-01

    We present experimental results on the study of spatiotemporally localized surface wave events on deep water that can be modeled using the Peregrine breather solution of the nonlinear Schrödinger equation. These are often considered as prototypes of oceanic rogue waves that can focus wave energy into a single wave packet. For small steepness values of the carrier gravity waves the Peregrine breathers are relatively wide, thus providing an excellent agreement between the theory and experimental results. For larger steepnesses the focusing leads to temporally and spatially shorter events. Nevertheless, agreement between measurements and the Peregrine breather theory remains reasonably good, with discrepancies of modulation gradients and spatiotemporal symmetries being tolerable. Lifetimes and travel distances of the spatiotemporally localized wave events determined from the experiment are in good agreement with the theory.

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

    PubMed

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

    2014-01-01

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

  8. One dimensional global and local solution for ICRF heating

    SciTech Connect

    Wang, C.Y.; Batchelor, D.B.; Jaeger, E.F.; Carter, M.D.

    1995-02-01

    A numerical code GLOSI [Global and Local One-dimensional Solution for Ion cyclotron range of frequencies (ICRF) heating] is developed to solve one-dimensional wave equations resulting from the use of radio frequency (RF) waves to heat plasmas. The code uses a finite difference method. Due to its numerical stability, the code can be used to find both global and local solutions when imposed with appropriate boundary conditions. Three types of boundary conditions are introduced to describe wave scattering, antenna wave excitation, and fixed tangential wave magnetic field. The scattering boundary conditions are especially useful for local solutions. The antenna wave excitation boundary conditions can be used to excite fast and slow waves in a plasma. The tangential magnetic field boundary conditions are used to calculate impedance matrices, which describe plasma and antenna coupling and can be used by an antenna code to calculate antenna loading. These three types of boundary conditions can also be combined to describe various physical situations in RF plasma heating. The code also includes plasma thermal effects and calculates collisionless power absorption and kinetic energy flux. The plasma current density is approximated by a second-order Larmor radius expansion, which results in a sixth-order ordinary differential equation.

  9. Local energy decay for linear wave equations with variable coefficients

    NASA Astrophysics Data System (ADS)

    Ikehata, Ryo

    2005-06-01

    A uniform local energy decay result is derived to the linear wave equation with spatial variable coefficients. We deal with this equation in an exterior domain with a star-shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data, and its proof is quite simple. This generalizes a previous famous result due to Morawetz [The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. Pure Appl. Math. 14 (1961) 561-568]. In order to prove local energy decay, we mainly apply two types of ideas due to Ikehata-Matsuyama [L2-behaviour of solutions to the linear heat and wave equations in exterior domains, Sci. Math. Japon. 55 (2002) 33-42] and Todorova-Yordanov [Critical exponent for a nonlinear wave equation with damping, J. Differential Equations 174 (2001) 464-489].

  10. Slanted snaking of localized Faraday waves

    NASA Astrophysics Data System (ADS)

    Pradenas, Bastián; Araya, Isidora; Clerc, Marcel G.; Falcón, Claudio; Gandhi, Punit; Knobloch, Edgar

    2017-06-01

    We report on an experimental, theoretical, and numerical study of slanted snaking of spatially localized parametrically excited waves on the surface of a water-surfactant mixture in a Hele-Shaw cell. We demonstrate experimentally the presence of a hysteretic transition to spatially extended parametrically excited surface waves when the acceleration amplitude is varied, as well as the presence of spatially localized waves exhibiting slanted snaking. The latter extend outside the hysteresis loop. We attribute this behavior to the presence of a conserved quantity, the liquid volume trapped within the meniscus, and introduce a universal model based on symmetry arguments, which couples the wave amplitude with such a conserved quantity. The model captures both the observed slanted snaking and the presence of localized waves outside the hysteresis loop, as demonstrated by numerical integration of the model equations.

  11. Testing local Lorentz invariance with gravitational waves

    DOE PAGES

    Kostelecký, V. Alan; Mewes, Matthew

    2016-04-20

    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. (C) 2016 The Authors. Published by Elsevier B.V.

  12. Localization of Waves in Merged Lattices

    PubMed Central

    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

  13. Localization of Waves in Merged Lattices.

    PubMed

    Alagappan, G; Png, C E

    2016-08-18

    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.

  14. Localization of Waves in Merged Lattices

    NASA Astrophysics Data System (ADS)

    Alagappan, G.; Png, C. E.

    2016-08-01

    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.

  15. Wave packet systems on local fields

    NASA Astrophysics Data System (ADS)

    Shah, Firdous A.; Ahmad, Owais

    2017-10-01

    In this paper, we introduce the notion of wave packet systems on local fields of positive characteristic and derive some characterizations of these systems by means of two basic equations in the Fourier domain. More precisely, we establish a complete characterization of orthogonal wave packet systems in L2(K) which include the corresponding results of wavelet analysis and Gabor theory as the special cases. We shall also provide a sufficient condition of the completeness of wave packet systems on local fields of positive characteristic subject to some mild conditions. The paper concludes with the necessary and sufficient conditions for the wave packet systems to be wave packet Parseval frames for L2(K) .

  16. Manipulating localized matter waves in multicomponent Bose-Einstein condensates.

    PubMed

    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.

  17. 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.

  18. 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.…

  19. 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.…

  20. Dynamics of Traveling Wave Solutions to a New Highly Nonlinear Shallow Water Wave Equation

    NASA Astrophysics Data System (ADS)

    Li, Jibin; Kou, Kit Ian

    In this paper, the dynamics of traveling wave solutions in a shallow water wave model with a regime for large-amplitude is studied. The corresponding traveling wave system is a singular planar dynamical system with one or two singular straight lines. By using the method of dynamical systems, bifurcation diagrams are presented. The existence of solitary wave solutions, periodic wave solutions, quasi-peakon solution, periodic peakon solutions and compacton solutions under different parameter conditions are determined.

  1. 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.

  2. Localized waves with spherical harmonic symmetries

    NASA Astrophysics Data System (ADS)

    Mills, M. S.; Siviloglou, G. A.; Efremidis, N.; Graf, T.; Wright, E. M.; Moloney, J. V.; Christodoulides, D. N.

    2012-12-01

    We introduce a class of propagation invariant spatiotemporal optical wave packets with spherical harmonic symmetries in their field configurations. The evolution of these light orbitals is considered theoretically in anomalously dispersive media, and their spinning dynamics are analyzed in terms of their corresponding energy flows. Similarly, localized waves generated via spherical superposition from Archimedean and Platonic solids in k⃗-ω space are investigated in this work.

  3. Spin wave localization in tangentially magnetized films

    PubMed Central

    Tartakovskaya, Elena V.; Pardavi-Horvath, Martha; McMichael, Robert D.

    2016-01-01

    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. PMID:27551693

  4. Deep-Water Waves: on the Nonlinear Schrödinger Equation and its Solutions

    NASA Astrophysics Data System (ADS)

    Vitanov, Nikolay K.; Chabchoub, Amin; Hoffmann, Norbert

    2013-06-01

    We present a brief discussion on the nonlinear Schrödinger equation for modelling the propagation of the deep-water wavetrains and a discussion on its doubly-localized breather solutions, that can be connected to the sudden formation of extreme waves, also known as rogue waves or freak waves.

  5. Interactions of localized wave structures and dynamics in the defocusing coupled nonlinear Schrödinger equations.

    PubMed

    Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong; Chen, Yong

    2017-04-01

    We investigate the defocusing coupled nonlinear Schrödinger equations from a 3×3 Lax pair. The Darboux transformations with the nonzero plane-wave solutions are presented to derive the newly localized wave solutions including dark-dark and bright-dark solitons, breather-breather solutions, and different types of new vector rogue wave solutions, as well as interactions between distinct types of localized wave solutions. Moreover, we analyze these solutions by means of parameters modulation. Finally, the perturbed wave propagations of some obtained solutions are explored by means of systematic simulations, which demonstrates that nearly stable and strongly unstable solutions. Our research results could constitute a significant contribution to explore the distinct nonlinear waves (e.g., dark solitons, breather solutions, and rogue wave solutions) dynamics of the coupled system in related fields such as nonlinear optics, plasma physics, oceanography, and Bose-Einstein condensates.

  6. Bifurcations of traveling wave solutions for an integrable equation

    SciTech Connect

    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.

  7. Oscillatory traveling wave solutions to an attractive chemotaxis system

    NASA Astrophysics Data System (ADS)

    Li, Tong; Liu, Hailiang; Wang, Lihe

    2016-12-01

    This paper investigates oscillatory traveling wave solutions to an attractive chemotaxis system. The convective part of this system changes its type when crossing a parabola in the phase space. The oscillatory nature of the traveling wave comes from the fact that one far-field state is in the elliptic region and another in the hyperbolic region. Such traveling wave solutions are shown to be linearly unstable. Detailed construction of some traveling wave solutions is presented.

  8. Different types of nonlinear localized and periodic waves in an erbium-doped fiber system

    NASA Astrophysics Data System (ADS)

    Ren, Yang; Yang, Zhan-Ying; Liu, Chong; Yang, Wen-Li

    2015-12-01

    We study nonlinear waves on a plane-wave background in an erbium-doped fiber system, which is governed by the coupled nonlinear Schrödinger and the Maxwell-Bloch equations. We find that prolific different types of nonlinear localized and periodic waves do exist in the system, including multi-peak soliton, periodic wave, antidark soliton, and W-shaped soliton (as well as the known bright soliton, breather, and rogue wave). In particular, the dynamics of these waves can be extracted from a unified exact solution, and the corresponding existence conditions are presented explicitly. Our results demonstrate the structural diversity of the nonlinear waves in this system.

  9. Traveling waves and their tails in locally resonant granular systems

    SciTech Connect

    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.

  10. Traveling waves and their tails in locally resonant granular systems

    DOE PAGES

    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

  11. Helping Ourselves: Local Solutions to Global Problems.

    ERIC Educational Resources Information Center

    Stokes, Bruce

    Solutions to global problems such as inflation, tightening energy supplies, and deteriorating environmental quality lie at the local level where the consequences are most obvious, the motivation to get involved is most direct, and the benefits of action are most immediate. Examples of problems regarding energy, the workplace, food production,…

  12. Solitary-wave interaction. [model equation solutions for long waves in dispersive media

    NASA Technical Reports Server (NTRS)

    Bona, J. L.; Pritchard, W. G.; Scott, L. R.

    1980-01-01

    The interaction of solitary-wave solutions of a model equation for long waves in dispersive media is examined numerically. It is found that the waves do not emerge from the interaction unscathed. Instead, two new solitary waves, having slightly different amplitudes from the original waves, together with a small dispersive tail are generated as a result of the interaction.

  13. Travelling wave solutions for higher-order wave equations of kdv type (iii).

    PubMed

    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.

  14. A Photonic mm-Wave Local Oscillator

    NASA Astrophysics Data System (ADS)

    Kimberk, Robert; Hunter, Todd R.; Tong, C.-Y. Edward; Blundell, Raymond

    2006-05-01

    A photonic millimeter wave local oscillator capable of producing two microwatts of radiated power at 224 GHz has been developed. The device was tested in one antenna of Smithsonian Institution's Submillimeter Array and was found to produce stable phase on multiple baselines. Graphical data is presented of correlator output phase and amplitude stability. A description of the system is given in both open and closed loop modes. A model is given which is used to predict the operational behavior. A novel method is presented to determine the safe operating point of the automated system.

  15. Black Plane Solutions and Localized Gravitational Energy

    PubMed Central

    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

  16. 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

  17. 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.

  18. Integro-differential equation of non-local wave interaction

    SciTech Connect

    Engibaryan, N B; Khachatryan, Aghavard Kh

    2007-06-30

    The integro-differential equation d{sup 2}f/dx{sup 2} + Af = {integral}{sub 0}{sup {infinity}}K(x-t)f(t)dt + g(x) with kernel K(x)={lambda}{integral}{sub a}{sup {infinity}}e{sup -|x|p}G(p)dp, a{>=}0, is considered, in which A>0, {lambda} element of 9-{infinity},{infinity}), G(p){>=}0, 2{integral}{sub a}{sup {infinity}}1/p g(p)dp=1. These equations arise, in particular, in the theory of non-local wave interaction. A factorization method of their analysis and solution is developed. Bibliography: 9 titles.

  19. 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.

  20. Bessel-Gauss pulse as an appropriate mathematical model for optically realizable localized waves.

    PubMed

    Reivelt, Kaido; Saari, Peeter

    2004-06-01

    We show that the field of the optically feasible luminal localized wave solutions of the scalar homogeneous wave equation can be modeled by means of Bessel-Gauss pulses. As the Bessel-Gauss pulses have a closed-form expression, this fact may be of great value in numerical simulations of various experimental situations.

  1. Peaked Periodic Wave Solutions to the Broer–Kaup Equation

    NASA Astrophysics Data System (ADS)

    Jiang, Bo; Bi, Qin-Sheng

    2017-01-01

    By qualitative analysis method, a sufficient condition for the existence of peaked periodic wave solutions to the Broer–Kaup equation is given. Some exact explicit expressions of peaked periodic wave solutions are also presented. Supported by National Nature Science Foundation of China under Grant No. 11102076 and Natural Science Fund for Colleges and Universities in Jiangsu Province under Grant No. 15KJB110005

  2. The Lifespan of Small Data Solutions in Two Dimensional Capillary Water Waves

    NASA Astrophysics Data System (ADS)

    Ifrim, Mihaela; Tataru, Daniel

    2017-09-01

    This article is concerned with the incompressible, irrotational infinite depth water wave equation in two space dimensions, without gravity but with surface tension. We consider this problem expressed in position-velocity potential holomorphic coordinates, and prove that small data solutions have at least cubic lifespan while small localized data leads to global solutions.

  3. Modeling Local and Regional Wave Propagation

    NASA Astrophysics Data System (ADS)

    Apoloner, Maria-Theresia; Bokelmann, Götz

    2013-04-01

    Seismograms reflect the combined effects of the source, recording instrument, ambient noise, and the propagation path. Especially for recording at distances smaller then 10° the signal is affected mainly by the crustal structure, as waves propagate in the crust and/or along Moho. Therefore appearance of regional seismograms varies strongly, which complicates record interpretation and phase identification severely. However, for earthquakes with small magnitudes, close distance records are the only ones available with a sufficient signal at all. Due to sparse seismic station coverage and the use of only the most distinct phases, typically Pg and Sg, localization can not always be ensured. Yet, retrieving accurate earthquake location, including depth information and the relation with faults is important for understanding tectonic processes and for estimating seismic hazard. Prior works by e.g. Ma (2010) show the benefit of using additional regional phases for localization, in particular depth. At local and regional distances the challenge lies in robustly detecting and identifying these phases correctly, which are usually superimposed by the coda of the P- and S-phase and sometimes even arrive simultaneously. In this work we want to shed light on the different influences on seismograms at local distances < 200 km. Starting with a simple crust-mantle model we calculate seismic recordings for sources at varying distances and depths. In addition we look at the changes induced by source mechanisms at diverse azimuths surrounding the source. Particularly the change in amplitude, time and frequency induced by the varying parameters is investigated. According to the phases identified in the diverse synthetic record sections, an overview of propagation characteristics is given. Our goal is to understand the usable information content of regional phases. Based on this information the theoretical performance of methods for identification of additional regional phases can be

  4. Localized waves in three-component coupled nonlinear Schrödinger equation

    NASA Astrophysics Data System (ADS)

    Xu, Tao; Chen, Yong

    2016-09-01

    We study the generalized Darboux transformation to the three-component coupled nonlinear Schrödinger equation. First- and second-order localized waves are obtained by this technique. In first-order localized wave, we get the interactional solutions between first-order rogue wave and one-dark, one-bright soliton respectively. Meanwhile, the interactional solutions between one-breather and first-order rogue wave are also given. In second-order localized wave, one-dark-one-bright soliton together with second-order rogue wave is presented in the first component, and two-bright soliton together with second-order rogue wave are gained respectively in the other two components. Besides, we observe second-order rogue wave together with one-breather in three components. Moreover, by increasing the absolute values of two free parameters, the nonlinear waves merge with each other distinctly. These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system. Project supported by the Global Change Research Program of China (Grant No. 2015CB953904), the National Natural Science Foundation of China (Grant Nos. 11275072 and 11435005), the Doctoral Program of Higher Education of China (Grant No. 20120076110024), the Network Information Physics Calculation of Basic Research Innovation Research Group of China (Grant No. 61321064), and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things, China (Grant No. ZF1213).

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

    USGS Publications Warehouse

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

    2017-01-01

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

  6. Phase patterns of dispersive waves from moving localized sources

    NASA Astrophysics Data System (ADS)

    Svirkunov, P. N.; Kalashnik, M. V.

    2014-01-01

    A general approach is proposed within which the phase structure of wave perturbations caused by a moving localized source can be described based on the wave dispersion law alone. Applying this approach, a simple analytical expression for the phase surfaces is obtained. It is used to study the details of phase patterns of gravity-capillary waves, the structure of wave trains in the ocean in the wake of a moving tropical hurricane, and the system of lee waves in Earth's atmosphere.

  7. Strongly nonlinear waves in locally resonant granular chains

    SciTech Connect

    Liu, Lifeng; James, Guillaume; Kevrekidis, Panayotis; Vainchtein, Anna

    2016-09-23

    In this paper, we explore a recently proposed locally resonant granular system bearing harmonic internal resonators in a chain of beads interacting via Hertzian elastic contacts. In this system, we propose the existence of two types of configurations: (a) small-amplitude periodic traveling waves and (b) dark-breather solutions, i.e. exponentially localized, time-periodic states mounted on top of a non-vanishing background. A remarkable feature distinguishing our results from other settings where dark breathers are observed is the complete absence of precompression in the system, i.e. the absence of a linear spectral band. We also identify conditions under which the system admits long-lived bright breather solutions. Our results are obtained by means of an asymptotic reduction to a suitably modified version of the so-called discrete p-Schrödinger (DpS) equation, which is established as controllably approximating the solutions of the original system for large but finite times (under suitable assumptions on the solution amplitude and the resonator mass). The findings are also corroborated by detailed numerical computations. Long-lived bright breathers are proved to exist over long but finite times, after which numerical simulations indicate that the breathers disintegrate. Finally, in line with these results, we prove that the only exact time-periodic bright breathers consist of trivial linear oscillations, without contact interactions between discrete elements.

  8. Strongly nonlinear waves in locally resonant granular chains

    DOE PAGES

    Liu, Lifeng; James, Guillaume; Kevrekidis, Panayotis; ...

    2016-09-23

    In this paper, we explore a recently proposed locally resonant granular system bearing harmonic internal resonators in a chain of beads interacting via Hertzian elastic contacts. In this system, we propose the existence of two types of configurations: (a) small-amplitude periodic traveling waves and (b) dark-breather solutions, i.e. exponentially localized, time-periodic states mounted on top of a non-vanishing background. A remarkable feature distinguishing our results from other settings where dark breathers are observed is the complete absence of precompression in the system, i.e. the absence of a linear spectral band. We also identify conditions under which the system admits long-livedmore » bright breather solutions. Our results are obtained by means of an asymptotic reduction to a suitably modified version of the so-called discrete p-Schrödinger (DpS) equation, which is established as controllably approximating the solutions of the original system for large but finite times (under suitable assumptions on the solution amplitude and the resonator mass). The findings are also corroborated by detailed numerical computations. Long-lived bright breathers are proved to exist over long but finite times, after which numerical simulations indicate that the breathers disintegrate. Finally, in line with these results, we prove that the only exact time-periodic bright breathers consist of trivial linear oscillations, without contact interactions between discrete elements.« less

  9. Strongly nonlinear waves in locally resonant granular chains

    NASA Astrophysics Data System (ADS)

    Liu, Lifeng; James, Guillaume; Kevrekidis, Panayotis; Vainchtein, Anna

    2016-11-01

    We explore a recently proposed locally resonant granular system bearing harmonic internal resonators in a chain of beads interacting via Hertzian elastic contacts. In this system, we propose the existence of two types of configurations: (a) small-amplitude periodic traveling waves and (b) dark-breather solutions, i.e. exponentially localized, time-periodic states mounted on top of a non-vanishing background. A remarkable feature distinguishing our results from other settings where dark breathers are observed is the complete absence of precompression in the system, i.e. the absence of a linear spectral band. We also identify conditions under which the system admits long-lived bright breather solutions. Our results are obtained by means of an asymptotic reduction to a suitably modified version of the so-called discrete p-Schrödinger (DpS) equation, which is established as controllably approximating the solutions of the original system for large but finite times (under suitable assumptions on the solution amplitude and the resonator mass). The findings are also corroborated by detailed numerical computations. Long-lived bright breathers are proved to exist over long but finite times, after which numerical simulations indicate that the breathers disintegrate. In line with these results, we prove that the only exact time-periodic bright breathers consist of trivial linear oscillations, without contact interactions between discrete elements.

  10. Unsteady evolution of localized unidirectional deep-water wave groups.

    PubMed

    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.

  11. Localization of Waves without Bistability: Worms in Nematic Electroconvection

    SciTech Connect

    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}

  12. 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.

  13. Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation

    NASA Astrophysics Data System (ADS)

    Bertola, Marco; El, Gennady A.; Tovbis, Alexander

    2016-10-01

    Rogue waves appearing on deep water or in optical fibres are often modelled by certain breather solutions of the focusing nonlinear Schrödinger (fNLS) equation which are referred to as solitons on finite background (SFBs). A more general modelling of rogue waves can be achieved via the consideration of multiphase, or finite-band, fNLS solutions of whom the standard SFBs and the structures forming due to their collisions represent particular, degenerate, cases. A generalized rogue wave notion then naturally enters as a large-amplitude localized coherent structure occurring within a finite-band fNLS solution. In this paper, we use the winding of real tori to show the mechanism of the appearance of such generalized rogue waves and derive an analytical criterion distinguishing finite-band potentials of the fNLS equation that exhibit generalized rogue waves.

  14. Stability of traveling wave solutions to the Whitham equation

    NASA Astrophysics Data System (ADS)

    Sanford, Nathan; Kodama, Keri; Carter, John D.; Kalisch, Henrik

    2014-06-01

    The Whitham equation was proposed as an alternate model equation for the simplified description of unidirectional wave motion at the surface of an inviscid fluid. An advantage of the Whitham equation over the KdV equation is that it provides a more faithful description of short waves of small amplitude. Recently, Ehrnström and Kalisch [19] established that the Whitham equation admits periodic traveling-wave solutions. The focus of this work is the stability of these solutions. The numerical results presented here suggest that all large-amplitude solutions are unstable, while small-amplitude solutions with large enough wavelength L are stable. Additionally, periodic solutions with wavelength smaller than a certain cut-off period always exhibit modulational instability. The cut-off wavelength is characterized by kh0=1.145, where k=2π/L is the wave number and h0 is the mean fluid depth.

  15. Nonlinear traveling wave solution for the MJO skeleton model

    NASA Astrophysics Data System (ADS)

    Chen, S.; Stechmann, S. N.

    2014-12-01

    Recently, a minimal dynamical model is presented for capturing MJO's fundamental features. The model is a nonlinear oscillator model for the MJO skeleton and it involves interactions between convection, moisture and circulation. I will present the exact nonlinear traveling wave solutions for the model based on its energy conservation. The exact nonlinear solution provides for an explicit comparison of features between linear and nonlinear waves such as dispersion relations and traveling wave speeds. Moreover, the nonlinear solutions, compared with the linear ones, produce a narrow region of active convection and a wider region of suppressed convection. These predictions offer nonlinear MJO features that could potentially be targets of observational investigations.

  16. A stationary phase solution for mountain waves with application to mesospheric mountain waves generated by Auckland Island

    NASA Astrophysics Data System (ADS)

    Broutman, Dave; Eckermann, Stephen D.; Knight, Harold; Ma, Jun

    2017-01-01

    A relatively general stationary phase solution is derived for mountain waves from localized topography. It applies to hydrostatic, nonhydrostatic, or anelastic dispersion relations, to arbitrary localized topography, and to arbitrary smooth vertically varying background temperature and vector wind profiles. A simple method is introduced to compute the ray Jacobian that quantifies the effects of horizontal geometrical spreading in the stationary phase solution. The stationary phase solution is applied to mesospheric mountain waves generated by Auckland Island during the Deep Propagating Gravity Wave Experiment. The results are compared to a Fourier solution. The emphasis is on interpretations involving horizontal geometrical spreading. The results show larger horizontal geometrical spreading for nonhydrostatic waves than for hydrostatic waves in the region directly above the island; the dominant effect of horizontal geometrical spreading in the lower ˜30 km of the atmosphere, compared to the effects of refraction and background density variation; and the enhanced geometrical spreading due to directional wind in the approach to a critical layer in the mesosphere.

  17. Finite difference solutions to shocked acoustic waves

    NASA Technical Reports Server (NTRS)

    Walkington, N. J.; Eversman, W.

    1983-01-01

    The MacCormack, Lambda and split flux finite differencing schemes are used to solve a one dimensional acoustics problem. Two duct configurations were considered, a uniform duct and a converging-diverging nozzle. Asymptotic solutions for these two ducts are compared with the numerical solutions. When the acoustic amplitude and frequency are sufficiently high the acoustic signal shocks. This condition leads to a deterioration of the numerical solutions since viscous terms may be required if the shock is to be resolved. A continuous uniform duct solution is considered to demonstrate how the viscous terms modify the solution. These results are then compared with a shocked solution with and without viscous terms. Generally it is found that the most accurate solutions are those obtained using the minimum possible viscosity coefficients. All of the schemes considered give results accurate enough for acoustic power calculations with no one scheme performing significantly better than the others.

  18. Exact and explicit solitary wave solutions to some nonlinear equations

    SciTech Connect

    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.

  19. Exact Interaction Solutions of an Extended (2+1)-Dimensional Shallow Water Wave Equation

    NASA Astrophysics Data System (ADS)

    Wang, Yun-Hu; Wang, Hui; Zhang, Hong-Sheng; Chaolu, TEMUER

    2017-08-01

    Applying the consistent Riccati expansion method, the extended (2+1)-dimensional shallow water wave equation is proved consistent Riccati solvable and the exact interaction solutions including soliton-cnoidal wave solutions, solitoff-typed solutions are obtained. With the help of the truncated Painlevé expansion, the corresponding nonlocal symmetry is also given, and furthermore, the nonlocal symmetry is localized by prolonging the related enlarged system. Supported by the National Natural Science Foundation of China under Grant Nos. 11405103, 11571008, 51679132, 11601321, and 11526137

  20. Theoretical and experimental evidence of non-symmetric doubly localized rogue waves.

    PubMed

    He, Jingsong; Guo, Lijuan; Zhang, Yongshuai; Chabchoub, Amin

    2014-11-08

    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.

  1. Theoretical and experimental evidence of non-symmetric doubly localized rogue waves

    PubMed Central

    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

  2. Sensitivity enhancement of traveling wave MRI using free local resonators: an experimental demonstration.

    PubMed

    Zhang, Xiaoliang

    2017-04-01

    Traveling wave MR uses the far fields in signal excitation and reception, therefore its acquisition efficiency is low in contrast to the conventional near field magnetic resonance (MR). Here we show a simple and efficient method based on the local resonator to improving sensitivity of traveling wave MR technique. The proposed method utilizes a standalone or free local resonator to amplify the radio frequency magnetic fields in the interested target. The resonators have no wire connections to the MR system and thus can be conveniently placed to any place around imaging simples. A rectangular loop L/C resonator to be used as the free local resonator was tuned to the proton Larmor frequency at 7T. Traveling wave MR experiments with and without the wireless free local resonator were performed on a living rat using a 7T whole body MR scanner. The signal-to-noise ratio (SNR) or sensitivity of the images acquired was compared and evaluated. In vivo 7T imaging results show that traveling wave MR with a wireless free local resonator placed near the head of a living rat achieves at least 10-fold SNR gain over the images acquired on the same rat using conventional traveling wave MR method, i.e. imaging with no free local resonators. The proposed free local resonator technique is able to enhance the MR sensitivity and acquisition efficiency of traveling wave MR at ultrahigh fields in vivo. This method can be a simple solution to alleviating low sensitivity problem of traveling wave MRI.

  3. Elastic parabolic equation solutions for oceanic T-wave generation and propagation from deep seismic sources.

    PubMed

    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.

  4. Travelling-wave solution in the Rapoport-Leas model

    NASA Astrophysics Data System (ADS)

    Tychkov, Sergey

    2017-02-01

    Rapoport-Leas model of motion of a two-phase flow on a plane is considered. Travelling-wave solutions for these equations are found. Wavefronts of these solutions may be circles, lines and parabolae. Ordinary differential equations for pressure and saturation on the wavefronts are established.

  5. Local effects of gravity wave propagation and saturation

    NASA Technical Reports Server (NTRS)

    Fritts, D. C.

    1985-01-01

    In recent years, gravity waves were recognized to play a major role in the dynamics of the middle atmosphere. Perhaps the major effect of such motions are the reversal of the vertical shear of the mean zonal wind and the occurrence of a large turbulent diffusivity in the mesosphere due to gravity wave saturation. Yet, despite the importance of these gravity wave effects, the processes and the consequences of gravity wave propagation and saturation are only beginning to be understood in detail. The linear saturation theory predicts drag and turbulent diffusion due to saturating wave motion. This theory, however, fails to address a number of issues that are certain to be important for gravity wave propagation and saturation in the middle atmosphere. These issues, including wave transience, wave superposition, local convective adjustment, and nonlinearity, are discussed.

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

    SciTech Connect

    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.

  7. A doubly-localized solution of plane Couette flow

    NASA Astrophysics Data System (ADS)

    Brand, Evan; Gibson, John

    2013-11-01

    We present a new equilibrium solution of plane Couette flow localized in two spatially extended directions. The solution is derived from the EQ7/HVS solution of plane Couette flow discovered independently by Itano and Generalis (PRL 2009) and Gibson et al. (JFM 2009), of which a spanwise localized version has also recently been produced (Gibson, these proceedings). The doubly localized solution displays relatively long length scales in comparison with the spatially periodic and spanwise localized solutions, suggesting the importance of these scales in capturing the spatial complexity of transitional and low-Reynolds number turbulence. The solution is comparable in size and appearance to the doubly-localized, chaotically evolving edge states previously computed in this flow by Duguet et al. (PoF 2009) and Schneider et al. (JFM 2010). Additionally, we address the structure of localized solutions in the ``tails,'' i.e. in the region approaching laminar.

  8. AdS waves as exact solutions to quadratic gravity

    SciTech Connect

    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.

  9. Heuristic approximations for sound fields produced by spherical waves incident on locally and non-locally reacting planar surfaces.

    PubMed

    Li, Kai Ming; Tao, Hongdan

    2014-01-01

    The classic Weyl-van der Pol (WVDP) formula is a well-known asymptotic solution for accurately predicting sound fields above a locally reacting ground surface. However, the form of the WVDP formula is inadequate for predicting sound fields in the vicinity of non-locally reacting surfaces; a correction term is often required in the formula to provide accurate numerical solutions. Even with this correction, there is a singularity in the diffraction wave term when the source is located directly above or below the receiver. This paper explores a heuristic method to remove this singularity and suggests an analytical form comparable to the WVDP formula. This improved formula offers a physically interpretable solution and allows for accurate predictions of the total sound field above locally and non-locally reacting surfaces for all geometrical configurations.

  10. Exact traveling wave solutions and L1 stability for the shallow water wave model of moderate amplitude

    NASA Astrophysics Data System (ADS)

    Wang, Ying; Guo, Yunxi

    2017-09-01

    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.

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

    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.

  12. POSSIBLE EXPERIMENTS ON WAVE FUNCTION LOCALIZATION DUE TO COMPTON SCATTERING

    SciTech Connect

    Aleksandrov, Alexander V; Danilov, Viatcheslav V; Gorlov, Timofey V; Liu, Yun; Shishlo, Andrei P; Nagaitsev,

    2013-01-01

    The reduction of a particle s wave function in the process of radiation or light scattering is a longstanding problem. Its solution will give a clue on processes that form, for example, wave functions of electrons constantly emitting synchrotron radiation quanta in storage rings. On a more global scale, it may shed light on wave function collapse due to the process of measurement. In this paper we consider various experimental options using Fermilab electron beams and a possible electron beam from the SNS linac and lasers to detect electron wave function change due to Compton scattering.

  13. 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.

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

    SciTech Connect

    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.

  15. Acoustic-wave localization in the presence of shear resonances

    NASA Astrophysics Data System (ADS)

    Graham, Ian S.; Piché, Luc; Levesque, Daniel; Grant, Martin

    1991-05-01

    We study, via both experiment and theory, localization of longitudinal-acoustic waves scattered from sites supporting transverse (shear) modes. The experimental system consists of a polymer melt solidifying by the growth of spherical semicrystalline nuclei. We excite this system with acoustic plane waves and measure the transmitted signal. For sufficiently high excitation frequencies we find renormalization of the sound speed and intense absorption peaks over a very narrow range of wave number. These data can be consistently interpreted as signs of localization within the sample. Standard theory, however does not predict localization in this system, since the longitudinal velocity in the scatterers is faster than that in the liquid. However, the solid scatterers support shear modes, which can significantly modify their scattering characteristics. We extend the theory of localization to allow for scatterers supporting shear. This model predicts shear-induced localization in the system we have studied.

  16. Realization of localized Bohr-like wave packets.

    PubMed

    Mestayer, J J; Wyker, B; Lancaster, J C; Dunning, F B; Reinhold, C O; Yoshida, S; Burgdörfer, J

    2008-06-20

    We demonstrate a protocol to create localized wave packets in very-high-n Rydberg states which travel in nearly circular orbits around the nucleus. Although these wave packets slowly dephase and eventually lose their localization, their motion can be monitored over several orbital periods. These wave packets represent the closest analog yet achieved to the original Bohr model of the hydrogen atom, i.e., an electron in a circular classical orbit around the nucleus. The possible extension of the approach to create "planetary atoms" in highly correlated stable multiply excited states is discussed.

  17. New Analytical Solution for Nonlinear Shallow Water-Wave Equations

    NASA Astrophysics Data System (ADS)

    Aydin, Baran; Kânoğlu, Utku

    2017-03-01

    We solve the nonlinear shallow water-wave equations over a linearly sloping beach as an initial-boundary value problem under general initial conditions, i.e., an initial wave profile with and without initial velocity. The methodology presented here is extremely simple and allows a solution in terms of eigenfunction expansion, avoiding integral transform techniques, which sometimes result in singular integrals. We estimate parameters, such as the temporal variations of the shoreline position and the depth-averaged velocity, compare with existing solutions, and observe perfect agreement with substantially less computational effort.

  18. New Analytical Solution for Nonlinear Shallow Water-Wave Equations

    NASA Astrophysics Data System (ADS)

    Aydin, Baran; Kânoğlu, Utku

    2017-08-01

    We solve the nonlinear shallow water-wave equations over a linearly sloping beach as an initial-boundary value problem under general initial conditions, i.e., an initial wave profile with and without initial velocity. The methodology presented here is extremely simple and allows a solution in terms of eigenfunction expansion, avoiding integral transform techniques, which sometimes result in singular integrals. We estimate parameters, such as the temporal variations of the shoreline position and the depth-averaged velocity, compare with existing solutions, and observe perfect agreement with substantially less computational effort.

  19. Local bifurcation of electrohydrodynamic waves on a conducting fluid

    NASA Astrophysics Data System (ADS)

    Lin, Zhi; Zhu, Yi; Wang, Zhan

    2017-03-01

    We are concerned with progressive waves propagating on a two-dimensional conducting fluid when a uniform electric field is applied in the direction perpendicular to the undisturbed free surface. The competing effects of gravity, surface tension, and electrically induced forces are investigated using both analytical and numerical techniques for an inviscid and incompressible fluid flowing irrotationally. We simplify the full Euler equations by expanding and truncating the Dirichlet-Neumann operators in the Hamiltonian formulation of the problem. The numerical results show that when the electric parameter is in a certain range, the bifurcation structure near the minimum of the phase speed is rich with Stokes, solitary, generalized solitary, and dark solitary waves. In addition to symmetric solutions, asymmetric solitary waves featuring a multi-packet structure are found to occur along a branch of asymmetric generalized solitary waves that itself bifurcates from Stokes waves of finite amplitude. The detailed bifurcation diagrams, together with typical wave profiles, are presented.

  20. Exact Solutions for a Local Fractional DDE Associated with a Nonlinear Transmission Line

    NASA Astrophysics Data System (ADS)

    Aslan, İsmail

    2016-09-01

    Of recent increasing interest in the area of fractional calculus and nonlinear dynamics are fractional differential-difference equations. This study is devoted to a local fractional differential-difference equation which is related to a nonlinear electrical transmission line. Explicit traveling wave solutions (kink/antikink solitons, singular, periodic, rational) are obtained via the discrete tanh method coupled with the fractional complex transform.

  1. Sound waves and modulational instabilities on continuous-wave solutions in spinor Bose-Einstein condensates

    NASA Astrophysics Data System (ADS)

    Tasgal, Richard S.; Band, Y. B.

    2015-01-01

    We analyze sound waves (phonons, i.e. Bogoliubov excitations) propagating on continuous-wave (cw) solutions of repulsive F =1 spinor Bose-Einstein condensates (BECs) such as 23Na (which is antiferromagnetic or polar) and 87Rb (which is ferromagnetic). Zeeman splitting by a uniform magnetic field is included. All cw solutions to ferromagnetic BECs with vanishing MF=0 particle density and nonzero components in both MF=±1 fields are subject to modulational instability (MI). Modulational instability increases with increasing particle density. Modulational instability also increases with differences in the components' wave numbers; this effect is larger at lower densities but becomes insignificant at higher particle densities. Continuous-wave solutions to antiferromagnetic (polar) BECs with vanishing MF=0 particle density and nonzero components in both MF=±1 fields do not suffer MI if the wave numbers of the components are the same. If there is a wave-number difference, MI initially increases with increasing particle density and then peaks before dropping to zero beyond a given particle density. The cw solutions with particles in both MF=±1 components and nonvanishing MF=0 components do not have MI if the wave numbers of the components are the same, but do exhibit MI when the wave numbers are different. Direct numerical simulations of a continuous wave with weak white noise confirm that weak noise grows fastest at wave numbers with the largest MI and show some of the results beyond small-amplitude perturbations. Phonon dispersion curves are computed numerically; we find analytic solutions for the phonon dispersion in a variety of limiting cases.

  2. Gauge invariant gluon spin operator for spinless nonlinear wave solutions

    NASA Astrophysics Data System (ADS)

    Lee, Bum-Hoon; Kim, Youngman; Pak, D. G.; Tsukioka, Takuya; Zhang, P. M.

    2017-04-01

    We consider nonlinear wave type solutions with intrinsic mass scale parameter and zero spin in a pure SU(2) quantum chromodynamics (QCD). A new stationary solution which can be treated as a system of static Wu-Yang monopole dressed in off-diagonal gluon field is proposed. A remarkable feature of such a solution is that it possesses a finite energy density everywhere. All considered nonlinear wave type solutions have common features: presence of the mass scale parameter, nonvanishing projection of the color fields along the propagation direction and zero spin. The last property requires revision of the gauge invariant definition of the spin density operator which is supposed to produce spin one states for the massless vector gluon field. We construct a gauge invariant definition of the classical gluon spin density operator which is unique and Lorentz frame independent.

  3. Breathers and localized solutions of complex modified Korteweg-de Vries equation

    NASA Astrophysics Data System (ADS)

    Liu, Yue-Feng; Guo, Rui; Li, Hua

    2015-07-01

    Under investigation is the complex modified Korteweg-de Vries (KdV) equation, which has many physical significance in fluid mechanics, plasma physics and so on. Via the Darboux transformation (DT) method, some breather and localized solutions are presented on two backgrounds: the continuous wave background u1 = kexp[i(Ax + Bt)] and the constant background u2 = a + ib. Some figures are plotted to illustrate the dynamical features of those solutions.

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

    PubMed

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

    2012-06-01

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

  5. 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.

  6. Resonance localization in tokamaks excited with ICRF waves

    NASA Astrophysics Data System (ADS)

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

    1985-06-01

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

  7. 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.

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

    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.

  9. Conservation laws, modulation instability and rogue waves for the localized magnetization with spin torque

    NASA Astrophysics Data System (ADS)

    Su, Chuan-Qi; Wang, Yong-Yan; Liu, Xue-Qing; Qin, Nan

    2017-07-01

    Under investigation in this paper is an integrable equation which can describe the localized magnetization with spin torque under the long-wavelength approximation. In order to obtain the rogue wave solutions, a new Lax pair is derived. Infinitely-many conservation laws are also constructed. Based on the generalized Darboux transformation, the first-, second- and third-order rogue wave solutions are derived. Property of the rogue waves are analyzed and influence of parameters α, β and separating function f(ɛ) on the rogue waves and spatial-temporal structures are also discussed (the meaning of α and β can be found in the paper). For the case of f(ɛ) = 0 , the modulus of the kth-order rogue wave (k = 1 , 2 , 3) is irrelevant to parameter α. Parameter β influences the spatial-temporal range where the rogue wave appears. Spatial-temporal range enlarges with the increase of β. In addition, β also produces a skew angle and the skew angle rotates in the counter clockwise direction with the increase of β. f(ɛ) influences the spatial-temporal structures of the second- and third-order rouge waves. If f(ɛ) ≠ 0, the second-order rogue wave will split into three single first-order rouge waves and the triangular pattern can be formed, while the third-order rogue wave will split into six ones and the triangular pattern and pentagon pattern can be formed. The linear stability analysis is carried out, which shows that the modulation instability process is influenced by the amplitude of the harmonic wave and the wave number.

  10. Optimized Equivalent Staggered-grid FD Method for Elastic Wave Modeling Based on Plane Wave Solutions

    NASA Astrophysics Data System (ADS)

    Yong, Peng; Huang, Jianping; Li, Zhenchun; Liao, Wenyuan; Qu, Luping; Li, Qingyang; Liu, Peijun

    2016-12-01

    In finite difference (FD) method, numerical dispersion is the dominant factor influencing the accuracy of seismic modeling. Various optimized FD schemes for scalar wave modeling have been proposed to reduce grid dispersion, while the optimized time-space domain FD schemes for elastic wave modeling have not been fully investigated yet. In this paper, an optimized FD scheme with Equivalent Staggered Grid (ESG) for elastic modelling has been developed. We start from the constant P- and S-wave speed elastic wave equations and then deduce analytical plane wave solutions in the wavenumber domain with eigenvalue decomposition method. Based on the elastic plane wave solutions, three new time-space domain dispersion relations of ESG elastic modeling are obtained, which are represented by three equations corresponding to P-, S- and converted wave terms in the elastic equations, respectively. By using these new relations, we can study the dispersion errors of different spatial FD terms independently. The dispersion analysis showed that different spatial FD terms have different errors. It is therefore suggested that different FD coefficients to be used to approximate the three spatial derivative terms. In addition, the relative dispersion error in L2-norm is minimized through optimizing FD coefficients using Newton's method. Synthetic examples have demonstrated that this new optimal FD schemes have superior accuracy for elastic wave modeling compared to Taylor-series expansion and optimized space domain FD schemes.

  11. Optimized equivalent staggered-grid FD method for elastic wave modelling based on plane wave solutions

    NASA Astrophysics Data System (ADS)

    Yong, Peng; Huang, Jianping; Li, Zhenchun; Liao, Wenyuan; Qu, Luping; Li, Qingyang; Liu, Peijun

    2017-02-01

    In finite-difference (FD) method, numerical dispersion is the dominant factor influencing the accuracy of seismic modelling. Various optimized FD schemes for scalar wave modelling have been proposed to reduce grid dispersion, while the optimized time-space domain FD schemes for elastic wave modelling have not been fully investigated yet. In this paper, an optimized FD scheme with Equivalent Staggered Grid (ESG) for elastic modelling has been developed. We start from the constant P- and S-wave speed elastic wave equations and then deduce analytical plane wave solutions in the wavenumber domain with eigenvalue decomposition method. Based on the elastic plane wave solutions, three new time-space domain dispersion relations of ESG elastic modelling are obtained, which are represented by three equations corresponding to P-, S- and converted-wave terms in the elastic equations, respectively. By using these new relations, we can study the dispersion errors of different spatial FD terms independently. The dispersion analysis showed that different spatial FD terms have different errors. It is therefore suggested that different FD coefficients to be used to approximate the three spatial derivative terms. In addition, the relative dispersion error in L2-norm is minimized through optimizing FD coefficients using Newton's method. Synthetic examples have demonstrated that this new optimal FD schemes have superior accuracy for elastic wave modelling compared to Taylor-series expansion and optimized space domain FD schemes.

  12. Localized finite-amplitude disturbances and selection of solitary waves

    PubMed

    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.

  13. Weak localization with nonlinear bosonic matter waves

    SciTech Connect

    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.

  14. Collision broadened resonance localization in tokamaks excited with ICRF waves

    NASA Astrophysics Data System (ADS)

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

    1985-08-01

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

  15. Symmetry and decay of traveling wave solutions to the Whitham equation

    NASA Astrophysics Data System (ADS)

    Bruell, Gabriele; Ehrnström, Mats; Pei, Long

    2017-04-01

    This paper is concerned with decay and symmetry properties of solitary-wave solutions to a nonlocal shallow-water wave model. An exponential decay result for supercritical solitary-wave solutions is given. Moreover, it is shown that all such solitary-wave solutions are symmetric and monotone on either side of the crest. The proof is based on the method of moving planes. Furthermore, a close relation between symmetric and traveling-wave solutions is established.

  16. Localized SXR Emission During Electron Bernstein Wave Injection in MST

    NASA Astrophysics Data System (ADS)

    Anderson, Jay; Forest, Cary; Seltzman, Andrew

    2008-11-01

    The electron Bernstein wave has been suggested as a solution to the RFP confinement problem: sustained, off-axis current drive stabilizes the resistive tearing modes which govern thermal transport. A staged experiment to test the feasibility of EBW heating and current drive is underway on MST. Experiments (˜10^5 W) aimed at a demonstration of EBW heating have produced a localized increase in SXR emission. This measured emission is consistent with modeling in its location, energy spectrum and dependence on radial diffusion within the plasma. Preliminary analysis indicates that the emission is strongest in the region where ray tracing predicts maximum deposition of the injected power. The multi-chord SXR camera used is sensitive to 4-7 keV photons which is consistent with Fokker-Plank modeling of EBW injection. The enhanced SXR emission vanishes quickly when radial diffusion in the plasma is high (as indicated by m=0 magnetic activity); this is also consistent with Fokker-Plank modeling. An increase of boron emission (and presumably boron within the plasma) is also observed during EBW injection. This presents an alternative explanation to the enhanced SXR emission; recent efforts have been made to isolate the two effects.

  17. Matter-wave localization in a weakly perturbed optical lattice

    SciTech Connect

    Cheng, Yongshan; Adhikari, S. K.

    2011-11-15

    By numerical solution and variational approximation of the Gross-Pitaevskii equation, we studied the localization of a noninteracting and weakly interacting Bose-Einstein condensate in a weakly perturbed optical lattice in one and three dimensions. The perturbation achieved through a weak delocalizing expulsive or a linear potential as well as a weak localizing harmonic potential removes the periodicity of the optical lattice and leads to localization. We also studied some dynamics of the localized state confirming its stability.

  18. Localization of a matter wave packet in a disordered potential

    SciTech Connect

    Piraud, M.; Bouyer, P.; Aspect, A.; Sanchez-Palencia, L.; Lugan, P.

    2011-03-15

    We theoretically study the Anderson localization of a matter wave packet in a one-dimensional disordered potential. We develop an analytical model which includes the initial phase-space density of the matter wave and the spectral broadening induced by the disorder. Our approach predicts a behavior of the localized density profile significantly more complex than a simple exponential decay. These results are confirmed by large-scale and long-time numerical calculations. They shed new light on recent experiments with ultracold atoms and may impact their analysis.

  19. 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.

  20. Guided Wave Based Crack Detection in the Rivet Hole Using Global Analytical with Local FEM Approach.

    PubMed

    Bhuiyan, Md Yeasin; Shen, Yanfeng; Giurgiutiu, Victor

    2016-07-21

    In this article, ultrasonic guided wave propagation and interaction with the rivet hole cracks has been formulated using closed-form analytical solution while the local damage interaction, scattering, and mode conversion have been obtained from finite element analysis. The rivet hole cracks (damage) in the plate structure gives rise to the non-axisymmetric scattering of Lamb wave, as well as shear horizontal (SH) wave, although the incident Lamb wave source (primary source) is axisymmetric. The damage in the plate acts as a non-axisymmetric secondary source of Lamb wave and SH wave. The scattering of Lamb and SH waves are captured using wave damage interaction coefficient (WDIC). The scatter cubes of complex-valued WDIC are formed that can describe the 3D interaction (frequency, incident direction, and azimuth direction) of Lamb waves with the damage. The scatter cubes are fed into the exact analytical framework to produce the time domain signal. This analysis enables us to obtain the optimum design parameters for better detection of the cracks in a multiple-rivet-hole problem. The optimum parameters provide the guideline of the design of the sensor installation to obtain the most noticeable signals that represent the presence of cracks in the rivet hole.

  1. Guided Wave Based Crack Detection in the Rivet Hole Using Global Analytical with Local FEM Approach

    PubMed Central

    Bhuiyan, Md Yeasin; Shen, Yanfeng; Giurgiutiu, Victor

    2016-01-01

    In this article, ultrasonic guided wave propagation and interaction with the rivet hole cracks has been formulated using closed-form analytical solution while the local damage interaction, scattering, and mode conversion have been obtained from finite element analysis. The rivet hole cracks (damage) in the plate structure gives rise to the non-axisymmetric scattering of Lamb wave, as well as shear horizontal (SH) wave, although the incident Lamb wave source (primary source) is axisymmetric. The damage in the plate acts as a non-axisymmetric secondary source of Lamb wave and SH wave. The scattering of Lamb and SH waves are captured using wave damage interaction coefficient (WDIC). The scatter cubes of complex-valued WDIC are formed that can describe the 3D interaction (frequency, incident direction, and azimuth direction) of Lamb waves with the damage. The scatter cubes are fed into the exact analytical framework to produce the time domain signal. This analysis enables us to obtain the optimum design parameters for better detection of the cracks in a multiple-rivet-hole problem. The optimum parameters provide the guideline of the design of the sensor installation to obtain the most noticeable signals that represent the presence of cracks in the rivet hole. PMID:28773724

  2. Accelerating Airy–Gauss–Kummer localized wave packets

    SciTech Connect

    Zhong, Wei-Ping; Belić, Milivoj; Zhang, Yiqi; Huang, Tingwen

    2014-01-15

    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. -- Highlights: •A general solution of 3D linear Schrödinger equation with an Airy time-dependence is reported. •We find that the Airy–Kummer spatiotemporal wave packets can carry infinite energy. •A class of the accelerating spatiotemporal optical pulses with special structures was found. •The spatiotemporal wave packets retain their energy features over several Rayleigh lengths.

  3. 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.

  4. Exact traveling wave solutions for system of nonlinear evolution equations.

    PubMed

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

    2016-01-01

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

  5. Rogue waves and unbounded solutions of the NLSE

    NASA Astrophysics Data System (ADS)

    Lechuga, Antonio

    2017-04-01

    Since the pioneering work of Zakharov has been generally admitted that rogue waves can be studied in the framework of the Nonlinear Schrödinger Equation (NLSE). Many researchers, Akhmediev, Peregrine, Matveev among others gave different solutions to this equation that, in some way, could be linked to rogue waves and also to its more important characteristic: its unexpectedness. Janssen (2003, 2004), Onorato (2004, 2006) and Waseda (2006) linked the coefficient of the nonlinear term of the Schrödinger equation with the Benjamin-Feir index (BFI) that, we know, is a measure of the modulational instability of the waves. From this point of view the value of this coefficient of the NLSE could be known from statistics. Thus the relationship between sea states and the mechanism of generation of rogue waves could be found out. Following the well-known Lie group theory researchers have been studying the Lie point symmetries of the NLSE: the scaling transformations, Galilean transformations and phase transformations. Basically these transformations turn the NLSE into a nonlinear ordinary differential equation called Duffing equation (also called eikonal equation). There are different ways to do this, but in most of them the independent variable that could be seen as a space variable is a kind of moving frame with the time incorporated in this way. The main aim of this work is to classify solutions of the Duffing equation (periodic and nonperiodic waves and also bounded and unbounded waves) bearing in mind that the coefficient of the nonlinear term in the NLSE is left unaltered in the process of the transformation.

  6. Plane wave solution for elastic wave scattering by a heterogeneous fracture

    NASA Astrophysics Data System (ADS)

    Nakagawa, Seiji; Nihei, Kurt T.; Myer, Larry R.

    2004-06-01

    A plane-wave method for computing the three-dimensional scattering of propagating elastic waves by a planar fracture with heterogeneous fracture compliance distribution is presented. This method is based upon the spatial Fourier transform of the seismic displacement-discontinuity (SDD) boundary conditions (also called linear slip interface conditions), and therefore, called the wave-number-domain SDD method (wd-SDD method). The resulting boundary conditions explicitly show the coupling between plane waves with an incident wave number component (specular component) and scattered waves which do not follow Snell's law (nonspecular components) if the fracture is viewed as a planar boundary. For a spatially periodic fracture compliance distribution, these boundary conditions can be cast into a linear system of equations that can be solved for the amplitudes of individual wave modes and wave numbers. We demonstrate the developed technique for a simulated fracture with a stochastic (correlated) surface compliance distribution. Low- and high-frequency solutions of the method are also compared to the predictions by low-order Born series in the weak and strong scattering limit.

  7. Transition between free-space Helmholtz equation solutions with plane sources and parabolic wave equation solutions.

    PubMed

    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.

  8. Discontinuous Galerkin Methods and Local Time Stepping for Wave Propagation

    SciTech Connect

    Grote, M. J.; Mitkova, T.

    2010-09-30

    Locally refined meshes impose severe stability constraints on explicit time-stepping methods for the numerical simulation of time dependent wave phenomena. To overcome that stability restriction, local time-stepping methods are developed, which allow arbitrarily small time steps precisely where small elements in the mesh are located. When combined with a discontinuous Galerkin finite element discretization in space, which inherently leads to a diagonal mass matrix, the resulting numerical schemes are fully explicit. Starting from the classical Adams-Bashforth multi-step methods, local time stepping schemes of arbitrarily high accuracy are derived. Numerical experiments validate the theory and illustrate the usefulness of the proposed time integration schemes.

  9. Shock waves as generalized solutions of thermoelastodynamics equations. On the uniqueness of boundary value problems solutions

    NASA Astrophysics Data System (ADS)

    Alipova, B. N.; Alexeyeva, L. A.; Dadayeva, A. N.

    2017-01-01

    Generalized solutions of coupled thermoelastodynamics equations are considered. By use of generalized functions theory, the conditions on jumps of stresses, velocities, temperature gradients and energy density on their fronts are received. The statements of four non-stationary boundary value problems of coupled thermoelasticity are given, for which uniqueness of decisions are proved by influence of shock thermoelastic waves.

  10. New Traveling Wave Solutions for a Class of Nonlinear Evolution Equations

    NASA Astrophysics Data System (ADS)

    Bai, Cheng-Jie; Zhao, Hong; Xu, Heng-Ying; Zhang, Xia

    The deformation mapping method is extended to solve a class of nonlinear evolution equations (NLEEs). Many types of explicit and exact traveling wave solutions, which contain solitary wave solutions, trigonometric function solutions, and Jacobian elliptic function solutions, are obtained by a simple algebraic transformation relation between the solutions of the NLEEs and those of the cubic nonlinear Klein-Gordon (NKG) equation.

  11. Ultrasonic wave-based defect localization using probabilistic modeling

    NASA Astrophysics Data System (ADS)

    Todd, M. D.; Flynn, E. B.; Wilcox, P. D.; Drinkwater, B. W.; Croxford, A. J.; Kessler, S.

    2012-05-01

    This work presents a new approach rooted in maximum likelihood estimation for defect localization in sparse array guided wave ultrasonic interrogation applications. The approach constructs a minimally-informed statistical model of the guided wave process, where unknown or uncertain model parameters are assigned non-informative Bayesian prior distributions and integrated out of the a posteriori probability calculation. The premise of this localization approach is straightforward: the most likely defect location is the point on the structure with the maximum a posteriori probability of actually being the location of damage (i.e., the most probable location given a set of sensor measurements). The proposed approach is tested on a complex stiffened panel against other common localization approaches and found to have superior performance in all cases.

  12. A physical solution for plane SH waves in anelastic media

    NASA Astrophysics Data System (ADS)

    Ursin, Bjorn; Carcione, José M.; Gei, Davide

    2017-05-01

    In a lossy medium with complex frequency-dependent wave speed both rays and plane waves at an interface should satisfy the dispersion relation (that is, the wave equation), the radiation condition (the amplitude should go to zero at infinity) and the horizontal complex slowness should be continuous (Snell's law). It is known that this may lead to a transmitted wave which violates the radiation condition and which also causes problems with the phase of the reflection coefficient. In fact, ray-tracing algorithms and analytical evaluations of the reflection and transmission coefficients in anelastic media may lead to non-physical solutions related to the complex square roots of the vertical slowness and polarizations. The steepest-descent approximation with complex horizontal slowness involves non-physical complex horizontal distances, and in some cases also a non-physical vertical slowness that violates the radiation condition. Similarly, the reflection and transmission coefficients and ray-tracing codes obtained with this approach yields wrong results. In order to tackle this problem, we choose the stationary-phase approximation with real horizontal slowness. This gives real horizontal distances, the radiation condition is always satisfied and the reflection and transmission coefficients are correct. This is shown by comparison to full-wave space-time modelling results by computing the reflection and transmission coefficients and respective phase angles from synthetic seismograms. This numerical evaluation is based on a 2-D wavenumber-frequency Fourier transform. The results indicate that the stationary-phase method with a real horizontal slowness provides the correct physical solution.

  13. On a problem for wave equation with local data on the whole boundary

    NASA Astrophysics Data System (ADS)

    Yessirkegenov, Nurgisa

    2016-12-01

    In the current paper we propose a new formulation of a local boundary value problem for a one-dimensional wave equation in a rectangular domain in which boundary conditions are given on the whole boundary. We prove the well-posedness of the boundary value problem in the classical and generalized senses. The proof of the well-posedness of the formulated problem is reduced to question of the existence and uniqueness of solutions of the corresponding functional equations.

  14. Sensitivity of an exothermic chemical wave front to a departure from local equilibrium.

    PubMed

    Nowakowski, B; Lemarchand, A

    2007-11-07

    We study the propagation of an exothermic chemical wave front in a reactive dilute gas and show that the particle velocity distribution departs from the Maxwellian form in the front zone. The analytical corrections to the balance equations for concentrations, temperature, and stream velocity induced by the departure from local equilibrium are derived from a perturbative solution of the Boltzmann equation. Our analytical predictions of the front properties, including its propagation speed, compare well with microscopic simulations of the particle dynamics.

  15. Local Solutions for National Challenges? Exploring Local Solutions through the Case of a National Succession Planning Strategy

    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…

  16. Local Solutions for National Challenges? Exploring Local Solutions through the Case of a National Succession Planning Strategy

    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…

  17. On the solutions of a model equation for shallow water waves of moderate amplitude

    NASA Astrophysics Data System (ADS)

    Mi, Yongsheng; Mu, Chunlai

    This paper is concerned with the Cauchy problem of a model equation for shallow water waves of moderate amplitude, which was proposed by A. Constantin and D. Lannes [The hydrodynamical relevance of the Camassa-Holmand Degasperis-Procesi equations, Arch. Ration. Mech. Anal. 192 (2009) 165-186]. First, the local well-posedness of the model equation is obtained in Besov spaces Bp,rs, p,r∈[1,∞], s>max{3/2,1+1/p} (which generalize the Sobolev spaces Hs) by using Littlewood-Paley decomposition and transport equation theory. Second, the local well-posedness in critical case (with s=3/2, p=2, r=1) is considered. Moreover, with analytic initial data, we show that its solutions are analytic in both variables, globally in space and locally in time. Finally, persistence properties on strong solutions are also investigated.

  18. Upgrading the local: Belgian cuisine in global waves.

    PubMed

    Scholliers, Peter; Geyzen, Anneke

    2010-01-01

    This essay touches upon questions about the use of food as an identity marker, the nature of local food, and the influence of foreign food. Since 1830, Belgium witnessed two international food waves that alternated with two local food waves, both opposing as well as using each other's characteristics. In this process, local food was continuously redefined. Belgium reveals a relationship between local and foreign food both in the sense of incorporation and exclusion. Foreign food always influenced local cooking and eating. The opposition between the “self” and the “other” is at times strongly upheld: local food is labeled as “our,” “authentic,” “national,” or “regional” (the “self”) to make the difference with “their,” “artificial,” or “international” (the “other”). This classification of foodways as national/regional is used to forge sentiments of belonging, especially in Belgium where strong separatist political feelings lead to intense regional reactions.

  19. Generation and classification of localized waves by Lorentz transformations in Fourier space.

    PubMed

    Saari, Peeter; Reivelt, Kaido

    2004-03-01

    The Lorentz transformations of propagation-invariant localized waves (also known as nondispersive or nondiffracting or undistorted progressive waves) are studied in the frequency-momentum space. For supports of wave functions in this space rules of transformation are derived which allow one to group all localized waves into distinct classes: subluminal, luminal, and superluminal localized waves. It is shown that for each class there is an inertial frame in which any given localized wave takes a particularly simple form. In other words, any localized wave is nothing but a relativistically aberrant and Doppler shifted version of a simple "seed" wave. Also discussed are the relations of the physical (subluminal) Lorentz tranformation to other mathematical tranformations used in the literature on localized waves, as well as physical interpretation of the substantial changes that localized waves undergo if observed and generated in different inertial frames.

  20. Lommel pulses: an analytic form for localized waves of the focus wave mode type with bandlimited spectrum.

    PubMed

    Sheppard, Colin J R; Saari, Peeter

    2008-01-07

    A criticism of the focus wave mode (FWM) solution for localized pulses is that it contains backward propagating components that are difficult to generate in many practical situations. We describe a form of FWM where the strength of the backward propagating components is identically zero and derive special cases where the field can be written in an analytic form. In particular, a free-space version of "backward light" pulse is considered, which moves in the opposite direction with respect to all its spectral constituents.

  1. Localized packets of acoustic gravity waves in the ionosphere

    NASA Astrophysics Data System (ADS)

    Skorokhod, T. V.; Lizunov, G. V.

    2012-02-01

    Using mass-spectrometric measurement data from the Dynamics Explorer 2 satellite, we investigated the distribution of medium-scale acoustic gravity waves (AGWs) at altitudes of the F-region of the ionosphere. It is shown that the planetary field of AGWs contains a regular and a sporadic component. The regular distribution of AGWs involves active polar areas (where the ionosphere is highly disturbed) and a relatively calm equatorial area. Sporadic AGWs are isolated and spatially localized wave packets that are distinguished against the background of the regular distribution of the wave field. We generated a directory containing observations of sporadic AGW for the period January-February 1983 and performed a statistical analysis of their relation to earthquakes.

  2. Verification of surface wave solutions obtained by the reciprocity theorem.

    PubMed

    Phan, Haidang; Cho, Younho; Achenbach, Jan D

    2014-09-01

    Surface wave motions generated by a time-harmonic point load applied at the surface of an isotropic linearly elastic half-space are conventionally solved by the use of integral transform techniques. The inverse transforms, are often complicated and will not always yield closed-form solutions. In this paper expressions for the displacements for surface wave motions radiated from point-load excitation are determined in a simple manner by the use of the elastodynamic reciprocity theorem. It is shown that the radiated amplitudes of the surface displacements obtained by the reciprocity approach are identical to the corresponding results obtained by the use of Hankel transform and by Lamb in his classical paper. Copyright © 2014 Elsevier B.V. All rights reserved.

  3. 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.

  4. Travelling Wave Solutions in Multigroup Age-Structured Epidemic Models

    NASA Astrophysics Data System (ADS)

    Ducrot, Arnaut; Magal, Pierre; Ruan, Shigui

    2010-01-01

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

  5. Viscosity of aqueous solutions and local microscopic structure.

    PubMed

    Corridoni, T; Mancinelli, R; Ricci, M A; Bruni, F

    2011-12-08

    The effect of solutes on the structure of water has been debated intensively over the past years. Typical scenarios label different ions as water structure "makers" or "breakers": this is a quite elusive definition, which has been first introduced in the description of the effect of solutes on the viscosity of water and, although criticized, is still used in the current literature. Here, using a combination of neutron diffraction and computer modeling, we present a possible relation between the viscosity B coefficient and a local structural property of the solution. In particular, B appears in the Jones-Dole relation and its sign is traditionally used to characterize a solute as "structure maker" or "breaker". We find that B is linearly correlated to the difference between the average solute-water distance and the water-water distance in the pure liquid, in the case of monovalent electrolyte solutions.

  6. A phase-plane analysis of localized frictional waves

    NASA Astrophysics Data System (ADS)

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

    2017-07-01

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

  7. Multifractal electronic wave functions in the Anderson model of localization

    SciTech Connect

    Schreiber, M.; Grussbach, H. )

    1992-06-20

    In this paper, investigations of the multifractal properties of electronic wave functions in disordered samples are reviewed. The characteristic mass exponents of the multifractal measure, the generalized dimensions and the singularity spectra are discussed for typical cases. New results for large 3D systems are reported, suggesting that the multifractal properties at the mobility edge which separates localized and extended states are independent of the microscopic details of the model.

  8. Local stability analysis for a planar shock wave

    NASA Technical Reports Server (NTRS)

    Salas, M. D.

    1984-01-01

    A procedure to study the local stability of planar shock waves is presented. The procedure is applied to a Rankine-Hugoniot shock in a divergent/convergent nozzle, to an isentropic shock in a divergent/convergent nozzle, and to Rankine-Hugoniot shocks attached to wedges and cones. It is shown that for each case, the equation governing the shock motion is equivalent to the damped harmonic oscillator equation.

  9. Localization of angular momentum in optical waves propagating through turbulence.

    PubMed

    Sanchez, Darryl J; Oesch, Denis W

    2011-12-05

    This is the first in a series of papers demonstrating that photons with orbital angular momentum can be created in optical waves propagating through distributed turbulence. The scope of this first paper is much narrower. Here, we demonstrate that atmospheric turbulence can impart non-trivial angular momentum to beams and that this non-trivial angular momentum is highly localized. Furthermore, creation of this angular momentum is a normal part of propagation through atmospheric turbulence.

  10. Transformations from traveling wave (TW) solutions to non-TW solutions of evolution equations via a direct method

    NASA Astrophysics Data System (ADS)

    Burde, Georgy I.

    2017-07-01

    Studying properties of evolution equations arising in different physical contexts commonly starts from assuming the traveling wave (TW) solution form which reduces the problem to an ordinary differential equation (ODE). A variety of direct methods for finding such solutions have been designed but usually there is no algorithmic way to proceed further from this stage. In the present study, a method, which allows constructing non-traveling wave solutions of an evolution equation from known traveling wave solutions, is developed and applied to some types of equations. The transformations yielded by the method can be naturally used for finding new solutions of a given equation. Having the TW solutions (for example, solitary wave solutions) defined in an explicit form, more general non-TW solutions can be also explicitly determined. The transformations can also give insight into some general properties of the equations.

  11. Localized solutions of extended discrete nonlinear Schrödinger equation

    NASA Astrophysics Data System (ADS)

    Umarov, B. A.; Ismail, Nazmi Hakim Bin; Hadi, Muhammad Salihi Abdul; Hassan, T. H.

    2017-09-01

    We consider the extended discrete nonlinear Schrödinger (EDNLSE) equation which includes the nearest neighbor nonlinear interaction in addition to the on-site cubic and quintic nonlinearities. This equation describes nonlinear excitations in dipolar Bose-Einstein condensate in a periodic optical lattice. We are particularly interested with the existence and stability conditions of localized nonlinear excitations of different types. The problem is tackled numerically, by application of Newton methods and by solving the eigenvalue problem for linearized system near the exact solution. Also the modulational instability of plane wave solution is discussed.

  12. Nonlinear Waves on Localized and Periodic Backgrounds with Time-Space Modulation

    NASA Astrophysics Data System (ADS)

    Liu, Mei-Kun; Yang, Zhan-Ying; Yang, Wen-Li

    2017-05-01

    We present one family of general analytical solutions for the generalized nonlinear Schrödinger equation with time-space modulation via the method of a combination of the Darboux transformation and similarity transformation. Nonlinear waves on different localized and periodic backgrounds depending on the corresponding nonlinearity modulations are obtained. In particular, we demonstrate the existence and property of localized modes on a double-periodic background under a special designed optical lattice potential. Our results may raise the possibility of related experiments and potential applications in nonlinear optics and Bose-Einstein condensates. Supported by the National Natural Science Foundation of China under Grant Nos. 11475135 and 11547302

  13. 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.

  14. 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.

  15. Shear wave arrival time estimates correlate with local speckle pattern.

    PubMed

    Mcaleavey, Stephen A; Osapoetra, Laurentius O; Langdon, Jonathan

    2015-12-01

    We present simulation and phantom studies demonstrating a strong correlation between errors in shear wave arrival time estimates and the lateral position of the local speckle pattern in targets with fully developed speckle. We hypothesize that the observed arrival time variations are largely due to the underlying speckle pattern, and call the effect speckle bias. Arrival time estimation is a key step in quantitative shear wave elastography, performed by tracking tissue motion via cross-correlation of RF ultrasound echoes or similar methods. Variations in scatterer strength and interference of echoes from scatterers within the tracking beam result in an echo that does not necessarily describe the average motion within the beam, but one favoring areas of constructive interference and strong scattering. A swept-receive image, formed by fixing the transmit beam and sweeping the receive aperture over the region of interest, is used to estimate the local speckle pattern. Metrics for the lateral position of the speckle are found to correlate strongly (r > 0.7) with the estimated shear wave arrival times both in simulations and in phantoms. Lateral weighting of the swept-receive pattern improved the correlation between arrival time estimates and speckle position. The simulations indicate that high RF echo correlation does not equate to an accurate shear wave arrival time estimate-a high correlation coefficient indicates that motion is being tracked with high precision, but the location tracked is uncertain within the tracking beam width. The presence of a strong on-axis speckle is seen to imply high RF correlation and low bias. The converse does not appear to be true-highly correlated RF echoes can still produce biased arrival time estimates. The shear wave arrival time bias is relatively stable with variations in shear wave amplitude and sign (-20 μm to 20 μm simulated) compared with the variation with different speckle realizations obtained along a given tracking

  16. Shear Wave Arrival Time Estimates Correlate with Local Speckle Pattern

    PubMed Central

    McAleavey, Stephen A.; Osapoetra, Laurentius O.; Langdon, Jonathan

    2016-01-01

    We present simulation and phantom studies demonstrating a strong correlation between errors in shear wave arrival time estimates and the lateral position of the local speckle pattern in targets with fully developed speckle. We hypothesize that the observed arrival time variations are largely due to the underlying speckle pattern, and call the effect speckle bias. Arrival time estimation is a key step in quantitative shear wave elastography, performed by tracking tissue motion via cross correlation of RF ultrasound echoes or similar methods. Variations in scatterer strength and interference of echoes from scatterers within the tracking beam result in an echo that does not necessarily describe the average motion within the beam, but one favoring areas of constructive interference and strong scattering. A swept-receive image, formed by fixing the transmit beam and sweeping the receive aperture over the region of interest, is used to estimate the local speckle pattern. Metrics for the lateral position of the speckle are found to correlate strongly (r>0.7) with the estimated shear wave arrival times both in simulations and in phantoms. Lateral weighting of the swept-receive pattern improved the correlation between arrival time estimates and speckle position. The simulations indicate that high RF echo correlation does not equate to an accurate shear wave arrival time estimate – a high correlation coefficient indicates that motion is being tracked with high precision, but the location tracked is uncertain within the tracking beam width. The presence of a strong on-axis speckle is seen to imply high RF correlation and low bias. The converse does not appear to be true – highly correlated RF echoes can still produce biased arrival time estimates. The shear wave arrival time bias is relatively stable with variations in shear wave amplitude and sign (−20 μm to 20 μm simulated) compared to the variation with different speckle realizations obtained along a given tracking

  17. A robust baseline removal method for guided wave damage localization

    NASA Astrophysics Data System (ADS)

    Liu, Chang; Harley, Joel B.; Bergés, Mario; Greve, David W.; Junker, Warren R.; Oppenheim, Irving J.

    2014-04-01

    Guided waves can propagate long distances and are sensitive to subtle structural damage. Guided-wave based damage localization often requires extracting the scatter signal(s) produced by damage, which is typically obtained by subtracting an intact baseline record from a record to be tested. However, in practical applications, environmental and operational conditions (EOC) dramatically affect guided wave signals. In this case, the baseline subtraction process can no longer perfectly remove the baseline, thereby defeating localization algorithms. In previous work, we showed that singular value decomposition (SVD) can be used to detect the presence of damage under large EOC variations, because it can differentiate the trends of damage from other EOC variations. This capability of differentiation implies that SVD can also robustly extract a scatter signal, originating from damage in the structure, that is not affected by temperature variation. This process allows us to extract a scatterer signal without the challenges associated with traditional temperature compensation and baseline subtraction routines. . In this work, we use to approach to localize structural damage in large, spatially and temporally varying EOCs. We collect pitch-catch records from randomly placed PZT transducers on an aluminum plate while undergoing temperature variations. Damage is introduced to the plate during the monitoring period. We then use our SVD method to extract the scatter signal from the records, and use the scatter signal to localize damage using the delay-and-sum method. To compare results, we also apply several temperature compensation methods to the records and then perform baseline subtraction. We show that our SVD-based approach successfully localize damage while current temperature-compensated baseline subtraction methods fail.

  18. Ethanol separation from ethanol-water solution by ultrasonic atomization and its proposed mechanism based on parametric decay instability of capillary wave

    NASA Astrophysics Data System (ADS)

    Sato, Masanori; Matsuura, Kazuo; Fujii, Toshitaka

    2001-02-01

    We show the experimental data of selective ethanol separation from ethanol-water solution, using ultrasonic atomization. Pure ethanol could be obtained directly from a solution with several mol% ethanol-water solution at 10 °C. This result can be explained in terms of parametric decay instability of capillary wave, in which high localization and accumulation of acoustic energy occur, leading to ultrasonic atomization. That is, parametric decay instability condenses the energy of longitudinal waves in a highly localized surface area of the capillary wave, and causes ultrasonic atomization.

  19. On the exploitation of mode localization in surface acoustic wave MEMS

    NASA Astrophysics Data System (ADS)

    Hanley, T. H.; Gallacher, B. J.; Grigg, H. T. D.

    2017-05-01

    Mode localization sensing has been recently introduced as an alternative resonant sensing protocol. It has been shown to exhibit several advantages over other resonant methods, in particular a potential for higher sensitivity and rejection of common mode noise. This paper expounds the principles of utilising surface acoustic waves (SAW) to create a mode localization sensor. A generalised geometry consisting of a pair of coupled resonant cavities is introduced and an analytical solution found for the displacement fields within the cavities. The solution is achieved by coupling the internal cavity solutions using a ray tracing method. The results of the analytical solution are compared to a numerical solution found using commercial finite element method (FEM) software; exact agreement is found between the two solutions. The insight gained from the analytical model enables the determination of critical design parameters. A brief analysis is presented showing analogous operation to previous examples of mode localization sensors. The sensitivity of the device is shown to depend nonlinearly on the number of periods in the array coupling the two cavities.

  20. Comparison between Regional and Local Pulse-Wave Velocity Data.

    PubMed

    Simova, Iana; Katova, Tzvetana; Santoro, Ciro; Galderisi, Maurizio

    2016-01-01

    Gold standard for pulse-wave velocity (PWV) measurement is determination of the carotid-femoral cfPWV, reflecting regional aortic PWV. Nevertheless, in several echocardiographic laboratories, PWV is measured locally, most commonly at the common carotid artery (CCA). The aim of this study was to compare regional and local PWV values in healthy volunteers. The study population consisted of 22 prospectively enrolled healthy subjects, mean age 38.7 ± 11.1 years, 50% male. For regional PWV measurement, we evaluated cfPWV with a standard echo scanner. Regional PWV was measured at the CCA, with semiautomated dedicated software (MyLab, EsaOte, Italy). cfPWV and local PWV values correlated significantly with high Pearson correlation coefficient (0.62, P = 0.002). Mean regional cfPWV (9.29 ± 3.73 m/s), however, was significantly higher than mean local PWV value (5.96 ± 1.08 m/s) (P < 0.001). The difference persisted in the subgroup analysis using different cfPWV cutoff values (10, 9, 8, and 7 m/s), except for subjects with cfPWV ≤7 m/s, where regional and local PWV values were similar. In a group of healthy volunteers, regional and local PWV values showed a good correlation. However, regional PWV was significantly higher than local PWV. These findings should be carefully taken into account when using this technique in the clinical setting. © 2015, Wiley Periodicals, Inc.

  1. Hybrid local FEM/global LISA modeling of guided wave propagation and interaction with damage in composite structures

    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

  2. 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.

  3. Large-amplitude hydromagnetic waves in collisionless relativistic plasma - Exact solution for the fast-mode magnetoacoustic wave

    NASA Technical Reports Server (NTRS)

    Barnes, A.

    1983-01-01

    An exact nonlinear solution is found to the relativistic kinetic and electrodynamic equations (in their hydromagnetic limit) that describes the large-amplitude fast-mode magnetoacoustic wave propagating normal to the magnetic field in a collisionless, previously uniform plasma. It is pointed out that a wave of this kind will be generated by transverse compression of any collisionless plasma. The solution is in essence independent of the detailed form of the particle momentum distribution functions. The solution is obtained, in part, through the method of characteristics; the wave exhibits the familiar properties of steepening and shock formation. A detailed analysis is given of the ultrarelativistic limit of this wave.

  4. WATER CONSERVATION: LOCAL SOLUTIONS TO A GLOBAL PROBLEM

    EPA Science Inventory

    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...

  5. WATER CONSERVATION: LOCAL SOLUTIONS TO A GLOBAL PROBLEM

    EPA Science Inventory

    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...

  6. A Magnetic Plethysmograph Probe for Local Pulse Wave Velocity Measurement.

    PubMed

    P M, Nabeel; Joseph, Jayaraj; Sivaprakasam, Mohanasankar

    2017-08-29

    We present the design and experimental validation of an arterial compliance probe with dual magnetic plethysmograph (MPG) transducers for local pulse wave velocity (PWV) measurement. The MPG transducers (positioned at 23 mm distance apart) utilizes Hall-effect sensors and permanent magnets for arterial blood pulse detection. The MPG probe was initially validated on an arterial flow phantom using a reference method. Further, 20 normotensive subjects (14 males, age = 24 ± 3.5 years) were studied under two different physical conditions: 1) Physically relaxed condition, 2) Postexercise condition. Local PWV was measured from the left carotid artery using the MPG probe. Brachial blood pressure (BP) was measured to investigate the correlation of BP with local PWV. The proposed MPG arterial compliance probe was capable of detecting high-fidelity blood pulse waveforms. Reliable local pulse transit time estimates were assessed by the developed measurement system. Beat-by-beat local PWV was measured from multiple subjects under different physical conditions. A profound increment was observed in the carotid local PWV for all subjects after exercise (average increment = 0.42 ± 0.22 m/s). Local PWV values and brachial BP parameters were significantly correlated (r ≥ 0.72), except for pulse pressure (r = 0.42). MPG arterial compliance probe for local PWV measurement was validated. Carotid local PWV measurement, its variations due to physical exercise and correlation with BP levels were examined during the in vivo study. A novel dual MPG probe for local PWV measurement and potential use in cuffless BP measurement.

  7. Constructing Quasi-Periodic Wave Solutions of Differential-Difference Equation by Hirota Bilinear Method

    NASA Astrophysics Data System (ADS)

    Wang, Qi

    2016-12-01

    In the present paper, based on the Riemann theta function, the Hirota bilinear method is extended to directly construct a kind of quasi-periodic wave solution of a new integrable differential-difference equation. The asymptotic property of the quasi-periodic wave solution is analyzed in detail. It will be shown that quasi-periodic wave solution converge to the soliton solutions under certain conditions and small amplitude limit.

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

    SciTech Connect

    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.

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

    NASA Astrophysics Data System (ADS)

    Marcotte, Christopher D.; Grigoriev, Roman O.

    2015-06-01

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

  10. Localized Heat Urticaria from 95-GHz Millimeter Waves.

    PubMed

    Gibbons, John A

    2017-06-01

    Local heat urticaria is a physical urticaria caused by the environmental stimulus of heat. Typically, the resultant lesion, a wheal, is pruritic (itches) and is sometimes accompanied by a burning sensation. It is a self-limited phenomenon that resolves after 1.5-2 h. The prevalence of local heat urticaria in the general population has been estimated as 1 in 200,000 persons. The subject, a 39-yr-old active duty man, participated in a test of a 95-GHz energy beam designed to heat the skin. He had delayed presentation of raised, erythematous, nonpruritic, nonpainful areas at five of the exposure sites where the skin temperature exceeded 54°C. All wheals resolved within 2 h of the exposures.Gibbons JA. Localized heat urticaria from 95-GHz millimeter waves. Aerosp Med Hum Perform. 2017; 88(6):586-588.

  11. Thermalized solution of the Galerkin-truncated Burgers equation: From the birth of local structures to thermalization

    NASA Astrophysics Data System (ADS)

    Feng, Peihua; Zhang, Jiazhong; Cao, Shengli; Prants, S. V.; Liu, Yan

    2017-04-01

    Discrepancy between truncated and exact solutions of the inviscid Burgers equation is studied by the pseudo-spectral method with setting all the Fourier modes with the wavenmubers beyond a truncated wavenumber KG to be zero. A localized short-wavelength oscillation, called as a "tyger", appears at occurrence of the shock in the truncated solution. The "tyger" shows very different shapes depending on the way of truncation of the nonlinear term. Moreover, the birth of the "tyger" is related to a period-doubling bifurcation which is illustrated by a map constructed by an iterative method at the center of the "tyger". In order to study the process of stability loss of the truncated wave solution, a perturbed wave is derived. The truncated wave solution loses its stability in every oscillator mode of the perturbed wave. Finally, the long-term process of thermalization is displayed by the perturbed wave coupled with a frozen wave profile containing a symmetric pair of shocks. Thermalization appears from the both sides of small structures around the center without symmetry breaking. The phenomenon of the birth of "a tyger" and its following thermalization can be understood from the view of stability loss of the truncated wave solution.

  12. Rogue waves: from nonlinear Schrödinger breather solutions to sea-keeping test.

    PubMed

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

    2013-01-01

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

  13. Rogue Waves: From Nonlinear Schrödinger Breather Solutions to Sea-Keeping Test

    PubMed Central

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

    2013-01-01

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

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

    PubMed

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

    2014-01-01

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

  15. Selection of Initial Solutions for Local Search in Multiobjective Genetic Local Search

    NASA Astrophysics Data System (ADS)

    Hitotsuyanagi, Yasuhiro; Wakamatsu, Yoshihiko; Nojima, Yusuke; Ishibuchi, Hisao

    In this paper, we propose a new selection scheme of initial solutions for the local search of a multiobjective genetic local search (MOGLS) algorithm. The MOGLS algorithm is the hybridization of an evolutionary multiobjective optimization (EMO) algorithm and local search. It is shown that the MOGLS algorithm has higher search ability than pure EMO algorithms. In the conventional MOGLS algorithm, the local search method is applied to the offspring population generated by the genetic operators. However, the generated offspring population often includes poor individuals because the genetic operators involve some random procedures and allow the generation of inferior offspring. The basic idea of our approach is to apply local search to the parent population. Thus our approach can apply local search to better solutions than the original MOGLS algorithm on average. Through computational experiments, we show that our approach improves the search ability of the MOGLS algorithm.

  16. An implicit difference scheme for the long-time evolution of localized solutions of a generalized Boussinesq system

    SciTech Connect

    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.

  17. Buffered lidocaine and bupivacaine mixture - the ideal local anesthetic solution?

    PubMed

    Best, Corliss A; Best, Alyssa A; Best, Timothy J; Hamilton, Danielle A

    2015-01-01

    The use of injectable local anesthetic solutions to facilitate pain-free surgery is an integral component of many procedures performed by the plastic surgeon. In many instances, a solution that has both rapid onset and prolonged duration of analgesia is optimal. A combination of lidocaine and bupivacaine, plain or with epinephrine, is readily available in most Canadian health care settings where such procedures are performed, and fulfills these criteria. However, commercially available solutions of both medications are acidic and cause a burning sensation on injection. Buffering to neutral pH with sodium bicarbonate is a practical method to mitigate the burning sensation, and has the added benefit of increasing the fraction of nonionized lipid soluble drug available. The authors report on the proportions of the three drugs to yield a neutral pH, and the results of an initial survey regarding the use of the combined solution with epinephrine in hand surgery.

  18. Inertial Alfvén wave localization and turbulent spectrum

    NASA Astrophysics Data System (ADS)

    Sharma, R. P.; Kumari, Anju; Yadav, Nitin

    2014-09-01

    The localization of pump inertial Alfvén wave (IAW) in low β plasmas (β ≪ me/ mi) has been investigated by developing a model based on weak IAW and finite amplitude background density fluctuations. When IAW is perturbed by these fluctuations which are in the form of magnetosonic and ion acoustic waves, its phase velocity gets modified and IAW breaks up into localized structures of very high intensity. Numerical simulation has been carried out to analyze the localized structures and magnetic fluctuation spectrum of pump IAW. We have also developed a simplified model to understand the physical insight into evolution pattern of IAW. Results obtained from simulation reveal that turbulent spectrum up to k⊥λe ≈ 1 follows Kolmogorov power law. Furthermore, at shorter wavelengths, dispersion starts and spectrum steepens with power law index ˜ - 3.8. Energy transport to smaller length scales through this mechanism may be accountable for the observed parallel electron heating in low β plasmas. Results obtained from the numerical simulation are consistent with the observations of various spacecraft like FAST and Hawkeye.

  19. Local surface skimming longitudinal wave velocity and residual stress mapping.

    PubMed

    Sathish, Shamachary; Martin, Richard W; Moran, Thomas J

    2004-01-01

    Local variation in surface skimming longitudinal wave (SSLW) velocity has been measured using a scanning acoustic microscope. A very narrow width electrical impulse has been used to excite the transducer of the acoustic lens. This permits the separation of the SSLW signal from the direct reflected signal in the time domain. A simple method of measuring the time delay between the directly reflected signal and the SSLW signal at two defocuses has been utilized for the local measurement of SSLW velocity. The variation in the SSLW velocity measured over an area of the sample is scaled and presented as an image. The method has been implemented to image the variation of the SSLW velocity around a crack tip in a sample of Ti-6Al-4V. Since the SSLW velocity is known to change linearly with the stress, the SSLW velocity image is considered as a representation of the image of stress around the crack tip. Local stress variation in the same region of the crack tip is directly measured using x-ray diffraction. The SSLW velocity image is compared with the x-ray diffraction stress image. The contrast in the two images, spatial resolution, and the penetration depth into the sample of acoustic waves and x rays are discussed.

  20. Localized spatially nonlinear matter waves in atomic-molecular Bose-Einstein condensates with space-modulated nonlinearity

    PubMed Central

    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

  1. Radiating dispersive shock waves in non-local optical media

    PubMed Central

    El, Gennady A.

    2016-01-01

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

  2. Surface wave tomography with USArray: Rayleigh wave phase velocity, ellipticity, and local amplification

    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.

  3. Dynamical behaviours and exact travelling wave solutions of modified generalized Vakhnenko equation

    NASA Astrophysics Data System (ADS)

    Xiao, Junjun; Feng, Dahe; Meng, Xia; Cheng, Yuanquan

    2017-01-01

    By using the bifurcation theory of planar dynamical systems and the qualitative theory of differential equations, we studied the dynamical behaviours and exact travelling wave solutions of the modified generalized Vakhnenko equation (mGVE). As a result, we obtained all possible bifurcation parametric sets and many explicit formulas of smooth and non-smooth travelling waves such as cusped solitons, loop solitons, periodic cusp waves, pseudopeakon solitons, smooth periodic waves and smooth solitons. Moreover, we provided some numerical simulations of these solutions.

  4. On full-wave solution for VLF waves in the near-Earth space

    NASA Astrophysics Data System (ADS)

    Kuzichev, I. V.; Shklyar, D. R.

    2010-08-01

    A VLF wave that propagates in the Earth's plasmasphere in the whistler mode must be converted into free space mode in order to be observed on the ground. This conversion takes place in collisional and highly inhomogeneous ionospheric plasma, which makes the description of the process not easy. Since an understanding of this process is vital for the analysis of VLF data, it has been in the focus of research since the beginning of whistler studies. A general approach to this problem, which is based on Maxwell's equations in magnetized plasma, is well developed and commonly accepted. However, its direct implementation meets serious difficulties which reveal themselves in numerical swamping. The intrinsic reason behind this is the existence of evanescent mode in the whistler frequency band. This leads to exponential growth of numerical solutions to the general set of equations. Various methods that have been developed to suppress this instability shift a solution of the physical problem to the field of simulation skill, so that the essential part of solution remains largely hidden. In this work we develop a new approach to the problem in which the evanescent mode is analytically excluded from consideration, making numerical calculations plain and straightforward. Using this approach, we find the field of whistler mode wave incident on the ionosphere from above in the whole span of altitudes, and calculate the reflection coefficient as a function of frequency for a number of incidence angles. We explain a quasiperiodic behaviour of the reflection coefficient by resonance absorption of the waves in the lower ionosphere.

  5. 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.

  6. Exciton localization in solution-processed organolead trihalide perovskites

    PubMed Central

    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

  7. Wave chaos in the stadium: Statistical properties of short-wave solutions of the Helmholtz equation

    SciTech Connect

    McDonald, S.W.; Kaufman, A.N.

    1988-04-15

    We numerically investigate statistical properties of short-wavelength normal modes and the spectrum for the Helmholtz equation in a two-dimensional stadium-shaped region. As the geometrical optics rays within this boundary (billiards) are nonintegrable, this wave problem serves as a simple model for the study of quantum chaos. The local spatial correlation function and the probability distribution P/sub n/(psi) of wave amplitude for normal modes psi/sub n/ are computed and compared with predictions based on semiclassical arguments applied to this nonintegrable Hamiltonian. The spectrum is analyzed in terms of the probability P(..delta..E) of neighboring energy-eigenvalue separations, which is shown to be similar to a Wigner distribution for the eigenvalues of a random matrix

  8. Local numerical modelling of ultrasonic guided waves in linear and nonlinear media

    NASA Astrophysics Data System (ADS)

    Packo, Pawel; Radecki, Rafal; Kijanka, Piotr; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.

    2017-04-01

    Nonlinear ultrasonic techniques provide improved damage sensitivity compared to linear approaches. The combination of attractive properties of guided waves, such as Lamb waves, with unique features of higher harmonic generation provides great potential for characterization of incipient damage, particularly in plate-like structures. Nonlinear ultrasonic structural health monitoring techniques use interrogation signals at frequencies other than the excitation frequency to detect changes in structural integrity. Signal processing techniques used in non-destructive evaluation are frequently supported by modeling and numerical simulations in order to facilitate problem solution. This paper discusses known and newly-developed local computational strategies for simulating elastic waves, and attempts characterization of their numerical properties in the context of linear and nonlinear media. A hybrid numerical approach combining advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE) is proposed for unique treatment of arbitrary strain-stress relations. The iteration equations of the method are derived directly from physical principles employing stress and displacement continuity, leading to an accurate description of the propagation in arbitrarily complex media. Numerical analysis of guided wave propagation, based on the newly developed hybrid approach, is presented and discussed in the paper for linear and nonlinear media. Comparisons to Finite Elements (FE) are also discussed.

  9. Solitary wave solution to a singularly perturbed generalized Gardner equation with nonlinear terms of any order

    NASA Astrophysics Data System (ADS)

    Zhou, J. B.; Xu, J.; Wei, J. D.; Yang, X. Q.

    2017-04-01

    This paper is concerned with the existence of travelling wave solutions to a singularly perturbed generalized Gardner equation with nonlinear terms of any order. By using geometric singular perturbation theory and based on the relation between solitary wave solution and homoclinic orbits of the associated ordinary differential equations, the persistence of solitary wave solutions of this equation is proved when the perturbation parameter is sufficiently small. The numerical simulations verify our theoretical analysis.

  10. On Hokusai's Great wave off Kanagawa: localization, linearity and a rogue wave in sub-Antarctic waters

    PubMed Central

    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

  11. On Hokusai's Great wave off Kanagawa: localization, linearity and a rogue wave in sub-Antarctic waters.

    PubMed

    Dudley, J M; Sarano, V; Dias, F

    2013-06-20

    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.

  12. Crystallization of Local Anesthetics When Mixed With Corticosteroid Solutions

    PubMed Central

    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

  13. Magnetic plethysmograph transducers for local blood pulse wave velocity measurement.

    PubMed

    Nabeel, P M; Joseph, Jayaraj; Sivaprakasam, Mohanasankar

    2014-01-01

    We present the design of magnetic plethysmograph (MPG) transducers for detection of blood pulse waveform and evaluation of local pulse wave velocity (PWV), for potential use in cuffless blood pressure (BP) monitoring. The sensors utilize a Hall effect magnetic field sensor to capture the blood pulse waveform. A strap based design is performed to enable reliable capture of large number of cardiac cycles with relative ease. The ability of the transducer to consistently detect the blood pulse is verified by in-vivo trials on few volunteers. A duality of such transducers is utilized to capture the local PWV at the carotid artery. The pulse transit time (PTT) between the two detected pulse waveforms, measured along a small section of the carotid artery, was evaluated using automated algorithms to ensure consistency of measurements. The correlation between the measured values of local PWV and BP was also investigated. The developed transducers provide a reliable, easy modality for detecting pulse waveform on superficial arteries. Such transducers, used for measurement of local PWV, could potentially be utilized for cuffless, continuous evaluation of BP at various superficial arterial sites.

  14. Simulation study of planar and nonplanar super rogue waves in an electronegative plasma: Local discontinuous Galerkin method

    NASA Astrophysics Data System (ADS)

    El-Tantawy, S. A.; Aboelenen, Tarek

    2017-05-01

    Planar and nonplanar (cylindrical and spherical) ion-acoustic super rogue waves in an unmagnetized electronegative plasma are investigated, both analytically (for planar geometry) and numerically (for planar and nonplanar geometries). Using a reductive perturbation technique, the basic set of fluid equations is reduced to a nonplanar/modified nonlinear Schrödinger equation (NLSE), which describes a slow modulation of the nonlinear wave amplitude. The local modulational instability of the ion-acoustic structures governed by the planar and nonplanar NLSE is reported. Furthermore, the existence region of rogue waves is strictly defined. The parameters used in our calculations are from the lab observation data. The local discontinuous Galerkin (LDG) method is used to find rogue wave solutions of the planar and nonplanar NLSE and to prove L2 stability of this method. Also, it is found that the numerical simulations and the exact (analytical) solutions of the planar NLSE match remarkably well and numerical examples show that the convergence orders of the proposed LDG method are N + 1 when polynomials of degree N are used. Moreover, it is noted that the spherical rogue waves travel faster than their cylindrical counterpart. Also, the numerical solution showed that the spherical and cylindrical amplitudes of the localized pulses decrease with the increase in the time | τ |.

  15. Pretend model of traveling wave solution of two-dimensional K-dV equation

    NASA Astrophysics Data System (ADS)

    Karim, Md Rezaul; Alim, Md Abdul; Andallah, Laek Sazzad

    2013-11-01

    Traveling wave resolution of Korteweg-de Vries (K-dV) solitary and numerical estimation of analytic solutions have been studied in this paper for imaginary concept. Pretend model of traveling wave deals with giant waves or series of waves created by an undersea earthquake, volcanic eruption or landslide. The concept of traveling wave is frequently used by mariners and in coastal, ocean and naval engineering. We have found some exact traveling wave solutions with relevant physical parameters using new auxiliary equation method introduced by Pang et al. (Appl. Math. Mech-Engl. Ed 31(7):929-936, 2010). We have solved the imaginary part of exact traveling wave equations analytically, and numerical results of time-dependent wave solutions have been presented graphically. This procedure has a potential to be used in more complex system for other types of K-dV equations.

  16. Localized nonlinear matter waves in two-component Bose-Einstein condensates with time- and space-modulated nonlinearities

    SciTech Connect

    Wang Dengshan; Hu Xinghua; Liu, W. M.

    2010-08-15

    We investigate the localized nonlinear matter waves in the two-component Bose-Einstein condensates with time- and space-modulated nonlinearities analytically and numerically. The similarity transformations are developed to solve the coupled Gross-Pitaevskii equations and two families of explicitly exact solutions are derived. Our results show that not only the attractive spatiotemporal inhomogeneous interactions but the repulsive ones support novel localized nonlinear matter waves in two-component Bose-Einstein condensates. The dynamics of these matter waves, including the breathing solitons, quasibreathing solitons, resonant solitons, and moving solitons, is discussed. We confirm the stability of the exact solutions by adding various initial stochastic noise and study the general cases of the interaction parameters numerically. We also provide the experimental parameters to produce these phenomena in future experiments.

  17. Two-dimensional envelope localized waves in the anomalous dispersion regime.

    PubMed

    Malaguti, Stefania; Bellanca, Gaetano; Trillo, Stefano

    2008-05-15

    Narrowband localized wave packets that are nondispersing and nondiffracting in one transverse dimension are characterized in anomalously dispersive media by means of a Fourier approach. Depending on the group velocity, waves with a dispersion relationship characterized by real wavenumbers can be O or X waves, while we also find waves with evanescent wavenumbers.

  18. Molecular quantum robotics: particle and wave solutions, illustrated by "leg-over-leg" walking along microtubules.

    PubMed

    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.

  19. Mesoscopic correlation within transmitted speckle pattern and wave localization

    NASA Astrophysics Data System (ADS)

    Hu, Bing

    This thesis is an experimental study of the statistical character of the field distribution within one-dimensional and transmitted through quasi-1D random samples. We measured the spatial extent of the field for extended, evanescent, and localized wave in random single-mode waveguide. We find that spectrally and spatially overlapping modes in a nominally localized region of an open dissipative system can be decomposed into quasi-normal-modes. Microwave field measurements of the near-field transmitted speckle pattern through random quasi-one-dimensional samples were carried out with polarization rotation, along a line, on a tight grid covering the full output surface. The field spectrum is Fourier transformed to give the temporal evolution of the speckle pattern. Field and intensity correlation versus displacement, frequency shift, and polarization rotation were studied to exhibit the growing impact of mesoscopic fluctuation and photon localization with time delay from a exciting pulse. The variation of key distributions and correlation functions with delay time were examined. We find a universal expression for the intensity correlation function which is valid for localized and diffusive waves in steady-state and in the time domain. It is a function only of the field correlation function which is the same in steady state and in the time domain and the degree of correlation, kappa, which also indicates the closeness of the random system to the localization transition. We also studied the microstatistics of the transmitted field in individual sample realizations, as opposed to the traditional focus on fluctuations relative to the ensemble average. We find that the field distribution in each configuration is Gaussian and that mesoscopic correlation arises as a result of fluctuation of the total transmission. The degree of correlation kappa is just the variance of total transmission normalized by its ensemble average. Other aspects on phase statistics of the speckle

  20. On periodic wave solutions and asymptotic behaviors to a generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt equation

    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.

  1. Propagation and localization of acoustic waves in Fibonacci phononic circuits

    NASA Astrophysics Data System (ADS)

    Aynaou, H.; El Boudouti, E. H.; Djafari-Rouhani, B.; Akjouj, A.; Velasco, V. R.

    2005-07-01

    A theoretical investigation is made of acoustic wave propagation in one-dimensional phononic bandgap structures made of slender tube loops pasted together with slender tubes of finite length according to a Fibonacci sequence. The band structure and transmission spectrum is studied for two particular cases. (i) Symmetric loop structures, which are shown to be equivalent to diameter-modulated slender tubes. In this case, it is found that besides the existence of extended and forbidden modes, some narrow frequency bands appear in the transmission spectra inside the gaps as defect modes. The spatial localization of the modes lying in the middle of the bands and at their edges is examined by means of the local density of states. The dependence of the bandgap structure on the slender tube diameters is presented. An analysis of the transmission phase time enables us to derive the group velocity as well as the density of states in these structures. In particular, the stop bands (localized modes) may give rise to unusual (strong normal) dispersion in the gaps, yielding fast (slow) group velocities above (below) the speed of sound. (ii) Asymmetric tube loop structures, where the loops play the role of resonators that may introduce transmission zeros and hence new gaps unnoticed in the case of simple diameter-modulated slender tubes. The Fibonacci scaling property has been checked for both cases (i) and (ii), and it holds for a periodicity of three or six depending on the nature of the substrates surrounding the structure.

  2. Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves.

    PubMed

    Baronio, Fabio; Degasperis, Antonio; Conforti, Matteo; Wabnitz, Stefan

    2012-07-27

    We construct and discuss a semirational, multiparametric vector solution of coupled nonlinear Schrödinger equations (Manakov system). This family of solutions includes known vector Peregrine solutions, bright- and dark-rogue solutions, and novel vector unusual freak waves. The vector rogue waves could be of great interest in a variety of complex systems, from optics and fluid dynamics to Bose-Einstein condensates and finance.

  3. Traveling Wave Solutions of the Gardner Equation and Motion of Plane Curves Governed by the mKdV Flow

    SciTech Connect

    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.

  4. Methylparaben concentration in commercial Brazilian local anesthetics solutions

    PubMed Central

    da SILVA, Gustavo Henrique Rodriguez; BOTTOLI, Carla Beatriz Grespan; GROPPO, Francisco Carlos; VOLPATO, Maria Cristina; RANALI, José; RAMACCIATO, Juliana Cama; MOTTA, Rogério Heládio Lopes

    2012-01-01

    Objective To detect the presence and concentration of methylparaben in cartridges of commercial Brazilian local anesthetics. Material and methods Twelve commercial brands (4 in glass and 8 in plastic cartridges) of local anesthetic solutions for use in dentistry were purchased from the Brazilian market and analyzed. Different lots of the commercial brands were obtained in different Brazilian cities (Piracicaba, Campinas and São Paulo). Separation was performed using high performance liquid chromatography (HPLC) with UV-Vis detector. The mobile phase used was acetonitrile:water (75:25 - v/v), pH 4.5, adjusted with acetic acid at a flow rate of 1.0 ml.min-1. Results When detected in the solutions, the methylparaben concentration ranged from 0.01% (m/v) to 0.16% (m/v). One glass and all plastic cartridges presented methylparaben. Conclusion 1. Methylparaben concentration varied among solutions from different manufacturers, and it was not indicated in the drug package inserts; 2. Since the presence of methylparaben in dental anesthetics is not regulated by the Brazilian National Health Surveillance Agency (ANVISA) and this substance could cause allergic reactions, it is important to alert dentists about its possible presence. PMID:23032206

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

    PubMed

    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.

  6. 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.

  7. Periodic wave, breather wave and travelling wave solutions of a (2 + 1)-dimensional B-type Kadomtsev-Petviashvili equation in fluids or plasmas

    NASA Astrophysics Data System (ADS)

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

    2016-11-01

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

  8. 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.

  9. New Travelling Solitary Wave and Periodic Solutions of the Generalized Kawahara Equation

    SciTech Connect

    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.

  10. 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.

  11. Numerical solution of plasma fluid equations using locally refined grids

    SciTech Connect

    Colella, P., LLNL

    1997-01-26

    This paper describes a numerical method for the solution of plasma fluid equations on block-structured, locally refined grids. The plasma under consideration is typical of those used for the processing of semiconductors. The governing equations consist of a drift-diffusion model of the electrons and an isothermal model of the ions coupled by Poisson's equation. A discretization of the equations is given for a uniform spatial grid, and a time-split integration scheme is developed. The algorithm is then extended to accommodate locally refined grids. This extension involves the advancement of the discrete system on a hierarchy of levels, each of which represents a degree of refinement, together with synchronization steps to ensure consistency across levels. A brief discussion of a software implementation is followed by a presentation of numerical results.

  12. Peakons and new exact solitary wave solutions of extended quantum Zakharov-Kuznetsov equation

    NASA Astrophysics Data System (ADS)

    Zhang, Ben-gong; Li, Weibo; Li, Xiangpeng

    2017-06-01

    In this paper, the three dimensional extended quantum Zakharov-Kuznetsov equation, which arises in the dimensionless hydrodynamic equations describing the nonlinear propagation of the quantum ion-acoustic waves, is investigated by an auxiliary equation method. As a result, peakons and a series of new exact traveling wave solutions, including bell-shaped, kink-type solitary wave, shock wave, periodic wave, and Jacobi elliptic solutions, are obtained. We also analyze the three kinds of nonlinear structures of our results, i.e., blowup, peakons, and shock wave. These new exact solutions will enrich the previous results and help us to further understand the physical structures and analyze the nonlinear propagation of the quantum ion-acoustic waves.

  13. Numerical Solution of Poroelastic Wave Equation Using Nodal Discontinuous Galerkin Finite Element Method

    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

  14. General set of traveling-wave solutions for amplitude equations in the phase field crystal model

    NASA Astrophysics Data System (ADS)

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

    2017-04-01

    Fronts dynamics of periodic crystalline state, which invades the homogeneous state (liquid phase), are analysed. These fronts are considered as traveling waves of atomic density amplitudes. The propagation of amplitudes is described by the hyperbolic equation of an extended Allen-Cahn type for which the complete set of analytical traveling-wave solutions are obtained by tanh-method. The set of solutions includes previously known traveling waves for the parabolic Allen-Cahn equation of both extended and standard form.

  15. 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.

  16. Addendum to "Travelling waves for a non-local Korteweg-de Vries-Burgers equation" [J. Differential Equations 257 (3) (2014) 720-758

    NASA Astrophysics Data System (ADS)

    Cuesta, C. M.; Achleitner, F.

    2017-01-01

    We add a theorem to F. Achleitner, C.M. Cuesta and S. Hittmeir (2014) [1]. In that paper we studied travelling wave solutions of a Korteweg-de Vries-Burgers type equation with a non-local diffusion term. In particular, the proof of existence and uniqueness of these waves relies on the assumption that the exponentially decaying functions are the only bounded solutions of the linearised equation. In this addendum we prove this assumption and thus close the existence and uniqueness proof of travelling wave solutions.

  17. 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.

  18. Inverse scattering transform analysis of rogue waves using local periodization procedure

    PubMed Central

    Randoux, Stéphane; Suret, Pierre; El, Gennady

    2016-01-01

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

  19. Inverse scattering transform analysis of rogue waves using local periodization procedure.

    PubMed

    Randoux, Stéphane; Suret, Pierre; El, Gennady

    2016-07-07

    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.

  20. Stimulated Brillouin scattering in the field of a two-dimensionally localized pumping wave

    SciTech Connect

    Solikhov, D. K.; Dvinin, S. A.

    2016-06-15

    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.

  1. 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.

  2. Wave field localization in a prestressed functionally graded layer

    NASA Astrophysics Data System (ADS)

    Belyankova, T. I.; Kalinchuk, V. V.

    2017-05-01

    Characteristic features of wave field formation caused by a surface source of harmonic vibration in a prestressed functionally graded layer are investigated. It is assumed that the elastic moduli and the density of the material vary with depth according to arbitrary laws. The initial material of the medium is represented by a model hyperelastic material with third-order elastic moduli. The boundary-value problem for a set of Lamè equations is reduced to a set of Cauchy problems with initial conditions, which is solved by the Runge-Kutta-Merson method modified to fit the specific problem under study. Considering shear vibrations of a functionally graded layer as an example, effects of the type of its inhomogeneity, variations in its properties, and nature of its initial stressed state on the displacement distribution in depth are investigated. Special attention is paid to characteristic features of displacement localization in a layer with an interface-type inclusion near critical frequencies. A direct relation between the inhomogeneous layer structure and the type of displacement localization in depth is demonstrated. It is found that the role of initial stresses and variations in material parameters considerably increases in the vicinities of critical frequencies.

  3. Global smooth solutions in R3 to short wave-long wave interactions in magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Frid, Hermano; Jia, Junxiong; Pan, Ronghua

    2017-04-01

    We consider a Benney-type system modeling short wave-long wave interactions in compressible viscous fluids under the influence of a magnetic field. Accordingly, this large system now consists of the compressible MHD equations coupled with a nonlinear Schrödinger equation along particle paths. We study the global existence of smooth solutions to the Cauchy problem in R3 when the initial data are small smooth perturbations of an equilibrium state. An important point here is that, instead of the simpler case having zero as the equilibrium state for the magnetic field, we consider an arbitrary non-zero equilibrium state B bar for the magnetic field. This is motivated by applications, e.g., Earth's magnetic field, and the lack of invariance of the MHD system with respect to either translations or rotations of the magnetic field. The usual time decay investigation through spectral analysis in this non-zero equilibrium case meets serious difficulties, for the eigenvalues in the frequency space are no longer spherically symmetric. Instead, we employ a recently developed technique of energy estimates involving evolution in negative Besov spaces, and combine it with the particular interplay here between Eulerian and Lagrangian coordinates.

  4. Transport and localization of waves in ladder-shaped lattices with locally PT -symmetric potentials

    NASA Astrophysics Data System (ADS)

    Nguyen, Ba Phi; Kim, Kihong

    2016-12-01

    We study numerically the transport and localization properties of waves in ordered and disordered ladder-shaped lattices with local PT symmetry. Using a transfer matrix method, we calculate the transmittance and the reflectance for the individual channels and the Lyapunov exponent for the whole system. In the absence of disorder, we find that when the gain or loss parameter ρ is smaller than the interchain coupling parameter tv, the transmittance and the reflectance are periodic functions of the system size, whereas when ρ is larger than tv, the transmittance is found to be an exponentially decaying function while the reflectance attains a saturation value in the thermodynamic limit. For a fixed system size, there appear perfect transmission resonances in each individual channel at several values of the gain or loss strength smaller than tv. A singular behavior of the transmittance is also found to appear at various values of ρ for a given system size. When disorder is inserted into the on-site potentials, these behaviors are changed substantially due to the interplay between disorder and the gain or loss effect. When ρ is smaller than tv, we find that the presence of locally PT -symmetric potentials suppresses Anderson localization, as compared to the localization in the corresponding Hermitian system. When ρ is larger than tv, we find that localization becomes more pronounced at higher gain or loss strengths. We also find that the phenomenon of anomalous localization occurs in disordered locally PT -symmetric systems precisely at the spectral positions E =0 and E =±√{tv2-ρ2 } . The anomaly at the band center manifests as a sharp peak, contrary to the conventional cases, whereas the anomalies at E =±√{tv2-ρ2 } manifest as sharp dips.

  5. An efficient algorithm for computation of solitary wave solutions to nonlinear differential equations

    NASA Astrophysics Data System (ADS)

    Ayub, Kamran; Khan, M. Yaqub; Mahmood-Ul-Hassan, Qazi; Ahmad, Jamshad

    2017-09-01

    Nonlinear mathematical problems and their solutions attain much attention in solitary waves. In soliton theory, an efficient tool to attain various types of soliton solutions is the \\exp (-φ (ζ ))-expansion technique. This article is devoted to find exact travelling wave solutions of Drinfeld-Sokolov equation via a reliable mathematical technique. By using the proposed technique, we attain soliton wave solution of various types. It is observed that the technique under discussion is user friendly with minimum computational work, and can be extended for physical problems of different nature in mathematical physics.

  6. Quantum stability of nonlinear wave type solutions with intrinsic mass parameter in QCD

    NASA Astrophysics Data System (ADS)

    Kim, Youngman; Lee, Bum-Hoon; Pak, D. G.; Park, Chanyong; Tsukioka, Takuya

    2017-09-01

    The problem of the existence of a stable vacuum field in pure QCD is revised. Our approach is based on using classical stationary nonlinear wave type solutions with an intrinsic mass scale parameter. Such solutions can be treated as quantum-mechanical wave functions describing massive spinless states in quantum theory. We verify whether nonlinear wave type solutions can form a stable vacuum field background within the framework of the effective action formalism. We demonstrate that there is a special class of stationary generalized Wu-Yang monopole solutions that are stable against quantum gluon fluctuations.

  7. Local ventilation solution for large, warm emission sources.

    PubMed

    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%.

  8. Benchmarking the solute transport module of the WAVE_MAT model

    NASA Astrophysics Data System (ADS)

    Mamadou, Sall; Vanclooster, Marnik; Vansteenkiste, Joachim; Diels, Jan

    2010-05-01

    Modelling water flow and solute transport through heterogeneous unsaturated zone soil under unsteady state conditions requires the use of numerical solutions. The WAVE model (Vanclooster et al., 1996), which solves numerically the 1-D flow and transport equation, is often used to simulate the water and chemical transport (pesticides, nutrients) in agricultural soil. The original version of the model has been encoded in Fortran77. The most recent version (WAVE3.1), has been submitted to many validation and benchmarking studies. To facilitate the future exploitation and development of the WAVE model, the code is currently transposed in a MATLABTM environment, referred to as WAVE_MAT. Following the principles of good modelling practice, version control for the new WAVE_MAT model is implemented. An essential part of the version control is the benchmarking of each new release. In this poster, we present the results of benchmarking of the solute transport module of WAVE_MAT_V0060610. We compare results of simulated solute transport with WAVE_MAT_V0060610 with the analytical solutions of the governing transport equation and with those obtained with the HYDRUS-1D model. The benchmarks are performed for three soil types (clay, loam, and sand) of 100 or 200 cm of profile length and for different solute transport parameters, and for different flow and boundary conditions. Although the correction of numerical dispersion is not yet applied to WAVE_MAT, the results agree well to the analytical solution for reasonable hydrodynamic dispersivity.

  9. Local radial point interpolation (MLRPI) method for solving time fractional diffusion-wave equation with damping

    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.

  10. Dynamic aspects of apparent attenuation and wave localization in layered media

    USGS Publications Warehouse

    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.

  11. Trapping and instability of directional gravity waves in localized water currents.

    PubMed

    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.

  12. Trapping and instability of directional gravity waves in localized water currents

    NASA Astrophysics Data System (ADS)

    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.

  13. Convection in binary fluid mixtures. II. Localized traveling waves

    NASA Astrophysics Data System (ADS)

    Barten, W.; Lücke, M.; Kamps, M.; Schmitz, R.

    1995-06-01

    Nonlinear, spatially localized structures of traveling convection rolls that are surrounded by quiescent fluid in horizontal layers of binary fluids heated from below are investigated in quantitative detail as a function of Rayleigh number for two different Soret coupling strengths (separation ratios) with Lewis and Prandtl numbers characterizing ethanol-water mixtures. A finite-difference method was used to solve the full hydrodynamic field equations numerically in a vertical cross section perpendicular to the roll axes subject to realistic horizontal and laterally periodic boundary conditions with different periodicity lengths. Structure and dynamics of these localized traveling waves (LTW's) are dominated by the concentration field. As in the spatially extended convective states that are investigated in an accompanying paper, the Soret-induced concentration variations strongly influence, via density changes, the buoyancy forces that drive convection. The spatiotemporal properties of this feedback mechanism, involving boundary layers and concentration plumes, show that LTW's are strongly nonlinear states. Light intensity distributions are determined that can be observed in side-view shadowgraphs done with horizontal light along the roll axes. Detailed analyses of all fields are made using color-coded isoplots, among others. In the frame comoving with their drift velocity, LTW's display a nontrivial spatiotemporal symmetry consisting of time translation by one-half an oscillation period combined with vertical reflection through the horizontal midplane of the layer. A time-averaged concentration current is driven by a phase difference between the waves of concentration and vertical velocity in the bulk of the LTW state. The associated large-scale concentration redistribution stabilizes the LTW and controls its drift velocity into the quiescent fluid by generating a buoyancy-reducing concentration ``barrier'' ahead of the leading LTW front. All considered LTW

  14. Exact solutions for semirelativistic problems with non-local potentials

    NASA Astrophysics Data System (ADS)

    Hall, Richard L.

    2006-01-01

    It is shown that exact solutions may be found for the energy eigenvalue problem generated by the class of semirelativistic Hamiltonians of the form H = \\sqrt{m^2+p^2} + \\hat{V} , where \\hat{V} is a non-local potential with a separable kernel of the form {\\cal V}(r,r^{\\prime}) = - \\sum_{i=1}^n v_i f_i(r)g_i(r^{\\prime}) . Explicit examples in one and three dimensions are discussed, including the Yamaguchi and Gauss potentials. The results are used to obtain lower bounds for the energy of the corresponding N-boson problem, with upper bounds provided by the use of a Gaussian trial function.

  15. Analytic solution of Hubbell's model of local community dynamics.

    PubMed

    McKane, Alan J; Alonso, David; Solé, Ricard V

    2004-02-01

    Recent theoretical approaches to community structure and dynamics reveal that many large-scale features of community structure (such as species-rank distributions and species-area relations) can be explained by a so-called neutral model. Using this approach, species are taken to be equivalent and trophic relations are not taken into account explicitly. Here we provide a general analytic solution to the local community model of Hubbell's neutral theory of biodiversity by recasting it as an urn model, i.e. a Markovian description of states and their transitions. Both stationary and time-dependent distributions are analysed. The stationary distribution-also called the zero-sum multinomial-is given in closed form. An approximate form for the time-dependence is obtained by using an expansion of the master equation. The temporal evolution of the approximate distribution is shown to be a good representation for the true temporal evolution for a large range of parameter values.

  16. 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.

  17. Nanohertz gravitational wave sources in the local universe

    NASA Astrophysics Data System (ADS)

    Mingarelli, Chiara M. F.; Croft, Steve; Ellis, Justin; Greene, Jenny E.; Lazio, Joseph; Ma, Chung-Pei; Sesana, Alberto; Burke-Spolaor, Sarah; Taylor, Stephen R.

    2017-01-01

    We look at the 2MASS galaxy catalog to identify potential supermassive black hole binary host galaxies, assess the likelihood of detecting one or more of these sources, and how much they might contribute to the nanohertz gravitational-wave (GW) background (GWB) and its anisotropy. We find that over 10,000 realizations of the local universe, out to 225 Mpc, that the number of sources per realization emitting GWs with f > 1 nHz can be described by a normal distribution with a mean of 130. We find that the detection of these sources is hampered by the small chirp mass of such binaries, and that with current best upper limits from the EPTA for continuous GW sources, the detection probability is < 1%. However, in the next 5-6 years we will begin to probe a region of the parameter space which is rich in sources, making a detection much more likely. Finally we find that a continuous GW source contributes < 1% to the isotropic GWB, but that some may contribute to the level of anisotropy by a few to 10%.

  18. Removal of a pinned spiral by generating target waves with a localized stimulus

    NASA Astrophysics Data System (ADS)

    Fu, Ya-Qing; Zhang, Hong; Cao, Zhoujian; Zheng, Bo; Hu, Gang

    2005-10-01

    Pinning of spiral waves by defects in cardiac muscle may cause permanent tachycardia. We numerically study the removal of a pinned spiral by a localized stimulus at the boundary of a two-dimensional excitable medium. It is shown that target waves may be generated by an external local force, and then the target waves will interact with the pinned spiral. When the external force is appropriately chosen, the generated target waves may suppress the pinned spiral, and the system is finally dominated by the target waves.

  19. Fast computation of synthetic seismograms within a medium containing remote localized perturbations: A numerical solution to the scattering problem

    NASA Astrophysics Data System (ADS)

    Masson, Yder; Romanowicz, Barbara

    2016-11-01

    We derive a fast discrete solution to the scattering problem. This solution allows us to compute accurate synthetic seismograms or waveforms for arbitrary locations of sources and receivers within a medium containing localized perturbations. The key to efficiency is that wave propagation modeling does not need to be carried out in the entire volume that encompasses the sources and the receivers but only within the sub-volume containing the perturbations or scatterers. The proposed solution has important applications, for example, it permits the imaging of remote targets located in regions where no sources or receivers are present. Our solution relies on domain decomposition: within a small volume that contains the scatterers, wave propagation is modeled numerically, while in the surrounding volume, where the medium isn't perturbed, the response is obtained through wavefield extrapolation. The originality of this work is the derivation of discrete formulas for representation theorems and Kirchhoff-Helmholtz integrals that naturally adapt to the numerical scheme employed for modeling wave propagation. Our solution applies, for example, to finite difference methods or finite/spectral elements methods. The synthetic seismograms obtained with our solution can be considered "exact" as the total numerical error is comparable to that of the method employed for modeling wave propagation. We detail a basic implementation of our solution in the acoustic case using the finite difference method and present numerical examples that demonstrate the accuracy of the method. We show that ignoring some terms accounting for higher order scattering effects in our solution has a limited effect on the computed seismograms and significantly reduces the computational effort. Finally, we show that our solution can be used to compute localised sensitivity kernels and we discuss applications to target oriented imaging. Extension to the elastic case is straightforward and summarised in a

  20. 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.

  1. Spherical Wave Propagation in a Poroelastic Medium with Infinite Permeability: Time Domain Solution

    PubMed Central

    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

  2. Joint analysis of refractions with surface waves: An inverse solution to the refraction-traveltime problem

    USGS Publications Warehouse

    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.

  3. Localized numerical impulse solutions in diffuse neural networks modeled by the complex fractional Ginzburg-Landau equation

    NASA Astrophysics Data System (ADS)

    Mvogo, Alain; Tambue, Antoine; Ben-Bolie, Germain H.; Kofané, Timoléon C.

    2016-10-01

    We investigate localized wave solutions in a network of Hindmarsh-Rose neural model taking into account the long-range diffusive couplings. We show by a specific analytical technique that the model equations in the infrared limit (wave number k → 0) can be governed by the complex fractional Ginzburg-Landau (CFGL) equation. According to the stiffness of the system, we propose both the semi and the linearly implicit Riesz fractional finite-difference schemes to solve efficiently the CFGL equation. The obtained fractional numerical solutions for the nerve impulse reveal localized short impulse properties. We also show the equivalence between the continuous CFGL and the discrete Hindmarsh-Rose models for relatively large network.

  4. Fingering patterns in Hele-Shaw flows are density shock wave solutions of dispersionless KdV hierarchy

    SciTech Connect

    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.

  5. The effect of ultrasonic waves in conducting polymer solution.

    PubMed

    de Azevedo, W M; de Oliveira Luna, A J H; Silva, E F V B N; Silva, R O

    2006-07-01

    The effects of ultrasonic wave on the conducting polymer polyaniline dissolved in DMSO were observed. The UV-visible, infrared and NMR analysis show that the polymer undergo a redox and doping transition when the ultrasound wave interacts with the polymer dissolved into the solvent. The proposed mechanism to explain these effects is based on the solvent's hygroscopicity properties. The interaction with the ultrasonic wave, homolitically dissociates the water molecule producing radical species, and these species interact with the dissolved conducting polymer changing its oxidation and doped state. The resulting effects of that interaction are the modification of oxidation state of the conducting polymer and the decrease of the amount of water molecule in the solvent. From those results, we have proposed one straightforward method to eliminate water contamination in the solvent DMSO using ultrasonic waves.

  6. Steady Detonation Wave Solutions Under the Reaction Heat Effect

    NASA Astrophysics Data System (ADS)

    Carvalho, Filipe; Soares, Ana Jacinta

    2010-04-01

    The dynamics of the steady detonation wave is studied in the frame of the kinetic theory for a binary reacting mixture undergoing a chemical reaction of type A + A ⇌ B + B. The influence of the reaction heat on the detonation wave structure is investigated for the first time. Some numerical results are provided for a generic symmetric chemical reaction of exothermic and endothermic type.

  7. Accessing Extreme Spatiotemporal Localization of High-Power Laser Radiation through Transformation Optics and Scalar Wave Equations.

    PubMed

    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.

  8. Modeling of nonlinear interactions between guided waves and fatigue cracks using local interaction simulation approach.

    PubMed

    Shen, Yanfeng; Cesnik, Carlos E S

    2017-02-01

    This article presents a parallel algorithm to model the nonlinear dynamic interactions between ultrasonic guided waves and fatigue cracks. The Local Interaction Simulation Approach (LISA) is further developed to capture the contact-impact clapping phenomena during the wave crack interactions based on the penalty method. Initial opening and closure distributions are considered to approximate the 3-D rough crack microscopic features. A Coulomb friction model is integrated to capture the stick-slip contact motions between the crack surfaces. The LISA procedure is parallelized via the Compute Unified Device Architecture (CUDA), which enables parallel computing on powerful graphic cards. The explicit contact formulation, the parallel algorithm, as well as the GPU-based implementation facilitate LISA's high computational efficiency over the conventional finite element method (FEM). This article starts with the theoretical formulation and numerical implementation of the proposed algorithm, followed by the solution behavior study and numerical verification against a commercial finite element code. Numerical case studies are conducted on Lamb wave interactions with fatigue cracks. Several nonlinear ultrasonic phenomena are addressed. The classical nonlinear higher harmonic and DC response are successfully captured. The nonlinear mode conversion at a through-thickness and a half-thickness fatigue crack is investigated. Threshold behaviors, induced by initial openings and closures of rough crack surfaces, are depicted by the proposed contact LISA model.

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

    NASA Technical Reports Server (NTRS)

    Collins, William

    1989-01-01

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

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

    NASA Technical Reports Server (NTRS)

    Collins, William

    1989-01-01

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

  11. Local run-up amplification by resonant wave interactions.

    PubMed

    Stefanakis, Themistoklis S; Dias, Frédéric; Dutykh, Denys

    2011-09-16

    Until now, the analysis of long wave run-up on a plane beach has been focused on finding its maximum value, failing to capture the existence of resonant regimes. One-dimensional numerical simulations in the framework of the nonlinear shallow water equations are used to investigate the boundary value problem for plane and nontrivial beaches. Monochromatic waves, as well as virtual wave-gage recordings from real tsunami simulations, are used as forcing conditions to the boundary value problem. Resonant phenomena between the incident wavelength and the beach slope are found to occur, which result in enhanced run-up of nonleading waves. The evolution of energy reveals the existence of a quasiperiodic state for the case of sinusoidal waves. Dispersion is found to slightly reduce the value of maximum run-up but not to change the overall picture. Run-up amplification occurs for both leading elevation and depression waves.

  12. A symmetric Trefftz-DG formulation based on a local boundary element method for the solution of the Helmholtz equation

    NASA Astrophysics Data System (ADS)

    Barucq, H.; Bendali, A.; Fares, M.; Mattesi, V.; Tordeux, S.

    2017-02-01

    A general symmetric Trefftz Discontinuous Galerkin method is built for solving the Helmholtz equation with piecewise constant coefficients. The construction of the corresponding local solutions to the Helmholtz equation is based on a boundary element method. A series of numerical experiments displays an excellent stability of the method relatively to the penalty parameters, and more importantly its outstanding ability to reduce the instabilities known as the "pollution effect" in the literature on numerical simulations of long-range wave propagation.

  13. Symbolic computation and abundant travelling wave solutions to KdV-mKdV equation

    NASA Astrophysics Data System (ADS)

    Raza Rizvi, Syed Tahir; Ali, Kashif; Sardar, Ali; Younis, Muhammad; Bekir, Ahmet

    2017-01-01

    In this article, the novel ( G '/ G)-expansion method is successfully applied to construct the abundant travelling wave solutions to the KdV-mKdV equation with the aid of symbolic computation. This equation is one of the most popular equation in soliton physics and appear in many practical scenarios like thermal pulse, wave propagation of bound particle, etc. The method is reliable and useful, and gives more general exact travelling wave solutions than the existing methods. The solutions obtained are in the form of hyperbolic, trigonometric and rational functions including solitary, singular and periodic solutions which have many potential applications in physical science and engineering. Many of these solutions are new and some have already been constructed. Additionally, the constraint conditions, for the existence of the solutions are also listed.

  14. Mathieu function solutions for photoacoustic waves in sinusoidal one-dimensional structures.

    PubMed

    Wu, Binbin; Diebold, Gerald J

    2012-07-01

    The photoacoustic effect for a one-dimensional structure, the sound speed of which varies sinusoidally in space, is shown to be governed by an inhomogeneous Mathieu equation with the forcing term dependent on the spatial and temporal properties of the exciting optical radiation. New orthogonality relations, traveling wave Mathieu functions, and solutions to the inhomogeneous Mathieu equation are found, which are used to determine the character of photoacoustic waves in infinite and finite length phononic structures. Floquet solutions to the Mathieu equation give the positions of the band gaps, the damping of the acoustic waves within the band gaps, and the dispersion relation for photoacoustic waves. The solutions to the Mathieu equation give the photoacoustic response of the structure, show the space equivalent of subharmonic generation and acoustic confinement when waves are excited within band gaps.

  15. Wave localization of linear gravity waves in shallow water: Global measurements and agreement between random matrix theory and experiments

    NASA Astrophysics Data System (ADS)

    Schmessane, Andrea; Laboratory of matter out equilibrium Team

    2012-11-01

    Wave localization explains how a perturbation is trapped by the randomness present in a propagation medium. As it propagates, the localized wave amplitude decreases strongly by multiple internal reflections with randomly positioned scatterers, effectively trapping the perturbation inside the random region. The characteristic length where a localized wave is propagated before being extinguish by randomness is called localization length. We carried experiments in a quasi-onedimensional channel with random bottom in a shallow water regime for surface gravity water waves, using a Perfilometry Fourier Transform method, which enables us to obtain global surface measurements. We discuss keys aspects of the control of variables, the experimental setup and the implementation of the measurement method. Thus, we can control, measure and evaluate fundamental variables present in the localization phenomenon such as the type of randomness, scattering intensity and sample length, which allows us to characterize wave localization. We use the scattering matrix method to compare the experimental measurements with theoretical and numerical predictions, using the Lyapunov exponent of the scattering matrix, and discuss their agreement. Conicyt

  16. Zooming in: From spatially extended traveling waves to localized structures: The case of the Sine-Gordon equation in (1+3) dimensions.

    PubMed

    Zarmi, Yair

    2017-01-01

    The Sine-Gordon equation in (1+3) dimensions has N-traveling front ("kink", "domain wall")- solutions for all N ≥ 1. A nonlinear functional of the solution, which vanishes on a single-front, maps multi-front solutions onto sets of infinitely long, but laterally bounded, rods, which move in space. Each rod is localized in the vicinity of the intersection of two Sine-Gordon fronts. The rod systems are solutions of the linear wave equation, driven by a term that is constructed out of Sine-Gordon fronts. An additional linear operation maps multi-rod systems onto sets of blobs. Each blob is localized in the vicinity of rod intersection, and moves in space. The blob systems are solutions of the linear wave equation, driven by a term that is also constructed out of Sine-Gordon fronts. The temporal evolution of multi-blob solutions mimics elastic collisions of systems of spatially extended particles.

  17. Explicit solutions to the intrinsic generalization for the wave and sine-Gordon equations

    NASA Astrophysics Data System (ADS)

    Gu, Chaohao; Hu, Hesheng

    1993-09-01

    The Darboux matrix method is used to study intrinsic generalized wave equation and intrinsic generalized sine-Gordon equation which have been studied by Beals and Tenenblat. Explicit formulas for exact solutions are obtained.

  18. Hodograph transformation and differential constraints for wave solutions to 2 × 2 quasilinear hyperbolic nonhomogeneous systems

    NASA Astrophysics Data System (ADS)

    Curró, C.; Fusco, D.; Manganaro, N.

    2012-05-01

    The differential constraint method is used to work out a reduction approach to determine solutions in a closed form to the highly nonlinear hodograph system arising from 2 × 2 hyperbolic nonhomogeneous models. These solutions inherit all of the features of the standard wave solutions obtainable via the classical hodograph transformation and in the meantime incorporate the dissipative effects induced on wave processes by the source-like term involved in the governing equations. Within such a theoretical framework the problem of integrating the standard linear hodograph system associated with 2 × 2 homogeneous models is also revisited and a number of results obtained elsewhere of relevant interest in wave problems are recovered as a particular case. Along the lines of the proposed reduction approach, different examples of 2 × 2 governing models are analysed thoroughly in order to highlight the flexibility of the provided solutions to describe hyperbolic dissipative wave processes.

  19. Contradiction within wave optics and its solution within a particle picture: comment.

    PubMed

    Délen, Xavier; Hanna, Marc; Balembois, François; Georges, Patrick; Bretenaker, Fabien

    2016-02-08

    An error in the rationale presented in the paper "Contradiction within wave optics and its solution within a particle picture" by Altmann [Opt. Express 23, 3731 (2015)10.1364/OE.23.003731] is discussed.

  20. Traveling wave solutions for epidemic cholera model with disease-related death.

    PubMed

    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.

  1. Traveling Wave Solutions for Epidemic Cholera Model with Disease-Related Death

    PubMed Central

    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

  2. Rogue wave solutions to the generalized nonlinear Schrödinger equation with variable coefficients.

    PubMed

    Zhong, Wei-Ping; Belić, Milivoj R; Huang, Tingwen

    2013-06-01

    A similarity transformation is utilized to reduce the generalized nonlinear Schrödinger (NLS) equation with variable coefficients to the standard NLS equation with constant coefficients, whose rogue wave solutions are then transformed back into the solutions of the original equation. In this way, Ma breathers, the first- and second-order rogue wave solutions of the generalized equation, are constructed. Properties of a few specific solutions and controllability of their characteristics are discussed. The results obtained may raise the possibility of performing relevant experiments and achieving potential applications.

  3. Traveling wave solution of higher-order traffic flow model with discontinuous fundamental diagram

    NASA Astrophysics Data System (ADS)

    Wu, Chun-Xiu

    2015-07-01

    The traveling wave solution of a unified higher-order traffic flow model is investigated with a discontinuous fundamental diagram under the Lagrange coordinate. The equilibrium velocity is a piecewise function which consists of two concave functions. The weak solution theory is applied to study the traveling wave solution of the model, in which a set of equations about the characteristic parameters are obtained. Through numerical simulation, the moving cluster solutions of the anisotropic and isotropic traffic flow models are reproduced, respectively. The numerical results agree with the analytical ones.

  4. Local diagnosis of gravity wave propagation during different background wind conditions

    NASA Astrophysics Data System (ADS)

    Schoon, Lena; Zülicke, Christoph

    2017-04-01

    A new method to diagnose gravity wave properties of a 3-dimensional data set is introduced. Based on the Hilbert transform the amplitude and 3-dimensional wave number is provided on every grid point with the possibility to analyze wave propagation locally. As an exemplary case study two situations with different wind conditions in early 2016 are chosen from ECMWF reanalysis data. These situations are analyzed for vertical gravity wave propagation. During a minor sudden stratospheric warming event gravity waves propagate from the tropopause into the lower stratosphere up to the wind reversal. There the gravity wave becomes shallower and it is absorbed. During strong westerly wind conditions gravity wave action indicates wave propagation to higher altitudes and damping by the model sponge layer leading to no gravity wave signals above about 50 km. Local and zonally averaged results show that consideration of the wave energy may mislead the interpretation of gravity wave behavior due to its dependence on density and background wind. The wave action is highlighted as a better measure for gravity wave propagation.

  5. 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.

  6. MicroResearch: finding sustainable local health solutions in East Africa through small local research studies.

    PubMed

    MacDonald, N E; Bortolussi, R; Kabakyenga, J; Pemba, S; Estambale, B; Kollmann, K H M; Odoi Adome, R; Appleton, M

    2014-09-01

    Sub-Saharan African countries have urged grassroots input to improve research capacity. In East Africa, MicroResearch is fostering local ability to find sustainable solutions for community health problems. At 5years, the following reports its progress. The MicroResearch program had three integrated components: (1) 2-week training workshops; (2) small proposal development with international peer review followed by project funding, implementation, knowledge translation; (3) coaching from experienced researchers. Evaluation included standardized questions after completion of the workshops, 2013 online survey of recent workshop participants and discussions at two East Africa MicroResearch Forums in 2013. Between 2008 and 2013, 15 workshops were conducted at 5 East Africa sites with 391 participants. Of the 29 projects funded by MicroResearch, 7 have been completed; of which 6 led to changes in local health policy/practice. MicroResearch training stimulated 13 other funded research projects; of which 8 were external to MicroResearch. Over 90% of participants rated the workshops as excellent with 20% spontaneously noting that MicroResearch changed how they worked. The survey highlighted three local research needs: mentors, skills and funding - each addressed by MicroResearch. On-line MicroResearch and alumni networks, two knowledge translation partnerships and an East Africa Leaders Consortium arose from the MicroResearch Forums. MicroResearch helped build local capacity for community-directed interdisciplinary health research. Copyright © 2014. Published by Elsevier Ltd.

  7. An analysis of spatiotemporal localized solutions in the variable coefficients (3 + 1)-dimensional nonlinear Schrödinger equation with six different forms of dispersion parameters

    NASA Astrophysics Data System (ADS)

    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.

  8. 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.

  9. Localization of ultra-low frequency waves in multi-ion plasmas of the planetary magnetosphere

    SciTech Connect

    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.

  10. Localized Nonlinear Waves in Nonlinear Schr¨odinger Equation with Nonlinearities Modulated in Space and Time

    NASA Astrophysics Data System (ADS)

    Chen, Junchao; Li, Biao

    2011-12-01

    In this paper, the generalized sub-equation method is extended to investigate localized nonlinear waves of the one-dimensional nonlinear Schrödinger equation (NLSE) with potentials and nonlinearities depending on time and on spatial coordinates. With the help of symbolic computation, three families of analytical solutions of this NLS-type equation are presented. Based on these solutions, periodically and quasiperiodically oscillating solitons (dark and bright) and moving solitons are observed. Some implications to Bose-Einstein condensates are also discussed

  11. Resonant emission of solitons from impurity-induced localized waves in nonlinear lattices.

    PubMed

    Yu, Gaokun; Wang, Xinlong; Tao, Zhiyong

    2011-02-01

    We propose a mechanism for soliton creation from resonantly excited localized waves via supratransmission in band gaps of nonlinear lattices. A nonlinear localized wave, which is formed by and vibrates around an impurity with an intrinsic frequency, is found to undergo a local resonance when subject to an external forcing. Under the resonance, an instability develops that leads to the efficient emission of solitons at a much lower rate than that in uniform lattices with no impurity. ©2011 American Physical Society

  12. Solution of the scalar wave equation over very long distances using nonlinear solitary waves: Relation to finite difference methods

    NASA Astrophysics Data System (ADS)

    Steinhoff, John; Chitta, Subhashini

    2012-08-01

    , as a wave equation with an added "confining" term that involves both a positive and a negative dissipation. Once we have the stable PDE, the discrete formulation is simply a multidimensional PDE with (stable) perturbations caused by the discretization. The resulting discrete solution can then be low order and very simple and yet remain stable over arbitrarily long times. When discretized and solved on an Eulerian grid, this new method allows far coarser grids than required by conventional resolution considerations, while still accounting for the effects of varying atmospheric and topographic features. An important point is that the new method is in the same form as conventional discrete wave equation methods. However, the conventional solution eventually decays, and only the "intermediate asymptotic" solution can be used. Simply by adding an extra term, we show that a nontrivial true asymptotic solution can be obtained. A similar solitary wave based approach has been used successfully in a different problem (involving "Vorticity Confinement"), for a number of years.

  13. Ammonia nitrogen removal from aqueous solution by local agricultural wastes

    NASA Astrophysics Data System (ADS)

    Azreen, I.; Lija, Y.; Zahrim, A. Y.

    2017-06-01

    Excess ammonia nitrogen in the waterways causes serious distortion to environment such as eutrophication and toxicity to aquatic organisms. Ammonia nitrogen removal from synthetic solution was investigated by using 40 local agricultural wastes as potential low cost adsorbent. Some of the adsorbent were able to remove ammonia nitrogen with adsorption capacity ranging from 0.58 mg/g to 3.58 mg/g. The highest adsorption capacity was recorded by Langsat peels with 3.58 mg/g followed by Jackfruit seeds and Moringa peels with 3.37 mg/g and 2.64 mg/g respectively. This experimental results show that the agricultural wastes can be utilized as biosorbent for ammonia nitrogen removal. The effect of initial ammonia nitrogen concentration, pH and stirring rate on the adsorption process were studied in batch experiment. The adsorption capacity reached maximum value at pH 7 with initial concentration of 500 mg/L and the removal rate decreased as stirring rate was applied.

  14. Local Existence of Solutions of Self Gravitating Relativistic Perfect Fluids

    NASA Astrophysics Data System (ADS)

    Brauer, Uwe; Karp, Lavi

    2014-01-01

    This paper deals with the evolution of the Einstein gravitational fields which are coupled to a perfect fluid. We consider the Einstein-Euler system in asymptotically flat spacestimes and therefore use the condition that the energy density might vanish or tend to zero at infinity, and that the pressure is a fractional power of the energy density. In this setting we prove local in time existence, uniqueness and well-posedness of classical solutions. The zero order term of our system contains an expression which might not be a C ∞ function and therefore causes an additional technical difficulty. In order to achieve our goals we use a certain type of weighted Sobolev space of fractional order. In Brauer and Karp (J Diff Eqs 251:1428-1446, 2011) we constructed an initial data set for these of systems in the same type of weighted Sobolev spaces. We obtain the same lower bound for the regularity as Hughes et al. (Arch Ratl Mech Anal 63(3):273-294, 1977) got for the vacuum Einstein equations. However, due to the presence of an equation of state with fractional power, the regularity is bounded from above.

  15. 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.

  16. Very weak solutions of wave equation for Landau Hamiltonian with irregular electromagnetic field

    NASA Astrophysics Data System (ADS)

    Ruzhansky, Michael; Tokmagambetov, Niyaz

    2016-11-01

    In this paper, we study the Cauchy problem for the Landau Hamiltonian wave equation, with time-dependent irregular (distributional) electromagnetic field and similarly irregular velocity. For such equations, we describe the notion of a `very weak solution' adapted to the type of solutions that exist for regular coefficients. The construction is based on considering Friedrichs-type mollifier of the coefficients and corresponding classical solutions, and their quantitative behaviour in the regularising parameter. We show that even for distributional coefficients, the Cauchy problem does have a very weak solution, and that this notion leads to classical or distributional-type solutions under conditions when such solutions also exist.

  17. Very weak solutions of wave equation for Landau Hamiltonian with irregular electromagnetic field

    NASA Astrophysics Data System (ADS)

    Ruzhansky, Michael; Tokmagambetov, Niyaz

    2017-04-01

    In this paper, we study the Cauchy problem for the Landau Hamiltonian wave equation, with time-dependent irregular (distributional) electromagnetic field and similarly irregular velocity. For such equations, we describe the notion of a `very weak solution' adapted to the type of solutions that exist for regular coefficients. The construction is based on considering Friedrichs-type mollifier of the coefficients and corresponding classical solutions, and their quantitative behaviour in the regularising parameter. We show that even for distributional coefficients, the Cauchy problem does have a very weak solution, and that this notion leads to classical or distributional-type solutions under conditions when such solutions also exist.

  18. 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.

  19. Translation of waves along quantum vortex filaments in the low-temperature two-dimensional local induction approximation

    SciTech Connect

    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

  20. Exact soliton solution of spin chain with an external magnetic field in linear wave background

    NASA Astrophysics Data System (ADS)

    Li, Qiu-Yan; Xie, Zheng-Wei; Li, Lu; Li, Zai-Dong; Liang, Jiu-Qing

    2004-07-01

    Employing a simple, straightforward Darboux transformation we construct exact N-soliton solution for anisotropic spin chain driven by an external magnetic field in linear wave background. As a special case the explicit one- and two-soliton solution dressed by the linear wave corresponding to magnon in quantum theory is obtained analytically and its property is discussed in detail. The dispersion law, effective soliton mass, and the energy of each soliton are investigated as well. Our result show that the stability criterion of soliton is related with anisotropic parameter and the amplitude of the linear wave.

  1. 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.

  2. Experimental signatures of localization in Langmuir wave turbulence

    SciTech Connect

    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.

  3. Local origin of slow EEG waves during sleep.

    PubMed

    Timofeev, Igor

    2013-01-01

    Neuronal activity mediating EEG slow waves consists of synchronous alternation of intracellular active and silent states. Recent data demonstrate that each active state of a sleep slow wave originates in a particular cortical location and propagate to involve other cortical areas. Preferential sites of origin of these waves are: the frontal cortex in adult humans, the associative cortex in cats and the somatosensory cortex in mice. In the site of origin of these slow waves any neuron can initiate a particular cycle, however there are neuronal groups with high likelihood of triggering a particular cycle. In epileptic patients, these neurons are mostly located in superficial layers, but in healthy experimental animals, populations ofintrinsically bursting neurons with a high probability of triggering spontaneous active states have been found in deeper cortical layers.

  4. Sensor structure concepts for the analysis or local radiation exposure of biological samples at terahertz and millimeter wave frequencies

    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.

  5. Two-state model based on the block-localized wave function method

    NASA Astrophysics Data System (ADS)

    Mo, Yirong

    2007-06-01

    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 π →π* transition for formamide upon solvation undergoes a redshift of 0.3eV, compared with the experimental data (0.40-0.5eV).

  6. Two-state model based on the block-localized wave function method.

    PubMed

    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).

  7. A simple and direct method for generating travelling wave solutions for nonlinear equations

    SciTech Connect

    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.

  8. Acoustic wave propagation in the solar atmosphere 1. Rediscussion of the linearized theory including nonstationary solutions

    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

  9. Simple Methods to Extract Analytical Solutions for Rossby Waves on Continuously Stratified Zonal Background Flows

    NASA Astrophysics Data System (ADS)

    Vianna, M. L.

    2016-02-01

    Observed westward phase speeds of Rossby waves in a subtropical region dominated by stratified eastward jets in the South Indian Ocean are about five times the traditional linear theory for propagation of Rossby waves in a stratified ocean. To date no simple analytical generalization of the standard dispersion relation with the inclusion of the effect of baroclinic eastward currents has been obtained, even for flat surface and bottom boundary conditions. One reason may be due to a kind of entanglement between the vertical profile of the jet and the phase speed eigenvalue, which makes this a nonlinear albeit separable eigenvalue problem even for linear theory. A quasi-exact entangled solution, separable by a Modified Bessel Transform, makes possible simple generalizations of the standard dispersion relation, away from critical layers. An interesting application of the method to Rossby waves over the South Indian Coutercurrent at 26° S using a parabolic approximation to the zonal velocity around its minimum at 500 m is offered here. The phase speed enhancement γ =c/c0, where c is the eigenvalue of the vertical velocity and c0 the phase speed given by the standard theory for the first baroclinic mode depends on a single parameter s=(π 2/12)U{zz(β N2/f2)-1, where Uzz is the curvature of the vertical profile of the mean zonal velocity. For (s/γ )≥{1} , the enhancement is simply given by γ = s2/3 , while for (s/γ )≤{1} , γ = 1+s . Examples near the critical layer and wavelengths of the order of the mean local Rossby radius (baroclinic instability) is also discussed in this context. The effects of adding sharp mid-oceanic ridges to the boundary conditions are also discussed.

  10. Alfvén wave collisions, the fundamental building block of plasma turbulence. I. Asymptotic solution

    SciTech Connect

    Howes, G. G.; Nielson, K. D.

    2013-07-15

    The nonlinear interaction between counterpropagating Alfvén waves is the physical mechanism underlying the cascade of energy to small scales in astrophysical plasma turbulence. Beginning with the equations for incompressible MHD, an asymptotic analytical solution for the nonlinear evolution of these Alfvén wave collisions is derived in the weakly nonlinear limit. The resulting qualitative picture of nonlinear energy transfer due to this mechanism involves two steps: first, the primary counterpropagating Alfvén waves interact to generate an inherently nonlinear, purely magnetic secondary fluctuation with no parallel variation; second, the two primary waves each interact with this secondary fluctuation to transfer energy secularly to two tertiary Alfvén waves. These tertiary modes are linear Alfvén waves with the same parallel wavenumber as the primary waves, indicating the lack of a parallel cascade. The amplitude of these tertiary modes increases linearly with time due to the coherent nature of the resonant four-wave interaction responsible for the nonlinear energy transfer. The implications of this analytical solution for turbulence in astrophysical plasmas are discussed. The solution presented here provides valuable intuition about the nonlinear interactions underlying magnetized plasma turbulence, in support of an experimental program to verify in the laboratory the nature of this fundamental building block of astrophysical plasma turbulence.

  11. Nonlinear wave structures as exact solutions of Vlasov-Maxwell equations.

    NASA Astrophysics Data System (ADS)

    Dasgupta, B.; Tsurutani, B. T.; Janaki, M. S.; Sharma, A. S.

    2001-12-01

    Many recent observations by POLAR and Geotail spacecraft of the low-latitudes magnetopause boundary layer (LLBL) and the polar cap boundary layer (PCBL) have detected nonlinear wave structures [Tsurutani et al, Geophys. Res. Lett., 25, 4117, 1998]. These nonlinear waves have electromagnetic signatures that are identified with Alfven and Whistler modes. Also solitary waves with mono- and bi-polar features were observed. In general such electromagnetic structures are described by the full Vlasov-Maxwell equations for waves propagating at an angle to the ambient magnetic field, but it has been a diffficult task obtaining the solutions because of the inherent nonlinearity. We have obtained an exact nonlinear solution of the full Vlasov-Maxwell equations in the presence of an electromagnetic wave propagating at an arbitrary direction with an ambient magnetic field. This is accomplished by finding the constants of motion of the charged particles in the electromagnetic field of the wave and then constructing a realistic distribution function as a function of these constants of motion. The corresponding trapping conditions for such waves are obtained, yielding the self-consistent description for the particles in the presence of the nonlinear waves. The interpretation of the observed nonlinear structures in terms of these general solutions will be presented.

  12. A research on solutions of a wave equation of shallow water for roll waves of debris flow

    NASA Astrophysics Data System (ADS)

    Arai, Muneyuki

    2015-04-01

    Intermittent surges of debris flow are observed in mountains region in Europe, Aisia and others. A purpose of this research is to obtain characteristic of wave equation on shallow water for debris flow surges. Considering a flow in a rectangular straight channel, where the width is very large compared to a flow depth, momentum correction factor β = 1 , constant friction factor over mean depth h0, a channel slope tanθ < 1, Froude number Fr > 1 , and a long wave condition by results of observations and experiments, a wave equation is obtained with δη' 'δη' δ2η' δ3η' δτ' + a1η δξ' - a2δξ'2 + a3δξ'3 = 0 (1) where, a1 = (3/2)c0'2, a2 = (1/2)( ) 1/c0'2 - 1/2tanθ (c0'/u0'), a3 = (1/2){ 4 2 } (2 + c0' )/(2c0')- 3/2 , and η : fluctuation of mean flow depth, h0 : mean depth, h = h0 + η : flow depth, η' = η/h0, x : coordinate axis of flow direction, x' = x/h0, ξ = ɛ1/2(x - vp0), ξ' = ξ/h0, vp0 : phase velocity, the velocity parameter of Gardner - Morikawa transformation, y : coordinate axis of depth direction, y' = y/h0, t : time, t' = tvp0/h0, τ = ɛ3/2t, τ' = (vp0/h0)τ, g : acceleration due to gravity, θ : slope angle of the channel, c0 = √-- gh0cosθ : wave velocity of a long wave, c0' = c0/vp0 u0 : mean velocity, u0' = u0/c0. Using for vp0 = c0 under a long wave condition by observations and experiments, above equation is expressed as δ-η' 3 ' δη' 1tanθ-δ2η' δ τ' + 2 η δξ' - 4 u0' δξ'2 = 0. (2) This equation is a kind of Burgers equation. Analytical solutions for different wave number k = 1/2, 3/2, 5/2 and k = 1,2,3 on initial conditions were obtained, and calculated by numerical analysis. These results show that the wave shape are deformed to a wave of wave number k = 1 for not multiple wave number. This indicates that a surge is formed with a wave length from the wave of a lot of wave numbers in initial state on actual surges or experimental surge flows.

  13. 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.

  14. Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators

    SciTech Connect

    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 evolution 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.

  15. Transient axial solution for plane and axisymmetric waves focused by a paraboloidal reflector.

    PubMed

    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.

  16. Multi-soliton, multi-breather and higher order rogue wave solutions to the complex short pulse equation

    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.

  17. 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.

  18. 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.

  19. Nonlinear spin wave magnetization of solution synthesized Ni nanoparticles

    NASA Astrophysics Data System (ADS)

    Vitta, Satish

    2007-03-01

    The magnetic properties of Ni nanoparticles synthesized using a soft chemical method followed by heat treatment in H2 atmosphere have been studied in detail. The powder consists of pure Ni with no additional phase and the average crystallite size is 30±5nm, determined using the modified Scherer relation. The crystallites tend to agglomerate into large particles of sizes 50-100nm, as observed by transmission electron microscopy. The saturation magnetization is found to be 46.42emug-1 at 5K, about 80% of the bulk magnetization value. The temperature dependence of saturation magnetization for T <0.5TC is found to deviate from the linear Bloch's T3/2 law indicating that spin wave interactions needs to be considered to understand the behavior. The spin wave stiffness constant obtained by fitting the saturation magnetization decay to a nonlinear spin wave model is lower by an order of magnitude compared to that of bulk Ni. The coercivity on the other hand decreases from 67Oe at 5Kto36Oe at 300K with a temperature dependence slower than the T1/2 behavior predicted for noninteracting superparamagnetic particles.

  20. Traveling waves solutions of isothermal chemical systems with decay

    NASA Astrophysics Data System (ADS)

    Qi, Yuanwei

    2015-02-01

    This article studies propagating traveling waves in a class of reaction-diffusion systems which include a model of microbial growth and competition in a flow reactor proposed by Smith and Zhao [17], and isothermal autocatalytic systems in chemical reaction of order m with a decay order n, where m and n are positive integers and m ≠ n. A typical system in autocatalysis is A + 2 B → 3 B (with rate k1 ab2) and B → C (with rate k2 b), where m = 2 and n = 1, involving two chemical species, a reactant A and an auto-catalyst B whose diffusion coefficients, DA and DB, are unequal due to different molecular weights and/or sizes. Here a is the concentration density of A, b that of B and C an inert chemical species. The two constants k1 and k2 are material constants measuring the relative strength of respective reactions. It is shown that there exist traveling waves when m > 1 and n = 1 with suitable relation between the ratio DB /DA, traveling speed c and rate constants k1, k2. On the other hand, it is proved that there exists no traveling wave when one of the chemical species is immobile, DB = 0 or n > m for all choices of other parameters.

  1. Classical implicit travelling wave solutions for a quasilinear convection-diffusion equation

    NASA Astrophysics Data System (ADS)

    Hearns, Jessica; Van Gorder, Robert A.

    2012-11-01

    We discuss classical implicit solutions to the partial differential equation ut=(H(u))xx+(G(u))x, a general convection-diffusion PDE with particular subcases appearing in many areas of fluids and astrophysics. As an illustrative example, and to compare our results with those present in the literature, we frequently consider travelling wave solutions for the quasilinear PDE ut=(um)xx+(un)x, which has been used to describe the flow of viscous fluids on an inclined bed and as a model of convection-diffusion processes. When n ⩾ m > 1, this equation can be used to model the flow of a fluid under gravity through a homogeneous and isotropic porous medium. The travelling wave ODE for both the general and more specific cases have a first integral which is used to obtain an implicit solution for the travelling wave profiles. We should mention that, for some values of m, the implicit relation can be solved in closed form for explicit exact solutions. In the case of n = 2m - 1, solving the implicit relation gives a general way of obtaining the solutions found in Vanaja [Vanaja, V., 2009. Physica Scripta 80, p. 045402] where the travelling wave solutions for the cases (m, n) = (2, 3) and (m, n) = (3, 5) were explicitly constructed using a more complicated ansatz method. For other more complicated cases where inversion cannot be performed, we apply the method of series reversion to construct series solutions from the implicit relations. Furthermore, we deduce the dependence of travelling wave solutions on the wave speed, even in cases where the explicit exact solution cannot be found.

  2. 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.

  3. An exact solution for effects of topography on free Rayleigh waves

    USGS Publications Warehouse

    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.

  4. 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.

  5. The Construction of Implicit and Explicit Solitary Wave Solutions of Nonlinear Partial Differential Equations.

    DTIC Science & Technology

    1987-08-01

    solution of the Korteweg-de Vries equation ( KdV ), working our way up to the derivation of the multi-soliton solution of the sine-Gordon equation (sG...SOLITARY WAVE SOLUTIONS OF NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS j DiS~~Uj~l. _’UDistribution/Willy Hereman AvaiiLi -itY Codes Technical Summary Report...Key Words: soliton theory, solitary waves, coupled KdV , evolution equations , direct methods, Harry Dym, sine-Gordon Mathematics Department, University

  6. Normal mode solutions for seismo-acoustic propagation resulting from shear and combined wave point sources.

    PubMed

    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.

  7. Traveling wave solutions for bistable fractional Allen-Cahn equations with a pyramidal front

    NASA Astrophysics Data System (ADS)

    Chan, Hardy; Wei, Juncheng

    2017-05-01

    Using the method of sub-super-solution, we construct a solution of (- Δ) s u - cuz - f (u) = 0 on R3 of pyramidal shape. Here (- Δ) s is the fractional Laplacian of sub-critical order 1 / 2 < s < 1 and f is a bistable nonlinearity. Hence, the existence of a traveling wave solution for the parabolic fractional Allen-Cahn equation with pyramidal front is asserted. The maximum of planar traveling wave solutions in various directions gives a sub-solution. A super-solution is roughly defined as the one-dimensional profile composed with the signed distance to a rescaled mollified pyramid. In the main estimate we use an expansion of the fractional Laplacian in the Fermi coordinates.

  8. Solitary Wave Solutions of KP equation, Cylindrical KP Equation and Spherical KP Equation

    NASA Astrophysics Data System (ADS)

    Li, Xiang-Zheng; Zhang, Jin-Liang; Wang, Ming-Liang

    2017-02-01

    Three (2+1)-dimensional equations–KP equation, cylindrical KP equation and spherical KP equation, have been reduced to the same KdV equation by different transformation of variables respectively. Since the single solitary wave solution and 2-solitary wave solution of the KdV equation have been known already, substituting the solutions of the KdV equation into the corresponding transformation of variables respectively, the single and 2-solitary wave solutions of the three (2+1)-dimensional equations can be obtained successfully. Supported by the National Natural Science Foundation of China under Grant No. 11301153 and the Doctoral Foundation of Henan University of Science and Technology under Grant No. 09001562, and the Science and Technology Innovation Platform of Henan University of Science and Technology under Grant No. 2015XPT001

  9. 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.

  10. Existence of traveling wave solutions for diffusive predator-prey type systems

    NASA Astrophysics Data System (ADS)

    Hsu, Cheng-Hsiung; Yang, Chi-Ru; Yang, Ting-Hui; Yang, Tzi-Sheng

    In this work we investigate the existence of traveling wave solutions for a class of diffusive predator-prey type systems whose each nonlinear term can be separated as a product of suitable smooth functions satisfying some monotonic conditions. The profile equations for the above system can be reduced as a four-dimensional ODE system, and the traveling wave solutions which connect two different equilibria or the small amplitude traveling wave train solutions are equivalent to the heteroclinic orbits or small amplitude periodic solutions of the reduced system. Applying the methods of Wazewski Theorem, LaSalle's Invariance Principle and Hopf bifurcation theory, we obtain the existence results. Our results can apply to various kinds of ecological models.

  11. Localization of ultra-low frequency waves in multi-ion plasmas of the planetary magnetosphere

    DOE PAGES

    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

  12. Water wave solutions of the coupled system Zakharov-Kuznetsov and generalized coupled KdV equations.

    PubMed

    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.

  13. Water Wave Solutions of the Coupled System Zakharov-Kuznetsov and Generalized Coupled KdV Equations

    PubMed Central

    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

  14. Spin waves in a two-sublattice antiferromagnet. A self-similar solution of the Landau-Lifshitz equation

    NASA Astrophysics Data System (ADS)

    Gorobets, Y. I.; Gorobets, Y.; Kulish, V. V.

    2017-01-01

    In the paper, spin waves in a uniaxial two-sublattice antiferromagnet are investigated. A new class of self-similar solutions of the Landau-Lifshitz equation is obtained and, therefore, a new type of spin waves is described. Examples of solutions of the found class are presented. New type of solution admits both linear and non-linear spin waves, including solitons. Space transformations used in the solution are mathematically analogous to the relativistic transformations.

  15. Matter-wave exact periodic solutions in optical lattices with periodic potential

    NASA Astrophysics Data System (ADS)

    Liu, Changfu; Zhu, Aijun

    2013-10-01

    Some special matter-wave periodic solutions for the Gross-Pitaevskii equation with periodic potential in the multidimensional optical lattices, are obtained through restricting parameters and some balance conditions between the optical potentials and interaction energies. The results show that the same type of periodic solutions in the same dimension possesses the same norm but different phases and they are all bounded. Especially, the numerics shows that two class (2+1)-dimensional periodic solutions are stable.

  16. A simplified method for thermal analysis of a cowl leading edge subject to intense local shock-wave-interference heating

    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.

  17. Self-similar wave produced by local perturbation of the Kelvin-Helmholtz shear-layer instability.

    PubMed

    Hoepffner, Jérôme; Blumenthal, Ralf; Zaleski, Stéphane

    2011-03-11

    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.

  18. On the Periodic Solutions of the Five-Dimensional Lorenz Equation Modeling Coupled Rosby Waves and Gravity Waves

    NASA Astrophysics Data System (ADS)

    Carvalho, Tiago; Llibre, Jaume

    2017-06-01

    Lorenz studied the coupled Rosby waves and gravity waves using the differential system U˙ = -VW + bVZ,V˙ = UW - bUZ,Ẇ = -UV,Ẋ = -Z,Ż = bUV + X. This system has the two first integrals H1 = U2 + V2,H 2 = V2 + W2 + X2 + Z2. Our main result shows that in each invariant set {H1 = h1 > 0}∩{H2 = h2 > 0} there are at least four (resp., 2) periodic solutions of the differential system with b≠0 and h2 > h1 (resp., h2 < h1).

  19. 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.

  20. 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.

  1. Spatial localization of nonlinear waves spreading in materials in the presence of dislocations and point defects

    NASA Astrophysics Data System (ADS)

    Erofeev, V. I.; Leontieva, A. V.; Malkhanov, A. O.

    2017-06-01

    Within the framework of self consistent dynamic problems, the impact of dislocations and point defects on the spatial localization of nonlinear acoustic waves propagating in materials has been studied.

  2. Lamb Wave Polarization Techniques for Structural Damage Localization and Quantification

    DTIC Science & Technology

    2011-11-01

    technological applications based on wave propagation, such as optics, seismology , telecommunications, and radar science. As opposed to other fields...Sorrento, Naples, Italy , 2010. 12. Sundaresan, M. J.; Pai, P. F.; Ghoshal, A.; Schulz, M.; Ferguson, F.; Chung, J. F. Methods of Distributed Sensing

  3. Exact numerical solutions for dark waves on the discrete nonlinear Schrödinger equation.

    PubMed

    Sánchez-Rey, Bernardo; Johansson, Magnus

    2005-03-01

    In this paper we study numerically existence and stability of exact dark waves on the (nonintegrable) discrete nonlinear Schrödinger equation for a finite one-dimensional lattice. These are solutions that bifurcate from stationary dark modes with constant background intensity and zero intensity at a site, and whose initial state translates exactly one site each period of the internal oscillations. We show that exact dark waves are characterized by an oscillatory background whose wavelength is closely related with the velocity. Faster dark waves require smaller wavelengths. For slow enough velocity dark waves are linearly stable, but when trying to continue numerically a solution towards higher velocities bifurcations appear, due to rearrangements in the oscillatory tail in order to make possible a decreasing of the wavelength. However, in principle, one might control the stability of an exact dark wave adjusting a phase factor which plays the role of a discreteness parameter. In addition, we also study the regimes of existence and stability for stationary discrete gray modes, which are exact solutions with phase-twisted constant-amplitude background and nonzero minimum intensity. Also such solutions develop envelope oscillations on top of the homogeneous background when continued into moving phase-twisted solutions.

  4. Spin wave localization in one-dimensional magnonic microcavity comprising yttrium iron garnet

    SciTech Connect

    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.

  5. Exact spherical wave solutions to Maxwell's equations with applications

    NASA Astrophysics Data System (ADS)

    Silvestri, Guy G.

    Electromagnetic radiation from bounded sources represent an important class of physical problems that can be solved for exactly. However, available texts on this subject almost always resort to approximate solution techniques that not only obscure the essential features of the problem but also restrict application to limited ranges of observation. This dissertation presents exact solutions for this important class of problems and demonstrates how these solutions can be applied to situations of genuine physical interest, in particular, the design of device structures with prespecified emission characteristics. The strategy employed is to solve Maxwell's equations in the spherical coordinate system. In this system, fundamental parameters such as electric and magnetic multipole moments fall out quite naturally. Expressions for radiated power, force, and torque assume especially illuminating and simple forms when expressed in terms of these multipole moments. All solutions are derived ab initio using first-principles arguments exclusively. Two operator equations that receive particularly detailed treatment are the vector Helmholtz equation for the time-independent potential vector-a and the 'covariant divergence' equation for the energy-momentum-stress tensor T(exp mu nu). An application of classical formulas, as modified by the requirements of statistical mechanics, to the case of heated black bodies leads to inquiries into the foundations of quantum mechanics and their relation to classical field theory. An application of formulas to various emission structures (spherically shaped antennas, surface diffraction gratings, collimated beams) provides a basis upon which to characterize these structures in an exact sense and, ultimately, to elicit clues as to their optimum design.

  6. Exact Spherical Wave Solutions to Maxwell's Equations with Applications

    NASA Astrophysics Data System (ADS)

    Silvestri, Guy G.

    Electromagnetic radiation from bounded sources represent an important class of physical problems that can be solved for exactly. However, available texts on this subject almost always resort to approximate solution techniques that not only obscure the essential features of the problem but also restrict application to limited ranges of observation. This dissertation presents exact solutions for this important class of problems and demonstrates how these solutions can be applied to situations of genuine physical interest, in particular, the design of device structures with prespecified emission characteristics. The strategy employed is to solve Maxwell's equations in the spherical coordinate system. In this system, fundamental parameters such as electric and magnetic multipole moments fall out quite naturally. Expressions for radiated power, force, and torque assume especially illuminating and simple forms when expressed in terms of these multipole moments. All solutions are derived ab initio using first-principles arguments exclusively. Two operator-equations that receive particularly detailed treatment are the vector Helmholtz equation for the time-independent potential vec a and the "covariant divergence" equation for the energy-momentum-stress tensor T^{mu nu}. An application of classical formulas, as modified by the requirements of statistical mechanics, to the case of heated blackbodies leads to inquiries into the foundations of quantum mechanics and their relation to classical field theory. An application of formulas to various emission structures (spherically-shaped antennas, surface diffraction gratings, collimated beams) provides a basis upon which to characterize these structures in an exact sense, and, ultimately, to elicit clues as to their optimum design.

  7. Detonation Waves Parameters for Fefo/nitrobenzene Solution

    NASA Astrophysics Data System (ADS)

    Mochalova, V. M.; Utkin, A. V.; Garanin, V. A.; Torunov, S. I.

    2009-12-01

    The dependence of detonation parameters for (bis-(2-fluoro-2, 2-dinitroethyl) formal)/nitrobenzene solution (FEFO/NB) on NB concentration was defined. Velocity profiles of the boundary between HE and water window were recorded by laser interferometer VISAR. It was found that particle velocity in a pure FEFO was strongly oscillating with the oscillation amplitude ˜50 m/s. It means that detonation front is unstable and heterogeneities size is about 10 μm. The average velocity profile corresponds to ZND model. The reaction time is equal to ˜400 ns, C-J pressure and particle velocity are 24 GPa and 2.0 km/s respectively. For FEFO/NB solution it was found that at low NB concentrations (10-20%) oscillations disappeared and detonation front was stable. When the NB concentration increased up to 30% high-frequency oscillations appeared again. The measurements of reaction zone structure up to critical concentration were conducted, it was about 45%. At average particle velocity profiles Von Neumann spike was distinctly registered. It was shown that in a pure FEFO and in solutions with NB concentration exceeding 30%) detonation front was unstable.

  8. Detonation waves parameters for FEFO/nitrobenzene solution

    NASA Astrophysics Data System (ADS)

    Mochalova, Valentina; Utkin, Alexander; Garanin, Victor; Torunov, Sergey

    2009-06-01

    The dependence of detonation parameters for (bis-(2-fluoro-2,2-dinitroethyl) formal)/nitrobenzene solution (FEFO/NB) from NB concentration was defined. Velocity profiles of the boundary between HE and water window were recorded by laser interferometer VISAR. It was found that particle velocity in a pure FEFO was strongly oscillating with the oscillation amplitude ˜50 m/s. It means that detonation front is unstable and irregularity size is about 10 mkm. The average velocity profile corresponds to ZND model. The reaction time is equal to ˜ 400ns, C-J pressure and particle velocity are 24 GPa and 2.0 km/s respectively. For FEFO/NB solution it was found that at low NB concentrations (10-20%) oscillations disappeared and detonation front was stable. When the NB concentration was increased up to 30 % high-frequency oscillations appeared again. The measurements of reaction zone structure up to critical concentration were conducted, it was about 45%. At average particle velocity profiles Von Neumann spike was distinctly registered. It was shown that in a pure FEFO and in solutions with NB concentration exceeding 30% detonation front was unstable.

  9. Solitons and nonlinear waves along quantum vortex filaments under the low-temperature two-dimensional local induction approximation

    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.

  10. Localized nonlinear waves in systems with time- and space-modulated nonlinearities.

    PubMed

    Belmonte-Beitia, Juan; Pérez-García, Víctor M; Vekslerchik, Vadym; Konotop, Vladimir V

    2008-04-25

    Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schrödinger 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.

  11. Localized Nonlinear Waves in Systems with Time- and Space-Modulated Nonlinearities

    SciTech Connect

    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.

  12. Approximate solutions to a nonintegrable problem of propagation of elliptically polarised waves in an isotropic gyrotropic nonlinear medium, and periodic analogues of multisoliton complexes

    SciTech Connect

    Makarov, V A; Petnikova, V M; Potravkin, N N; Shuvalov, V V

    2014-02-28

    Using the linearization method, we obtain approximate solutions to a one-dimensional nonintegrable problem of propagation of elliptically polarised light waves in an isotropic gyrotropic medium with local and nonlocal components of the Kerr nonlinearity and group-velocity dispersion. The consistent evolution of two orthogonal circularly polarised components of the field is described analytically in the case when their phases vary linearly during propagation. The conditions are determined for the excitation of waves with a regular and 'chaotic' change in the polarisation state. The character of the corresponding nonlinear solutions, i.e., periodic analogues of multisoliton complexes, is analysed. (nonlinear optical phenomena)

  13. Localization Effects on the Dissipation of Gravity Wave Packet in the Upper Mesosphere and Lower Thermosphere

    NASA Astrophysics Data System (ADS)

    Walterscheid, R. L.; Heale, C. J.; Snively, J. B.

    2016-12-01

    A question of fundamental importance is the altitudes to which waves originating in the lower atmosphere can propagate. It is well-known that high-frequency waves may propagate to great heights, while slow waves are damped at lower altitudes. Less well known is that the nature of the disturbance, whether it is a localized wave packet excited by transient forcing or a steady-state wave excited by sustained forcing, also controls wave decay. Wave packets may diminish in amplitude by the spreading of wave energy due to dispersion, whereas steady-state waves are already fully dispersed. For steady-state waves dissipation always gives an increase in the vertical wavelength, for wavepackets localization (bandwidth) plays a key role and depending on the degree of localization scale-dependent dissipation may preferentially absorb either short vertical wavelength components of a wavetrain (slow waves), or long vertical wavelength components (fast waves). If the dispersed wavetrain is long compared to the scale height for kinematic viscosity then clipping of the waveform occurs that preferentially damps fast waves with longer vertical wavelengths at the leading edge of the packet, with the result that the central wavelength decreases. This causes the dissipating packet to ascend slower and damp sooner than would be indicated by the inviscid group velocity [Heale et al., JGR, 2014]. On the other hand, if the wavepacket is highly localized initially and remains that way (is not too dispersive) so that viscosity does not vary too strongly across the packet then the small scale components are damped first because the rate of dissipation is higher for these components. This shifts the central wavelength to larger values and causes the dissipating packets to ascent higher and more rapidly than inviscid theory would indicate [Walterscheid, JGR, 2013]. The theory of wave packet propagation subject to decay in a viscous media will be reviewed and results of calculations with a time

  14. Insights to caving processes from localization of microseismic swarms induced by salt solution mining

    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

  15. ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS: Heteroclinic Breather-Wave Solutions for Davey-Stewartson Equation

    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.

  16. Transient localized wave patterns and their application to migraine.

    PubMed

    Dahlem, Markus A; Isele, Thomas M

    2013-05-29

    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.

  17. Nonlinear Schrödinger equation: generalized Darboux transformation and rogue wave solutions.

    PubMed

    Guo, Boling; Ling, Liming; Liu, Q P

    2012-02-01

    In this paper, we construct a generalized Darboux transformation for the nonlinear Schrödinger equation. The associated N-fold Darboux transformation is given in terms of both a summation formula and determinants. As applications, we obtain compact representations for the Nth-order rogue wave solutions of the focusing nonlinear Schrödinger equation and Hirota equation. In particular, the dynamics of the general third-order rogue wave is discussed and shown to exhibit interesting structures.

  18. 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.

  19. Classifying the hierarchy of nonlinear-Schrödinger-equation rogue-wave solutions.

    PubMed

    Kedziora, David J; Ankiewicz, Adrian; Akhmediev, Nail

    2013-07-01

    We present a systematic classification for higher-order rogue-wave solutions of the nonlinear Schrödinger equation, constructed as the nonlinear superposition of first-order breathers via the recursive Darboux transformation scheme. This hierarchy is subdivided into structures that exhibit varying degrees of radial symmetry, all arising from independent degrees of freedom associated with physical translations of component breathers. We reveal the general rules required to produce these fundamental patterns. Consequently, we are able to extrapolate the general shape for rogue-wave solutions beyond order 6, at which point accuracy limitations due to current standards of numerical generation become non-negligible. Furthermore, we indicate how a large set of irregular rogue-wave solutions can be produced by hybridizing these fundamental structures.

  20. Traveling wave solutions in a plant population model with a seed bank.

    PubMed

    Li, Bingtuan

    2012-11-01

    We propose an integro-difference equation model to predict the spatial spread of a plant population with a seed bank. The formulation of the model consists of a nonmonotone convolution integral operator describing the recruitment and seed dispersal and a linear contraction operator addressing the effect of the seed bank. The recursion operator of the model is noncompact, which poses a challenge to establishing the existence of traveling wave solutions. We show that the model has a spreading speed, and prove that the spreading speed can be characterized as the slowest speed of a class of traveling wave solutions by using an asymptotic fixed point theorem. Our numerical simulations show that the seed bank has the stabilizing effect on the spatial patterns of traveling wave solutions.

  1. 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.

  2. High order local absorbing boundary conditions for acoustic waves in terms of farfield expansions

    NASA Astrophysics Data System (ADS)

    Villamizar, Vianey; Acosta, Sebastian; Dastrup, Blake

    2017-03-01

    We devise a new high order local absorbing boundary condition (ABC) for radiating problems and scattering of time-harmonic acoustic waves from obstacles of arbitrary shape. By introducing an artificial boundary S enclosing the scatterer, the original unbounded domain Ω is decomposed into a bounded computational domain Ω- and an exterior unbounded domain Ω+. Then, we define interface conditions at the artificial boundary S, from truncated versions of the well-known Wilcox and Karp farfield expansion representations of the exact solution in the exterior region Ω+. As a result, we obtain a new local absorbing boundary condition (ABC) for a bounded problem on Ω-, which effectively accounts for the outgoing behavior of the scattered field. Contrary to the low order absorbing conditions previously defined, the error at the artificial boundary induced by this novel ABC can be easily reduced to reach any accuracy within the limits of the computational resources. We accomplish this by simply adding as many terms as needed to the truncated farfield expansions of Wilcox or Karp. The convergence of these expansions guarantees that the order of approximation of the new ABC can be increased arbitrarily without having to enlarge the radius of the artificial boundary. We include numerical results in two and three dimensions which demonstrate the improved accuracy and simplicity of this new formulation when compared to other absorbing boundary conditions.

  3. ROSSBY WAVE INSTABILITY IN LOCALLY ISOTHERMAL AND POLYTROPIC DISKS: THREE-DIMENSIONAL LINEAR CALCULATIONS

    SciTech Connect

    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.

  4. Localized Electromagnetic Waves: Interactions with Surfaces and Nanostructures

    NASA Astrophysics Data System (ADS)

    Anderson, Nicholas R.

    The interaction of electromagnetic waves with nanostructures is an important area of research for signal processing devices, magnetic data storage, biosensors and a variety of other applications. In this work, we present analytic and numerical calculations for oscillating electric and magnetic fields coupling with excitations in magnetic materials as well as metallic and dielectric materials, near their resonance frequencies. One of the problems with the miniaturization of signal processing components is that there is a cutoff frequency associated with the transverse electric (TE) mode in waveguides. However, it is usually the TE mode which is used to achieve nonreciprocity for devices such as isolators. As a first step to circumvent this problem we looked at the absorption of electromagnetic waves in an antiferromagnet and a ferrite when the incident wave is at an arbitrary angle with respect to the magnetization direction. We calculated reflectivity and attenuated total reflectivity and found absorption and nonreciprocity, asymmetric behavior for waves traveling in opposite directions, for a broad range of propagation angles. Subsequently we also performed calculations for a transverse magnetic mode in a waveguide. The wave was allowed to propagate at an arbitrary angle with respect to the magnetization direction of the ferrite in the waveguide. We again found nonreciprocity for a wide range of angles. Our results show that this system could be used as an on-chip isolator with isolation values over 75 dB/cm in the 50 GHz range. We explored another signal processing device operating in the GHz range: a nonlinear phase shifter. Using Fe as the magnetic material allows the phase shifter to operate over a wide frequency and power range. We found a differential phase shift of greater than 50° over 3 cm for this device. The theoretical results compared well with experimental measurements. Finally, we study surface plasmon polaritons propagating along a metallic

  5. Rogue wave solutions for a generalized nonautonomous nonlinear equation in a nonlinear inhomogeneous fiber

    SciTech Connect

    Xie, Xi-Yang; Tian, Bo Wang, Yu-Feng; Sun, Ya; Jiang, Yan

    2015-11-15

    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.

  6. Contradiction within wave optics and its solution within a particle picture.

    PubMed

    Altmann, Konrad

    2015-02-09

    It is shown that the condition provided by paraxial wave optics for the resonance frequencies of the eigenmodes of an optical resonator leads to a contradiction, if the resonator is divided into subcavities. Moreover, it is shown that the results obtained in this way imply a violation of energy conservation. Since for nearly plane waves, paraxial wave optics becomes exact within wave optics, this contradiction also concerns wave optics. A solution for this problem is proposed within a particle picture as presented recently by the author. It is based on a consideration of the change of momentum of a photon bouncing between two equiphase surfaces with vanishing distance. This leads to a transverse force exerted on the photon. Assigning a relativistic mass to the photon leads to a Schrödinger equation describing a transverse motion of the photon. In this way the transverse modes of an optical resonator can be understood as the quantum mechanical eigenfunctions of a single photon.

  7. 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.

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

    PubMed

    Feng, Wei; Li, Yong; Jin, Depeng; Su, Li; Chen, Sheng

    2016-06-16

    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.

  9. A study on dust acoustic traveling wave solutions and quasiperiodic route to chaos in nonthermal magnetoplasmas

    NASA Astrophysics Data System (ADS)

    Saha, Asit; Pal, Nikhil; Saha, Tapash; Ghorui, M. K.; Chatterjee, Prasanta

    2016-12-01

    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.

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

    USGS Publications Warehouse

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

    2010-01-01

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

  11. Three-dimensional analytical solution for transient guided wave propagation in liquid-filled pipe systems.

    PubMed

    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.

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

    PubMed

    Wang, Ken Kang-Hsin; Ye, Zhen

    2003-12-01

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

  13. Exact soliton-on-plane-wave solutions for two-component Bose-Einstein condensates.

    PubMed

    Li, Lu; Malomed, Boris A; Mihalache, Dumitru; Liu, W M

    2006-06-01

    By means of the Darboux transformation, we obtain analytical solutions for a soliton set on top of a plane-wave background in coupled Gross-Pitaevskii equations describing a binary Bose-Einstein condensate. We consider basic properties of the solutions with and without the cross interaction [cross phase modulation (XPM)] between the two components of the background. In the absence of the XPM, this solutions maintain properties of one-component condensates, such as the modulation instability (MI); in the presence of the cross interaction, the solutions exhibit different properties, such as restriction of the MI and soliton splitting.

  14. Exact soliton-on-plane-wave solutions for two-component Bose-Einstein condensates

    SciTech Connect

    Li Lu; Malomed, Boris A.; Mihalache, Dumitru; Liu, W. M.

    2006-06-15

    By means of the Darboux transformation, we obtain analytical solutions for a soliton set on top of a plane-wave background in coupled Gross-Pitaevskii equations describing a binary Bose-Einstein condensate. We consider basic properties of the solutions with and without the cross interaction [cross phase modulation (XPM)] between the two components of the background. In the absence of the XPM, this solutions maintain properties of one-component condensates, such as the modulation instability (MI); in the presence of the cross interaction, the solutions exhibit different properties, such as restriction of the MI and soliton splitting.

  15. An Automated Algebraic Method for Finding a Series of Exact Travelling Wave Solutions of Nonlinear Evolution Equations

    NASA Astrophysics Data System (ADS)

    Liu, Yin-Ping; Li, Zhi-Bin

    2003-03-01

    Based on a type of elliptic equation, a new algebraic method to construct a series of exact solutions for nonlinear evolution equations is proposed, meanwhile, its complete implementation TRWS in Maple is presented. The TRWS can output a series of travelling wave solutions entirely automatically, which include polynomial solutions, exponential function solutions, triangular function solutions, hyperbolic function solutions, rational function solutions, Jacobi elliptic function solutions, and Weierstrass elliptic function solutions. The effectiveness of the package is illustrated by applying it to a variety of equations. Not only are previously known solutions recovered but also new solutions and more general form of solutions are obtained.

  16. Extended nonlinear Schrödinger equation with higher-order odd and even terms and its rogue wave solutions.

    PubMed

    Ankiewicz, Adrian; Wang, Yan; Wabnitz, Stefan; Akhmediev, Nail

    2014-01-01

    We consider an extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms with variable coefficients. The resulting equation has soliton solutions and approximate rogue wave solutions. We present these solutions up to second order. Moreover, specific constraints on the parameters of higher-order terms provide integrability of the resulting equation, providing a corresponding Lax pair. Particular cases of this equation are the Hirota and the Lakshmanan-Porsezian-Daniel equations. The resulting integrable equation admits exact rogue wave solutions. In particular cases, mentioned above, these solutions are reduced to the rogue wave solutions of the corresponding equations.

  17. Breather and rogue wave solutions of a generalized nonlinear Schrödinger equation.

    PubMed

    Wang, L H; Porsezian, K; He, J S

    2013-05-01

    In this paper, using the Darboux transformation, we demonstrate the generation of first-order breather and higher-order rogue waves from a generalized nonlinear Schrödinger equation with several higher-order nonlinear effects representing femtosecond pulse propagation through nonlinear silica fiber. The same nonlinear evolution equation can also describe the soliton-type nonlinear excitations in classical Heisenberg spin chain. Such solutions have a parameter γ(1), denoting the strength of the higher-order effects. From the numerical plots of the rational solutions, the compression effects of the breather and rogue waves produced by γ(1) are discussed in detail.

  18. Rogue-wave solutions of a three-component coupled nonlinear Schrödinger equation.

    PubMed

    Zhao, Li-Chen; Liu, Jie

    2013-01-01

    We investigate rogue-wave solutions in a three-component coupled nonlinear Schrödinger equation. With certain requirements on the backgrounds of components, we construct a multi-rogue-wave solution that exhibits a structure like a four-petaled flower in temporal-spatial distribution, in contrast to the eye-shaped structure in one-component or two-component systems. The results could be of interest in such diverse fields as Bose-Einstein condensates, nonlinear fibers, and superfluids.

  19. 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.

  20. Quantum Hasimoto transformation and nonlinear waves on a superfluid vortex filament under the quantum local induction approximation.

    PubMed

    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.

  1. Charged particle behavior in localized ultralow frequency waves: Theory and observations

    NASA Astrophysics Data System (ADS)

    Li, Li; Zhou, Xu-Zhi; Zong, Qiu-Gang; Rankin, Robert; Zou, Hong; Liu, Ying; Chen, Xing-Ran; Hao, Yi-Xin

    2017-06-01

    The formation and variability of the Van Allen radiation belts are highly influenced by charged particles accelerated via drift-resonant interactions with ultralow frequency (ULF) waves. In the prevailing theory of drift resonance, the ULF wave amplitude is assumed independent of magnetic longitude. This assumption is not generally valid in Earth's magnetosphere, as supported by numerous observations that point to the localized nature of ULF waves. Here we introduce a longitude dependence of the ULF wave amplitude, achieved via a von Mises function, into the theoretical framework of ULF wave-particle drift resonance. To validate the revised theory, the predicted particle signatures are compared with observational data through a best fit procedure. It is demonstrated that incorporation of nonlocal effects in drift-resonance theory provides an improved understanding of charged particle behavior in the inner magnetosphere through the intermediary of ULF waves.

  2. Transient Localized Wave Patterns and Their Application to Migraine

    PubMed Central

    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

  3. Low frequency dynamics of disordered XY spin chains and pinned density waves: from localized spin waves to soliton tunneling.

    PubMed

    Fogler, Michael M

    2002-05-06

    A long-standing problem of the low-energy dynamics of a disordered XY spin chain is reexamined. The case of a rigid chain is studied, where the quantum effects can be treated quasiclassically. It is shown that, as the frequency decreases, the relevant excitations change from localized spin waves to two-level systems to soliton-antisoliton pairs. The linear-response correlation functions are calculated. The results apply to other periodic glassy systems such as pinned density waves, planar vortex lattices, stripes, and disordered Luttinger liquids.

  4. One Single Static Measurement Predicts Wave Localization in Complex Structures.

    PubMed

    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.

  5. Dynamics of analytical three-dimensional matter-wave solutions in Bose-Einstein condensates with multi-body interactions

    NASA Astrophysics Data System (ADS)

    Jin, Hai-Qin; Dai, Wei; Tong, Aihong; Cai, Ze-Bin; Liang, Jian-Chu; He, Jun-Rong

    2014-03-01

    Using the F-expansion method we obtain a class of analytical matter-wave solutions to Bose-Einstein condensates with multi-body interactions through the three-dimensional quintic Gross-Pitaevskii equation. Our results demonstrate that the dynamics of matter-wave solutions can be controlled by selecting the potential, quintic nonlinearity, and gain coefficients. The obtained matter-wave solutions may be generated by tuning the cubic nonlinearity to zero via the Feschbach resonance technique and making the quintic nonlinearity increasing rapidly enough toward the periphery. The stability analysis of the obtained matter-wave solutions is investigated analytically and numerically.

  6. A solution for TM-mode plane waves incident on a two-dimensional inhomogeneity

    SciTech Connect

    Lee, K. H.; Morrison, H. F.

    1985-07-01

    A solution for the electromagnetic fields scattered from a two-dimensional inhomogeneity in a conducting half space has been obtained for an incident TM mode plane wave; the magnetic field is polarized parallel to the strike of the inhomogeneity. The approach has been to determine the scattering currents within the inhomogeneity using an integral equation for the electric fields. This solution is similar in concept to earlier studies of TE mode scattering from two-dimensional inhomogeneities, and it completes the analysis of the scattering of arbitrary plane waves using the integral equation approach. For simple bodies in the earth integral equation solution offers significant computational advantages over alternate finite element or finite difference methods of solution.

  7. Initial Value Problem Solution of Nonlinear Shallow Water-Wave Equations

    SciTech Connect

    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.

  8. Initial value problem solution of nonlinear shallow water-wave equations.

    PubMed

    Kânoğlu, 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.

  9. Self-similar solutions for the Hasselmann equation and experimental scaling of wind-wave spectra

    NASA Astrophysics Data System (ADS)

    Badulin, S. I.; Pushkarev, A. N.; Resio, D.; Zakharov, V. E.

    2003-04-01

    The solutions for the Hasselmann equation (kinetic equation for wind-driven waves) are studied numerically for the case of duration-limited growth and different conventional parameterizations of wave sources and sinks (Snyderet al. 1981; Plant 1982; Hsiao &Shemdin 1983; Komen, Hasselmann & Hasselmann 1984; Donelan, Pierson 1987). The strong self-similar behavior of the numerical solutions is found for all the parameterizations in a wide range of wind speeds and wave ages. Moreover, the resulting self-similar solutions are found to be surprisingly close to experimentally established approximations in magnitudes and shapes of frequency spectra. The comparison with JONSWAP modified spectra (Donelan et al. 1985) is detailed. It is found that this approximation being obtained for the case of fetch-limited growth fits quite well the corresponding spectra for the numerical duration limited solutions in a wide range of wave ages (C_p/U10 ≈ 0.4div 1.4 ). Theoretical overview of self-similar solutions for the kinetic equation is given in its relation to the experimentally observed dependencies of mean parameters (i.e. mean energy, frequency) of wind-driven waves both in cases of fetch-limited and duration limited growth. Universality features of the dependencies are treated as a result of dominating nonlinear transfer in wind-wave field. The research was conducted under the U.S. Army Corps of Engineers, RDT&E program, grant DACA 42-00-C0044, ONR grant N00014-98-1-0070 and NSF grant NDMS0072803, INTAS grant 01-234 and Russian Foundation for Basic Research 01-05-64603, 01-05-64464, 02-05-65140. This support is gratefully acknowledged.

  10. Traveling wave solutions in a two-group epidemic model with latent period

    NASA Astrophysics Data System (ADS)

    Zhao, Lin; Wang, Zhi-Cheng; Ruan, Shigui

    2017-04-01

    In this paper, we propose a susceptible-infective-recovered (SIR) epidemic model to describe the geographic spread of an infectious disease in two groups/sub-populations living in a spatially continuous habitat. It is assumed that the susceptibility of individuals for infection and the infectivity of individuals are distinct between these two groups/sub-populations. It is also assumed that the infectious disease has a fixed latent period and the latent individuals may diffuse. We investigate the traveling wave solutions and obtain complete information about the existence and nonexistence of nontrivial traveling wave solutions. We prove that when the basic reproduction number {{R}0}≤ft(S10,S20\\right)>1 at the disease free equilibrium ≤ft(S10,S20,0,0\\right) , there exists a critical number c *  >  0 such that for each c  >  c *, the system admits a nontrivial traveling wave solution with wave speed c, and for c  <  c *, the system admits no nontrivial traveling wave solution. When {{R}0}≤ft(S10,S20\\right)≤slant 1 , we show that there exists no nontrivial traveling wave solution. In addition, for the case {{R}0}≤ft(S10,S20\\right)>1 and c  >  c *, we also find that the final sizes of susceptible individuals, denoted by ≤ft({{S}1,0},{{S}2,0}\\right) , satisfies {{R}0}≤ft({{S}1,0},{{S}2,0}\\right)<1 , which means that there is no outbreak of this the infectious disease anymore. At last, we analyze and simulate the continuous dependence of the minimal speed c * on the parameters.

  11. Three-dimensional two-fluid investigation of 3D-localized magnetic reconnection and its relation to whistler waves

    NASA Astrophysics Data System (ADS)

    Yoon, Young Dae; Bellan, Paul M.

    2016-10-01

    A full three-dimensional computer code was developed in order to simulate a 3D-localized magnetic reconnection. We assume an incompressible two-fluid regime where the ions are stationary, and electron inertia and Hall effects are present. We solve a single dimensionless differential equation for perturbed magnetic fields with arbitrary background fields. The code has successfully reproduced both experimental and analytic solutions to resonance and Gendrin mode whistler waves in a uniform background field. The code was then modified to model 3D-localized magnetic reconnection as a 3D-localized perturbation on a hyperbolic-tangent background field. Three-dimensional properties that are asymmetric in the out-of-plane direction have been observed. These properties pertained to magnetic field lines, electron currents and their convection. Helicity and energy have also been examined, as well as the addition of a guide field.

  12. Existence of periodic travelling wave solutions for a regularized Benjamin-Ono system

    NASA Astrophysics Data System (ADS)

    Pipicano, Felipe Alexander; Muñoz Grajales, Juan Carlos

    2015-12-01

    In this paper, we discuss the existence of periodic travelling wave solutions of a regularized Benjamin-Ono system by using the topological-degree theory of positive operators on Banach spaces. Furthermore, we use a high-accuracy pseudospectral solver based on a Fourier decomposition to construct numerical approximations of these stationary solutions. The numerical simulations are in perfect agreement with the theoretical results.

  13. Dispersive matched filtering of ultrasonic guided waves for improved sparse array damage localization

    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.

  14. 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.

  15. Observation of two-dimensional classical wave localization: third sound on superfluid 4He films on a disordered substrate.

    PubMed

    Luhman, D R; Herrmann, J C; Hallock, R B

    2005-05-06

    We present the results of measurements of the propagation of third sound waves on superfluid 4He adsorbed to two-dimensional ordered and disordered substrates. In the disordered case we compare the experimental results to theoretical predictions of classical wave localization in such systems and conclude that classical wave localization is present in our system.

  16. Exact solution for eigenfunction statistics at the center-of-band anomaly in the Anderson localization model

    NASA Astrophysics Data System (ADS)

    Kravtsov, V. E.; Yudson, V. I.

    2010-11-01

    An exact solution is found for the problem of the center-of-band (E=0) anomaly in the one-dimensional Anderson model of localization. By deriving and solving an equation for the generating function Φ(u,ϕ) we obtained an exact expression in quadratures for statistical moments Iq=⟨|ψE(r)|2q⟩ of normalized wave functions ψE(r) which show violation of one-parameter scaling and emergence of an additional length scale at E≈0 .

  17. Extensions of 1d Bgk Electron Solitary Wave Solutions To 3d Magnetized and Unmagnetized Plasmas

    NASA Astrophysics Data System (ADS)

    Chen, Li-Jen; Parks, George K.

    This paper will compare the key results for BGK electron solitary waves in 3D mag- netized and unmagnetized plasmas. For 3D magnetized plasmas with highly magnetic field-aligned electrons, our results predict that the parallel widths of the solitary waves can be smaller than one Debye length, the solitary waves can be large scale features of the magnetosphere, and the parallel width-amplitude relation has a dependence on the perpendicular size. We can thus obtain an estimate on the typical perpendicular size of the observed solitary waves assuming a series of consecutive solitary waves are in the same flux tude with a particular perpendicular span. In 3D unmagnetized plasma systems such as the neutral sheet and magnetic reconnection sites, our theory indi- cates that although mathematical solutions can be constructed as the time-stationary solutions for the nonlinear Vlasov-Poisson equations, there does not exist a param- eter range for the solutions to be physical. We conclude that single-humped solitary potential pulses cannot be self-consistently supported by charged particles in 3D un- magnetized plasmas.

  18. Wave gradiometry and its link with Helmholtz equation solutions applied to USArray in the eastern U.S.

    NASA Astrophysics Data System (ADS)

    Liu, Yuanyuan; Holt, William E.

    2015-08-01

    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 the displacement spatial gradients to seismogram displacements and velocities through two unknown coefficients, A→ and B→. These coefficients are solved for through iterative, damped least squares 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 wave slowness. A→ and B→ 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 ∇·B→ and changes in geometrical spreading, which can be further linked with areas of strong energy focusing and defocusing. We finally obtain isotropic Rayleigh wave phase velocity maps for 15 periods between 20 and 150 s, by stacking results from 37 earthquakes, which show a velocity change along the approximate boundary of the early Paleozoic continental margin. We also observe two low-velocity anomalies, one centered over the central Appalachians where Eocene basaltic volcanism has occurred and the other within the northeastern U.S., possibly associated with the Great Meteor Hotspot track.

  19. Regional acidosis locally inhibits but remotely stimulates Ca2+ waves in ventricular myocytes.

    PubMed

    Ford, Kerrie L; Moorhouse, Emma L; Bortolozzi, Mario; Richards, Mark A; Swietach, Pawel; Vaughan-Jones, Richard D

    2017-07-01

    Spontaneous Ca2+ waves in cardiomyocytes are potentially arrhythmogenic. A powerful controller of Ca2+ waves is the cytoplasmic H+ concentration ([H+]i), which fluctuates spatially and temporally in conditions such as myocardial ischaemia/reperfusion. H+-control of Ca2+ waves is poorly understood. We have therefore investigated how [H+]i co-ordinates their initiation and frequency. Spontaneous Ca2+ waves were imaged (fluo-3) in rat isolated ventricular myocytes, subjected to modest Ca2+-overload. Whole-cell intracellular acidosis (induced by acetate-superfusion) stimulated wave frequency. Pharmacologically blocking sarcolemmal Na+/H+ exchange (NHE1) prevented this stimulation, unveiling inhibition by H+. Acidosis also increased Ca2+ wave velocity. Restricting acidosis to one end of a myocyte, using a microfluidic device, inhibited Ca2+ waves in the acidic zone (consistent with ryanodine receptor inhibition), but stimulated wave emergence elsewhere in the cell. This remote stimulation was absent when NHE1 was selectively inhibited in the acidic zone. Remote stimulation depended on a locally evoked, NHE1-driven rise of [Na+]i that spread rapidly downstream. Acidosis influences Ca2+ waves via inhibitory Hi+ and stimulatory Nai+ signals (the latter facilitating intracellular Ca2+-loading through modulation of sarcolemmal Na+/Ca2+ exchange activity). During spatial [H+]i-heterogeneity, Hi+-inhibition dominates in acidic regions, while rapid Nai+ diffusion stimulates waves in downstream, non-acidic regions. Local acidosis thus simultaneously inhibits and stimulates arrhythmogenic Ca2+-signalling in the same myocyte. If the principle of remote H+-stimulation of Ca2+ waves also applies in multicellular myocardium, it raises the possibility of electrical disturbances being driven remotely by adjacent ischaemic areas, which are known to be intensely acidic.

  20. Various Kinds Waves and Solitons Interaction Solutions of Boussinesq Equation Describing Ultrashort Pulse in Quadratic Nonlinear Medium

    NASA Astrophysics Data System (ADS)

    Guo, Bang-Xing; Gao, Zhan-Jie; Lin, Ji

    2016-12-01

    The consistent tanh expansion (CTE) method is applied to the (2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution, and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlevé truncated expansion method. And we investigate interactive properties of solitons and periodic waves. Supported by the National Natural Science Foundation of Zhejiang Province under Grant No. LZ15A050001 and the National Natural Science Foundation of China under Grant No. 11675164

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

    PubMed

    Brujan, Emil-Alexandru

    2008-09-01

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

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

    SciTech Connect

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

    2010-10-15

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

  3. Testing spontaneous localization theories with matter-wave interferometry

    SciTech Connect

    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.

  4. 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.

  5. Integrability Test and Travelling-Wave Solutions of Higher-Order Shallow- Water Type Equations

    NASA Astrophysics Data System (ADS)

    Maldonado, Mercedes; Molinero, María Celeste; Pickering, Andrew; Prada, Julia

    2010-04-01

    We apply the Weiss-Tabor-Carnevale (WTC) Painlevé test to members of a sequence of higher-order shallow-water type equations. We obtain the result that the equations considered are non-integrable, although compatibility conditions at real resonances are satisfied. We also construct travelling-wave solutions for these and related equations.

  6. 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].

  7. Similarity solution to fractional nonlinear space-time diffusion-wave equation

    NASA Astrophysics Data System (ADS)

    Costa, F. Silva; Marão, J. A. P. F.; Soares, J. C. Alves; de Oliveira, E. Capelas

    2015-03-01

    In this article, the so-called fractional nonlinear space-time wave-diffusion equation is presented and discussed. This equation is solved by the similarity method using fractional derivatives in the Caputo, Riesz-Feller, and Riesz senses. Some particular cases are presented and the corresponding solutions are shown by means of 2-D and 3-D plots.

  8. 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.

  9. Localized modes of the Hirota equation: Nth order rogue wave and a separation of variable technique

    NASA Astrophysics Data System (ADS)

    Mu, Gui; Qin, Zhenyun; Chow, Kwok Wing; Ee, Bernard K.

    2016-10-01

    The Hirota equation is a special extension of the intensively studied nonlinear Schrödinger equation, by incorporating third order dispersion and one form of the self-steepening effect. Higher order rogue waves of the Hirota equation can be calculated theoretically through a Darboux-dressing transformation by a separation of variable approach. A Taylor expansion is used and no derivative calculation is invoked. Furthermore, stability of these rogue waves is studied computationally. By tracing the evolution of an exact solution perturbed by random noise, it is found that second order rogue waves are generally less stable than first order ones.

  10. On the accurate long-time solution of the wave equation in exterior domains: Asymptotic expansions and corrected boundary conditions

    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.

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

    NASA Astrophysics Data System (ADS)

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

    2017-01-01

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

  12. 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.

  13. 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.

  14. Time-domain solutions for nonlinear elastic 1-D plane wave propagation

    SciTech Connect

    Korneev, V.A.

    1998-06-01

    Time-domain solutions are obtained for 1-D nonlinear elastic wave propagation problems using a five-constant nonlinear theory. The assumption of weak attenuation was used throughout the development. The strongest nonlinear effects are obtained for the case of single compressional wave propagation, for single compressional or shear wave propagation through a longitudinally pre-stressed elastic material, and for shear wave propagation in a shear pre-stressed elastic material. Estimates of the size of these effects indicate that nonlinear phenomena are likely to be observable in real seismic data. The results may be useful for the measurement of nonlinear constants in elastic materials, for explaining the frequency content of seismograms, and for monitoring strain fields in the earth`s crust.

  15. Preparation of magnesium ferrite nanoparticles by ultrasonic wave-assisted aqueous solution ball milling.

    PubMed

    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.

  16. Solitary wave solution to a class of higher-order viscous traffic flow model

    NASA Astrophysics Data System (ADS)

    Wu, Chun-Xiu; Zhang, Peng

    2017-05-01

    Traveling waves of a class of higher-order traffic flow models with viscosity are studied with the reduction perturbation method, which leads to the well-known Kortweg-de Vries equation and the approximate solitary wave solution to the model. The fifth-order accuracy weighted essentially nonoscillatory scheme is adopted for comparison between the analytical and numerical results. The numerical tests show that the solitary wave evolves with little deformation of its profile and that a globally perturbed equilibrium traffic state is able to evolve into a profile similar to that of a solitary wave, which is identified by the same total number of vehicles on the ring road. These results are compared with those in the literature and demonstrate that the approximation to the model is more accurate.

  17. Influence of the intrapulse Raman scattering on the localized pulsating solutions of generalized complex-quintic Ginzburg-Landau equation

    NASA Astrophysics Data System (ADS)

    Uzunov, Ivan M.; Georgiev, Zhivko D.

    2014-10-01

    We study the dynamics of the localized pulsating solutions of generalized complex cubic- quintic Ginzburg-Landau equation (CCQGLE) in the presence of intrapulse Raman scattering (IRS). We present an approach for identification of periodic attractors of the generalized CCQGLE. At first using ansatz of the travelling wave, and fixing some relations between the material parameters, we derive the strongly nonlinear Lienard - Van der Pol equation for the amplitude of the nonlinear wave. Next, we apply the Melnikov method to this equation to analyze the possibility of existence of limit cycles. For a set of fixed material parameters we show the existence of limit cycle that arises around a closed phase trajectory of the unperturbed system and prove its stability.

  18. Single-image-based solution for optics temperature-dependent nonuniformity correction in an uncooled long-wave infrared camera.

    PubMed

    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.

  19. Solitary and Jacobi elliptic wave solutions of the generalized Benjamin-Bona-Mahony equation

    NASA Astrophysics Data System (ADS)

    Belobo, Didier Belobo; Das, Tapas

    2017-07-01

    Exact bright, dark, antikink solitary waves and Jacobi elliptic function solutions of the generalized Benjamin-Bona-Mahony equation with arbitrary power-law nonlinearity will be constructed in this work. The method used to carry out the integration is the F-expansion method. Solutions obtained have fractional and integer negative or positive power-law nonlinearities. These solutions have many free parameters such that they may be used to simulate many experimental situations, and to precisely control the dynamics of the system.

  20. Localization estimates for a random discrete wave equation at high frequency

    SciTech Connect

    Faris, W.G.

    1987-02-01

    It is shown that at high frequencies matrix elements of the Green's function of a random discrete wave equation decay exponentially at long distances. This is the input to the proof of dense point spectrum with localized eigenfunctions in this frequency range. The proof uses techniques of Froehlich and Spencer. A sequence of renormalization transformations shows that large regions where wave propagation is easily maintained become increasingly sparse as resonance is approached.

  1. Localization of RF Breakdowns in a Standing Wave Cavity

    SciTech Connect

    Wang, Faya; Adolphsen, Chris; /SLAC

    2009-08-03

    At SLAC, a 5-cell, normal-conducting, L-band (1.3 GHz), standing-wave (SW) cavity was built as a prototype positron capture accelerator for the ILC. The structure met the ILC gradient goal but required extensive rf processing. When rf breakdowns occurred, a large variation was observed in the decay rate of the stored energy in the cavity after the input power was shut off. It appeared that the breakdowns were isolating sections of the cavity, and that the trapped energy in those sections was then partitioned among its natural modes, producing a distinct beating pattern during the decay. To explore this phenomenon further, an equivalent circuit model of cavity was created that reproduces well its normal operating characteristics. The model was then used to compute the spectra of trapped energy for different numbers of isolated cells. The resulting modal patterns agree well with those of the breakdown data, and thus such a comparison appears to provide a means of identifying the irises on which the breakdowns occurred.

  2. THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN

    PubMed Central

    Jiang, H.; Liu, F.; Meerschaert, M. M.; McGough, R. J.

    2013-01-01

    Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n) (n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko’s Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi-term time-space fractional models including fractional Laplacian. PMID:26425384

  3. THE FUNDAMENTAL SOLUTIONS FOR MULTI-TERM MODIFIED POWER LAW WAVE EQUATIONS IN A FINITE DOMAIN.

    PubMed

    Jiang, H; Liu, F; Meerschaert, M M; McGough, R J

    2013-01-01

    Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals (1, 2], [2, 3), [2, 4) or (0, n) (n > 2), respectively. Analytical solutions of the multi-term modified power law wave equations are derived. These new techniques are based on Luchko's Theorem, a spectral representation of the Laplacian operator, a method of separating variables and fractional derivative techniques. Then these general methods are applied to the special cases of the Szabo wave equation and the power law wave equation. These methods and techniques can also be extended to other kinds of the multi-term time-space fractional models including fractional Laplacian.

  4. 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.

  5. Non-local features of a hydrodynamic pilot-wave system

    NASA Astrophysics Data System (ADS)

    Nachbin, Andre; Couchman, Miles; Bush, John

    2016-11-01

    A droplet walking on the surface of a vibrating fluid bath constitutes a pilot-wave system of the form envisaged for quantum dynamics by Louis de Broglie: a particle moves in resonance with its guiding wave field. We here present an examination of pilot-wave hydrodynamics in a confined domain. Specifically, we present a one-dimensional water wave model that describes droplets walking in single and multiple cavities. The cavities are separated by a submerged barrier, and so allow for the study of tunneling. They also highlight the non-local dynamical features arising due to the spatially-extended wave field. Results from computational simulations are complemented by laboratory experiments.

  6. A Local Parabolic Method for Long Distance Wave Propagation

    DTIC Science & Technology

    2005-09-21

    centroid motion and total integrated amplitude at each point along the pulse surface. The main issue in computing these cases is that conventional...This is necessary because the Lattice Confinement terms should not depend on the scale of the quantity being confined. Another important point is that...4,VD2 2+ E5,VD xb where b is a local harmonic mean of 3 at each grid point : B~f FI N’ where 6, and VD denote discrete operators and Eqn. 1.2 was

  7. 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.

  8. Acoustical model of small calibre ballistic shock waves in air for automatic sniper localization applications

    NASA Astrophysics Data System (ADS)

    Aguilar, Juan R.; Salinas, Renato A.; Abidi, Mongi A.

    2007-04-01

    The phenomenon of ballistic shock wave emission by a small calibre projectile at supersonic speed is quite relevant in automatic sniper localization applications. When available, ballistic shock wave analysis makes possible the estimation of the main ballistic features of a gunfire event. The propagation of ballistic shock waves in air is a process which mainly involves nonlinear distortion, or steepening, and atmospheric absorption. Current ballistic shock waves propagation models used in automatic sniper localization systems only consider nonlinear distortion effects. This means that only the rates of change of shock peak pressure and the N-wave duration with distance are considered in the determination of the miss distance. In the present paper we present an improved acoustical model of small calibre ballistic shock wave propagation in air, intended to be used in acoustics-based automatic sniper localization applications. In our approach, we have considered nonlinear distortion, but additionally we have also introduced the effects of atmospheric sound absorption. Atmospheric absorption is implemented in the time domain in order to get faster calculation times than those computed in frequency domain. Furthermore, we take advantage of the fact that atmospheric absorption plays a fundamental role in the rise times of the shocks, and introduce the rate of change of the rise time with distance as a third parameter to be used in the determination of the miss distance. This lead us to a more accurate and robust estimation of the miss distance, and consequently of the projectile trajectory, and the spatial coordinates of the gunshot origin.

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

    SciTech Connect

    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}.

  10. 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.

  11. Broadband Lamb wave trapping in cellular metamaterial plates with multiple local resonances.

    PubMed

    Zhao, De-Gang; Li, Yong; Zhu, Xue-Feng

    2015-03-20

    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.

  12. Quantifying local exciton, charge resonance, and multiexciton character in correlated wave functions of multichromophoric systems

    SciTech Connect

    Casanova, David; Krylov, Anna I.

    2016-01-07

    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.

  13. Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations.

    PubMed

    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.

  14. 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.

  15. Rescaled Local Interaction Simulation Approach for Shear Wave Propagation Modelling in Magnetic Resonance Elastography

    PubMed Central

    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

  16. Spin-polarized local density of states around vortex in helical p-wave superconductors

    NASA Astrophysics Data System (ADS)

    Tanaka, Kenta K.; Ichioka, Masanori; Onari, Seiichiro

    2017-07-01

    Based on the quasi-classical Eilenberger theory, we investigate the magnetic field dependence of order-parameters and spin-polarized local density of states (LDOS) in the vortex lattice state of helical p-wave superconductors. The spin-polarized LDOS is induced by the vorticity coupling to the chirality of up-spin pair or down-spin pair, even when Knight shift does not change. We clarify the instability of the helical p-wave state at high field, and that the spin-polarized LDOS shows the unique behaviors of the helical p-wave state.

  17. Spin-polarized local density of states in the vortex state of helical p -wave superconductors

    NASA Astrophysics Data System (ADS)

    Tanaka, Kenta K.; Ichioka, Masanori; Onari, Seiichiro

    2017-04-01

    Properties of the vortex state in helical p -wave superconductor are studied by the quasiclassical Eilenberger theory. We confirm the instability of the helical p -wave state at high fields and that the spin-polarized local density of states M (E ,r ) appears even when Knight shift does not change. This is because the vorticity couples to the chirality of up-spin pair or down-spin pair of the helical state. In order to identify the helical p -wave state at low fields, we investigate the structure of the zero-energy M (E =0 ,r ) in the vortex states, and also the energy spectra of M (E ,r ) .

  18. Open waveguides in a thin Dirichlet lattice: II. localized waves and radiation conditions

    NASA Astrophysics Data System (ADS)

    Nazarov, S. A.

    2017-02-01

    Wave processes localized near an angular open waveguide obtained by thickening two perpendicular semi-infinite rows of ligaments in a thin square lattice of quantum waveguides (Dirichlet problem for the Helmholtz equation) are investigated. Waves of two types are discovered: the first are observed near the lattice nodes and almost do not affect the ligaments, while the second, on the contrary, excite oscillations in the ligaments, whereas the nodes stay relatively at rest. Asymptotic representations of the wave fields are derived, and radiation conditions are imposed on the basis of the Umov-Mandelstam energy principle.

  19. Modified Kubelka-Munk equations for localized waves inside a layered medium.

    PubMed

    Haney, Matthew M; van Wijk, Kasper

    2007-03-01

    We present a pair of coupled partial differential equations to describe the evolution of the average total intensity and intensity flux of a wave field inside a randomly layered medium. These equations represent a modification of the Kubelka-Munk equations, or radiative transfer. Our modification accounts for wave interference (e.g., localization), which is neglected in radiative transfer. We numerically solve the modified Kubelka-Munk equations and compare the results to radiative transfer as well as to simulations of the wave equation with randomly located thin layers.

  20. Local wave grouping in a parameter-gradient system and its formation mechanism

    NASA Astrophysics Data System (ADS)

    Liao, Huimin; Wu, Yangle; Yu, Jianglei; Ouyang, Qi

    2008-01-01

    In a ferroin-catalyzed Belousov-Zhabotinsky (BZ) reaction-diffusion system with reagent concentration gradients, we observed in the experiment a type of spirals with local waves forming groups. Here, we propose an interpretation of the wave grouping phenomenon. The wave grouping mechanism can be well explained in terms of the cooperation of the excitability gradient and the Doppler effect induced by spiral tip’s meandering. In the simulation based on three-dimensional reaction-diffusion system using Oregonator model, spiral patterns analogous to the experiment observation are well reproduced when the parameter gradient in the z direction is introduced.

  1. Local wave grouping in a parameter-gradient system and its formation mechanism.

    PubMed

    Liao, Huimin; Wu, Yangle; Yu, Jianglei; Ouyang, Qi

    2008-01-01

    In a ferroin-catalyzed Belousov-Zhabotinsky (BZ) reaction-diffusion system with reagent concentration gradients, we observed in the experiment a type of spirals with local waves forming groups. Here, we propose an interpretation of the wave grouping phenomenon. The wave grouping mechanism can be well explained in terms of the cooperation of the excitability gradient and the Doppler effect induced by spiral tip's meandering. In the simulation based on three-dimensional reaction-diffusion system using Oregonator model, spiral patterns analogous to the experiment observation are well reproduced when the parameter gradient in the z direction is introduced.

  2. Computation of homoclinic solutions to periodic orbits in a reduced water-wave problem

    NASA Astrophysics Data System (ADS)

    Champneys, A. R.; Lord, G. J.

    1997-02-01

    This paper concerns homoclinic solutions to periodic orbits in a fourth-order Hamiltonian system arising from a reduction of the classical water-wave problem in the presence of surface tension. These solutions correspond to travelling solitary waves which converge to non-decaying ripples at infinity. An analytical result of Amick and Toland (1992), showing the existence of such homoclinic orbits to small-amplitude periodic orbits in a singular limit, is extended numerically. Also, a related result by Amick and McLeod (1991), showing the non-existence of homoclinic solutions to zero, is motivated geometrically. A general boundary-value method is constructed for continuation of homoclinic orbits to periodic orbits in Hamiltonian and reversible systems. Numerical results are presented using the path-following software AUTO, showing that the Amick-Toland solutions persist well away from the singular limit and for large-amplitude periodic orbits. Special account is taken of the phase shift between the two periodic solutions in the asymptotic limits. Furthermore, new multi-modal homoclinic solutions to periodic orbits are shown to exist under a transversality hypothesis, which is verified a posteriori by explicit computation. Continuation of these new solutions reveals limit points with respect to the singular parameter.

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

    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.; Hartman, M. T.; Haster, C.-J.; Haughian, K.; Heidmann, A.; Heintze, M. C.; Heitmann, H.; Hello, P.; Hemming, G.; Hendry, M.; Heng, I. S.; Hennig, J.; Heptonstall, A. W.; Heurs, M.; Hild, S.; Hoak, D.; Hodge, K. A.; Hofman, D.; Hollitt, S. E.; Holt, K.; Holz, D. E.; Hopkins, P.; Hosken, D. J.; Hough, J.; Houston, E. A.; Howell, E. J.; Hu, Y. M.; Huang, S.; Huerta, E. A.; Huet, D.; Hughey, B.; Husa, S.; Huttner, S. H.; Huynh-Dinh, T.; Idrisy, A.; Indik, N.; Ingram, D. R.; Inta, R.; Isa, H. N.; Isac, J.-M.; Isi, M.; Islas, G.; Isogai, T.; Iyer, B. R.; Izumi, K.; Jacqmin, T.; Jang, H.; Jani, K.; Jaranowski, P.; Jawahar, S.; Jiménez-Forteza, F.; Johnson, W. W.; Jones, D. I.; Jones, R.; Jonker, R. J. G.; Ju, L.; K, Haris; Kalaghatgi, C. V.; Kalogera, V.; Kandhasamy, S.; Kang, G.; Kanner, J. B.; Karki, S.; Kasprzack, M.; Katsavounidis, E.; Katzman, W.; Kaufer, S.; Kaur, T.; Kawabe, K.; Kawazoe, F.; Kéfélian, F.; Kehl, M. S.; Keitel, D.; Kelley, D. B.; Kells, W.; Kennedy, R.; Key, J. S.; Khalaidovski, A.; Khalili, F. Y.; Khan, S.; Khan, Z.; Khazanov, E. A.; Kijbunchoo, N.; Kim, C.; Kim, J.; Kim, K.; Kim, N.; Kim, N.; Kim, Y.-M.; King, E. J.; King, P. J.; Kinzel, D. L.; Kissel, J. S.; Kleybolte, L.; Klimenko, S.; Koehlenbeck, S. M.; Kokeyama, K.; Koley, S.; Kondrashov, V.; Kontos, A.; Korobko, M.; Korth, W. Z.; Kowalska, I.; Kozak, D. B.; Kringel, V.; Krishnan, B.; Królak, A.; Krueger, C.; Kuehn, G.; Kumar, P.; Kuo, L.; Kutynia, A.; Lackey, B. D.; Landry, M.; Lange, J.; Lantz, B.; Lasky, P. D.; Lazzarini, A.; Lazzaro, C.; Leaci, P.; Leavey, S.; Lebigot, E.; Lee, C. H.; Lee, H. K.; Lee, H. M.; Lee, K.; Lenon, A.; Leonardi, M.; Leong, J. R.; Leroy, N.; Letendre, N.; Levin, Y.; Levine, B. M.; Li, T. G. F.; Libson, A.; Littenberg, T. B.; Lockerbie, N. A.; Logue, J.; Lombardi, A. L.; Lord, J. E.; Lorenzini, M.; Loriette, V.; Lormand, M.; Losurdo, G.; Lough, J. D.; Lück, H.; Lundgren, A. P.; Luo, J.; Lynch, R.; Ma, Y.; MacDonald, T.; Machenschalk, B.; MacInnis, M.; Macleod, D. M.; Magana-Sandoval, F.; Magee, R. M.; Mageswaran, M.; Majorana, E.; Maksimovic, I.; Malvezzi, V.; Man, N.; Mandel, I.; Mandic, V.; Mangano, V.; Mansell, G. L.; Manske, M.; Mantovani, M.; Marchesoni, F.; Marion, F.; Márka, S.; Márka, Z.; Markosyan, A. S.; Maros, E.; Martelli, F.; Martellini, L.; Martin, I. W.; Martin, R. M.; Martynov, D. V.; Marx, J. N.; Mason, K.; Masserot, A.; Massinger, T. J.; Masso-Reid, M.; Matichard, F.; Matone, L.; Mavalvala, N.; Mazumder, N.; Mazzolo, G.; McCarthy, R.; McClelland, D. E.; McCormick, S.; McGuire, S. C.; McIntyre, G.; McIver, J.; McManus, D. J.; McWilliams, S. T.; Meacher, D.; Meadors, G. D.; Meidam, J.; Melatos, A.; Mendell, G.; Mendoza-Gandara, D.; Mercer, R. A.; Merilh, E.; Merzougui, M.; Meshkov, S.; Messenger, C.; Messick, C.; Meyers, P. M.; Mezzani, F.; Miao, H.; Michel, C.; Middleton, H.; Mikhailov, E. E.; Milano, L.; Miller, J.; Millhouse, M.; Minenkov, Y.; Ming, J.; Mirshekari, S.; Mishra, C.; Mitra, S.; Mitrofanov, V. P.; Mitselmakher, G.; Mittleman, R.; Moggi, A.; Mohan, M.; Mohapatra, S. R. P.; Montani, M.; Moore, B. C.; Moore, C. J.; Moraru, D.; Moreno, G.; Morriss, S. R.; Mossavi, K.; Mours, B.; Mow-Lowry, C. M.; Mueller, C. L.; Mueller, G.; Muir, A. W.; Mukherjee, Arunava; Mukherjee, D.; Mukherjee, S.; Mullavey, A.; Munch, J.; Murphy, D. J.; Murray, P. G.; Mytidis, A.; Nardecchia, I.; Naticchioni, L.; Nayak, R. K.; Necula, V.; Nedkova, K.; Nelemans, G.; Neri, M.; Neunzert, A.; Newton, G.; Nguyen, T. T.; Nielsen, A. B.; Nissanke, S.; Nitz, A.; Nocera, F.; Nolting, D.; Normandin, M. E. N.; Nuttall, L. K.; Oberling, J.; Ochsner, E.; O'Dell, J.; Oelker, E.; Ogin, G. H.; Oh, J. J.; Oh, S. H.; Ohme, F.; Oliver, M.; Oppermann, P.; Oram, Richard J.; O'Reilly, B.; O'Shaughnessy, R.; Ott, C. D.; Ottaway, D. J.; Ottens, R. S.; Overmier, H.; Owen, B. J.; Pai, A.; Pai, S. A.; Palamos, J. R.; Palashov, O.; Palomba, C.; Pal-Singh, A.; Pan, H.; Pankow, C.; Pannarale, F.; Pant, B. C.; Paoletti, F.; Paoli, A.; Papa, M. A.; Paris, H. R.; Parker, W.; Pascucci, D.; Pasqualetti, A.; Passaquieti, R.; Passuello, D.; Patrick, Z.; Pearlstone, B. L.; Pedraza, M.; Pedurand, R.; Pekowsky, L.; Pele, A.; Penn, S.; Pereira, R.; Perreca, A.; Phelps, M.; Piccinni, O.; Pichot, M.; Piergiovanni, F.; Pierro, V.; Pillant, G.; Pinard, L.; Pinto, I. M.; Pitkin, M.; Poggiani, R.; Post, A.; Powell, J.; Prasad, J.; Predoi, V.; Premachandra, S. S.; Prestegard, T.; Price, L. R.; Prijatelj, M.; Principe, M.; Privitera, S.; Prodi, G. A.; Prokhorov, L.; Punturo, M.; Puppo, P.; Pürrer, M.; Qi, H.; Qin, J.; Quetschke, V.; Quintero, E. A.; Quitzow-James, R.; Raab, F. J.; Rabeling, D. S.; Radkins, H.; Raffai, P.; Raja, S.; Rakhmanov, M.; Rapagnani, P.; Raymond, V.; Razzano, M.; Re, V.; Read, J.; Reed, C. M.; Regimbau, T.; Rei, L.; Reid, S.; Reitze, D. H.; Rew, H.; Ricci, F.; Riles, K.; Robertson, N. A.; Robie, R.; Robinet, F.; Rocchi, A.; Rolland, L.; Rollins, J. G.; Roma, V. J.; Romano, J. D.; Romano, R.; Romanov, G.; Romie, J. H.; Rosińska, D.; Rowan, S.; Rüdiger, A.; Ruggi, P.; Ryan, K.; Sachdev, S.; Sadecki, T.; Sadeghian, L.; Saleem, M.; Salemi, F.; Samajdar, A.; Sammut, L.; Sanchez, E. J.; Sandberg, V.; Sandeen, B.; Sanders, J. R.; Sassolas, B.; Sathyaprakash, B. S.; Saulson, P. R.; Sauter, O.; Savage, R. L.; Sawadsky, A.; Schale, P.; Schilling, R.; Schmidt, J.; Schmidt, P.; Schnabel, R.; Schofield, R. M. S.; Schönbeck, A.; Schreiber, E.; Schuette, D.; Schutz, B. F.; Scott, J.; Scott, S. M.; Sellers, D.; Sentenac, D.; Sequino, V.; Sergeev, A.; Serna, G.; Setyawati, Y.; Sevigny, A.; Shaddock, D. A.; Shah, S.; Shahriar, M. S.; Shaltev, M.; Shao, Z.; Shapiro, B.; Shawhan, P.; Sheperd, A.; Shoemaker, D. H.; Shoemaker, D. M.; Siellez, K.; Siemens, X.; Sigg, D.; Silva, A. D.; Simakov, D.; Singer, A.; Singer, L. P.; Singh, A.; Singh, R.; Sintes, A. M.; Slagmolen, B. J. J.; Smith, J. R.; Smith, N. D.; Smith, R. J. E.; Son, E. J.; Sorazu, B.; Sorrentino, F.; Souradeep, T.; Srivastava, A. K.; Staley, A.; Steinke, M.; Steinlechner, J.; Steinlechner, S.; Steinmeyer, D.; Stephens, B. C.; Stone, R.; Strain, K. A.; Straniero, N.; Stratta, G.; Strauss, N. A.; Strigin, S.; Sturani, R.; Stuver, A. L.; Summerscales, T. Z.; Sun, L.; Sutton, P. J.; Swinkels, B. L.; Szczepanczyk, M. J.; Tacca, M.; Talukder, D.; Tanner, D. B.; Tápai, M.; Tarabrin, S. P.; Taracchini, A.; Taylor, R.; Theeg, T.; Thirugnanasambandam, M. P.; Thomas, E. G.; Thomas, M.; Thomas, P.; Thorne, K. A.; Thorne, K. S.; Thrane, E.; Tiwari, S.; Tiwari, V.; Tokmakov, K. V.; Tomlinson, C.; Tonelli, M.; Torres, C. V.; Torrie, C. I.; Töyrä, D.; Travasso, F.; Traylor, G.; Trifirò, D.; Tringali, M. C.; Trozzo, L.; Tse, M.; Turconi, M.; Tuyenbayev, D.; Ugolini, D.; Unnikrishnan, C. S.; Urban, A. L.; Usman, S. A.; Vahlbruch, H.; Vajente, G.; Valdes, G.; van Bakel, N.; van Beuzekom, M.; van den Brand, J. F. J.; van den Broeck, C.; Vander-Hyde, D. C.; van der Schaaf, L.; van der Sluys, M. V.; van Heijningen, J. V.; van Veggel, A. A.; Vardaro, M.; Vass, S.; Vasúth, M.; Vaulin, R.; Vecchio, A.; Vedovato, G.; Veitch, J.; Veitch, P. J.; Venkateswara, K.; Verkindt, D.; Vetrano, F.; Viceré, A.; Vinciguerra, S.; Vine, D. J.; Vinet, J.-Y.; Vitale, S.; Vo, T.; Vocca, H.; Vorvick, C.; Vousden, W. D.; Vyatchanin, S. P.; Wade, A. R.; Wade, L. E.; Wade, M.; Walker, M.; Wallace, L.; Walsh, S.; Wang, G.; Wang, H.; Wang, M.; Wang, X.; Wang, Y.; Ward, R. L.; Warner, J.; Was, M.; Weaver, B.; Wei, L.-W.; Weinert, M.; Weinstein, A. J.; Weiss, R.; Welborn, T.; Wen, L.; Weßels, P.; Westphal, T.; Wette, K.; Whelan, J. T.; White, D. J.; Whiting, B. F.; Williams, R. D.; Williamson, A. R.; Willis, J. L.; Willke, B.; Wimmer, M. H.; Winkler, W.; Wipf, C. C.; Wittel, H.; Woan, G.; Worden, J.; Wright, J. L.; Wu, G.; Yablon, J.; Yam, W.; Yamamoto, H.; Yancey, C. C.; Yap, M. J.; Yu, H.; Yvert, M.; Zadrożny, A.; Zangrando, L.; Zanolin, M.; Zendri, J.-P.; Zevin, M.; Zhang, F.; Zhang, L.; Zhang, M.; Zhang, Y.; Zhao, C.; Zhou, M.; Zhou, Z.; Zhu, X. J.; Zucker, M. E.; Zuraw, S. E.; Zweizig, J.; LIGO Scientific Collaboration; Virgo Collaboration

    2016-12-01

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

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

    NASA Technical Reports Server (NTRS)

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

    2016-01-01

    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 sq. deg to 20 sq. deg will require at least three detectors of sensitivity within a factor of approximately 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.

  5. DETECTION, LOCALIZATION, AND CHARACTERIZATION OF GRAVITATIONAL WAVE BURSTS IN A PULSAR TIMING ARRAY

    SciTech Connect

    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.

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

    PubMed

    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; Castro, J M Gonzalez; Gopakumar, A; Gordon, N A; Gorodetsky, M L; Gossan, S E; Gosselin, M; Gouaty, R; Graef, C; Graff, P B; Granata, M; Grant, A; Gras, S; Gray, C; Greco, G; Green, A C; Groot, P; Grote, H; Grunewald, S; Guidi, G M; Guo, X; Gupta, A; Gupta, M K; Gushwa, K E; Gustafson, E K; Gustafson, R; Hacker, J J; Hall, B R; Hall, E D; Hammond, G; Haney, M; Hanke, M M; Hanks, J; Hanna, C; Hannam, M D; Hanson, J; Hardwick, T; Harms, J; Harry, G M; Harry, I W; Hart, M J; Hartman, M T; Haster, C-J; Haughian, K; Heidmann, A; Heintze, M C; Heitmann, H; Hello, P; Hemming, G; Hendry, M; Heng, I S; Hennig, J; Heptonstall, A W; Heurs, M; Hild, S; Hoak, D; Hodge, K A; Hofman, D; Hollitt, S E; Holt, K; Holz, D E; Hopkins, P; Hosken, D J; Hough, J; Houston, E A; Howell, E J; Hu, Y M; Huang, S; Huerta, E A; Huet, D; Hughey, B; Husa, S; Huttner, S H; Huynh-Dinh, T; Idrisy, A; Indik, N; Ingram, D R; Inta, R; Isa, H N; Isac, J-M; Isi, M; Islas, G; Isogai, T; Iyer, B R; Izumi, K; Jacqmin, T; Jang, H; Jani, K; Jaranowski, P; Jawahar, S; Jiménez-Forteza, F; Johnson, W W; Jones, D I; Jones, R; Jonker, R J G; Ju, L; Haris, K; Kalaghatgi, C V; Kalogera, V; Kandhasamy, S; Kang, G; Kanner, J B; Karki, S; Kasprzack, M; Katsavounidis, E; Katzman, W; Kaufer, S; Kaur, T; Kawabe, K; Kawazoe, F; Kéfélian, F; Kehl, M S; Keitel, D; Kelley, D B; Kells, W; Kennedy, R; Key, J S; Khalaidovski, A; Khalili, F Y; Khan, S; Khan, Z; Khazanov, E A; Kijbunchoo, N; Kim, C; Kim, J; Kim, K; Kim, N; Kim, Y-M; King, E J; King, P J; Kinzel, D L; Kissel, J S; Kleybolte, L; Klimenko, S; Koehlenbeck, S M; Kokeyama, K; Koley, S; Kondrashov, V; Kontos, A; Korobko, M; Korth, W Z; Kowalska, I; Kozak, D B; Kringel, V; Krishnan, B; Królak, A; Krueger, C; Kuehn, G; Kumar, P; Kuo, L; Kutynia, A; Lackey, B D; Landry, M; Lange, J; Lantz, B; Lasky, P D; Lazzarini, A; Lazzaro, C; Leaci, P; Leavey, S; Lebigot, E; Lee, C H; Lee, H K; Lee, H M; Lee, K; Lenon, A; Leonardi, M; Leong, J R; Leroy, N; Letendre, N; Levin, Y; Levine, B M; Li, T G F; Libson, A; Littenberg, T B; Lockerbie, N A; Logue, J; Lombardi, A L; Lord, J E; Lorenzini, M; Loriette, V; Lormand, M; Losurdo, G; Lough, J D; Lück, H; Lundgren, A P; Luo, J; Lynch, R; Ma, Y; MacDonald, T; Machenschalk, B; MacInnis, M; Macleod, D M; Magaña-Sandoval, F; Magee, R M; Mageswaran, M; Majorana, E; Maksimovic, I; Malvezzi, V; Man, N; Mandel, I; Mandic, V; Mangano, V; Mansell, G L; Manske, M; Mantovani, M; Marchesoni, F; Marion, F; Márka, S; Márka, Z; Markosyan, A S; Maros, E; Martelli, F; Martellini, L; Martin, I W; Martin, R M; Martynov, D V; Marx, J N; Mason, K; Masserot, A; Massinger, T J; Masso-Reid, M; Matichard, F; Matone, L; Mavalvala, N; Mazumder, N; Mazzolo, G; McCarthy, R; McClelland, D E; McCormick, S; McGuire, S C; McIntyre, G; McIver, J; McManus, D J; McWilliams, S T; Meacher, D; Meadors, G D; Meidam, J; Melatos, A; Mendell, G; Mendoza-Gandara, D; Mercer, R A; Merilh, E; Merzougui, M; Meshkov, S; Messenger, C; Messick, C; Meyers, P M; Mezzani, F; Miao, H; Michel, C; Middleton, H; Mikhailov, E E; Milano, L; Miller, J; Millhouse, M; Minenkov, Y; Ming, J; Mirshekari, S; Mishra, C; Mitra, S; Mitrofanov, V P; Mitselmakher, G; Mittleman, R; Moggi, A; Mohan, M; Mohapatra, S R P; Montani, M; Moore, B C; Moore, C J; Moraru, D; Moreno, G; Morriss, S R; Mossavi, K; Mours, B; Mow-Lowry, C M; Mueller, C L; Mueller, G; Muir, A W; Mukherjee, Arunava; Mukherjee, D; Mukherjee, S; Mullavey, A; Munch, J; Murphy, D J; Murray, P G; Mytidis, A; Nardecchia, I; Naticchioni, L; Nayak, R K; Necula, V; Nedkova, K; Nelemans, G; Neri, M; Neunzert, A; Newton, G; Nguyen, T T; Nielsen, A B; Nissanke, S; Nitz, A; Nocera, F; Nolting, D; Normandin, M E N; Nuttall, L K; Oberling, J; Ochsner, E; O'Dell, J; Oelker, E; Ogin, G H; Oh, J J; Oh, S H; Ohme, F; Oliver, M; Oppermann, P; Oram, R J; O'Reilly, B; O'Shaughnessy, R; Ott, C D; Ottaway, D J; Ottens, R S; Overmier, H; Owen, B J; Pai, A; Pai, S A; Palamos, J R; Palashov, O; Palomba, C; Pal-Singh, A; Pan, H; Pankow, C; Pannarale, F; Pant, B C; Paoletti, F; Paoli, A; Papa, M A; Paris, H R; Parker, W; Pascucci, D; Pasqualetti, A; Passaquieti, R; Passuello, D; Patrick, Z; Pearlstone, B L; Pedraza, M; Pedurand, R; Pekowsky, L; Pele, A; Penn, S; Pereira, R; Perreca, A; Phelps, M; Piccinni, O; Pichot, M; Piergiovanni, F; Pierro, V; Pillant, G; Pinard, L; Pinto, I M; Pitkin, M; Poggiani, R; Post, A; Powell, J; Prasad, J; Predoi, V; Premachandra, S S; Prestegard, T; Price, L R; Prijatelj, M; Principe, M; Privitera, S; Prodi, G A; Prokhorov, L; Punturo, M; Puppo, P; Pürrer, M; Qi, H; Qin, J; Quetschke, V; Quintero, E A; Quitzow-James, R; Raab, F J; Rabeling, D S; Radkins, H; Raffai, P; Raja, S; Rakhmanov, M; Rapagnani, P; Raymond, V; Razzano, M; Re, V; Read, J; Reed, C M; Regimbau, T; Rei, L; Reid, S; Reitze, D H; Rew, H; Ricci, F; Riles, K; Robertson, N A; Robie, R; Robinet, F; Rocchi, A; Rolland, L; Rollins, J G; Roma, V J; Romano, J D; Romano, R; Romanov, G; Romie, J H; Rosińska, D; Rowan, S; Rüdiger, A; Ruggi, P; Ryan, K; Sachdev, S; Sadecki, T; Sadeghian, L; Saleem, M; Salemi, F; Samajdar, A; Sammut, L; Sanchez, E J; Sandberg, V; Sandeen, B; Sanders, J R; Sassolas, B; Sathyaprakash, B S; Saulson, P R; Sauter, O; Savage, R L; Sawadsky, A; Schale, P; Schilling, R; Schmidt, J; Schmidt, P; Schnabel, R; Schofield, R M S; Schönbeck, A; Schreiber, E; Schuette, D; Schutz, B F; Scott, J; Scott, S M; Sellers, D; Sentenac, D; Sequino, V; Sergeev, A; Serna, G; Setyawati, Y; Sevigny, A; Shaddock, D A; Shah, S; Shahriar, M S; Shaltev, M; Shao, Z; Shapiro, B; Shawhan, P; Sheperd, A; Shoemaker, D H; Shoemaker, D M; Siellez, K; Siemens, X; Sigg, D; Silva, A D; Simakov, D; Singer, A; Singer, L P; Singh, A; Singh, R; Sintes, A M; Slagmolen, B J J; Smith, J R; Smith, N D; Smith, R J E; Son, E J; Sorazu, B; Sorrentino, F; Souradeep, T; Srivastava, A K; Staley, A; Steinke, M; Steinlechner, J; Steinlechner, S; Steinmeyer, D; Stephens, B C; Stone, R; Strain, K A; Straniero, N; Stratta, G; Strauss, N A; Strigin, S; Sturani, R; Stuver, A L; Summerscales, T Z; Sun, L; Sutton, P J; Swinkels, B L; Szczepanczyk, M J; Tacca, M; Talukder, D; Tanner, D B; Tápai, M; Tarabrin, S P; Taracchini, A; Taylor, R; Theeg, T; Thirugnanasambandam, M P; Thomas, E G; Thomas, M; Thomas, P; Thorne, K A; Thorne, K S; Thrane, E; Tiwari, S; Tiwari, V; Tokmakov, K V; Tomlinson, C; Tonelli, M; Torres, C V; Torrie, C I; Töyrä, D; Travasso, F; Traylor, G; Trifirò, D; Tringali, M C; Trozzo, L; Tse, M; Turconi, M; Tuyenbayev, D; Ugolini, D; Unnikrishnan, C S; Urban, A L; Usman, S A; Vahlbruch, H; Vajente, G; Valdes, G; van Bakel, N; van Beuzekom, M; van den Brand, J F J; van den Broeck, C; Vander-Hyde, D C; van der Schaaf, L; van der Sluys, M V; van Heijningen, J V; van Veggel, A A; Vardaro, M; Vass, S; Vasúth, M; Vaulin, R; Vecchio, A; Vedovato, G; Veitch, J; Veitch, P J; Venkateswara, K; Verkindt, D; Vetrano, F; Viceré, A; Vinciguerra, S; Vine, D J; Vinet, J-Y; Vitale, S; Vo, T; Vocca, H; Vorvick, C; Vousden, W D; Vyatchanin, S P; Wade, A R; Wade, L E; Wade, M; Walker, M; Wallace, L; Walsh, S; Wang, G; Wang, H; Wang, M; Wang, X; Wang, Y; Ward, R L; Warner, J; Was, M; Weaver, B; Wei, L-W; Weinert, M; Weinstein, A J; Weiss, R; Welborn, T; Wen, L; Weßels, P; Westphal, T; Wette, K; Whelan, J T; White, D J; Whiting, B F; Williams, R D; Williamson, A R; Willis, J L; Willke, B; Wimmer, M H; Winkler, W; Wipf, C C; Wittel, H; Woan, G; Worden, J; Wright, J L; Wu, G; Yablon, J; Yam, W; Yamamoto, H; Yancey, C C; Yap, M J; Yu, H; Yvert, M; Zadrożny, A; Zangrando, L; Zanolin, M; Zendri, J-P; Zevin, M; Zhang, F; Zhang, L; Zhang, M; Zhang, Y; Zhao, C; Zhou, M; Zhou, Z; Zhu, X J; Zucker, M E; Zuraw, S E; Zweizig, J

    2016-01-01

    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.

  7. Local heating of human skin by millimeter waves: a kinetics study.

    PubMed

    Alekseev, S I; Ziskin, M C

    2003-12-01

    Heating rates of human skin exposed locally to 42.25 GHz mm waves, coming from a waveguide (WG) opening or a YAV device designed for therapeutic application, were studied in vivo using infrared (IR) thermography. For both radiators, the power density distribution was described by a circularly symmetrical Gaussian type function on the exposed skin surface. Insertion of a small thermocouple (d = 0.1 mm) in the exposed area did not produce any significant artifact, either in the power density distribution or kinetics measurement, providing it was perpendicular to the E vector. The heating kinetics in the skin exposed with either the WG opening or the YAV device were well fitted to solutions of the 2-D bio-heat transfer equation for homogeneous tissue. Changes in irradiating beam size (1-8 mm) had no detectable effect on the initial (0.3-3.0 s) phase of the heating kinetics. However, the amplitude of the kinetics decreased substantially with decreasing the beam size. As the temperature rise in the time interval necessary for reliable measurement of the initial temperature rise rate was very small, an accurate experimental determination of specific absorption rate (SAR) becomes practically impossible at the low intensities normally used in our experiments. The correct SAR values may be found from fitting of the model to the heating kinetics. Bioelectromagnetics 24:571-581, 2003.

  8. 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.

  9. 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.

  10. Localization of sleep spindles, k-complexes, and vertex waves with subdural electrodes in children.

    PubMed

    Pinto, Anna L R; Fernández, Iván S; Peters, Jurriaan M; Manganaro, Sheryl; Singer, Jedediah M; Vendrame, Martina; Prabhu, Sanjay P; Loddenkemper, Tobias; Kothare, Sanjeev V

    2014-08-01

    To describe for the first time in children the localization of sleep spindles, K-complexes, and vertex waves using subdural electrodes. We enrolled children who underwent presurgical evaluation of refractory epilepsy with subdural grid electrodes. We analyzed electroencephalogram data from subdural electrodes and simultaneous recording with Cz scalp electrode. Sleep spindles, K-complexes, and vertex waves were identified and localized based on their morphology on the subdural electrodes. Sixteen patients (9 boys; age range, 3-18 years) were enrolled in the study. The inter-rater reliability on identification and localization of maximal amplitude was high with an intraclass correlation coefficient of 0.85 for vertex waves, 0.94 for sleep spindles, and 0.91 for K-complexes. Sleep spindles presented maximum amplitude around the perirolandic area with a field extending to the frontal regions. K-complexes presented maximum amplitude around the perirolandic area with a field extending to the frontal regions. Vertex waves presented maximum amplitude around the perirolandic areas. In our series of pediatric patients, sleep spindles, K-complexes, and vertex waves were localized around the perirolandic area.

  11. Generalized Darboux transformation and rogue wave solution of the coherently-coupled nonlinear Schrödinger system

    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.

  12. Periodic wave solutions of coupled integrable dispersionless equations by residue harmonic balance

    NASA Astrophysics Data System (ADS)

    Leung, A. Y. T.; Yang, H. X.; Guo, Z. J.

    2012-11-01

    We introduce the residue harmonic balance method to generate periodic solutions for nonlinear evolution equations. A PDE is firstly transformed into an associated ODE by a wave transformation. The higher-order approximations to the angular frequency and periodic solution of the ODE are obtained analytically. To improve the accuracy of approximate solutions, the unbalanced residues appearing in harmonic balance procedure are iteratively considered by introducing an order parameter to keep track of the various orders of approximations and by solving linear equations. Finally, the periodic solutions of PDEs result. The proposed method has the advantage that the periodic solutions are represented by Fourier functions rather than the sophisticated implicit functions as appearing in most methods.

  13. On the Formation of Shock Waves in Subsonic Flows With Local Supersonic Velocities

    NASA Technical Reports Server (NTRS)

    Frankl, F. I.

    1950-01-01

    In the flow about a body with large subsonic velocity if the velocity of the approaching flow is sufficiently large, regions of local supersonic velocities are formed about the body. It is known from experiment that these regions downstream of the flow are always bounded by shock waves; a continuous transition of the supersonic velocity to the subsonic under the conditions indicated has never been observed. A similar phenomenon occurs in pipes. If at two cross sections of the pipe the velocity is subsonic and between these sections regions of local supersonic velocity are formed without completely occupying a single cross section, these regions are always bounded by shock waves.

  14. Traveling wave solutions in a chain of periodically forced coupled nonlinear oscillators

    DOE PAGES

    Duanmu, M.; Whitaker, N.; Kevrekidis, P. G.; ...

    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

  15. Multi-rogue waves solutions: from the NLS to the KP-I equation

    NASA Astrophysics Data System (ADS)

    Dubard, P.; Matveev, V. B.

    2013-12-01

    Our discovery of multi-rogue wave (MRW) solutions in 2010 completely changed the viewpoint on the links between the theory of rogue waves and integrable systems, and helped explain many phenomena which were never understood before. It is enough to mention the famous Three Sister waves observed in oceans, the creation of a regular approach to studying higher Peregrine breathers, and the new understanding of 2 + 1 dimensional rogue waves via the NLS-KP correspondence. This article continues the study of the MRW solutions of the NLS equation and their links with the KP-I equation started in a previous series of articles (Dubard et al 2010 Eur. Phys. J. 185 247-58, Dubard and Matveev 2011 Natural Hazards Earth Syst. Sci. 11 667-72, Matveev and Dubard 2010 Proc. Int. Conf. FNP-2010 (Novgorod, St Petersburg) pp 100-101, Dubard 2010 PhD Thesis). In particular, it contains a discussion of the large parametric asymptotics of these solutions, which has never been studied before.

  16. Selective localization of myosin-I proteins in macropinosomes and actin waves.

    PubMed

    Brzeska, Hanna; Koech, Hilary; Pridham, Kevin J; Korn, Edward D; Titus, Margaret A

    2016-02-01

    Class I myosins are widely expressed with roles in endocytosis and cell migration in a variety of cell types. Dictyostelium express multiple myosin Is, including three short-tailed (Myo1A, Myo1E, Myo1F) and three long-tailed (Myo1B, Myo1C, Myo1D). Here we report the molecular basis of the specific localizations of short-tailed Myo1A, Myo1E, and Myo1F compared to our previously determined localization of long-tailed Myo1B. Myo1A and Myo1B have common and unique localizations consistent with the various features of their tail region; specifically the BH sites in their tails are required for their association with the plasma membrane and heads are sufficient for relocalization to the front of polarized cells. Myo1A does not localize to actin waves and macropinocytic protrusions, in agreement with the absence of a tail region which is required for these localizations of Myo1B. However, in spite of the overall similarity of their domain structures, the cellular distributions of Myo1E and Myo1F are quite different from Myo1A. Myo1E and Myo1F, but not Myo1A, are associated with macropinocytic cups and actin waves. The localizations of Myo1E and Myo1F in macropinocytic structures and actin waves differ from the localization of Myo1B. Myo1B colocalizes with F-actin in the actin waves and at the tips of mature macropinocytic cups whereas Myo1E and Myo1F are in the interior of actin waves and along the entire surface of macropinocytic cups. Our results point to different mechanisms of targeting of short- and long-tailed myosin Is, and are consistent with these myosins having both shared and divergent cellular functions.

  17. 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.

  18. Diffusive and localization behavior of electromagnetic waves in a two-dimensional random medium.

    PubMed

    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)].

  19. Over-reflection of slow magnetosonic waves by homogeneous shear flow: Analytical solution

    SciTech Connect

    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.

  20. The iterative solution of wave propagation in transverse magnetic mode for graded positive-negative

    NASA Astrophysics Data System (ADS)

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

    2017-01-01

    The iterative solution was used to obtain the electromagnetic wave propagation in transverse magnetic (TM) mode for a graded positive-negative refractive index. The graded graphs of negative permittivity and negative permeability were obtained in hyperbolic functions. By using hyperbolic function for permittivity and permeability in Maxwell equation and by separation variable, we obtained the electromagnetic differential equation. From the differential equation, we used the approachment using MacLaurin series to obtain the wave vector and magnetic fields equation. The distribution of the magnetic fields were given in graph visualization using Matlab software.

  1. [Micro-wave local area network for radiological image transmission].

    PubMed

    Takizawa, M; Sone, S; Kasuga, T; Oguchi, K; Kondo, S; Fuwa, Y; Yamaura, I; Wako, T; Okazaki, Y; Maruyama, Y

    1994-10-25

    Shinshu University consists of five campuses in different locations, a situation that presents some problems in communication. To solve this problem, the Shinshu University Video and Data Network System (SUNS), which includes a high-speed audio-visual transfer function, has been developed and utilized for pre- and postgraduate education, administrative teleconferences, and local telephone (PBX) and Fax services. In 1988, a cooperative group for the study of radiographic image processing was organized, consisting of staff members of Shinshu University Hospital in Matsumoto, the Faculty of Engineering in Nagano (75 km from Matsumoto) and the Faculty of Textile Science and Technology in Ueda (45 km from Matsumoto). The system has been developed with a pair of personal computer (PC)-based interactive image workstations and high-speed digital telecommunication interfaces to the SUNS. A transmission time of 878 kbps has been attained, including the time needed for read/write onto the PC hard disk. Image data thus transferred from the hospital have been utilized for the study of image processing by researchers in the Faculty of Engineering, and the processed images have been sent back to the hospital for evaluation of clinical efficacy of the processing by diagnostic radiologists. This kind of microwave network is a promising alternative for high-speed data transmission for radiological images and their processing.

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

    SciTech Connect

    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.

  3. Dissipative MHD solutions for resonant Alfven waves in 1-dimensional magnetic flux tubes

    NASA Technical Reports Server (NTRS)

    Goossens, Marcel; Ruderman, Michail S.; Hollweg, Joseph V.

    1995-01-01

    The present paper extends the analysis by Sakurai, Goossens, and Hollweg (1991) on resonant Alfven waves in nonuniform magnetic flux tubes. It proves that the fundamental conservation law for resonant Alfven waves found in ideal MHD by Sakurai, Goossens, and Hollweg remains valid in dissipative MHD. This guarantees that the jump conditions of Sakurai, Goossens, and Hollweg, that connect the ideal MHD solutions for xi(sub r), and P' across the dissipative layer, are correct. In addition, the present paper replaces the complicated dissipative MHD solutions obtained by Sakurai, Goossens, and Hollweg for xi(sub r), and P' in terms of double integrals of Hankel functions of complex argument of order 1/3 with compact analytical solutions that allow a straight- forward mathematical and physical interpretation. Finally, it presents an analytical dissipative MHD solution for the component of the Lagrangian displacement in the magnetic surfaces perpen- dicular to the magnetic field lines xi(sub perpendicular) which enables us to determine the dominant dynamics of resonant Alfven waves in dissipative MHD.

  4. On the cubic zero-order solution of electromagnetic waves. II. Isolated particles with lossy plasmas

    SciTech Connect

    Lee, Hyoung-In; Mok, Jinsik

    2010-07-15

    Electromagnetic waves are examined for a single isolated nanoparticle, which is composed of lossy plasmonic components and immersed in an unbounded homogeneous dielectric host medium. Wave characteristics thus obtained on resonance play crucial roles as the zero-order solution for periodic structures such as linear particle chains. The dispersion relation with cubic nonlinearity in frequency accounts for radiation damping in addition to dynamic depolarization. It is theoretically analyzed on the parameter plane spanned by the material loss and the plasma frequency. As in the preceding companion paper of Paper I, analysis shows two types of solutions: propagating waves and stationary states. In addition, the temporal attenuation rate exhibits a maximum feature at a certain material loss in confirmation of experimental results. However, physical behaviors of a nanoparticle turn out quite distinct from those illustrated in Paper I. The reasons are that the different mathematical structures are involved, and different geometries require different underlying assumptions. In special, the issue of series convergence in choosing proper solutions will be addressed. In addition, solutions to nanoparticles made of polarizable dielectric materials are found not to exist.

  5. Dynamic Sensing of Localized Corrosion at the Metal/Solution Interface

    PubMed Central

    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

  6. On the dispersionless Kadomtsev-Petviashvili equation with arbitrary nonlinearity and dimensionality: exact solutions, longtime asymptotics of the Cauchy problem, wave breaking and shocks

    NASA Astrophysics Data System (ADS)

    Santucci, F.; Santini, P. M.

    2016-10-01

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

  7. Some new traveling wave exact solutions of the (2+1)-dimensional Boiti-Leon-Pempinelli equations.

    PubMed

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

    2014-01-01

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

  8. Local Slow Waves in Superficial Layers of Primary Cortical Areas during REM Sleep.

    PubMed

    Funk, Chadd M; Honjoh, Sakiko; Rodriguez, Alexander V; Cirelli, Chiara; Tononi, Giulio

    2016-02-08

    Sleep is traditionally constituted of two global behavioral states, non-rapid eye movement (NREM) and rapid eye movement (REM), characterized by quiescence and reduced responsiveness to sensory stimuli [1]. NREM sleep is distinguished by slow waves and spindles throughout the cerebral cortex and REM sleep by an "activated," low-voltage fast electroencephalogram (EEG) paradoxically similar to that of wake, accompanied by rapid eye movements and muscle atonia. However, recent evidence has shown that cortical activity patterns during wake and NREM sleep are not as global as previously thought. Local slow waves can appear in various cortical regions in both awake humans [2] and rodents [3-5]. Intracranial recordings in humans [6] and rodents [4, 7] have shown that NREM sleep slow waves most often involve only a subset of brain regions that varies from wave to wave rather than occurring near synchronously across all cortical areas. Moreover, some cortical areas can transiently "wake up" [8] in an otherwise sleeping brain. Yet until now, cortical activity during REM sleep was thought to be homogenously wake-like. We show here, using local laminar recordings in freely moving mice, that slow waves occur regularly during REM sleep, but only in primary sensory and motor areas and mostly in layer 4, the main target of relay thalamic inputs, and layer 3. This finding may help explain why, during REM sleep, we remain disconnected from the environment even though the bulk of the cortex shows wake-like, paradoxical activation.

  9. Disorder in Quantum Vacuum: Casimir-Induced Localization of Matter Waves

    SciTech Connect

    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.

  10. Localization of Short Duration Gravitational-wave Transients with the Early Advanced LIGO and Virgo Detectors

    NASA Astrophysics Data System (ADS)

    Essick, Reed; Vitale, Salvatore; Katsavounidis, Erik; Vedovato, Gabriele; Klimenko, Sergey

    2015-02-01

    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 deg2 in 2015 and 60-110 deg2 in 2016, although knowledge of the waveform can reduce this to as little as 22 deg2. 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.

  11. LOCALIZATION OF SHORT DURATION GRAVITATIONAL-WAVE TRANSIENTS WITH THE EARLY ADVANCED LIGO AND VIRGO DETECTORS

    SciTech Connect

    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.

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

    PubMed

    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.

  13. Directional cloaking of flexural waves in a plate with a locally resonant metamaterial.

    PubMed

    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.

  14. New concept for the pairing anti-halo effect as a localized wave packet of quasiparticles

    NASA Astrophysics Data System (ADS)

    Hagino, K.; Sagawa, H.

    2017-02-01

    The pairing anti-halo effect is a phenomenon that a pairing correlation suppresses a divergence of nuclear radius, which happens for single-particle states with orbital angular momenta of l =0 and 1 in the limit of vanishing binding energy. While this effect has mainly been discussed in terms of Hartree-Fock-Bogoliubov (HFB) theory, we here use a three-body model and provide its new intuitive concept as a localized wave packet for a quasiparticle, that is, a coherent superposition of a weakly bound and continuum wave functions due to a pairing interaction. We show that the one-particle density in the three-body model can be directly expressed with such quasiparticle wave functions, which have a close analog to wave functions in the HFB approximation.

  15. Localization of 3D inertial Alfvén wave and generation of turbulence

    NASA Astrophysics Data System (ADS)

    Sharma, R. P.; Sharma, Prachi; Yadav, N.

    2015-06-01

    The present paper deals with the nonlinear interaction of Inertial Alfvén wave (IAW) and fast magnetosonic wave in the low beta plasma, where beta is the ratio of thermal pressure to the background magnetic pressure. In this paper, the localization and turbulent spectra of IAW along with the density dips correlated with the fast magnetosonic wave have been investigated. Variation of parallel electric field along and across the field lines has also been studied. Taking ponderomotive nonlinear effect in the dynamics of fast magnetosonic wave, couple of dimensionless equations has been derived. These coupled equations have been simulated numerically using the pseudo-spectral method. The obtained results reveal that the Kolmogorov scaling is followed by a steeper scaling in magnetic power spectrum, which is consistent with the observations by the FAST and Hawkeye spacecraft in auroral region. The relevance of present investigation has been discussed for auroral plasmas.

  16. Local chiral symmetry and charge-density waves in one-dimensional conductors

    NASA Astrophysics Data System (ADS)

    Sakita, B.; Shizuya, K.

    1990-09-01

    Symmetry-related features of charge-density-wave transport phenomena are studied using a non-mean-field effective Lagrangian approach. It is pointed out that a local chiral symmetry (based on the Kač-Moody algebra) emerges in the low-energy structure of one-dimensional electron-phonon systems. From this symmetry follow directly power-law correlations of both electrons and phonons. The Peierls instability is suppressed owing to one-dimensional fluctuations. Still the charge-density wave arises and the chiral anomaly can account for acceleration of a sliding charge-density wave along with a phonon-drag effect. The problem of pinning of charge-density waves is discussed in relation to explicit breakings of the chiral symmetry.

  17. 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.

  18. 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.

  19. Photonic nanojets as a versatile optical tool for wave super-localization

    SciTech Connect

    Geints, Yu. E.; Zemlyanov, A. A.; Panina, E. K.

    2016-08-02

    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.

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

    SciTech Connect

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

    2015-11-15

    We study vector localized waves on continuous wave background with higher-order effects in a two-mode optical fiber. The striking properties of transition, coexistence, and interaction of these localized waves arising from higher-order effects are revealed in combination with corresponding modulation instability (MI) characteristics. It shows that these vector localized wave properties have no analogues in the case without higher-order effects. Specifically, compared to the scalar case, an intriguing transition between bright–dark rogue waves and w-shaped–anti-w-shaped solitons, which occurs as a result of the attenuation of MI growth rate to vanishing in the zero-frequency perturbation region, is exhibited with the relative background frequency. In particular, our results show that the w-shaped–anti-w-shaped solitons can coexist with breathers, coinciding with the MI analysis where the coexistence condition is a mixture of a modulation stability and MI region. It is interesting that their interaction is inelastic and describes a fusion process. In addition, we demonstrate an annihilation phenomenon for the interaction of two w-shaped solitons which is identified essentially as an inelastic collision in this system. -- Highlights: •Vector rogue wave properties induced by higher-order effects are studied. •A transition between vector rogue waves and solitons is obtained. •The link between the transition and modulation instability (MI) is demonstrated. •The coexistence of vector solitons and breathers coincides with the MI features. •An annihilation phenomenon for the vector two w-shaped solitons is presented.

  1. Exact solutions for the source-excited cylindrical electromagnetic waves in a nonlinear nondispersive medium.

    PubMed

    Es'kin, V A; Kudrin, A V; Petrov, E Yu

    2011-06-01

    The behavior of electromagnetic fields in nonlinear media has been a topical problem since the discovery of materials with a nonlinearity of electromagnetic properties. The problem of finding exact solutions for the source-excited nonlinear waves in curvilinear coordinates has been regarded as unsolvable for a long time. In this work, we present the first solution of this type for a cylindrically symmetric field excited by a pulsed current filament in a nondispersive medium that is simultaneously inhomogeneous and nonlinear. Assuming that the medium has a power-law permittivity profile in the linear regime and lacks a center of inversion, we derive an exact solution for the electromagnetic field excited by a current filament in such a medium and discuss the properties of this solution.

  2. Solutions of kW Continuous-wave All-fiber Laser

    NASA Astrophysics Data System (ADS)

    Dapeng, Yan; Libo, Li; Xiaoxu, Liu; Dayong, Min

    2011-02-01

    Solutions of kW continuous-wave (CW) all-fiber laser are proposed. In our solutions, master oscillator power amplifier (MOPA) configuration is applied. Output power of master oscillator is 10W, and then is amplified to 70W with 1st pre-amplifier and next scaled up to 400W. Finally, 400W fiber laser is used as a basic power unit, and 1000W all-fiber laser can be achieved by means of beam combining with large core double clad fiber (DCF) combiner. In this solution, fiber laser has good stability and reliability for dispersion coupling of pump source and inhibition of photon darkening effect in the fiber. In addition, this solution assures us realize a 1000W all-fiber laser product easily, and the cost is low.

  3. Multiple scales analysis and travelling wave solutions for KdV type nonlinear evolution equations

    NASA Astrophysics Data System (ADS)

    Ayhan, Burcu; Ozer, M. Naci; Bekir, Ahmet

    2017-01-01

    Nonlinear evolution equations are the mathematical models of problems that arise in many field of science. These equations has become an important field of study in applied mathematics in recent years. We apply exact solution methods and multiple scale method which is known as a perturbation method to nonlinear evolution equations. Using exact solution methods we get travelling wave solutions expressed by hyperbolic functions, trigonometric functions and rational functions. Also we derive Nonlinear Schrödinger (NLS) type equations from Korteweg-de Vries (KdV) type nonlinear evolution equations and we get approximate solutions for KdV type equations using multiple scale method. The proposed methods are direct and effective and can be used for many nonlinear evolution equations. It is shown that these methods provide a powerful mathematical tool to solve nonlinear evolution equations in mathematical physics.

  4. Traveling wave solutions of degenerate coupled multi-KdV equations

    NASA Astrophysics Data System (ADS)

    Gürses, Metin; Pekcan, Aslı

    2016-10-01

    Traveling wave solutions of degenerate coupled ℓ-KdV equations are studied. Due to symmetry reduction these equations reduce to one ordinary differential equation (ODE), i.e., (f')2 = Pn(f) where Pn(f) is a polynomial function of f of degree n = ℓ + 2, where ℓ ≥ 3 in this work. Here ℓ is the number of coupled fields. There is no known method to solve such ordinary differential equations when ℓ ≥ 3. For this purpose, we introduce two different types of methods to solve the reduced equation and apply these methods to degenerate three-coupled KdV equation. One of the methods uses the Chebyshev's theorem. In this case, we find several solutions, some of which may correspond to solitary waves. The second method is a kind of factorizing the polynomial Pn(f) as a product of lower degree polynomials. Each part of this product is assumed to satisfy different ODEs.

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

    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.

  6. Equilibria and Travelling wave solutions for Couette and channel flows with longitudinal grooves

    NASA Astrophysics Data System (ADS)

    Vadarevu, Sabarish; Sharma, Ati; Ganapathisubramani, Bharathram

    2016-11-01

    Several classes of exact solutions for canonical flows have been computed by earlier researchers. These solutions are known to inform the flow of turbulence in state-space. We extend two classes of exact solutions, equilibria and travelling wave solutions, from flat-walled Couette and channel flows to grooved geometries with groove-amplitudes as high as 20% of channel half-height. These solutions provide insight into the mechanics of how a wavy wall could influence turbulent flow. Plotting scalars such as the average shear stress at the wall and the bulk velocity (for channel flows) allows us to identify branches of solutions that could have greater contributions to turbulence, and reconcile the curious phenomenon of drag reduction observed in some riblet-mounted boundary layer flows. Earlier researchers have proposed using modified boundary conditions (imposed on flat surfaces) as a substitute to imposing the traditional no-slip and impermeability conditions on a rough wall. We compare solutions for grooved flows to those for flat-walled flows with modified boundary conditions to evaluate the validity of such simplification to non-laminar solutions.

  7. 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

  8. Global existence of solutions for semilinear damped wave equation in 2-D exterior domain

    NASA Astrophysics Data System (ADS)

    Ikehata, Ryo

    We consider a mixed problem of a damped wave equation utt-Δ u+ ut=| u| p in the two dimensional exterior domain case. Small global in time solutions can be constructed in the case when the power p on the nonlinear term | u| p satisfies p ∗=2solution in the exterior domain. A new device developed in Ikehata-Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.

  9. Exact time-dependent nonlinear dispersive wave solutions in compressible magnetized plasmas exhibiting collapse.

    PubMed

    Chakrabarti, Nikhil; Maity, Chandan; Schamel, Hans

    2011-04-08

    Compressional waves in a magnetized plasma of arbitrary resistivity are treated with the lagrangian fluid approach. An exact nonlinear solution with a nontrivial space and time dependence is obtained with boundary conditions as in Harris' current sheet. The solution shows competition among hydrodynamic convection, magnetic field diffusion, and dispersion. This results in a collapse of density and the magnetic field in the absence of dispersion. The dispersion effects arrest the collapse of density but not of the magnetic field. A possible application is in the early stage of magnetic star formation.

  10. Solution of an inverse scattering problem for the acoustic wave equation in three-dimensional media

    NASA Astrophysics Data System (ADS)

    Baev, A. V.

    2016-12-01

    A three-dimensional inverse scattering problem for the acoustic wave equation is studied. The task is to determine the density and acoustic impedance of a medium. A necessary and sufficient condition for the unique solvability of this problem is established in the form of an energy conservation law. The interpretation of the solution to the inverse problem and the construction of medium images are discussed.

  11. Double-wave solutions to quasilinear hyperbolic systems of first-order PDEs

    NASA Astrophysics Data System (ADS)

    Curró, C.; Manganaro, N.

    2017-10-01

    A reduction procedure for determining double-wave exact solutions to first-order hyperbolic systems of PDEs is proposed. The basic idea is to reduce the integration of the governing hyperbolic set of N partial differential equations to that of a 2 × 2 reduced hyperbolic model along with a further differential constraint. Therefore, the method of differential constraints is used in order to solve the auxiliary 2 × 2 system. An example of interest to viscoelasticity is presented.

  12. Solitary, explosive and periodic solutions for electron acoustic solitary waves with non-thermal hot ions

    NASA Astrophysics Data System (ADS)

    Elwakil, S. A.; Abulwafa, E. M.; El-Shewy, E. K.; Abd-El-Hamid, H. M.

    2011-11-01

    A theoretical investigation has been made for electron acoustic waves propagating in a system of unmagnetized collisionless plasma consists of a cold electron fluid and ions with two different temperatures in which the hot ions obey the non-thermal distribution. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small but finite amplitude electrostatic waves. It is found that the presence of the energetic population of non-thermal hot ions δ, initial normalized equilibrium density of low temperature ions μ and the ratio of temperatures of low temperature ions to high temperature ions β do not only significantly modify the basic properties of solitary structure, but also change the polarity of the solitary profiles. At the critical hot ions density, the KdV equation is not appropriate for describing the system. Hence, a new set of stretched coordinates is considered to derive the modified KdV equation. In the vicinity of the critical hot ions density, neither KdV nor modified KdV equation is appropriate for describing the electron acoustic waves. Therefore, a further modified KdV equation is derived. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the various KdV-type equations, is used here. Numerical studies have been reveals different solutions e.g., bell-shaped solitary pulses, singular solitary "blowup" solutions, Jacobi elliptic doubly periodic wave, Weierstrass elliptic doubly periodic type solutions, in addition to explosive pulses. The results of the present investigation may be applicable to some plasma environments, such as Earth's magnetotail region.

  13. Parallel iterative procedures for approximate solutions of wave propagation by finite element and finite difference methods

    SciTech Connect

    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.

  14. Excitation of ship waves by a submerged object: New solution to the classical problem.

    PubMed

    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.

  15. 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.

  16. On travelling wave solutions of a generalized Davey-Stewartson system

    NASA Astrophysics Data System (ADS)

    Eden, Alp; Erbay, Saadet

    2005-02-01

    The generalized Davey-Stewartson (GDS) equations, as derived by Babaoglu & Erbay (2004, Int. J. Non-Linear Mech., 39, 941-949), is a system of three coupled equations in (2 + 1) dimensions modelling wave propagation in an infinite elastic medium. The physical parameters ({gamma}, m1, m2, {lambda} and n) of the system allow one to classify the equations as elliptic-elliptic-elliptic (EEE), elliptic-elliptic-hyperbolic (EEH), elliptic-hyperbolic-hyperbolic (EHH), hyperbolic-elliptic-elliptic (HEE), hyperbolic-hyperbolic-hyperbolic (HHH) and hyperbolic-elliptic-hyperbolic (HEH) (Babaoglu et alE, 2004, preprint). In this note, we only consider the EEE and HEE cases and seek travelling wave solutions to GDS systems. By deriving Pohozaev-type identities we establish some necessary conditions on the parameters for the existence of travelling waves, when solutions satisfy some integrability conditions. Using the explicit solutions given in Babaoglu & Erbay (2004) we also show that the parameter constraints must be weaker in the absence of such integrability conditions.

  17. On the cubic zero-order solution of electromagnetic waves. I. Periodic slabs with lossy plasmas

    SciTech Connect

    Lee, Hyoung-In; Mok, Jinsik

    2010-07-15

    Electromagnetic waves are considered for periodic structures consisting of lossy plasmonic components and dielectric host media. For the plasmonic components, not only low-loss metals but also high-loss gas plasmas are taken into consideration. For small filling fractions of the plasmonic components, the intercell interactions are kept to a minimum. In this way, the zero-order solution to the dispersion relation is solved by focusing on its cubic nonlinearity in frequency. Analysis shows that there are two types of solutions: propagating waves and stationary states, depending on the magnitudes of the temporal attenuation rates. Depending on the relative strengths of the material loss of the plasmonic component and its filling fraction, several key critical parameters for the transitions between these two solution types are thus identified. In the following companion paper of Paper II, the cubic nonlinearities in frequency of the dispersion relations stem from different origins. Notwithstanding, they lead to strikingly similar features such as the transitions in wave types and Hopf bifurcations.

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

    PubMed Central

    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

  19. Analytical solution of the problem of a shock wave in the collapsing gas in Lagrangian coordinates

    NASA Astrophysics Data System (ADS)

    Kuropatenko, V. F.; Shestakovskaya, E. S.

    2016-10-01

    It is proposed the exact solution of the problem of a convergent shock wave and gas dynamic compression in a spherical vessel with an impermeable wall in Lagrangian coordinates. At the initial time the speed of cold ideal gas is equal to zero, and a negative velocity is set on boundary of the sphere. When t > t0 the shock wave spreads from this point into the gas. The boundary of the sphere will move under the certain law correlated with the motion of the shock wave. The trajectories of the gas particles in Lagrangian coordinates are straight lines. The equations determining the structure of the gas flow between the shock front and gas border have been found as a function of time and Lagrangian coordinate. The dependence of the entropy on the velocity of the shock wave has been found too. For Lagrangian coordinates the problem is first solved. It is fundamentally different from previously known formulations of the problem of the self-convergence of the self-similar shock wave to the center of symmetry and its reflection from the center, which was built up for the infinite area in Euler coordinates.

  20. Wave propagation through random media: A local method of small perturbations based on the Helmholtz equation

    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.

  1. Localizing high-lying Rydberg wave packets with two-color laser fields

    NASA Astrophysics Data System (ADS)

    Larimian, Seyedreza; Lemell, Christoph; Stummer, Vinzenz; Geng, Ji-Wei; Roither, Stefan; Kartashov, Daniil; Zhang, Li; Wang, Mu-Xue; Gong, Qihuang; Peng, Liang-You; Yoshida, Shuhei; Burgdörfer, Joachim; Baltuška, Andrius; Kitzler, Markus; Xie, Xinhua

    2017-08-01

    We demonstrate control over the localization of high-lying Rydberg wave packets in argon atoms with phase-locked orthogonally polarized two-color laser fields. With a reaction microscope, we measure ionization signals of high-lying Rydberg states induced by a weak dc field and blackbody radiation as a function of the relative phase between the two-color fields. We find that the dc-field-ionization yield of high-lying Rydberg argon atoms oscillates with the relative two-color phase with a period of 2 π while the photoionization signal by blackbody radiation shows a period of π . Accompanying simulations show that these observations are a clear signature of the asymmetric localization of electrons recaptured into very elongated (low angular momentum) high-lying Rydberg states after conclusion of the laser pulse. Our findings thus open an effective pathway to control the localization of high-lying Rydberg wave packets.

  2. Improving the local solution accuracy of large-scale digital image-based finite element analyses.

    PubMed

    Charras, G T; Guldberg, R E

    2000-02-01

    Digital image-based finite element modeling (DIBFEM) has become a widely utilized approach for efficiently meshing complex biological structures such as trabecular bone. While DIBFEM can provide accurate predictions of apparent mechanical properties, its application to simulate local phenomena such as tissue failure or adaptation has been limited by high local solution errors at digital model boundaries. Furthermore, refinement of digital meshes does not necessarily reduce local maximum errors. The purpose of this study was to evaluate the potential to reduce local mean and maximum solution errors in digital meshes using a post-processing filtration method. The effectiveness of a three-dimensional, boundary-specific filtering algorithm was found to be mesh size dependent. Mean absolute and maximum errors were reduced for meshes with more than five elements through the diameter of a cantilever beam considered representative of a single trabecula. Furthermore, mesh refinement consistently decreased errors for filtered solutions but not necessarily for non-filtered solutions. Models with more than five elements through the beam diameter yielded absolute mean errors of less than 15% for both Von Mises stress and maximum principal strain. When applied to a high-resolution model of trabecular bone microstructure, boundary filtering produced a more continuous solution distribution and reduced the predicted maximum stress by 30%. Boundary-specific filtering provides a simple means of improving local solution accuracy while retaining the model generation and numerical storage efficiency of the DIBFEM technique.

  3. Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves

    NASA Astrophysics Data System (ADS)

    Seadawy, Aly R.

    2017-01-01

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

  4. Shock compression modeling of metallic single crystals: comparison of finite difference, steady wave, and analytical solutions

    SciTech Connect

    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

  5. Shock compression modeling of metallic single crystals: comparison of finite difference, steady wave, and analytical solutions

    DOE PAGES

    Lloyd, Jeffrey T.; Clayton, John D.; Austin, Ryan A.; ...

    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

  6. Local Structure and Short-Range Order in a NiCoCr Solid Solution Alloy

    DOE PAGES

    Zhang, F. X.; Zhao, Shijun; Jin, Ke; ...

    2017-05-19

    Multi-element solid solution alloys are intrinsically disordered on the atomic scale, and many of their advanced properties originate from the unique local structural characteristics. We measured the local structure of a NiCoCr solid solution alloy with X-ray/neutron total scattering and extended X-ray absorption fine structure (EXAFS) techniques. The atomic pair distribution function analysis (PDF) did not exhibit distinct structural distortion. But, EXAFS analysis suggested that the Cr atoms are favorably bonded with Ni and Co in the solid solution alloys. This short-range order (SRO) plays a role in the distinct low values of electrical and thermal conductivities in Ni-based solidmore » solution alloys when Cr is incorporated. Both the long-range and local structures of the NiCoCr alloy upon Ni ion irradiation were studied and an irradiation-induced enhancement of SRO was found.« less

  7. 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

  8. 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.

  9. 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.

  10. F-string solution in AdS4 ×𝒞𝒫3 pp-wave background

    NASA Astrophysics Data System (ADS)

    Banerjee, Gourav; Panda, Binata

    2017-01-01

    We present supergravity solution for F-string in pp-wave background obtained from AdS4 ×𝒞𝒫3 with zero flat direction. The classical solution is shown to break all space-time supersymmetries. We explicitly write down the standard as well as supernumerary Killing spinors both for the background and F-string solution.

  11. Modulational instability, higher-order localized wave structures, and nonlinear wave interactions for a nonautonomous Lenells-Fokas equation in inhomogeneous fibers.

    PubMed

    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.

  12. Localization of nonlinear shallow water waves over a randomly rough seabed

    NASA Astrophysics Data System (ADS)

    Mei, Chiang; Grataloup, Geraldine; Li, Yile

    2003-11-01

    Localization or spatial attenuation of sea waves can be caused by bottom friction and by radiation of scattered waves. We describe a theory of shallow-water waves scattered by a long stretch of randomly rough seabed, where the root-mean-square height of the roughness is moderately small. Boussinesq equations are used as the starting point. By using two-scale expansions and Green's functions, multiple scattering by the rough bottom and the nonlinear exchanges of energy between different frequencies are accounted for. For monochromatic incident waves, the evolution equations for all harmonics are shown to be nonlinearly coupled ordinary differential equations with damping, whose coefficients are related to the correlation functions of the roughess. Examples of localization and generation of harmonics are shown by numerical examples. For an incident soliton, the evolution equation is shown to be a KdV-Burgers equation with new diffusion and dispersion terms in integral form, implying memory. Numerical results on soliton deformation, fission and localization will be discussed. Long fetch approximation will be described. This theory differs from several existing ones where random potentials are added to the evolution equations.

  13. Nonlinear, Local Kinetic Damping of Finite-Size Plasma Waves Relevant to Stimulated Raman Scattering

    NASA Astrophysics Data System (ADS)

    Mori, Warren; Fahlen, Jay; Winjum, Benjamin; Grismayer, Thomas; Decyk, Viktor

    2009-11-01

    Computer simulations of stimulated Raman scattering (SRS) indicate that the instability is bursty in time and space, leading to finite-size plasma waves in both the longitudinal and transverse directions. Using particle-in-cell (PIC) simulations with an external, ponderomotive impulse driver, we present the results of detailed study of the nonlinear behavior of finite-sized plasma waves in order to better understand the long-time behavior of SRS reflectivities. In one dimension, we present recently published results (Fahlen et al., PRL 102, 245002 (2009)) showing that finite-length plasma waves erode from the rear edge as new resonant particles enter and locally damp the packet. In multiple dimensions, recent results show that finite-width plasma waves localize about their axis due primarily to local, kinetic damping at the edges. The simulations are performed using a 1D and 2D electrostatic PIC code, and also using a 2D Darwin PIC code. This work was supported by DOE under Grant Nos. DE-FG52-03-NA00065, DE-FG52-06NA26195, and DE-FG02-03ER54721.

  14. Effects of ULF waves on local and global energetic particles: Particle energy and species dependences

    NASA Astrophysics Data System (ADS)

    Li, L. Y.; Yu, J.; Cao, J. B.; Wang, Z. Q.; Yu, Y. Q.; Reeves, G. D.; Li, X.

    2016-11-01

    After 06:13 UT on 24 August 2005, an interplanetary shock triggers large-amplitude ultralow-frequency (ULF) waves (|δB| ≥ 15 nT) in the Pc4-Pc5 wave band (1.6-9 mHz) near the noon geosynchronous orbit (6.6 RE). The local and global effects of ULF waves on energetic particles are observed by five Los Alamos National Laboratory satellites at different magnetic local times. The large-amplitude ULF waves cause the synchronous oscillations of energetic electrons and protons (≥75 keV) at the noon geosynchronous orbit. When the energetic particles have a negative phase space density radial gradient, they undergo rapid outward radial diffusion and loss in the wave activity region. In the particle drift paths without strong ULF waves, only the rapidly drifting energetic electrons (≥225 keV) display energy-dispersive oscillations and flux decays, whereas the slowly drifting electrons (<225 keV) and protons (75-400 keV) have no ULF oscillation and loss feature. When the dayside magnetopause is compressed to the geosynchronous orbit, most of energetic electrons and protons are rapidly lost because of open drift trajectories. The global and multicomposition particle measurements demonstrate that the effect of ULF waves on nonlocal particle flux depends on the particle energy and species, whereas magnetopause shadowing effect is independent of the energetic particle species. For the rapidly drifting outer radiation belt particles (≥225 keV), nonlocal particle loss/acceleration processes could also change their fluxes in the entire drift trajectory in the absence of "Dst effect" and substorm injection.

  15. Noninvasive Method for Measuring Local Pulse Wave Velocity by Dual Pulse Wave Doppler: In Vitro and In Vivo Studies

    PubMed Central

    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

  16. New analytical solutions for propagation of small but finite amplitude ion-acoustic waves in a dense plasma

    NASA Astrophysics Data System (ADS)

    Hafez, M. G.; Talukder, M. R.; Ali, M. Hossain

    2016-01-01

    The theoretical and numerical studies have been investigated on the nonlinear propagation of electrostatic ion-acoustic waves (IAWs) in an un-magnetized Thomas-Fermi plasma system consisting of electron, positrons, and positive ions for both of ultra-relativistic and non-relativistic degenerate electrons. Korteweg-de Vries (K-dV) equation is derived from the model equations by using the well-known reductive perturbation method. This equation is solved by employing the generalized Riccati equation mapping method. The hyperbolic functions type solutions to the K-dV equation are only considered for describing the effect of plasma parameters on the propagation of electrostatic IAWs for both of ultra-relativistic and non-relativistic degenerate electrons. The obtained results may be helpful in proper understanding the features of small but finite amplitude localized IAWs in degenerate plasmas and provide the mathematical foundation in plasma physics.

  17. Travelling-wave and separated variable solutions of a nonlinear Schroedinger equation

    NASA Astrophysics Data System (ADS)

    Bountis, Tassos; Nobre, Fernando D.

    2016-08-01

    Some interesting nonlinear generalizations have been proposed recently for the linear Schroedinger, Klein-Gordon, and Dirac equations of quantum and relativistic physics. These novel equations involve a real parameter q and reduce to the corresponding standard linear equations in the limit q → 1. Their main virtue is that they possess plane-wave solutions expressed in terms of a q-exponential function that can vanish at infinity, while preserving the Einstein energy-momentum relation for all q. In this paper, we first present new travelling wave and separated variable solutions for the main field variable Ψ ( x → , t ) , of the nonlinear Schroedinger equation (NLSE), within the q-exponential framework, and examine their behavior at infinity for different values of q. We also solve the associated equation for the second field variable Φ ( x → , t ) , derived recently within the context of a classical field theory, which corresponds to Ψ ∗ ( x → , t ) for the linear Schroedinger equation in the limit q → 1. For x ∈ ℜ, we show that certain perturbations of these q-exponential solutions Ψ(x, t) and Φ(x, t) are unbounded and hence would lead to divergent probability densities over the full domain -∞ < x < ∞. However, we also identify ranges of q values for which these solutions vanish at infinity, and may therefore be physically important.

  18. Computer simulation of flagellar movement VIII: coordination of dynein by local curvature control can generate helical bending waves.

    PubMed

    Brokaw, Charles J

    2002-10-01

    Computer simulations have been carried out with a model flagellum that can bend in three dimensions. A pattern of dynein activation in which regions of dynein activity propagate along each doublet, with a phase shift of approximately 1/9 wavelength between adjacent doublets, will produce a helical bending wave. This pattern can be termed "doublet metachronism." The simulations show that doublet metachronism can arise spontaneously in a model axoneme in which activation of dyneins is controlled locally by the curvature of each outer doublet microtubule. In this model, dyneins operate both as sensors of curvature and as motors. Doublet metachronism and the chirality of the resulting helical bending pattern are regulated by the angular difference between the direction of the moment and sliding produced by dyneins on a doublet and the direction of the controlling curvature for that doublet. A flagellum that is generating a helical bending wave experiences twisting moments when it moves against external viscous resistance. At high viscosities, helical bending will be significantly modified by twist unless the twist resistance is greater than previously estimated. Spontaneous doublet metachronism must be modified or overridden in order for a flagellum to generate the planar bending waves that are required for efficient propulsion of spermatozoa. Planar bending can be achieved with the three-dimensional flagellar model by appropriate specification of the direction of the controlling curvature for each doublet. However, experimental observations indicate that this "hard-wired" solution is not appropriate for real flagella. Copyright 2002 Wiley-Liss, Inc.

  19. Kinetic Alfvén wave turbulence and formation of localized structures

    SciTech Connect

    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.

  20. 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.