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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. 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'.

  10. 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'.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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

  17. 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.

  18. 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

  19. 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.

  20. 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}

  1. 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.

  2. 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].

  3. 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.

  4. 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

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.…

  10. 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

  11. 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.

  12. 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.

  13. 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.

  14. 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

  15. 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.

  16. 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.

  17. 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,…

  18. 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

  19. 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

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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).

  6. 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}

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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

  12. 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.

  13. 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.

  14. 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.

  15. 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

  16. 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.

  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. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. PML solution of longitudinal wave propagation in heterogeneous media

    NASA Astrophysics Data System (ADS)

    Farzanian, M.; Arbabi, Freydoon; Pak, Ronald

    2016-06-01

    This paper describes the development of a model for unbounded heterogeneous domains with radiation damping produced by an unphysical wave absorbing layer. The Perfectly Matched Layer (PML) approach is used along with a displacement-based finite element. The heterogeneous model is validated using the closed-form solution of a benchmark problem: a free rod with two-part modulus subjected to a specified time history. Both elastically supported and unsupported semi-infinite rods with different degrees of inhomogeneity and loading are considered. Numerical results illustrate the effects of inhomogeneity on the response and are compared with those for equivalent homogeneous domains. The effects of characteristic features of the inhomogeneous problem, presence of local maxima and cut-off frequency are determined. A degenerate case of a homogeneous semi-infinite rod on elastic foundations is produced by tending the magnitude of the foundation stiffness to zero. The response of the latter is compared with that of a free rod. The importance of proper selection of the PML parameters to highly accurate and efficient results is demonstrated by example problems.

  14. Local Marangoni number at the onset of hydrothermal waves

    NASA Astrophysics Data System (ADS)

    Pelacho, Miguel Angel; Garcimartín, Angel; Burguete, Javier

    2000-07-01

    We report the results of an experiment in which a layer of fluid, placed in a container open to the air, is subjected to a horizontal temperature difference ΔT. The fluid height h is kept constant and both the horizontal temperature difference and the horizontal dimensions of the fluid layer are changed. In this configuration, when ΔT goes beyond a certain threshold, waves propagating from the cold to the hot side appear (hydrothermal waves) with a determined group velocity. We study the influence of the container geometry on these waves. Close to the threshold, they are spatially localized near the hot side and a local Marangoni number is defined to describe this behavior. If ΔT is further increased, the waves fill the whole fluid layer. We also find an agreement between our experimental results and theoretical works and simulations.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. Filamentation of laser beam and suppression of stimulated Raman scattering due to localization of electron plasma wave

    NASA Astrophysics Data System (ADS)

    Purohit, Gunjan; Sharma, Prerana; Sharma, R. P.

    2012-02-01

    This paper presents the effect of laser beam filamentation on the localization of electron plasma wave (EPW) and stimulated Raman scattering (SRS) in unmagnetized plasma when relativistic and ponderomotive nonlinearities are operative. The splitted profile of the laser beam is obtained due to uneven focusing of the off-axial rays. The semi-analytical solution of the nonlinearly coupled EPW equation in the presence of laser beam filaments has been found. It is observed that due to this nonlinear coupling between these two waves, localization of EPW takes place. Stimulated Raman scattering of this EPW is studied and back reflectivity has been calculated. Further, the localization of EPW affects the eigenfrequency and damping of plasma wave. The new enhanced damping of the plasma wave has been calculated and it is found that the SRS process gets suppressed due to the localization of plasma wave in laser beam filamentary structures.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  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. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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

  4. 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.

  5. 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.

  6. 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...

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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

  16. 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

  17. 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.

  18. 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.

  19. 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

  20. 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.

  1. 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

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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

  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. 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.

  10. 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.

  11. Suppression of stimulated Raman scattering due to localization of electron plasma wave in laser beam filaments

    SciTech Connect

    Sharma, Prerana; Sharma, R. P.

    2009-03-15

    The filamentation of the high power laser beam by taking off-axial contribution is investigated when ponderomotive nonlinearity is taken into account. The splitted profile of the laser beam is obtained due to uneven focusing of the off-axial rays. It is observed that the weak electron plasma wave (EPW) propagating in the z direction is nonlinearly coupled in the modified filamentary regions of the laser beam. The semianalytical solution of the nonlinear coupled EPW equation in the presence of laser beam filaments has been found and it is observed that the nonlinear coupling between these two waves leads to localization of the EPW. Stimulated Raman scattering (SRS) of this EPW is studied and backreflectivity has been calculated. Further, the localization of EPW affects the eigenfrequency and damping of plasma wave. As a result of this, mismatch and modified enhanced Landau damping lead to the disruption of SRS process and a substantial reduction in the backreflectivity. For the typical laser beam and plasma parameters with wavelength ({lambda}=1064 nm), power flux ({approx_equal}10{sup 16} W cm{sup -2}), and plasma density (n/n{sub cr})=0.2; the backreflectivity was found to be suppressed by a factor of around 20%.

  12. Suppression of stimulated Raman scattering due to localization of electron plasma wave in laser beam filaments

    NASA Astrophysics Data System (ADS)

    Sharma, Prerana; Sharma, R. P.

    2009-03-01

    The filamentation of the high power laser beam by taking off-axial contribution is investigated when ponderomotive nonlinearity is taken into account. The splitted profile of the laser beam is obtained due to uneven focusing of the off-axial rays. It is observed that the weak electron plasma wave (EPW) propagating in the z direction is nonlinearly coupled in the modified filamentary regions of the laser beam. The semianalytical solution of the nonlinear coupled EPW equation in the presence of laser beam filaments has been found and it is observed that the nonlinear coupling between these two waves leads to localization of the EPW. Stimulated Raman scattering (SRS) of this EPW is studied and backreflectivity has been calculated. Further, the localization of EPW affects the eigenfrequency and damping of plasma wave. As a result of this, mismatch and modified enhanced Landau damping lead to the disruption of SRS process and a substantial reduction in the backreflectivity. For the typical laser beam and plasma parameters with wavelength (λ =1064 nm), power flux (≈1016 W cm-2), and plasma density (n /ncr)=0.2; the backreflectivity was found to be suppressed by a factor of around 20%.

  13. Suppression of stimulated Raman scattering due to localization of electron plasma wave in laser beam filaments

    NASA Astrophysics Data System (ADS)

    Sharma, Prerana; Sharma, Rampal

    2009-11-01

    The filamentation of the high power laser beam by taking off-axial contribution is investigated when ponderomotive nonlinearity is taken into account. The splitted profile of the laser beam is obtained due to uneven focusing of the off-axial rays. It is observed that the weak electron plasma wave (EPW) propagating in the z direction is nonlinearly coupled in the modified filamentary regions of the laser beam. The semi-analytical solution of the nonlinear coupled EPW equation in the presence of laser beam filaments has been found and it is observed that the nonlinear coupling between these two waves leads to localization of the EPW. Stimulated Raman scattering (SRS) of this EPW is studied and back reflectivity has been calculated. Further, the localization of EPW affects the eigen frequency and damping of plasma wave. As a result of this, mismatch and modified enhanced Landau damping lead to the disruption of SRS process and a substantial reduction in the back reflectivity. For the typical laser beam and plasma parameters with wavelength (λ=1064nm), power flux ( 10^16 W cm-2), and plasma density (n/ncr) = 0.2; the back reflectivity was found to be suppressed by a factor of around 20%.

  14. 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.

  15. 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.

  16. 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

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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

  6. 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.

  7. 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.

  8. 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

  9. 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.

  10. 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.

  11. 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%.

  12. 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.

  13. 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.

  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. 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.

  16. 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.

  17. 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.

  18. 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

  19. 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.

  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. 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.

  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. 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

  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. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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

  19. 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.

  20. 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).

  1. 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.

  2. 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.

  3. 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.

  4. 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

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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

  11. 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.

  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. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  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. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  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. 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.

  7. 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.

  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. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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

  17. 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

  18. 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.

  19. 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

  20. 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

  1. Stable and accurate difference methods for seismic wave propagation on locally refined meshes

    NASA Astrophysics Data System (ADS)

    Petersson, A.; Rodgers, A.; Nilsson, S.; Sjogreen, B.; McCandless, K.

    2006-12-01

    To overcome some of the shortcomings of previous numerical methods for the elastic wave equation subject to stress-free boundary conditions, we are incorporating recent results from numerical analysis to develop a new finite difference method which discretizes the governing equations in second order displacement formulation. The most challenging aspect of finite difference methods for time dependent hyperbolic problems is clearly stability and some previous methods are known to be unstable when the material has a compressional velocity which exceeds about three times the shear velocity. Since the material properties in seismic applications often vary rapidly on the computational grid, the most straight forward approach for guaranteeing stability is through an energy estimate. For a hyperbolic system in second order formulation, the key to an energy estimate is a spatial discretization which is self-adjoint, i.e. corresponds to a symmetric or symmetrizable matrix. At the same time we want the scheme to be efficient and fully explicit, so only local operations are necessary to evolve the solution in the interior of the domain as well as on the free-surface boundary. Furthermore, we want the solution to be accurate when the data is smooth. Using these specifications, we developed an explicit second order accurate discretization where stability is guaranteed through an energy estimate for all ratios Cp/Cs. An implementation of our finite difference method was used to simulate ground motions during the 1906 San Francisco earthquake on a uniform grid with grid sizes down to 100 meters corresponding to over 4 Billion grid points. These simulations were run on 1024 processors on one of the supercomputers at Lawrence Livermore National Lab. To reduce the computational requirements for these simulations, we are currently extending the numerical method to use a locally refined mesh where the mesh size approximately follows the velocity structure in the domain. Some

  2. 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.

  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. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  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 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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 .

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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}.

  4. 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.

  5. 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.

  6. 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

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. 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].

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. [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.

  5. 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.

  6. 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

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

    NASA Astrophysics Data System (ADS)

    Adur, Rohan; Du, Chunhui; Manuilov, Sergei A.; Wang, Hailong; Yang, Fengyuan; Pelekhov, Denis V.; Hammel, P. Chris

    2015-05-01

    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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. 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

  16. 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.

  17. 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.

  18. Saturation of SRS-LDI with Non-local Growth of SRS Driven Electron Plasma Wave

    NASA Astrophysics Data System (ADS)

    Salcedo, A.; Bers, A.; Ram, A. K.

    2000-10-01

    Experimental observations have shown the coupling of SRS and Langmuir decay interaction (LDI), in ICF experiments where the SRS backscattering is dependent on the damping of ion acoustic waves.(Juan P. Fernandez, et al., Phys. Rev. Lett.) 77, 2702 (1996); R. K. Kirkwood, et al., Phys. Rev. Lett. 77, 13, (1996). A model 3-wave interaction equations for LDI with a growing EPW (driven by SRS) and its non-local Landau damping, gives a simple description of the effect of LDI on the saturation of SRS and its dependence on IAW damping. ( A. Salcedo, A. Bers, A. K. Ram, in Proc. 1st IFSA), Bordeaux, France (1999), pp. 343-348. We present results on the extension of this model to include the non-local growth of the SRS driven EPW, and a comparison with simulations of the full five-wave interaction equations for SRS coupled to LDI. (J. A. Heikkinen, J. Karttunen, Phys. Fluids) 29 (4), (1986).

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. Chaotic Solutions of Nonlinear Wave-Wave Interacting Systems in Plasmas.

    DTIC Science & Technology

    1980-06-01

    that a quasi-periodic function of time " does not have the mixing property (i.e., the autocovariance P1 R(t) of x does not decay to zero as t - x...2.1, where it is assumed that the vii s in (2.1) are zero for N= 3,4. For N =3, the first frequency matching condition has two degrees of freedom and...has a solution X(t) = _X, the zero -vector in the X-space, or X(t) = (0,0, x3(0)exp(-y 3t)) T on the set in the X-space corresponding to E09 and they

  11. 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.

  12. 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

  13. 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.

  14. 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.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

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

    NASA Astrophysics Data System (ADS)

    Arzhannikov, A. V.; Kotelnikov, I. A.

    2016-08-01

    We have proposed a new method for solving the problem of ship waves excited on the surface of a nonviscous liquid by a submerged object that moves at a variable speed. As a first application of this method, we have obtained a new solution to the classic problem of ship waves generated by a submerged ball that moves rectilinearly with constant velocity parallel to the equilibrium surface of the liquid. For this example, we have derived asymptotic expressions describing the vertical displacement of the liquid surface in the limit of small and large values of the Froude number. The exact solution is presented in the form of two terms, each of which is reduced to one-dimensional integrals. One term describes the "Bernoulli hump" and another term the "Kelvin wedge." As a second example, we considered vertical oscillation of the submerged ball. In this case, the solution leads to the calculation of one-dimensional integral and describes surface waves propagating from the epicenter above the ball.

  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 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.

  17. Estimation of local pulse wave velocity using arterial diameter waveforms: Experimental validation in sheep

    NASA Astrophysics Data System (ADS)

    Graf, S.; Craiem, D.; Barra, J. G.; Armentano, R. L.

    2011-12-01

    Increased arterial stiffness is associated with an increased risk of cardiovascular events. Estimation of arterial stiffness using local pulse wave velocity (PWV) promises to be very useful for noninvasive diagnosis of arteriosclerosis. In this work we estimated in an instrumented sheep, the local aortic pulse wave velocity using two sonomicrometry diameter sensors (separated 7.5 cm) according to the transit time method (PWVTT) with a sampling rate of 4 KHz. We simultaneously measured aortic pressure in order to determine from pressure-diameter loops (PWVPDLoop), the "true" local aortic pulse wave velocity. A pneumatic cuff occluder was implanted in the aorta in order to compare both methods under a wide range of pressure levels. Mean pressure values ranged from 47 to 101 mmHg and mean proximal diameter values from 12.5. to 15.2 mm. There were no significant differences between PWVTT and PWVPDLoop values (451±43 vs. 447±48 cm/s, p = ns, paired t-test). Both methods correlated significantly (R = 0.81, p<0.05). The mean difference between both methods was only -4±29 cm/s, whereas the range of the limits of agreement (mean ± 2 standard deviation) was -61 to +53 cm/s, showing no trend. In conclusion, the diameter waveforms transit time method was found to allow an accurate and precise estimation of the local aortic PWV.

  18. Local wave particle resonant interaction causing energetic particle prompt loss in DIII-D plasmas

    NASA Astrophysics Data System (ADS)

    Zhang, R. B.; Fu, G. Y.; White, R. B.; Wang, X. G.

    2015-11-01

    A new wave particle resonance mechanism is found explaining the first-orbit prompt neutral beam-ion losses induced by shear Alfvén Eigenmodes (AEs) in the DIII-D tokamak. Because of the large banana width, a typical trapped beam ion can only interact locally with a core localised Alfvén Eigenmode for a fraction of its orbit, i.e. part of its inner leg of the banana orbit. These trapped beam ions can experience substantial radial kick within one bounce as long as the phases of the wave seen by the particles are nearly constant during this local interaction. A wave particle resonant condition is found based on the locally averaged particle orbit frequencies over the interaction part of the particle orbit. It is further found that the frequency width of the local resonance is quite large because the interaction time is short. This implies that particles over a considerable region of phase space can interact effectively with the localised AEs and experience large radial kicks within one bounce orbit. The radial kick size is found numerically and analytically to scale linearly in AE amplitude and is about 5 cm for typical experimental parameters. These results are consistent with experimental measurement.

  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. 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

  1. 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.

  2. 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

  3. 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

  4. Local finite-amplitude wave activity as an objective diagnostic of midlatitude extreme weather

    SciTech Connect

    Chen, Gang; Lu, Jian; Burrows, Alex D.; Leung, Lai-Yung R.

    2015-12-28

    Midlatitude extreme weather events are responsible for a large part of climate related damage, yet our understanding of these extreme events is limited, partly due to the lack of a theoretical basis for midlatitude extreme weather. In this letter, the local finite-amplitude wave activity (LWA) of Huang and Nakamura [2015] is introduced as a diagnostic of the 500-hPa geopotential height (Z500) to characterizing midlatitude weather events. It is found that the LWA climatology and its variability associated with the Arctic Oscillation (AO) agree broadly with the previously reported blocking frequency in literature. There is a strong seasonal and spatial dependence in the trend13 s of LWA in recent decades. While there is no observational evidence for a hemispheric-scale increase in wave amplitude, robust trends in wave activity can be identified at the regional scales, with important implications for regional climate change.

  5. Model-based compressive sensing for damage localization in Lamb wave inspection.

    PubMed

    Perelli, Alessandro; Di Ianni, Tommaso; Marzani, Alessandro; De Marchi, Luca; Masetti, Guido

    2013-10-01

    Compressive sensing (CS) has emerged as a potentially viable technique for the efficient compression and analysis of high-resolution signals that have a sparse representation in a fixed basis. In this work, we have developed a CS approach for ultrasonic signal decomposition suitable to achieve high performance in Lamb-wave-based defect detection procedures. In the proposed approach, a CS algorithm based on an alternating minimization (AM) procedure is adopted to extract the information about both the system impulse response and the reflectivity function. The implemented tool exploits the dispersion compensation properties of the warped frequency transform as a means to generate the sparsifying basis for the signal representation. The effectiveness of the decomposition task is demonstrated on synthetic signals and successfully tested on experimental Lamb waves propagating in an aluminum plate. Compared with available strategies, the proposed approach provides an improvement in the accuracy of wave propagation path length estimation, a fundamental step in defect localization procedures.

  6. 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.

  7. Fatigue damage localization using time-domain features extracted from nonlinear Lamb waves

    NASA Astrophysics Data System (ADS)

    Hong, Ming; Su, Zhongqing; Lu, Ye; Cheng, Li

    2014-03-01

    Nonlinear guided waves are sensitive to small-scale fatigue damage that may hardly be identified by traditional techniques. A characterization method for fatigue damage is established based on nonlinear Lamb waves in conjunction with the use of a piezoelectric sensor network. Theories on nonlinear Lamb waves for damage detection are first introduced briefly. Then, the ineffectiveness of using pure frequency-domain information of nonlinear wave signals for locating damage is discussed. With a revisit to traditional gross-damage localization techniques based on the time of flight, the idea of using temporal signal features of nonlinear Lamb waves to locate fatigue damage is introduced. This process involves a time-frequency analysis that enables the damage-induced nonlinear signal features, which are either undiscernible in the original time history or uninformative in the frequency spectrum, to be revealed. Subsequently, a finite element modeling technique is employed, accounting for various sources of nonlinearities in a fatigued medium. A piezoelectric sensor network is configured to actively generate and acquire probing Lamb waves that involve damageinduced nonlinear features. A probability-based diagnostic imaging algorithm is further proposed, presenting results in diagnostic images intuitively. The approach is experimentally verified on a fatigue-damaged aluminum plate, showing reasonably good accuracy. Compared to existing nonlinear ultrasonics-based inspection techniques, this approach uses a permanently attached sensor network that well accommodates automated online health monitoring; more significantly, it utilizes time-domain information of higher-order harmonics from time-frequency analysis, and demonstrates a great potential for quantitative characterization of small-scale damage with improved localization accuracy.

  8. 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.

  9. Generation of localized magnetic moments in the charge-density-wave state

    NASA Astrophysics Data System (ADS)

    Akzyanov, Ramil S.; Rozhkov, Alexander V.

    2015-08-01

    We propose a mechanism explaining the generation of localized magnetic moments in charge-density-wave compounds. Our model Hamiltonian describes an Anderson impurity placed in a host material exhibiting the charge-density wave. There is a region of the model's parameter space, where even weak Coulomb repulsion on the impurity site is able to localize the magnetic moment on the impurity. The phase diagram of a single impurity at T = 0 is mapped. To establish the connection with experiment, the thermodynamic properties of a random impurity ensemble is studied. Magnetic susceptibility of the ensemble diverges at low temperature; heat capacity as a function of the magnetic field demonstrates pronounced low field peak. Both features are consistent with experiments on orthorhombic TaS3 and blue bronze.

  10. Joint Inversion for Earthquake Depths Using Local Waveforms and Amplitude Spectra of Rayleigh Waves

    NASA Astrophysics Data System (ADS)

    Jia, Zhe; Ni, Sidao; Chu, Risheng; Zhan, Zhongwen

    2017-01-01

    Reliable earthquake depth is fundamental to many seismological problems. In this paper, we present a method to jointly invert for centroid depths with local (distance < 5°) seismic waveforms and regional (distance of 5°-15°) Rayleigh wave amplitude spectra on sparse networks. We use earthquake focal mechanisms and magnitudes retrieved with the Cut-and-Paste (CAP) method to compute synthetic amplitude spectra of fundamental mode Rayleigh wave for a range of depths. Then we grid search to find the optimal depth that minimizes the joint misfit of amplitude spectra and local waveforms. As case studies, we apply this method to the 2008 Wells, Nevada Mw6.0 earthquake and a Mw5.6 outer-rise earthquake to the east of Japan Trench in 2013. Uncertainties estimated with a bootstrap re-sampling approach show that this joint inversion approach constrains centroid depths well, which are also verified by independent teleseismic depth-phase data.

  11. Local probing of propagating acoustic waves in a gigahertz echo chamber

    NASA Astrophysics Data System (ADS)

    Gustafsson, Martin V.; Santos, Paulo V.; Johansson, Göran; Delsing, Per

    2012-04-01

    In the same way that micro-mechanical resonators resemble guitar strings and drums, surface acoustic waves resemble the sound these instruments produce, but moving over a solid surface rather than through air. In contrast with oscillations in suspended resonators, such propagating mechanical waves have not before been studied near the quantum mechanical limits. Here, we demonstrate local probing of surface acoustic waves with a displacement sensitivity of 30amRMSHz-1/2 and detection sensitivity on the single-phonon level after averaging, at a frequency of 932MHz. Our probe is a piezoelectrically coupled single-electron transistor, which is sufficiently fast, non-destructive and localized to enable us to track pulses echoing back and forth in a long acoustic cavity, self-interfering and ringing the cavity up and down. We project that strong coupling to quantum circuits will enable new experiments, and hybrids using the unique features of surface acoustic waves. Prospects include quantum investigations of phonon-phonon interactions, and acoustic coupling to superconducting qubits for which we present favourable estimates.

  12. Wave scattering of complex local site in a layered half-space by using a multidomain IBEM: incident plane SH waves

    NASA Astrophysics Data System (ADS)

    Ba, Zhenning; Yin, Xiao

    2016-06-01

    A multidomain indirect boundary element method (IBEM) is proposed to study the wave scattering of plane SH waves by complex local site in a layered half-space. The new method, using both the full-space and layered half-space Green's functions as its fundamental solutions can also be regarded as a coupled method of the full-space IBEM and half-space IBEM. First, the whole model is decomposed into independent closed regions and an opened layered half-space region with all of the irregular interfaces; then, fictitious uniformly distributed loads are applied separately on the boundaries of each region, and scattered fields of the closed regions and the opened layered half-space region are constructed by calculating the full-space and layered half-space Green's functions, respectively; finally, all of the regions are assembled to establish the linear algebraic system that arises from discretization. The densities of the distributed loads are determined directly by solving the algebraic system. The accuracy and capability of the new approach are verified extensively by comparing its results with those of published approaches for a class of hills, valleys and embedded inclusions. And the capability of the new method is further displayed when it is used to investigate a hill-triple layered valley-hill coupled topography in a multilayered half-space. All of the numerical calculations presented in this paper demonstrate that the new method is very suitable for solving multidomain coupled multilayered wave scattering problems with the merits of high accuracy and representing the scattered fields in different kinds of regions more reasonably and flexibly.

  13. Long-wave approximation for hybridization modeling of local surface plasmonic resonance in nanoshells.

    PubMed

    Li, Ben Q; Liu, Changhong

    2011-01-15

    A hybridization model for the localized surface plasmon resonance of a nanoshell is developed within the framework of long-wave approximation. Compared with the existing hybridization model derived from the hydrodynamic simulation of free electron gas, this approach is much simpler and gives identical results for a concentric nanoshell. Also, with this approach, the limitations associated with the original hybridization model are succinctly stated. Extension of this approach to hybridization modeling of more complicated structures such as multiplayered nanoshells is straightforward.

  14. Experimental investigation of the local wave speed in a draft tube with cavitation vortex rope

    NASA Astrophysics Data System (ADS)

    Landry, C.; Favrel, A.; Müller, A.; Nicolet, C.; Yamamoto, K.; Avellan, F.

    2014-03-01

    Hydraulic machines operating in a wider range are subjected to cavitation developments inducing undesirable pressure pulsations which could lead to potential instability of the power plant. The occurrence of pulsating cavitation volumes in the runner and the draft tube is considered as a mass source of the system and is depending on the cavitation compliance. This dynamic parameter represents the cavitation volume variation with the respect to a variation of pressure and defines implicitly the local wave speed in the draft tube. This parameter is also decisive for an accurate prediction of system eigen frequencies. Therefore, the local wave speed in the draft tube is intrinsically linked to the eigen frequencies of the hydraulic system. Thus, if the natural frequency of a hydraulic system can be determined experimentally, it also becomes possible to estimate a local wave speed in the draft tube with a numerical model. In the present study, the reduced scale model of a Francis turbine (v=0.29) was investigated at off-design conditions. In order to measure the first eigenmode of the hydraulic test rig, an additional discharge was injected at the inlet of the hydraulic turbine at a variable frequency and amplitude to excite the system. Thus, with different pressure sensors installed on the test rig, the first eigenmode was determined. Then, a hydro-acoustic test rig model was developed with the In-house EPFL SIMSEN software and the local wave speed in the draft tube was adjusted to obtain the same first eigen frequency as that measured experimentally. Finally, this method was applied for different Thoma and Froude numbers at part load conditions.

  15. Self adaptive solution strategies: Locally bound constrained Newton Raphson solution algorithms

    NASA Technical Reports Server (NTRS)

    Padovan, Joe

    1991-01-01

    A summary is given of strategies which enable the automatic adjustment of the constraint surfaces recently used to extend the range and numerical stability/efficiency of nonlinear finite element equation solvers. In addition to handling kinematic and material induced nonlinearity, both pre-and postbuckling behavior can be treated. The scheme employs localized bounds on various hierarchical partitions of the field variables. These are used to resize, shape, and orient the global constraint surface, thereby enabling essentially automatic load/deflection incrementation. Due to the generality of the approach taken, it can be implemented in conjunction with the constraints of an arbitrary functional type. To benchmark the method, several numerical experiments are presented. These include problems involving kinematic and material nonlinearity, as well as pre- and postbuckling characteristics. Also included is a list of papers published in the course of the work.

  16. Forests as a natural seismic metamaterial: Rayleigh wave bandgaps induced by local resonances

    NASA Astrophysics Data System (ADS)

    Colombi, Andrea; Roux, Philippe; Guenneau, Sebastien; Gueguen, Philippe; Craster, Richard V.

    2016-01-01

    We explore the thesis that resonances in trees result in forests acting as locally resonant metamaterials for Rayleigh surface waves in the geophysics context. A geophysical experiment demonstrates that a Rayleigh wave, propagating in soft sedimentary soil at frequencies lower than 150 Hz, experiences strong attenuation, when interacting with a forest, over two separate large frequency bands. This experiment is interpreted using finite element simulations that demonstrate the observed attenuation is due to bandgaps when the trees are arranged at the sub-wavelength scale with respect to the incident Rayleigh wave. The repetitive bandgaps are generated by the coupling of the successive longitudinal resonances of trees with the vertical component of the Rayleigh wave. For wavelengths down to 5 meters, the resulting bandgaps are remarkably large and strongly attenuating when the acoustic impedance of the trees matches the impedance of the soil. Since longitudinal resonances of a vertical resonator are inversely proportional to its length, a man-made engineered array of resonators that attenuates Rayleigh waves at frequency ≤10 Hz could be designed starting from vertical pillars coupled to the ground with longitudinal resonance ≤10 Hz.

  17. Forests as a natural seismic metamaterial: Rayleigh wave bandgaps induced by local resonances.

    PubMed

    Colombi, Andrea; Roux, Philippe; Guenneau, Sebastien; Gueguen, Philippe; Craster, Richard V

    2016-01-11

    We explore the thesis that resonances in trees result in forests acting as locally resonant metamaterials for Rayleigh surface waves in the geophysics context. A geophysical experiment demonstrates that a Rayleigh wave, propagating in soft sedimentary soil at frequencies lower than 150 Hz, experiences strong attenuation, when interacting with a forest, over two separate large frequency bands. This experiment is interpreted using finite element simulations that demonstrate the observed attenuation is due to bandgaps when the trees are arranged at the sub-wavelength scale with respect to the incident Rayleigh wave. The repetitive bandgaps are generated by the coupling of the successive longitudinal resonances of trees with the vertical component of the Rayleigh wave. For wavelengths down to 5 meters, the resulting bandgaps are remarkably large and strongly attenuating when the acoustic impedance of the trees matches the impedance of the soil. Since longitudinal resonances of a vertical resonator are inversely proportional to its length, a man-made engineered array of resonators that attenuates Rayleigh waves at frequency ≤10 Hz could be designed starting from vertical pillars coupled to the ground with longitudinal resonance ≤10 Hz.

  18. Forests as a natural seismic metamaterial: Rayleigh wave bandgaps induced by local resonances

    PubMed Central

    Colombi, Andrea; Roux, Philippe; Guenneau, Sebastien; Gueguen, Philippe; Craster, Richard V.

    2016-01-01

    We explore the thesis that resonances in trees result in forests acting as locally resonant metamaterials for Rayleigh surface waves in the geophysics context. A geophysical experiment demonstrates that a Rayleigh wave, propagating in soft sedimentary soil at frequencies lower than 150 Hz, experiences strong attenuation, when interacting with a forest, over two separate large frequency bands. This experiment is interpreted using finite element simulations that demonstrate the observed attenuation is due to bandgaps when the trees are arranged at the sub-wavelength scale with respect to the incident Rayleigh wave. The repetitive bandgaps are generated by the coupling of the successive longitudinal resonances of trees with the vertical component of the Rayleigh wave. For wavelengths down to 5 meters, the resulting bandgaps are remarkably large and strongly attenuating when the acoustic impedance of the trees matches the impedance of the soil. Since longitudinal resonances of a vertical resonator are inversely proportional to its length, a man-made engineered array of resonators that attenuates Rayleigh waves at frequency ≤10 Hz could be designed starting from vertical pillars coupled to the ground with longitudinal resonance ≤10 Hz. PMID:26750489

  19. Exact density functional and wave function embedding schemes based on orbital localization

    NASA Astrophysics Data System (ADS)

    Hégely, Bence; Nagy, Péter R.; Ferenczy, György G.; Kállay, Mihály

    2016-08-01

    Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.

  20. Asymptotic solutions of weakly nonlinear, dispersive wave-propagation problems by Fourier analysis

    SciTech Connect

    Srinivasan, R.

    1989-01-01

    A perturbation method based on Fourier analysis and multiple scales is introduced for solving weakly nonlinear, dispersive wave propagation problems with Fourier transformable initial conditions. Asymptotic solutions are derived for the weakly nonlinear cubic Schroedinger (NLS) equation with variable coefficients and the weakly nonlinear Kortewegde-Vries (KdV) equation; the results for the NLS equation are verified by comparison with numerical solutions. In the special case of constant coefficients, the asymptotic solution for the weakly nonlinear NLS equation agrees to leading order with previously derived results in the literature; in general, this is not true to higher orders. Therefore previous asymptotic results for the strongly nonlinear Schroedinger equation can be valid only for restricted initial conditions. Similar conclusions apply to the KdV equation.

  1. Maximum a posteriori probability estimation for localizing damage using ultrasonic guided waves

    NASA Astrophysics Data System (ADS)

    Flynn, Eric B.; Todd, Michael D.; Wilcox, Paul D.; Drinkwater, Bruce W.; Croxford, Anthony J.

    2011-04-01

    Presented is an approach to damage localization for guided wave structural health monitoring (GWSHM) in plate-like structures. In this mode of SHM, transducers excite and sense guided waves in order to detect and characterize the presence of damage. The premise of the presented localization approach is simple: use as the estimated damage location the point on the structure with the maximum a posteriori probability (MAP) of being the location of damage (i.e., the most probable location given a set of sensor measurements). This is accomplished by constructing a minimally-informed statistical model of the GWSHM process. Parameters of the model which are unknown, such as scattered wave amplitude, are assigned non-informative Bayesian prior distributions and averaged out of the a posteriori probability calculation. Using an ensemble of measurements from an instrumented plate with stiffening stringers, the performance of the MAP estimate is compared to that of what were found to be the two most effective previously reported algorithms. The MAP estimate proved superior in nearly all test cases and was particularly effective in localizing damage using very sparse arrays of as few as three transducers.

  2. Hybrid local FEM/global LISA modeling of damped guided wave propagation in complex composite structures

    NASA Astrophysics Data System (ADS)

    Shen, Yanfeng; Cesnik, Carlos E. S.

    2016-09-01

    This paper presents a new hybrid modeling technique for the efficient simulation of guided wave generation, propagation, and interaction with damage in complex composite structures. A local finite element model is deployed to capture the piezoelectric effects and actuation dynamics of the transmitter, while the global domain wave propagation and interaction with structural complexity (structure features and damage) are solved utilizing a local interaction simulation approach (LISA). This hybrid approach allows the accurate modeling of the local dynamics of the transducers and keeping the LISA formulation in an explicit format, which facilitates its readiness for parallel computing. The global LISA framework was extended through the 3D Kelvin-Voigt viscoelasticity theory to include anisotropic damping effects for composite structures, as an improvement over the existing LISA formulation. The global LISA framework was implemented using the compute unified device architecture running on graphic processing units. A commercial preprocessor is integrated seamlessly with the computational framework for grid generation and material property allocation to handle complex structures. The excitability and damping effects are successfully captured by this hybrid model, with experimental validation using the scanning laser doppler vibrometry. To demonstrate the capability of our hybrid approach for complex structures, guided wave propagation and interaction with a delamination in a composite panel with stiffeners is presented.

  3. Broadband Lamb Wave Trapping in Cellular Metamaterial Plates with Multiple Local Resonances

    PubMed Central

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

    2015-01-01

    We have investigated the Lamb wave propagation in cellular metamaterial plates constructed by bending-dominated and stretch-dominated unit-cells with the stiffness differed by orders of magnitude at an ultralow density. The simulation results show that ultralight metamaterial plates with textured stubs deposited on the surface can support strong local resonances for both symmetric and anti-symmetric modes at low frequencies, where Lamb waves at the resonance frequencies are highly localized in the vibrating stubs. The resonance frequency is very sensitive to the geometry of textured stubs. By reasonable design of the geometry of resonant elements, we establish a simple loaded-bar model with the array of oscillators having a gradient relative density (or weight) that can support multiple local resonances, which permits the feasibility of a broadband Lamb wave trapping. Our study could be potentially significant in designing ingenious weight-efficient acoustic devices for practical applications, such as shock absorption, cushioning, and vibrations traffic, etc. PMID:25790858

  4. On Locally Deformed Stratified Media : Applications To Rough Surfaces And Guided Wave Devices With Corrugated Boundaries

    NASA Astrophysics Data System (ADS)

    Petit, R.; Hugonin, J. P.

    1984-12-01

    In 1977, we published two papers on the diffraction of electromagnetic waves at a locally deformed flat boundary surface and at a locally deformed plane wave-guide. Since this time, an important theoretical and numerical study of locally deformed stratified media has been carried out in our lab. This study has been summarized three years ago in the J.O.S.A. and it has been presented last year as a thesis dissertation. But both the J.O.S.A. paper and the thesis are difficult to read for non specialists because the involved mathematics are rather subtle and, at least, tedious for experimenters. In other words, an important work has been done, which seems to be unknown to most of "practical people". We thought that a SPIE meeting is a good opportunity to cure this regrettable situation. A computer program is now available which probably might be very useful for those working on rough dielectric surfaces and on guided wave devices with corrugated boundaries. We would like to present to engineers the possibilities and the limits of this big computer code called hereafter Program (P)

  5. Characterizing wave propagation to improve indoor step-level person localization using floor vibration

    NASA Astrophysics Data System (ADS)

    Mirshekari, Mostafa; Pan, Shijia; Zhang, Pei; Noh, Hae Young

    2016-04-01

    The objective of this paper is to characterize frequency-dependent wave propagation of footstep induced floor vibration to improve robustness of vibration-based occupant localization. Occupant localization is an essential part of many smart structure applications (e.g., energy management, patient/customer tracking, etc.). Exist- ing techniques include visual (e.g. cameras and IR sensors), acoustic, RF, and load-based approaches. These approaches have many deployment and operational requirements that limits their adaptation. To overcome these limitations, prior work has utilized footstep-induced vibrations to allow sparse sensor configuration and non-intrusive detection. However, frequency dependent propagation characteristics and low signal-to-noise ratio (SNR) of footstep-induced vibrations change the shape of the signal. Furthermore, estimating the wave propagation velocity for forming the multilateration equations and localizing the footsteps is a challenging task. They, in turn, lead to large errors of localization. In this paper, we present a structural vibration based indoor occupant localization technique using improved time-difference-of-arrival between multiple vibration sensors. In particular we overcome signal distortion by decomposing the signal into frequency components and focusing on high energy components for accurate indoor localization. Such decomposition leverages the frequency-specific propagation characteristics and reduces the effect of low SNR (by choosing the components of highest energy). Furthermore, we develop a velocity calibration method that finds the optimal velocity which minimizes the localization error. We validate our approach through field experiments in a building with human participants. We are able to achieve an average localization error of less than 0.21 meters, which corresponds to a 13X reduction in error when compared to the baseline method using raw data.

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

    PubMed

    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.

  7. Full 3D dispersion curve solutions for guided waves in generally anisotropic media

    NASA Astrophysics Data System (ADS)

    Hernando Quintanilla, F.; Lowe, M. J. S.; Craster, R. V.

    2016-02-01

    Dispersion curves of guided waves provide valuable information about the physical and elastic properties of waves propagating within a given waveguide structure. Algorithms to accurately compute these curves are an essential tool for engineers working in non-destructive evaluation and for scientists studying wave phenomena. Dispersion curves are typically computed for low or zero attenuation and presented in two or three dimensional plots. The former do not always provide a clear and complete picture of the dispersion loci and the latter are very difficult to obtain when high values of attenuation are involved and arbitrary anisotropy is considered in single or multi-layered systems. As a consequence, drawing correct and reliable conclusions is a challenging task in the modern applications that often utilize multi-layered anisotropic viscoelastic materials. These challenges are overcome here by using a spectral collocation method (SCM) to robustly find dispersion curves in the most complicated cases of high attenuation and arbitrary anisotropy. Solutions are then plotted in three-dimensional frequency-complex wavenumber space, thus gaining much deeper insight into the nature of these problems. The cases studied range from classical examples, which validate this approach, to new ones involving materials up to the most general triclinic class for both flat and cylindrical geometry in multi-layered systems. The apparent crossing of modes within the same symmetry family in viscoelastic media is also explained and clarified by the results. Finally, the consequences of the centre of symmetry, present in every crystal class, on the solutions are discussed.

  8. Distribution of energy of solutions of the wave equation on singular spaces of constant curvature and on a homogeneous tree

    NASA Astrophysics Data System (ADS)

    Tsvetkova, A. V.

    2016-10-01

    In the paper, the Cauchy problem for the wave equation on singular spaces of constant curvature and on an infinite homogeneous tree is studied. Two singular spaces are considered: the first one consists of a three-dimensional Euclidean space to which a ray is glued, and the other is formed by two three-dimensional Euclidean spaces joined by a segment. The solution of the Cauchy problem for the wave equation on these objects is described and the behavior of the energy of a wave as time tends to infinity is studied. The Cauchy problem for the wave equation on an infinite homogeneous tree is also considered, where the matching conditions for the Laplace operator at the vertices are chosen in the form generalizing the Kirchhoff conditions. The spectrum of such an operator is found, and the solution of the Cauchy problem for the wave equation is described. The behavior of wave energy as time tends to infinity is also studied.

  9. Wide localized solutions of the parity-time-symmetric nonautonomous nonlinear Schrödinger equation

    NASA Astrophysics Data System (ADS)

    Meza, L. E. Arroyo; Dutra, A. de Souza; Hott, M. B.; Roy, P.

    2015-01-01

    By using canonical transformations we obtain localized (in space) exact solutions of the nonlinear Schrödinger equation (NLSE) with cubic and quintic space and time modulated nonlinearities and in the presence of time-dependent and inhomogeneous external potentials and amplification or absorption (source or drain) coefficients. We obtain a class of wide localized exact solutions of NLSE in the presence of a number of non-Hermitian parity-time (PT )-symmetric external potentials, which are constituted by a mixing of external potentials and source or drain terms. The exact solutions found here can be applied to theoretical studies of ultrashort pulse propagation in optical fibers with focusing and defocusing nonlinearities. We show that, even in the presence of gain or loss terms, stable solutions can be found and that the PT symmetry is an important feature to guarantee the conservation of the average energy of the system.

  10. Using wave intensity analysis to determine local reflection coefficient in flexible tubes.

    PubMed

    Li, Ye; Parker, Kim H; Khir, Ashraf W

    2016-09-06

    It has been shown that reflected waves affect the shape and magnitude of the arterial pressure waveform, and that reflected waves have physiological and clinical prognostic values. In general the reflection coefficient is defined as the ratio of the energy of the reflected to the incident wave. Since pressure has the units of energy per unit volume, arterial reflection coefficient are traditionally defined as the ratio of reflected to the incident pressure. We demonstrate that this approach maybe prone to inaccuracies when applied locally. One of the main objectives of this work is to examine the possibility of using wave intensity, which has units of energy flux per unit area, to determine the reflection coefficient. We used an in vitro experimental setting with a single inlet tube joined to a second tube with different properties to form a single reflection site. The second tube was long enough to ensure that reflections from its outlet did not obscure the interactions of the initial wave. We generated an approximately half sinusoidal wave at the inlet of the tube and took measurements of pressure and flow along the tube. We calculated the reflection coefficient using wave intensity (RdI and RdI(0.5)) and wave energy (RI and RI(0.5)) as well as the measured pressure (RdP) and compared these results with the reflection coefficient calculated theoretically based on the mechanical properties of the tubes. The experimental results show that the reflection coefficients determined by all the techniques we studied increased or decreased with distance from the reflection site, depending on the type of reflection. In our experiments, RdP, RdI(0.5) and RI(0.5) are the most reliable parameters to measure the mean reflection coefficient, whilst RdI and RI provide the best measure of the local reflection coefficient, closest to the reflection site. Additional work with bifurcations, tapered tubes and in vivo experiments are needed to further understand, validate the method

  11. Local problems, local solutions: improving tuberculosis control at the district level in Malawi.

    PubMed Central

    Kelly, P. M.

    2001-01-01

    OBJECTIVE: To examine the causes of a low cure rate at the district level of a tuberculosis (TB) control programme and to formulate, implement, and evaluate an intervention to improve the situation. METHODS: The study setting was Mzuzu (population 60,000), where the annual smear-positive pulmonary TB incidence was 160 per 100,000 and the human immunodeficiency virus (HIV) seroprevalence was 67% among TB patients. There is one TB treatment unit, but several other organizations are involved with TB control. An examination of case-holding activities was carried out, potential areas for improvement were identified, and interventions performed. FINDINGS: In 1990-91, the cure rate was 24% among smear-positive cases (29% among survivors to end of treatment). Problems identified included a fragmented TB control programme; inadequate training and supervision; suboptimal recording of patients' addresses; and nonadherence to national TB control programme protocols. These problems were addressed, and in 1992-93 the cure rate rose to 68% (relative risk (RR) = 2.85 (95% confidence interval (CI) = 1.63, 4.96)) and to 92% among survivors to the end of treatment (RR = 3.12 (95% CI = 1.84, 5.29)). High cure rates are therefore achievable despite high HIV prevalence. CONCLUSIONS: Simple, inexpensive, local programmatic interventions can dramatically improve TB case holding. This study demonstrates the need for evaluation, training, and supervision at all levels of the programme. PMID:11242817

  12. An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations

    NASA Astrophysics Data System (ADS)

    Parkes, E. J.; Duffy, B. R.

    1996-11-01

    The tanh-function method for finding explicit travelling solitary wave solutions to non-linear evolution equations is described. The method is usually extremely tedious to use by hand. We present a Mathematica package ATFM that deals with the tedious algebra and outputs directly the required solutions. The use of the package is illustrated by applying it to a variety of equations; not only are previously known solutions recovered but in some cases more general forms of solution are obtained.

  13. Interfacial wave theory of dendrite growth - Global mode solution and quantum condition

    NASA Technical Reports Server (NTRS)

    Xu, Jian-Jun

    1990-01-01

    The signal feedback process at the edge of the dendrite tip is investigated, and the global instability mechanism of the system is derived. A mechanism is developed to describe a discrete set of unstable global modes for the system. Called WEASR, the method considers the wave emission at the turning point and signal reflections between the turning point and the front edge of the tip. It is shown that the method can obtain the asymptotic solutions for the unstable global modes and the quantum condition for the corresponding eigenvalues. A turning point called the pattern formation condition is shown to be crucial in the formation of dendritic structure and the choice of the final tip velocity. The wave emission process is outlined, and the importance of a signal feedback process at the edge of the dendrite tip is demonstrated. Parameters such as stability and surface tension can be analyzed in terms of their effects on WEASR modes.

  14. MicroResearch--Finding sustainable solutions to local health challenges in East Africa.

    PubMed

    Kollmann, Tobias R; Bortolussi, Robert; MacDonald, Noni E

    2015-06-01

    The urgent need in Africa for research capacity building has been recognized by African leaders and governments for many years. However, lack of large research funding opportunities has been seen as a major obstacle to improving research capacity in precisely those countries that need it the most. Microfinance has shown that a small infusion of capital can "prime the pump" to creative local economic productivity. In a similar way, MicroResearch has proven effective in promoting a similar bottom-up strategy to find sustainable solutions to local health challenges through local community focused research. Specifically, MicroResearch through hands-on didactic courses, mentoring and small-scale research funding promotes small research projects that improve research skills across the entire health-care provider spectrum to unleash a culture of inquiry. This in turn stimulates health care providers to identify the locally most relevant obstacles that need to be overcome and implement locally feasible and sustainable solutions. MicroResearch is a bottom-up strategy proven effective at finding sustainable solutions to local health challenges.

  15. From plane waves to local Gaussians for the simulation of correlated periodic systems

    NASA Astrophysics Data System (ADS)

    Booth, George H.; Tsatsoulis, Theodoros; Chan, Garnet Kin-Lic; Grüneis, Andreas

    2016-08-01

    We present a simple, robust, and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on the representation of the Gaussians within a finite bandwidth by their underlying plane wave coefficients. The core region is handled within the projected augment wave framework, by pseudizing the Gaussian functions within a cutoff radius around each nucleus, smoothing the functions so that they are faithfully represented by a plane wave basis with only moderate kinetic energy cutoff. To mitigate the effects of the basis set superposition error and incompleteness at the mean-field level introduced by the Gaussian basis, we also propose a hybrid approach, whereby the complete occupied space is first converged within a large plane wave basis, and the Gaussian basis used to construct a complementary virtual space for the application of correlated methods. We demonstrate that these pseudized Gaussians yield compact and systematically improvable spaces with an accuracy comparable to their non-pseudized Gaussian counterparts. A key advantage of the described method is its ability to efficiently capture and describe electronic correlation effects of weakly bound and low-dimensional systems, where plane waves are not sufficiently compact or able to be truncated without unphysical artifacts. We investigate the accuracy of the pseudized Gaussians for the water dimer interaction, neon solid, and water adsorption on a LiH surface, at the level of second-order Møller-Plesset perturbation theory.

  16. Low-frequency four-wave mixing spectroscopy of biomolecules in aqueous solutions

    SciTech Connect

    Bunkin, Aleksei F; Pershin, S M

    2011-01-24

    Four-wave mixing (FWM) spectroscopy is used to detect the rotational resonances of H{sub 2}O and H{sub 2}O{sub 2} molecules in DNA and denatured DNA aqueous solutions in the range {+-}10 cm{sup -1} with a spectral resolution of 3 GHz. It is found that the resonance contribution of the rotational transitions of these molecules increases significantly in solutions rather than in distilled water. This fact is interpreted as a manifestation of specific properties of a hydration layer at DNA-water and denatured DNA-water interfaces. Analysis of the FWM spectra shows that the concentration of H{sub 2}O{sub 2} molecules in the hydration layer of the DNA solution increases by a factor of 3 after denaturation. The FWM spectra of aqueous solutions of {alpha}-chymotrypsin protein are obtained in the range {+-}7cm{sup -1} at the protein concentrations between 0 and 20 mg cm{sup -3}. It is found that the hypersound velocity in the protein aqueous solution, measured by the shift of Brillouin components in the scattering spectrum, obeys a cubic dependence on the protein concentration and reaches a value of about 3000 m s{sup -1} at 20 mg cm{sup -3}. (application of lasers and laser-optical methods in life sciences)

  17. A shifted Jacobi collocation algorithm for wave type equations with non-local conservation conditions

    NASA Astrophysics Data System (ADS)

    Doha, Eid H.; Bhrawy, Ali H.; Abdelkawy, Mohammed A.

    2014-09-01

    In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach

  18. On the numerical solution of two-dimensional, laminar compressible flows with imbedded shock waves.

    NASA Technical Reports Server (NTRS)

    Goodrich, W. D.; Lamb, J. P.; Bertin, J. J.

    1972-01-01

    The complete, time-dependent Navier-Stokes equations are expressed in conservation form and solved by employing an explicit finite difference numerical technique which incorporates artificial viscosity terms of the form first suggested by Rusanov for numerical stability in the vicinity of shock waves. Surface boundary conditions are developed in a consistent and unique manner through the use of a physically oriented extrapolation procedure. From numerical experimentation an extended range for the explicit stability parameter is established. Also employed is an additional convergence parameter which relates incremental spatial steps. Convergence of the transient solution to a steady state flow was obtained after 400 to 500 time steps.

  19. Transport solutions of the Lamé equations and shock elastic waves

    NASA Astrophysics Data System (ADS)

    Alexeyeva, L. A.; Kaishybaeva, G. K.

    2016-07-01

    The Lamé system describing the dynamics of an isotropic elastic medium affected by a steady transport load moving at subsonic, transonic, or supersonic speed is considered. Its fundamental and generalized solutions in a moving frame of reference tied to the transport load are analyzed. Shock waves arising in the medium at supersonic speeds are studied. Conditions on the jump in the stress, displacement rate, and energy across the shock front are obtained using distribution theory. Numerical results concerning the dynamics of an elastic medium influenced by concentrated transport loads moving at sub-, tran- and supersonic speeds are presented.

  20. A Comparison of Solutions of Two Model Equations for Long Waves.

    DTIC Science & Technology

    1983-02-01

    focused on solutions of (A) and (B) that correspond to the initial condition that u(x,0) is a given function. Equation (A) is the Korteweg -de Vries...waves on the surface of water, two models have received particular attention. One is the equation of Korteweg and de Vries (1895) ( equation (A) or the...channel is the equation proposed by Korteweg and de Vries (1895), 3 1:’il nt * nx + 7 nnx + F n + . l= O. (la) In this equation n - n(x,t) represents

  1. Asymptotic property of solutions to the random cauchy problem for wave equations

    NASA Astrophysics Data System (ADS)

    Dôku, Isamu

    1986-01-01

    Based on the existence and uniqueness theorem for random wave equations, we consider asymptotic behaviors of solutions to the random initial value problem. We describe conditions for the equipartition of stochastic energy (or SE for short) by making use of the random spectral theory and, according to Goldstein's semigroup method, we prove the asymptotically equipartitioned SE theorem and the so-called virial theorem of classical mechanics, and also study the probabilistic characterization of the conditions for equipartition. In addition, we show at last the equipartition of SE from a finite time onwards.

  2. Photonic crystal fiber based evanescent-wave sensor for detection of biomolecules in aqueous solutions.

    PubMed

    Jensen, Jesper B; Pedersen, Lars H; Hoiby, Poul E; Nielsen, Lars B; Hansen, T P; Folkenberg, J R; Riishede, J; Noordegraaf, Danny; Nielsen, Kristian; Carlsen, A; Bjarklev, A

    2004-09-01

    We demonstrate highly efficient evanescent-wave detection of fluorophore-labeled biomolecules in aqueous solutions positioned in the air holes of the microstructured part of a photonic crystal fiber. The air-suspended silica structures located between three neighboring air holes in the cladding crystal guide light with a large fraction of the optical field penetrating into the sample even at wavelengths in the visible range. An effective interaction length of several centimeters is obtained when a sample volume of less than 1 microL is used.

  3. Acoustic carrier transportation induced by surface acoustic waves in graphene in solution

    NASA Astrophysics Data System (ADS)

    Okuda, Satoshi; Ikuta, Takashi; Kanai, Yasushi; Ono, Takao; Ogawa, Shinpei; Fujisawa, Daisuke; Shimatani, Masaaki; Inoue, Koichi; Maehashi, Kenzo; Matsumoto, Kazuhiko

    2016-04-01

    The acoustic charge transportation induced by surface acoustic wave (SAW) propagation in graphene in solution was investigated. The sign of acoustic current (I A) was found to switch when crossing the Dirac point because the major carrier was transitioned from holes to electrons by the change in electrolyte-gate voltage. I A also exhibited a peak value under conditions of both hole and electron conduction. These results can be explained on the basis of a change in the type of major carrier in graphene, as well as a change in the carrier mobility of graphene.

  4. In vivo noninvasive method for measuring local wave velocity in femoral arteries of pig

    NASA Astrophysics Data System (ADS)

    Zhang, Xiaoming; Kinnick, Randall; Pislaru, Cristina; Fatemi, Mostafa; Greenleaf, James

    2005-09-01

    We have proposed generating a bending wave in the arterial wall using ultrasound radiation force and measuring the wave velocity along the arterial wall [Zhang et al., IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52, 642-652 (2005)]. Here, we report the results of in vivo studies on pigs. The pig was anesthetized, and a micromanometer tip catheter was inserted into the femoral artery to measure luminal pressure. A water bath was created on the animal's groin to allow unimpeded access of the ultrasound beams to the femoral artery. The femoral artery was first located using a 13-MHz linear-array transducer. Then, a vibro-acoustography image was obtained to ensure precise positioning of the excitation force relative to the artery. The artery was excited by the force transducer and the resulting vibration of the arterial wall was measured by a sensing Doppler transceiver. Measured wave velocity was 3.1 m/s at 300 Hz. With this new method wave velocity over a distance of 5 mm, and therefore stiffness of arteries, can be measured locally and non-invasively. Measurement time is short in a few tens of milliseconds, which allows pressure dependence and pharmacological effect on the wall properties to be measured at different cardiac times.

  5. Exact Solutions in the Invariant Manifolds of the Generalized Integrable Hénon-Heiles System and Exact Traveling Wave Solutions of Klein-Gordon-Schrödinger Equations

    NASA Astrophysics Data System (ADS)

    Li, Jibin

    In this paper, we consider the exact explicit solutions for the famous generalized Hénon-Heiles (H-H) system. Corresponding to the three integrable cases, on the basis of the investigation of the dynamical behavior and level curves of the planar dynamical systems, we find all possible explicit exact parametric representations of solutions in the invariant manifolds of equilibrium points in the four-dimensional phase space. These solutions contain quasi-periodic solutions, homoclinic solutions, periodic solutions as well as blow-up solutions. Therefore, we answer the question: what are the flows in the center manifolds and homoclinic manifolds of the generalized Hénon-Heiles (H-H) system. As an application of the above results, we consider the traveling wave solutions for the coupled (n + 1)-dimensional Klein-Gordon-Schrödinger Equations with quadratic power nonlinearity.

  6. An Operator Method for Field Moments from the Extended Parabolic Wave Equation and Analytical Solutions of the First and Second Moments for Atmospheric Electromagnetic Wave Propagation

    NASA Technical Reports Server (NTRS)

    Manning, Robert M.

    2004-01-01

    The extended wide-angle parabolic wave equation applied to electromagnetic wave propagation in random media is considered. A general operator equation is derived which gives the statistical moments of an electric field of a propagating wave. This expression is used to obtain the first and second order moments of the wave field and solutions are found that transcend those which incorporate the full paraxial approximation at the outset. Although these equations can be applied to any propagation scenario that satisfies the conditions of application of the extended parabolic wave equation, the example of propagation through atmospheric turbulence is used. It is shown that in the case of atmospheric wave propagation and under the Markov approximation (i.e., the delta-correlation of the fluctuations in the direction of propagation), the usual parabolic equation in the paraxial approximation is accurate even at millimeter wavelengths. The comprehensive operator solution also allows one to obtain expressions for the longitudinal (generalized) second order moment. This is also considered and the solution for the atmospheric case is obtained and discussed. The methodology developed here can be applied to any qualifying situation involving random propagation through turbid or plasma environments that can be represented by a spectral density of permittivity fluctuations.

  7. Initial-Boundary Value Problem Solution of the Nonlinear Shallow-water Wave Equations

    NASA Astrophysics Data System (ADS)

    Kanoglu, U.; Aydin, B.

    2014-12-01

    The hodograph transformation solutions of the one-dimensional nonlinear shallow-water wave (NSW) equations are usually obtained through integral transform techniques such as Fourier-Bessel transforms. However, the original formulation of Carrier and Greenspan (1958 J Fluid Mech) and its variant Carrier et al. (2003 J Fluid Mech) involve evaluation integrals. Since elliptic integrals are highly singular as discussed in Carrier et al. (2003), this solution methodology requires either approximation of the associated integrands by smooth functions or selection of regular initial/boundary data. It should be noted that Kanoglu (2004 J Fluid Mech) partly resolves this issue by simplifying the resulting integrals in closed form. Here, the hodograph transform approach is coupled with the classical eigenfunction expansion method rather than integral transform techniques and a new analytical model for nonlinear long wave propagation over a plane beach is derived. This approach is based on the solution methodology used in Aydın & Kanoglu (2007 CMES-Comp Model Eng) for wind set-down relaxation problem. In contrast to classical initial- or boundary-value problem solutions, here, the NSW equations are formulated to yield an initial-boundary value problem (IBVP) solution. In general, initial wave profile with nonzero initial velocity distribution is assumed and the flow variables are given in the form of Fourier-Bessel series. The results reveal that the developed method allows accurate estimation of the spatial and temporal variation of the flow quantities, i.e., free-surface height and depth-averaged velocity, with much less computational effort compared to the integral transform techniques such as Carrier et al. (2003), Kanoglu (2004), Tinti & Tonini (2005 J Fluid Mech), and Kanoglu & Synolakis (2006 Phys Rev Lett). Acknowledgments: This work is funded by project ASTARTE- Assessment, STrategy And Risk Reduction for Tsunamis in Europe. Grant 603839, 7th FP (ENV.2013.6.4-3 ENV

  8. Attraction of spiral waves by localized inhomogeneities with small-world connections in excitable media

    NASA Astrophysics Data System (ADS)

    Wang, Xiaonan; Lu, Ying; Jiang, Minxi; Ouyang, Qi

    2004-05-01

    Trapping and untrapping of spiral tips in a two-dimensional homogeneous excitable medium with local small-world connections are studied by numerical simulation. In a homogeneous medium which can be simulated with a lattice of regular neighborhood connections, the spiral wave is in the meandering regime. When changing the topology of a small region from regular connections to small-world connections, the tip of the spiral waves is attracted by the small-world region, where the average path length declines with the introduction of long distant connections. The “trapped” phenomenon also occurs in regular lattices where the diffusion coefficient of the small region is increased. The above results can be explained by the eikonal equation, the Luther equation, and the relation between the core radius and the diffusion coefficient.

  9. Shock wave synthesis of amino acids from solutions of ammonium formate and ammonium bicarbonate

    NASA Astrophysics Data System (ADS)

    Suzuki, Chizuka; Furukawa, Yoshihiro; Kobayashi, Takamichi; Sekine, Toshimori; Nakazawa, Hiromoto; Kakegawa, Takeshi

    2015-07-01

    The emergence of life's building blocks, such as amino acids and nucleobases, on the prebiotic Earth was a critical step for the beginning of life. Reduced species with low mass, such as ammonia, amines, or carboxylic acids, are potential precursors for these building blocks of life. These precursors may have been provided to the prebiotic ocean by carbonaceous chondrites and chemical reactions related to meteorite impacts on the early Earth. The impact of extraterrestrial objects on Earth occurred more frequently during this period than at present. Such impacts generated shock waves in the ocean, which have the potential to progress chemical reactions to form the building blocks of life from reduced species. To simulate shock-induced reactions in the prebiotic ocean, we conducted shock-recovery experiments on ammonium bicarbonate solution and ammonium formate solution at impact velocities ranging from 0.51 to 0.92 km/s. In the products from the ammonium formate solution, several amino acids (glycine, alanine, ß-alanine, and sarcosine) and aliphatic amines (methylamine, ethylamine, propylamine, and butylamine) were detected, although yields were less than 0.1 mol % of the formic acid reactant. From the ammonium bicarbonate solution, smaller amounts of glycine, methylamine, ethylamine, and propylamine were formed. The impact velocities used in this study represent minimum cases because natural meteorite impacts typically have higher velocities and longer durations. Our results therefore suggest that shock waves could have been involved in forming life's building blocks in the ocean of prebiotic Earth, and potentially in aquifers of other planets, satellites, and asteroids.

  10. Wave Impact on a Wall: Comparison of Experiments with Similarity Solutions

    NASA Astrophysics Data System (ADS)

    Wang, A.; Duncan, J. H.; Lathrop, D. P.

    2014-11-01

    The impact of a steep water wave on a fixed partially submerged cube is studied with experiments and theory. The temporal evolution of the water surface profile upstream of the front face of the cube in its center plane is measured with a cinematic laser-induced fluorescence technique using frame rates up to 4,500 Hz. For a small range of cube positions, the surface profiles are found to form a nearly circular arc with upward curvature between the front face of the cube and a point just downstream of the wave crest. As the crest approaches the cube, the effective radius of this portion of the profile decreases rapidly. At the same time, the portion of the profile that is upstream of the crest approaches a straight line with a downward slope of about 15°. As the wave impact continues, the circular arc shrinks to zero radius with very high acceleration and a sudden transition to a high-speed vertical jet occurs. This flow singularity is modeled with a power-law scaling in time, which is used to create a time-independent system of equations of motion. The scaled governing equations are solved numerically and the similarly scaled measured free surface shapes, are favorably compared with the solutions. The support of the Office of Naval Research is gratefully acknowledged.

  11. Stability and collapse of localized solutions of the controlled three-dimensional Gross-Pitaevskii equation

    NASA Astrophysics Data System (ADS)

    Fedele, R.; Jovanović, D.; Eliasson, B.; de Nicola, S.; Shukla, P. K.

    2010-03-01

    On the basis of recent investigations, a newly developed analytical procedure is used for constructing a wide class of localized solutions of the controlled three-dimensional (3D) Gross-Pitaevskii equation (GPE) that governs the dynamics of Bose-Einstein condensates (BECs) in the presence of a spatio-temporally varying external potential. The controlled 3D GPE is decomposed into a two-dimensional (2D) linear Schrödinger equation (called the `transverse equation’) and a one-dimensional (1D) nonlinear Schrödinger equation (called the `longitudinal equation’), constrained by a variational condition for the controlling potential. The latter corresponds to the requirement for the minimization of the control operation in the transverse plane. Then, the above class of localized solutions are constructed as the product of the solutions of the transverse and longitudinal equations. A consistency condition between the transverse and longitudinal solutions yields a relationship between the transverse and longitudinal restoring forces produced by the external trapping potential well through a `controlling parameter’ (i.e. the average, with respect to the transverse profile, of the nonlinear inter-atomic interaction term of the GPE). It is found that the longitudinal profile supports localized solutions in the form of bright, dark or grey solitons with time-dependent amplitudes, widths and centroids. The related longitudinal phase is varying in space and time with time-dependent curvature radius and wavenumber. In turn, all the above parameters (i.e. amplitudes, widths, centroids, curvature radius and wavenumbers) can be easily expressed in terms of the controlling parameter. It is also found that the transverse profile has the form of Hermite-Gauss functions (depending on the transverse coordinates), and the explicit spatio-temporal dependence of the controlling potential is self-consistently determined. On the basis of these exact 3D analytical solutions, a stability

  12. Localization of electronic states in finite ladder models: Participation ratio and localization length as measures of the wave-function extension

    NASA Astrophysics Data System (ADS)

    Carrillo-Nuñez, H.; Schulz, Peter A.

    2008-12-01

    In this work we discuss and compare different definitions for localization of electronic states in low-dimensional systems. We choose a heuristic model for DNA-like molecules as a system prototype in order to establish ranges of equivalence for the localization length obtained from both the conductance and participation ratios. The results suggest also criteria to infer the extension of wave function in mesoscopic systems within the diffusive transport regime as complementary information to the localization length.

  13. Existence and numerical simulation of periodic traveling wave solutions to the Casimir equation for the Ito system

    NASA Astrophysics Data System (ADS)

    Abbasbandy, S.; Van Gorder, R. A.; Hajiketabi, M.; Mesrizadeh, M.

    2015-10-01

    We consider traveling wave solutions to the Casimir equation for the Ito system (a two-field extension of the KdV equation). These traveling waves are governed by a nonlinear initial value problem with an interesting nonlinearity (which actually amplifies in magnitude as the size of the solution becomes small). The nonlinear problem is parameterized by two initial constant values, and we demonstrate that the existence of solutions is strongly tied to these parameter values. For our interests, we are concerned with positive, bounded, periodic wave solutions. We are able to classify parameter regimes which admit such solutions in full generality, thereby obtaining a nice existence result. Using the existence result, we are then able to numerically simulate the positive, bounded, periodic solutions. We elect to employ a group preserving scheme in order to numerically study these solutions, and an outline of this approach is provided. The numerical simulations serve to illustrate the properties of these solutions predicted analytically through the existence result. Physically, these results demonstrate the existence of a type of space-periodic structure in the Casimir equation for the Ito model, which propagates as a traveling wave.

  14. Complex-periodic spiral waves in confluent cardiac cell cultures induced by localized inhomogeneities

    NASA Astrophysics Data System (ADS)

    Hwang, Seong-min; Kim, Tae Yun; Lee, Kyoung J.

    2005-07-01

    Spatiotemporal wave activities in excitable heart tissues have long been the subject of numerous studies because they underlie different forms of cardiac arrhythmias. In particular, understanding the dynamics and the instabilities of spiral waves have become very important because they can cause reentrant tachycardia and their subsequent transitions to fibrillation. Although many aspects of cardiac spiral waves have been investigated through experiments and model simulations, their complex properties are far from well understood. Here, we show that intriguing complex-periodic (such as period-2, period-3, period-4, or aperiodic) spiral wave states can arise in monolayer tissues of cardiac cell culture in vitro, and demonstrate that these different dynamic states can coexist with abrupt and spontaneous transitions among them without any change in system parameters; in other words, the medium supports multistability. Based on extensive image data analysis, we have confirmed that these spiral waves are driven by their tips tracing complex orbits whose unusual, meandering shapes are formed by delicate interplay between localized conduction blocks and nonlinear properties of the culture medium. Author contributions: S.-m.H. and K.J.L. designed research; S.-m.H. and T.Y.K. performed research; S.-m.H. contributed new reagents/analytic tools; S.-m.H., T.Y.K., and K.J.L. analyzed data; and S.-m.H. and K.J.L. wrote the paper.This paper was submitted directly (Track II) to the PNAS office.Abbreviations: IBI, interbeat interval; P-n, period-n.

  15. The Method of Decomposition in Invariant Structures: Exact Solutions for N Internal Waves in Three Dimensions

    NASA Astrophysics Data System (ADS)

    Miroshnikov, Victor

    2015-11-01

    The Navier-Stokes system of PDEs is reduced to a system of the vorticity, continuity, Helmholtz, and Lamb-Helmholtz PDEs. The periodic Dirichlet problems are formulated for conservative internal waves vanishing at infinity in upper and lower domains. Stationary kinematic Fourier (SKF) structures, stationary kinematic Euler-Fourier (SKEF) structures, stationary dynamic Euler-Fourier (SDEF) structures, and SKEF-SDEF structures of three spatial variables and time are constructed to consider kinematic and dynamic problems of the three-dimensional theory of the Newtonian flows with harmonic velocity. Exact solutions for propagation and interaction of N internal waves in the upper and lower domains are developed by the method of decomposition in invariant structures and implemented through experimental and theoretical programming in Maple. Main results are summarized in a global existence theorem for the strong solutions. The SKEF, SDEF, and SKEF-SDEF structures of the cumulative flows are visualized by two-parametric surface plots for six fluid-dynamic variables.

  16. Fast solution of elliptic partial differential equations using linear combinations of plane waves

    NASA Astrophysics Data System (ADS)

    Pérez-Jordá, José M.

    2016-02-01

    Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations A x =b , where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O (N logN ) memory and executing an iteration in O (N log2N ) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.

  17. Fast solution of elliptic partial differential equations using linear combinations of plane waves.

    PubMed

    Pérez-Jordá, José M

    2016-02-01

    Given an arbitrary elliptic partial differential equation (PDE), a procedure for obtaining its solution is proposed based on the method of Ritz: the solution is written as a linear combination of plane waves and the coefficients are obtained by variational minimization. The PDE to be solved is cast as a system of linear equations Ax=b, where the matrix A is not sparse, which prevents the straightforward application of standard iterative methods in order to solve it. This sparseness problem can be circumvented by means of a recursive bisection approach based on the fast Fourier transform, which makes it possible to implement fast versions of some stationary iterative methods (such as Gauss-Seidel) consuming O(NlogN) memory and executing an iteration in O(Nlog(2)N) time, N being the number of plane waves used. In a similar way, fast versions of Krylov subspace methods and multigrid methods can also be implemented. These procedures are tested on Poisson's equation expressed in adaptive coordinates. It is found that the best results are obtained with the GMRES method using a multigrid preconditioner with Gauss-Seidel relaxation steps.

  18. Stability of localized solutions in a subcritically unstable pattern-forming system under a global delayed control.

    PubMed

    Rubinstein, B Y; Nepomnyashchy, A A; Golovin, A A

    2007-04-01

    The formation of spatially localized patterns in a system with subcritical instability under feedback control with delay is investigated within the framework of globally controlled Ginzburg-Landau equation. It is shown that feedback control can stabilize spatially localized solutions. With the increase of delay, these solutions undergo oscillatory instability that, for large enough control strength, results in the formation of localized oscillating pulses. With further increase of the delay the solution blows up.

  19. Buffered lidocaine and bupivacaine mixture – the ideal local anesthetic solution?

    PubMed Central

    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. PMID:26090348

  20. Higher-order vector discrete rogue-wave states in the coupled Ablowitz-Ladik equations: Exact solutions and stability.

    PubMed

    Wen, Xiao-Yong; Yan, Zhenya; Malomed, Boris A

    2016-12-01

    An integrable system of two-component nonlinear Ablowitz-Ladik equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system. Then, new higher-order discrete two-component RW solutions of the system are found by means of a newly derived discrete version of a generalized Darboux transformation. Finally, the perturbed evolution of these RW states is explored in terms of systematic simulations, which demonstrates that tightly and loosely bound RWs are, respectively, nearly stable and strongly unstable solutions.

  1. Higher-order vector discrete rogue-wave states in the coupled Ablowitz-Ladik equations: Exact solutions and stability

    NASA Astrophysics Data System (ADS)

    Wen, Xiao-Yong; Yan, Zhenya; Malomed, Boris A.

    2016-12-01

    An integrable system of two-component nonlinear Ablowitz-Ladik equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system. Then, new higher-order discrete two-component RW solutions of the system are found by means of a newly derived discrete version of a generalized Darboux transformation. Finally, the perturbed evolution of these RW states is explored in terms of systematic simulations, which demonstrates that tightly and loosely bound RWs are, respectively, nearly stable and strongly unstable solutions.

  2. Self-localization of planetary wave structures in the ionosphere upon interaction with nonuniform geomagnetic field and zonal wind

    NASA Astrophysics Data System (ADS)

    Aburjania, G. D.

    2011-08-01

    The generation and further linear and nonlinear dynamics of planetary magnetized Rossby waves (MRWs) in the rotating dissipative ionosphere are studied in the presence of a zonal wind (shear flow). MRWs are caused by interaction with the spatially nonuniform geomagnetic field and are ionospheric manifestations of ordinary tropospheric Rossby waves. A simplified self-consistent set of model equations describing MRW-shear flow interaction is derived on the basis of complete equations of ionospheric magnetohydrodynamics. Based on an analysis of an exact analytical solution to the derived dynamic equations, an effective linear mechanism of MRW amplification in the interaction with nonuniform zonal wind is ascertained. It is shown that operators of linear problems are non-self-adjoint in the case of shear flows, and the corresponding eigenfunctions are nonorthogonal; therefore, the canonically modal approach is of little use when studying such flows; a so-called nonmodal mathematical analysis is required. It is ascertained that MRWs effectively get shear flow energy during the linear stage of evolution and significantly increase (by several orders of magnitude) their energy and amplitude. The necessary and sufficient condition of shear flow instability in an ionospheric medium is derived. Nonlinear self-localization begins with the development of shear instability and an increase in the amplitude, and the process ends with the self-organization of strongly localized isolated large-scale nonlinear vortex structures. Thus, a new degree of freedom and a way for perturbation evolution to occur appear in medium with shear flow. The nonlinear systems can be a pure monopole vortex, a vortex streets, or vortex chains depending of the shape of the sheared flow velocity profile. The accumulation of such vortices in the ionospheric medium can produce a strongly turbulent state.

  3. Long-range traveling waves of activity triggered by local dichoptic stimulation in V1 of behaving monkeys

    PubMed Central

    Yang, Zhiyong; Heeger, David J.; Blake, Randolph

    2014-01-01

    Traveling waves of cortical activity, in which local stimulation triggers lateral spread of activity to distal locations, have been hypothesized to play an important role in cortical function. However, there is conflicting physiological evidence for the existence of spreading traveling waves of neural activity triggered locally. Dichoptic stimulation, in which the two eyes view dissimilar monocular patterns, can lead to dynamic wave-like fluctuations in visual perception and therefore, provides a promising means for identifying and studying cortical traveling waves. Here, we used voltage-sensitive dye imaging to test for the existence of traveling waves of activity in the primary visual cortex of awake, fixating monkeys viewing dichoptic stimuli. We find clear traveling waves that are initiated by brief, localized contrast increments in one of the monocular patterns and then, propagate at speeds of ∼30 mm/s. These results demonstrate that under an appropriate visual context, circuitry in visual cortex in alert animals is capable of supporting long-range traveling waves triggered by local stimulation. PMID:25343785

  4. Shear Wave Splitting from Local Earthquakes in the New Madrid Seismic Zone

    NASA Astrophysics Data System (ADS)

    Martin, P.; Arroucau, P.; Vlahovic, G.

    2012-12-01

    In this study we investigate crustal anisotropy in the New Madrid seismic zone (NMSZ), by analyzing shear wave splitting from local earthquake data. The NMSZ is centrally located in the United States, spanning portions of western Tennessee, northeastern Arkansas, and southeastern Missouri. The NMSZ is also the location in which three of the largest known earthquakes took place in North America, occurring in 1811-1812. Although many seismic studies have been performed in this region, there is no consensus about which driving mechanism could satisfy both the current observations, as well as the historically observed seismicity. Therefore, it is important to continue investigating the NMSZ, to gain a better understanding of its seismicity, and the possible mechanisms that drive it. The automated technique developed by Savage et al. (2010) is used to perform the shear wave splitting measurements at 120 seismic stations within the NMSZ. The Center for Earthquake Research and Information (CERI) at the University of Memphis provided data for 1151 earthquakes spanning the years 2003-2011. The initial event selection was reduced to 245 earthquakes ranging in magnitude from 2.0 to 4.6, which fell within the shear wave window of one or more of the stations. The results of this study provide information about orientation of microcracks in the upper portion of the crust; future work will include analysis for temporal and spatial variations in order to assess the state of stress in the region.

  5. Detection and localization of single-source gravitational waves with pulsar timing arrays

    NASA Astrophysics Data System (ADS)

    Zhu, X.-J.; Wen, L.; Hobbs, G.; Zhang, Y.; Wang, Y.; Madison, D. R.; Manchester, R. N.; Kerr, M.; Rosado, P. A.; Wang, J.-B.

    2015-05-01

    Pulsar timing arrays (PTAs) can be used to search for very low frequency (10-9-10-7 Hz) gravitational waves (GWs). In this paper, we present a general method for the detection and localization of single-source GWs using PTAs. We demonstrate the effectiveness of this new method for three types of signals: monochromatic waves as expected from individual supermassive binary black holes in circular orbits, GWs from eccentric binaries and GW bursts. We also test its implementation in realistic data sets that include effects such as uneven sampling and heterogeneous data spans and measurement precision. It is shown that our method, which works in the frequency domain, performs as well as published time-domain methods. In particular, we find it equivalent to the Fe-statistic for monochromatic waves. We also discuss the construction of null streams - data streams that have null response to GWs, and the prospect of using null streams as a consistency check in the case of detected GW signals. Finally, we present sensitivities to individual supermassive binary black holes in eccentric orbits. We find that a monochromatic search that is designed for circular binaries can efficiently detect eccentric binaries with both high and low eccentricities, while a harmonic summing technique provides greater sensitivities only for binaries with moderate eccentricities.

  6. Many-body Localization Transition in Rokhsar-Kivelson-type wave functions

    NASA Astrophysics Data System (ADS)

    Chen, Xiao; Yu, Xiongjie; Cho, Gil Young; Clark, Bryan; Fradkin, Eduardo

    We construct a family of many-body wave functions to study the many-body localization phase transition. The wave functions have a Rokhsar-Kivelson form, in which the weight for the configurations are chosen from the Gibbs weights of a classical spin glass model, known as the Random Energy Model, multiplied by a random sign structure to represent a highly excited state. These wave functions show a phase transition into an MBL phase. In addition, we see three regimes of entanglement scaling with subsystem size: scaling with entanglement corresponding to an infinite temperature thermal phase, constant scaling, and a sub-extensive scaling between these limits. Near the phase transition point, the fluctuations of the Renyi entropies are non-Gaussian. We find that Renyi entropies with different Renyi index transition into the MBL phase at different points and have different scaling behavior, suggesting a multifractal behavior. This work was supported in part by DMR-1064319 and DMR-1408713 (XC,GYC,EF) at the University of Illinois, PHY11-25915 at KITP (EF), DOE, SciDAC FG02-12ER46875 (BKC and XY), and the Brain Korea 21 PLUS Project of Korea Government (GYC).

  7. Guided wave interaction with hole damage using the local interaction simulation approach

    NASA Astrophysics Data System (ADS)

    Obenchain, Matthew B.; Cesnik, Carlos E. S.

    2014-12-01

    This paper considers the effects of hole damage on guided wave propagation in isotropic and composite plates using both the local interaction simulation approach (LISA) and experimental methods. Guided wave generation from piezoceramic wafers is modeled using the recently developed LISA hybrid approach. First, holes in isotropic plates are simulated to establish LISA's ability to capture the guided wave scattering effects of various hole sizes. Experimental results are compared with the simulations to aid in evaluating the LISA model. Next, hole damage in cross-ply composite laminates is modeled and compared with experimental results. Various hole sizes and azimuthal locations are simulated to determine the effects of varying those parameters. Results from both the isotropic and composite damage studies clearly display the ability of LISA to model hole damage. Both the simulation and experimental results illustrate the advantages and disadvantages of various sensor locations relative to the actuator and damage locations. Finally, the study shows the ability of the LISA model to capture mode conversions resulting from partial thickness holes.

  8. Localization and broadband follow-up of the gravitational-wave transient GW150914

    DOE PAGES

    Abbott, B. P.

    2016-07-20

    A gravitational-wave (GW) transient was identified in data recorded by the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) detectors on 2015 September 14. The event, initially designated G184098 and later given the name GW150914, is described in detail elsewhere. By prior arrangement, preliminary estimates of the time, significance, and sky location of the event were shared with 63 teams of observers covering radio, optical, near-infrared, X-ray, and gamma-ray wavelengths with ground- and space-based facilities. In this Letter we describe the low-latency analysis of the GW data and present the sky localization of the first observed compact binary merger. We summarize themore » follow-up observations reported by 25 teams via private Gamma-ray Coordinates Network circulars, giving an overview of the participating facilities, the GW sky localization coverage, the timeline and depth of the observations. As this event turned out to be a binary black hole merger, there is little expectation of a detectable electromagnetic (EM) signature. Nevertheless, this first broadband campaign to search for a counterpart of an Advanced LIGO source represents a milestone and highlights the broad capabilities of the transient astronomy community and the observing strategies that have been developed to pursue neutron star binary merger events. Furthermore, detailed investigations of the EM data and results of the EM follow-up campaign are being disseminated in papers by the individual teams.« less

  9. Spatial localization of resistive drift wave structure in tokamak edge plasmas with an embedded magnetic island

    SciTech Connect

    Hu, Shilin; Qu, Hongpeng; Li, Jiquan; Kishimoto, Y.

    2014-10-15

    Resistive drift wave instability is investigated numerically in tokamak edge plasma confined by sheared slab magnetic field geometry with an embedded magnetic island. The focus is on the structural characteristics of eigenmode inside the island, where the density profile tends to be flattened. A transition of the dominant eigenmode occurs around a critical island width w{sub c}. For thin islands with a width below w{sub c}, two global long wavelength eigenmodes with approximately the same growth rate but different eigenfrequency are excited, which are stabilized by the magnetic island through two-dimensional mode coupling in both x and y (corresponding to radial and poloidal in tokamak) directions. On the other hand, a short wavelength eigenmode, which is destabilized by thick islands with a width above w{sub c}, dominates the edge fluctuation, showing a prominent structural localization in the region between the X-point and the O-point of the magnetic island. The main destabilization mechanism is identified as the mode coupling in the y direction, which is similar to the so-called toroidal coupling in tokamak plasmas. These three eigenmodes may coexist in the drift wave fluctuation for the island with a width around w{sub c}. It is demonstrated that the structural localization results mainly from the quasilinear flattening of density profile inside the magnetic island.

  10. Localization and broadband follow-up of the gravitational-wave transient GW150914

    SciTech Connect

    Abbott, B. P.

    2016-07-20

    A gravitational-wave (GW) transient was identified in data recorded by the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) detectors on 2015 September 14. The event, initially designated G184098 and later given the name GW150914, is described in detail elsewhere. By prior arrangement, preliminary estimates of the time, significance, and sky location of the event were shared with 63 teams of observers covering radio, optical, near-infrared, X-ray, and gamma-ray wavelengths with ground- and space-based facilities. In this Letter we describe the low-latency analysis of the GW data and present the sky localization of the first observed compact binary merger. We summarize the follow-up observations reported by 25 teams via private Gamma-ray Coordinates Network circulars, giving an overview of the participating facilities, the GW sky localization coverage, the timeline and depth of the observations. As this event turned out to be a binary black hole merger, there is little expectation of a detectable electromagnetic (EM) signature. Nevertheless, this first broadband campaign to search for a counterpart of an Advanced LIGO source represents a milestone and highlights the broad capabilities of the transient astronomy community and the observing strategies that have been developed to pursue neutron star binary merger events. Furthermore, detailed investigations of the EM data and results of the EM follow-up campaign are being disseminated in papers by the individual teams.

  11. Detection and localization of continuous gravitational waves with pulsar timing arrays: the role of pulsar terms

    NASA Astrophysics Data System (ADS)

    Zhu, X.-J.; Wen, L.; Xiong, J.; Xu, Y.; Wang, Y.; Mohanty, S. D.; Hobbs, G.; Manchester, R. N.

    2016-09-01

    A pulsar timing array is a Galactic-scale detector of nanohertz gravitational waves (GWs). Its target signals contain two components: the `Earth term' and the `pulsar term' corresponding to GWs incident on the Earth and pulsar, respectively. In this work we present a Frequentist method for the detection and localization of continuous waves that takes into account the pulsar term and is significantly faster than existing methods. We investigate the role of pulsar terms by comparing a full-signal search with an Earth-term-only search for non-evolving black hole binaries. By applying the method to synthetic data sets, we find that (i) a full-signal search can slightly improve the detection probability (by about five per cent); (ii) sky localization is biased if only Earth terms are searched for and the inclusion of pulsar terms is critical to remove such a bias; (iii) in the case of strong detections (with signal-to-noise ratio ≳30), it may be possible to improve pulsar distance estimation through GW measurements.

  12. Localization and Broadband Follow-up of the Gravitational-wave Transient GW150914

    NASA Astrophysics Data System (ADS)

    Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M. R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R. X.; Adya, V. B.; Affeldt, C.; Agathos, M.; Agatsuma, K.; Aggarwal, N.; Aguiar, O. D.; Aiello, L.; Ain, A.; Ajith, P.; Allen, B.; Allocca, A.; Altin, P. A.; Anderson, S. B.; Anderson, W. G.; Arai, K.; Araya, M. C.; Arceneaux, C. C.; Areeda, J. S.; Arnaud, N.; Arun, K. G.; Ascenzi, S.; Ashton, G.; Ast, M.; Aston, S. M.; Astone, P.; Aufmuth, P.; Aulbert, C.; Babak, S.; Bacon, P.; Bader, M. K. M.; Baker, P. T.; Baldaccini, F.; Ballardin, G.; Ballmer, S. W.; Barayoga, J. C.; Barclay, S. E.; Barish, B. C.; Barker, D.; Barone, F.; Barr, B.; Barsotti, L.; Barsuglia, M.; Barta, D.; Barthelmy, S.; Bartlett, J.; Bartos, I.; Bassiri, R.; Basti, A.; Batch, J. C.; Baune, C.; Bavigadda, V.; Bazzan, M.; Behnke, B.; Bejger, M.; Bell, A. S.; Bell, C. J.; Berger, B. K.; Bergman, J.; Bergmann, G.; Berry, C. P. 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. G.; 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.; Boom, B. A.; Bork, R.; Boschi, V.; Bose, S.; Bouffanais, Y.; 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.; Bustillo, J. C.; Callister, T.; Calloni, E.; Camp, J. B.; Cannon, K. C.; Cao, J.; Capano, C. D.; Capocasa, E.; Carbognani, F.; Caride, S.; Diaz, J. C.; Casentini, C.; Caudill, S.; Cavagliá, M.; Cavalier, F.; Cavalieri, R.; Cella, G.; Cepeda, C. B.; Baiardi, L. C.; 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.; Cominsky, L.; Constancio, M., Jr.; 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.; Cowan, E. E.; 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. T.; De Rosa, R.; DeSalvo, R.; Dhurandhar, S.; Díaz, M. C.; Di Fiore, L.; Di Giovanni, M.; Di Lieto, A.; Di Pace, S.; 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.; 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.; Fiorucci, D.; Fisher, R. P.; Flaminio, R.; Fletcher, M.; Fournier, J.-D.; Franco, S.; Frasca, S.; Frasconi, F.; Frei, Z.; Freise, A.; Frey, R.; Frey, V.; 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. G.; 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.; Haris, K.; 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.; 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, I.; 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.; 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. O.; 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, A.; Mukherjee, D.; Mukherjee, S.; Mukund, N.; 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.; Ottaway, D. J.; Ottens, R. S.; Overmier, H.; Owen, B. J.; Pai, A.; Pai, S. A.; Palamos, J. R.; Palashov, O.; Palliyaguru, N.; 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.; Patricelli, B.; Patrick, Z.; Pearlstone, B. L.; Pedraza, M.; Pedurand, R.; Pekowsky, L.; Pele, A.; Penn, S.; Perreca, A.; Phelps, M.; Piccinni, O.; Pichot, M.; Piergiovanni, F.; Pierro, V.; Pillant, G.; Pinard, L.; Pinto, I. M.; Pitkin, M.; Poggiani, R.; Popolizio, P.; 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.; Puncken, O.; 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.; Reyes, S. D.; Ricci, F.; Riles, K.; Robertson, N. A.; Robie, R.; Robinet, F.; Rocchi, A.; Rolland, L.; Rollins, J. G.; Roma, V. J.; Romano, R.; Romanov, G.; Romie, J. H.; Rosińska, D.; Rowan, S.; Rüdiger, A.; Ruggi, P.; Ryan, K.; Sachdev, S.; Sadecki, T.; Sadeghian, L.; Salconi, 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.; Singh, A.; Singh, R.; Singhal, A.; 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.; Szczepańczyk, 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 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.; Voss, D.; 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; Allison, J.; Bannister, K.; Bell, M. E.; Chatterjee, S.; Chippendale, A. P.; Edwards, P. G.; Harvey-Smith, L.; Heywood, Ian; Hotan, A.; Indermuehle, B.; Marvil, J.; McConnell, D.; Murphy, T.; Popping, A.; Reynolds, J.; Sault, R. J.; Voronkov, M. A.; Whiting, M. T.; Australian Square Kilometer Array Pathfinder (ASKAP) Collaboration; Castro-Tirado, A. J.; Cunniffe, R.; Jelínek, M.; Tello, J. C.; Oates, S. R.; Hu, Y.-D.; Kubánek, P.; Guziy, S.; Castellón, A.; García-Cerezo, A.; Muñoz, V. F.; Pérez del Pulgar, C.; Castillo-Carrión, S.; Castro Cerón, J. M.; Hudec, R.; Caballero-García, M. D.; Páta, P.; Vitek, S.; Adame, J. A.; Konig, S.; Rendón, F.; Mateo Sanguino, T. de J.; Fernández-Muñoz, R.; Yock, P. C.; Rattenbury, N.; Allen, W. H.; Querel, R.; Jeong, S.; Park, I. H.; Bai, J.; Cui, Ch.; Fan, Y.; Wang, Ch.; Hiriart, D.; Lee, W. H.; Claret, A.; Sánchez-Ramírez, R.; Pandey, S. B.; Mediavilla, T.; Sabau-Graziati, L.; BOOTES Collaboration; Abbott, T. M. C.; Abdalla, F. B.; Allam, S.; Annis, J.; Armstrong, R.; Benoit-Lévy, A.; Berger, E.; Bernstein, R. A.; Bertin, E.; Brout, D.; Buckley-Geer, E.; Burke, D. L.; Capozzi, D.; Carretero, J.; Castander, F. J.; Chornock, R.; Cowperthwaite, P. S.; Crocce, M.; Cunha, C. E.; D'Andrea, C. B.; da Costa, L. N.; Desai, S.; Diehl, H. T.; Dietrich, J. P.; Doctor, Z.; Drlica-Wagner, A.; Drout, M. R.; Eifler, T. F.; Estrada, J.; Evrard, A. E.; Fernandez, E.; Finley, D. A.; Flaugher, B.; Foley, R. J.; Fong, W.-F.; Fosalba, P.; Fox, D. B.; Frieman, J.; Fryer, C. L.; Gaztanaga, E.; Gerdes, D. W.; Goldstein, D. A.; Gruen, D.; Gruendl, R. A.; Gutierrez, G.; Herner, K.; Honscheid, K.; James, D. J.; Johnson, M. D.; Johnson, M. W. G.; Karliner, I.; Kasen, D.; Kent, S.; Kessler, R.; Kim, A. G.; Kind, M. C.; Kuehn, K.; Kuropatkin, N.; Lahav, O.; Li, T. S.; Lima, M.; Lin, H.; Maia, M. A. G.; Margutti, R.; Marriner, J.; Martini, P.; Matheson, T.; Melchior, P.; Metzger, B. D.; Miller, C. J.; Miquel, R.; Neilsen, E.; Nichol, R. C.; Nord, B.; Nugent, P.; Ogando, R.; Petravick, D.; Plazas, A. A.; Quataert, E.; Roe, N.; Romer, A. K.; Roodman, A.; Rosell, A. C.; Rykoff, E. S.; Sako, M.; Sanchez, E.; Scarpine, V.; Schindler, R.; Schubnell, M.; Scolnic, D.; Sevilla-Noarbe, I.; Sheldon, E.; Smith, N.; Smith, R. C.; Soares-Santos, M.; Sobreira, F.; Stebbins, A.; Suchyta, E.; Swanson, M. E. C.; Tarle, G.; Thaler, J.; Thomas, D.; Thomas, R. C.; Tucker, D. L.; Vikram, V.; Walker, A. R.; Wechsler, R. H.; Wester, W.; Yanny, B.; Zhang, Y.; Zuntz, J.; Dark Energy Survey; Dark Energy Camera GW-EM Collaboration; Connaughton, V.; Burns, E.; Goldstein, A.; Briggs, M. S.; Zhang, B.-B.; Hui, C. M.; Jenke, P.; Wilson-Hodge, C. A.; Bhat, P. N.; Bissaldi, E.; Cleveland, W.; Fitzpatrick, G.; Giles, M. M.; Gibby, M. H.; Greiner, J.; von Kienlin, A.; Kippen, R. M.; McBreen, S.; Mailyan, B.; Meegan, C. A.; Paciesas, W. S.; Preece, R. D.; Roberts, O.; Sparke, L.; Stanbro, M.; Toelge, K.; Veres, P.; Yu, H.-F.; Blackburn, L.; Fermi GBM Collaboration; Ackermann, M.; Ajello, M.; Albert, A.; Anderson, B.; Atwood, W. B.; Axelsson, M.; Baldini, L.; Barbiellini, G.; Bastieri, D.; Bellazzini, R.; Bissaldi, E.; Blandford, R. D.; Bloom, E. D.; Bonino, R.; Bottacini, E.; Brandt, T. J.; Bruel, P.; Buson, S.; Caliandro, G. A.; Cameron, R. A.; Caragiulo, M.; Caraveo, P. A.; Cavazzuti, E.; Charles, E.; Chekhtman, A.; Chiang, J.; Chiaro, G.; Ciprini, S.; Cohen-Tanugi, J.; Cominsky, L. R.; Costanza, F.; Cuoco, A.; D'Ammando, F.; de Palma, F.; Desiante, R.; Digel, S. W.; Di Lalla, N.; Di Mauro, M.; Di Venere, L.; Domínguez, A.; Drell, P. S.; Dubois, R.; Favuzzi, C.; Ferrara, E. C.; Franckowiak, A.; Fukazawa, Y.; Funk, S.; Fusco, P.; Gargano, F.; Gasparrini, D.; Giglietto, N.; Giommi, P.; Giordano, F.; Giroletti, M.; Glanzman, T.; Godfrey, G.; Gomez-Vargas, G. A.; Green, D.; Grenier, I. A.; Grove, J. E.; Guiriec, S.; Hadasch, D.; Harding, A. K.; Hays, E.; Hewitt, J. W.; Hill, A. B.; Horan, D.; Jogler, T.; Jóhannesson, G.; Johnson, A. S.; Kensei, S.; Kocevski, D.; Kuss, M.; La Mura, G.; Larsson, S.; Latronico, L.; Li, J.; Li, L.; Longo, F.; Loparco, F.; Lovellette, M. N.; Lubrano, P.; Magill, J.; Maldera, S.; Manfreda, A.; Marelli, M.; Mayer, M.; Mazziotta, M. N.; McEnery, J. E.; Meyer, M.; Michelson, P. F.; Mirabal, N.; Mizuno, T.; Moiseev, A. A.; Monzani, M. E.; Moretti, E.; Morselli, A.; Moskalenko, I. V.; Negro, M.; Nuss, E.; Ohsugi, T.; Omodei, N.; Orienti, M.; Orlando, E.; Ormes, J. F.; Paneque, D.; Perkins, J. S.; Pesce-Rollins, M.; Piron, F.; Pivato, G.; Porter, T. A.; Racusin, J. L.; Rainò, S.; Rando, R.; Razzaque, S.; Reimer, A.; Reimer, O.; Salvetti, D.; Saz Parkinson, P. M.; Sgrò, C.; Simone, D.; Siskind, E. J.; Spada, F.; Spandre, G.; Spinelli, P.; Suson, D. J.; Tajima, H.; Thayer, J. B.; Thompson, D. J.; Tibaldo, L.; Torres, D. F.; Troja, E.; Uchiyama, Y.; Venters, T. M.; Vianello, G.; Wood, K. S.; Wood, M.; Zhu, S.; Zimmer, S.; Fermi LAT Collaboration; Brocato, E.; Cappellaro, E.; Covino, S.; Grado, A.; Nicastro, L.; Palazzi, E.; Pian, E.; Amati, L.; Antonelli, L. A.; Capaccioli, M.; D'Avanzo, P.; D'Elia, V.; Getman, F.; Giuffrida, G.; Iannicola, G.; Limatola, L.; Lisi, M.; Marinoni, S.; Marrese, P.; Melandri, A.; Piranomonte, S.; Possenti, A.; Pulone, L.; Rossi, A.; Stamerra, A.; Stella, L.; Testa, V.; Tomasella, L.; Yang, S.; GRAvitational Wave Inaf TeAm (GRAWITA); Bazzano, A.; Bozzo, E.; Brandt, S.; Courvoisier, T. J.-L.; Ferrigno, C.; Hanlon, L.; Kuulkers, E.; Laurent, P.; Mereghetti, S.; Roques, J. P.; Savchenko, V.; Ubertini, P.; INTEGRAL Collaboration; Kasliwal, M. M.; Singer, L. P.; Cao, Y.; Duggan, G.; Kulkarni, S. R.; Bhalerao, V.; Miller, A. A.; Barlow, T.; Bellm, E.; Manulis, I.; Rana, J.; Laher, R.; Masci, F.; Surace, J.; Rebbapragada, U.; Cook, D.; Van Sistine, A.; Sesar, B.; Perley, D.; Ferreti, R.; Prince, T.; Kendrick, R.; Horesh, A.; Intermediate Palomar Transient Factory (iPTF) Collaboration; Hurley, K.; Golenetskii, S. V.; Aptekar, R. L.; Frederiks, D. D.; Svinkin, D. S.; Rau, A.; von Kienlin, A.; Zhang, X.; Smith, D. M.; Cline, T.; Krimm, H.; InterPlanetary Network; Abe, F.; Doi, M.; Fujisawa, K.; Kawabata, K. S.; Morokuma, T.; Motohara, K.; Tanaka, M.; Ohta, K.; Yanagisawa, K.; Yoshida, M.; J-GEM Collaboration; Baltay, C.; Rabinowitz, D.; Ellman, N.; Rostami, S.; La Silla–QUEST Survey; Bersier, D. F.; Bode, M. F.; Collins, C. A.; Copperwheat, C. M.; Darnley, M. J.; Galloway, D. K.; Gomboc, A.; Kobayashi, S.; Mazzali, P.; Mundell, C. G.; Piascik, A. S.; Pollacco, Don; Steele, I. A.; Ulaczyk, K.; Liverpool Telescope Collaboration; Broderick, J. W.; Fender, R. P.; Jonker, P. G.; Rowlinson, A.; Stappers, B. W.; Wijers, R. A. M. J.; Low Frequency Array (LOFAR) Collaboration; Lipunov, V.; Gorbovskoy, E.; Tyurina, N.; Kornilov, V.; Balanutsa, P.; Kuznetsov, A.; Buckley, D.; Rebolo, R.; Serra-Ricart, M.; Israelian, G.; Budnev, N. M.; Gress, O.; Ivanov, K.; Poleshuk, V.; Tlatov, A.; Yurkov, V.; MASTER Collaboration; Kawai, N.; Serino, M.; Negoro, H.; Nakahira, S.; Mihara, T.; Tomida, H.; Ueno, S.; Tsunemi, H.; Matsuoka, M.; MAXI Collaboration; Croft, S.; Feng, L.; Franzen, T. M. O.; Gaensler, B. M.; Johnston-Hollitt, M.; Kaplan, D. L.; Morales, M. F.; Tingay, S. J.; Wayth, R. B.; Williams, A.; Murchison Wide-field Array (MWA) Collaboration; Smartt, S. J.; Chambers, K. C.; Smith, K. W.; Huber, M. E.; Young, D. R.; Wright, D. E.; Schultz, A.; Denneau, L.; Flewelling, H.; Magnier, E. A.; Primak, N.; Rest, A.; Sherstyuk, A.; Stalder, B.; Stubbs, C. W.; Tonry, J.; Waters, C.; Willman, M.; Pan-STARRS Collaboration; Olivares E., F.; Campbell, H.; Kotak, R.; Sollerman, J.; Smith, M.; Dennefeld, M.; Anderson, J. P.; Botticella, M. T.; Chen, T.-W.; Della Valle, M.; Elias-Rosa, N.; Fraser, M.; Inserra, C.; Kankare, E.; Kupfer, T.; Harmanen, J.; Galbany, L.; Le Guillou, L.; Lyman, J. D.; Maguire, K.; Mitra, A.; Nicholl, M.; Razza, A.; Terreran, G.; Valenti, S.; Gal-Yam, A.; PESSTO Collaboration; Ćwiek, A.; Ćwiok, M.; Mankiewicz, L.; Opiela, R.; Zaremba, M.; Żarnecki, A. F.; Pi of Sky Collaboration; Onken, C. A.; Scalzo, R. A.; Schmidt, B. P.; Wolf, C.; Yuan, F.; SkyMapper Collaboration; Evans, P. A.; Kennea, J. A.; Burrows, D. N.; Campana, S.; Cenko, S. B.; Giommi, P.; Marshall, F. E.; Nousek, J.; O'Brien, P.; Osborne, J. P.; Palmer, D.; Perri, M.; Siegel, M.; Tagliaferri, G.; Swift Collaboration; Klotz, A.; Turpin, D.; Laugier, R.; TAROT, Zadko, Algerian National Observatory, C2PU Collaboration; Beroiz, M.; Peñuela, T.; Macri, L. M.; Oelkers, R. J.; Lambas, D. G.; Vrech, R.; Cabral, J.; Colazo, C.; Dominguez, M.; Sanchez, B.; Gurovich, S.; Lares, M.; Marshall, J. L.; DePoy, D. L.; Padilla, N.; Pereyra, N. A.; Benacquista, M.; TOROS Collaboration; Tanvir, N. R.; Wiersema, K.; Levan, A. J.; Steeghs, D.; Hjorth, J.; Fynbo, J. P. U.; Malesani, D.; Milvang-Jensen, B.; Watson, D.; Irwin, M.; Fernandez, C. G.; McMahon, R. G.; Banerji, M.; Gonzalez-Solares, E.; Schulze, S.; de Ugarte Postigo, A.; Thoene, C. C.; Cano, Z.; Rosswog, S.; VISTA Collaboration

    2016-07-01

    A gravitational-wave (GW) transient was identified in data recorded by the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) detectors on 2015 September 14. The event, initially designated G184098 and later given the name GW150914, is described in detail elsewhere. By prior arrangement, preliminary estimates of the time, significance, and sky location of the event were shared with 63 teams of observers covering radio, optical, near-infrared, X-ray, and gamma-ray wavelengths with ground- and space-based facilities. In this Letter we describe the low-latency analysis of the GW data and present the sky localization of the first observed compact binary merger. We summarize the follow-up observations reported by 25 teams via private Gamma-ray Coordinates Network circulars, giving an overview of the participating facilities, the GW sky localization coverage, the timeline, and depth of the observations. As this event turned out to be a binary black hole merger, there is little expectation of a detectable electromagnetic (EM) signature. Nevertheless, this first broadband campaign to search for a counterpart of an Advanced LIGO source represents a milestone and highlights the broad capabilities of the transient astronomy community and the observing strategies that have been developed to pursue neutron star binary merger events. Detailed investigations of the EM data and results of the EM follow-up campaign are being disseminated in papers by the individual teams.

  13. Premerger localization of gravitational-wave standard sirens with LISA: Harmonic mode decomposition

    NASA Astrophysics Data System (ADS)

    Kocsis, Bence; Haiman, Zoltán; Menou, Kristen; Frei, Zsolt

    2007-07-01

    The continuous improvement in localization errors (sky position and distance) in real time as LISA observes the gradual inspiral of a supermassive black hole binary can be of great help in identifying any prompt electromagnetic counterpart associated with the merger. We develop a new method, based on a Fourier decomposition of the time-dependent, LISA-modulated gravitational-wave signal, to study this intricate problem. The method is faster than standard Monte Carlo simulations by orders of magnitude. By surveying the parameter space of potential LISA sources, we find that counterparts to supermassive black hole binary mergers with total mass M˜105 107M⊙ and redshifts z≲3 can be localized to within the field of view of astronomical instruments (˜deg2) typically hours to weeks prior to coalescence. This will allow a triggered search for variable electromagnetic counterparts as the merger proceeds, as well as monitoring of the most energetic coalescence phase. A rich set of astrophysical and cosmological applications would emerge from the identification of electromagnetic counterparts to these gravitational-wave standard sirens.

  14. A trade-off solution between model resolution and covariance in surface-wave inversion

    USGS Publications Warehouse

    Xia, J.; Xu, Y.; Miller, R.D.; Zeng, C.

    2010-01-01

    Regularization is necessary for inversion of ill-posed geophysical problems. Appraisal of inverse models is essential for meaningful interpretation of these models. Because uncertainties are associated with regularization parameters, extra conditions are usually required to determine proper parameters for assessing inverse models. Commonly used techniques for assessment of a geophysical inverse model derived (generally iteratively) from a linear system are based on calculating the model resolution and the model covariance matrices. Because the model resolution and the model covariance matrices of the regularized solutions are controlled by the regularization parameter, direct assessment of inverse models using only the covariance matrix may provide incorrect results. To assess an inverted model, we use the concept of a trade-off between model resolution and covariance to find a proper regularization parameter with singular values calculated in the last iteration. We plot the singular values from large to small to form a singular value plot. A proper regularization parameter is normally the first singular value that approaches zero in the plot. With this regularization parameter, we obtain a trade-off solution between model resolution and model covariance in the vicinity of a regularized solution. The unit covariance matrix can then be used to calculate error bars of the inverse model at a resolution level determined by the regularization parameter. We demonstrate this approach with both synthetic and real surface-wave data. ?? 2010 Birkh??user / Springer Basel AG.

  15. Local heating of human skin by millimeter waves: effect of blood flow.

    PubMed

    Alekseev, S I; Radzievsky, A A; Szabo, I; Ziskin, M C

    2005-09-01

    We investigated the influence of blood perfusion on local heating of the forearm and middle finger skin following 42.25 GHz exposure with an open ended waveguide (WG) and with a YAV mm wave therapeutic device. Both sources had bell-shaped distributions of the incident power density (IPD) with peak intensities of 208 and 55 mW/cm(2), respectively. Blood perfusion was changed in two ways: by blood flow occlusion and by externally applied vasodilator (nonivamide/nicoboxil) cream to the skin. For thermal modeling, we used the bioheat transfer equation (BHTE) and the hybrid bioheat equation (HBHE) which combines the BHTE and the scalar effective thermal conductivity equation (ETCE). Under normal conditions with the 208 mW/cm(2) exposure, the cutaneous temperature elevation (DeltaT) in the finger (2.5 +/- 0.3 degrees C) having higher blood flow was notably smaller than the cutaneous DeltaT in the forearm (4.7 +/- 0.4 degrees C). However, heating of the forearm and finger skin with blood flow occluded was the same, indicating that the thermal conductivity of tissue in the absence of blood flow at both locations was also the same. The BHTE accurately predicted local hyperthermia in the forearm only at low blood flow. The HBHE made accurate predictions at both low and high perfusion rates. The relationship between blood flow and the effective thermal conductivity (k(eff)) was found to be linear. The heat dissipating effect of higher perfusion was mostly due to an apparent increase in k(eff). It was shown that mm wave exposure could result in steady state heating of tissue layers located much deeper than the penetration depth (0.56 mm). The surface DeltaT and heat penetration into tissue increased with enlarging the irradiating beam area and with increasing exposure duration. Thus, mm waves at sufficient intensities could thermally affect thermo-sensitive structures located in the skin and underlying tissue.

  16. Rapid guided wave delamination detection and quantification in composites using global-local sensing

    NASA Astrophysics Data System (ADS)

    Tian, Zhenhua; Yu, Lingyu; Leckey, Cara

    2016-08-01

    This paper presents a rapid guided ultrasonic wave inspection approach through global inspection by phased array beamforming and local damage evaluation via wavenumber analysis. The global-local approach uses a hybrid system consisting of a PZT wafer and a non-contact laser vibrometer. The overall inspection is performed in two steps. First, a phased array configured by a small number of measurements performs beamforming and beamsteering over the entire plate in order to detect and locate the presence of the damage. A local area is identified as target damage area for the second step. Then a high density wavefield measurement is taken over the target damage area and a spatial wavenumber imaging is performed to quantitatively evaluate the damage. The two-step inspection has been applied to locate and quantify impact-induced delamination damage in a carbon fiber reinforced polymer composite plate. The detected delamination location, size and shape agree well with those of an ultrasonic C-scan. For the test case studied in this work the global-local approach reduced the total composite inspection (damage detection and characterization) time by ∼97% compared to using a full scan approach.

  17. Response of a chemical wave to local pulse irradiation in the ruthenium-catalyzed Belousov-Zhabotinsky reaction.

    PubMed

    Nakata, Satoshi; Suzuki, Shogo; Ezaki, Takato; Kitahata, Hiroyuki; Nishi, Kei; Nishiura, Yasumasa

    2015-04-14

    The photo-sensitive Belousov-Zhabotinsky (BZ) reaction system was investigated to understand the response of wave propagation to local pulse stimulation in an excitable field. When the chemical wave was irradiated with a bright pulse or a dark pulse, the speed of wave propagation decreased or increased. The timing of pulse irradiation that significantly affected the speed of chemical wave propagation was different with the bright and dark pulses. That is, there is a sensitive point in the chemical wave. The experimental results were qualitatively reproduced by a numerical calculation based on a three-variable Oregonator model that was modified for the photosensitive BZ reaction. These results suggest that the chemical wave is sensitive to the timing of pulse irradiation due to the rates of production of an activator and an inhibitor in the photochemical reaction.

  18. On some qualitative results for the solution to a Dirichlet problem in local generalized Morrey spaces

    NASA Astrophysics Data System (ADS)

    Scapellato, Andrea

    2017-01-01

    Aim of this study is to obtain an interior estimate for the solution of the Dirichlet problem for a linear elliptic partial differential equations having the coefficients of the principal part that belong to the Sarason class VMO of functions with vanishing mean oscillation. In order to obtain the desidered result we use some estimates for singular integral operators and commutators on Generalized Local Morrey Spaces.

  19. Local L∞-estimates, weak Harnack inequality, and stochastic continuity of solutions of SPDEs

    NASA Astrophysics Data System (ADS)

    Dareiotis, Konstantinos; Gerencsér, Máté

    2017-01-01

    We consider stochastic partial differential equations under minimal assumptions: the coefficients are merely bounded and measurable and satisfy the stochastic parabolicity condition. In particular, the diffusion term is allowed to be scaling-critical. We derive local supremum estimates with a stochastic adaptation of De Giorgi's iteration and establish a weak Harnack inequality for the solutions. The latter is then used to obtain pointwise almost sure continuity.

  20. [Search for a new rinsing solution for the local lysis of calcium-containing urinary calculi].

    PubMed

    Leskovar, P; Hropot, M; Wellnhofer, E

    1982-04-01

    Due to improved rinsing techniques local chemolitholysis is again becoming more important. Good result good results in the local chemolysis of phosphate calculi (calculi caused by remains of Struvit) with Renacidin and other rinsing solutions (Fam, Rossier, Gittes, Jacobs, Smith, Royle, Nemoy, Stamey) have led to a revival chemolitholysis (Alken) in the last 4--5 years, however only in the case of phosphate calculi, which account for 60--80%, cannot be dissolved by Renacidin, as is explicitly pointed out by the manufacturer. The experiments carried out by the group headed by Kallistratos and Timmermann in the 60's using rinsing solutions based on EDTA were discontinued, probably because of physiological reservations concerning the chemicals used and the long duration of treatment at physiologically tolerable concentrations and pH values. In order to extend the range of rinsing solutions to be tested, we tested new substances, including some which complex not only the anion (oxalate) but also the cation (Ca). Alternating treatment with oxalate binding and Ca binding rinsing solutions has been found to give particularly good results.

  1. Warped AdS 6 × S 2 in Type IIB supergravity I: local solutions

    NASA Astrophysics Data System (ADS)

    D'Hoker, Eric; Gutperle, Michael; Karch, Andreas; Uhlemann, Christoph F.

    2016-08-01

    We investigate the existence of solutions with 16 residual supersymmetries to Type IIB supergravity on a space-time of the formc AdS 6× S 2 warped over a two-dimensional Riemann surface Σ. The SO(2 , 5) × SO(3) isometry extends to invariance under the exceptional Lie superalgebra F (4). In the present paper, we construct the general Ansatz compatible with these symmetries, derive the corresponding reduced BPS equations, and obtain their complete local solution in terms of two locally holomorphic functions {A}_{± } on Σ, subject to certain positivity and regularity conditions. Globally, ( {A}+ , {A}- ) are allowed to be multiple-valued on Σ and be holomorphic sections of a holomorphic bundle over Σ with structure group contained in SU(1,1)× C . Globally regular solutions are expected to provide the near-horizon geometry of ( p, q) 5-brane and 7-brane webs which are holographic duals to five-dimensional conformal field theories. A preliminary analysis of the positivity and regularity conditions will be presented here, leaving the construction of globally regular solutions to a subsequent paper.

  2. Pulsed plane wave analytic solutions for generic shapes and the validation of Maxwell's equations solvers

    NASA Technical Reports Server (NTRS)

    Yarrow, Maurice; Vastano, John A.; Lomax, Harvard

    1992-01-01

    Generic shapes are subjected to pulsed plane waves of arbitrary shape. The resulting scattered electromagnetic fields are determined analytically. These fields are then computed efficiently at field locations for which numerically determined EM fields are required. Of particular interest are the pulsed waveform shapes typically utilized by radar systems. The results can be used to validate the accuracy of finite difference time domain Maxwell's equations solvers. A two-dimensional solver which is second- and fourth-order accurate in space and fourth-order accurate in time is examined. Dielectric media properties are modeled by a ramping technique which simplifies the associated gridding of body shapes. The attributes of the ramping technique are evaluated by comparison with the analytic solutions.

  3. Global existence and exponential decay of the solution for a viscoelastic wave equation with a delay

    NASA Astrophysics Data System (ADS)

    Dai, Qiuyi; Yang, Zhifeng

    2014-10-01

    In this paper, we consider initial-boundary value problem of viscoelastic wave equation with a delay term in the interior feedback. Namely, we study the following equation together with initial-boundary conditions of Dirichlet type in Ω × (0, + ∞) and prove that for arbitrary real numbers μ 1 and μ 2, the above-mentioned problem has a unique global solution under suitable assumptions on the kernel g. This improve the results of the previous literature such as Nicaise and Pignotti (SIAM J. Control Optim 45:1561-1585, 2006) and Kirane and Said-Houari (Z. Angew. Math. Phys. 62:1065-1082, 2011) by removing the restriction imposed on μ 1 and μ 2. Furthermore, we also get an exponential decay results for the energy of the concerned problem in the case μ 1 = 0 which solves an open problem proposed by Kirane and Said-Houari (Z. Angew. Math. Phys. 62:1065-1082, 2011).

  4. Experimental Validation of a Branched Solution Model for Magnetosonic Ionization Waves in Plasma Accelerators

    NASA Astrophysics Data System (ADS)

    Underwood, Thomas; Loebner, Keith; Cappelli, Mark

    2015-11-01

    Detailed measurements of the thermodynamic and electrodynamic plasma state variables within the plume of a pulsed plasma accelerator are presented. A quadruple Langmuir probe operating in current-saturation mode is used to obtain time resolved measurements of the plasma density, temperature, potential, and velocity along the central axis of the accelerator. This data is used in conjunction with a fast-framing, intensified CCD camera to develop and validate a model predicting the existence of two distinct types of ionization waves corresponding to the upper and lower solution branches of the Hugoniot curve. A deviation of less than 8% is observed between the quasi-steady, one-dimensional theoretical model and the experimentally measured plume velocity. This work is supported by the U.S. Department of Energy Stewardship Science Academic Program in addition to the National Defense Science Engineering Graduate Fellowship.

  5. Single-scattering parabolic equation solutions for elastic media propagation, including Rayleigh waves.

    PubMed

    Metzler, Adam M; Siegmann, William L; Collins, Michael D

    2012-02-01

    The parabolic equation method with a single-scattering correction allows for accurate modeling of range-dependent environments in elastic layered media. For problems with large contrasts, accuracy and efficiency are gained by subdividing vertical interfaces into a series of two or more single-scattering problems. This approach generates several computational parameters, such as the number of interface slices, an iteration convergence parameter τ, and the number of iterations n for convergence. Using a narrow-angle approximation, the choices of n=1 and τ=2 give accurate solutions. Analogous results from the narrow-angle approximation extend to environments with larger variations when slices are used as needed at vertical interfaces. The approach is applied to a generic ocean waveguide that includes the generation of a Rayleigh interface wave. Results are presented in both frequency and time domains.

  6. Class of solitary wave solutions of the one-dimensional Gross-Pitaevskii equation.

    PubMed

    Atre, Rajneesh; Panigrahi, Prasanta K; Agarwal, G S

    2006-05-01

    We present a large family of exact solitary wave solutions of the one-dimensional Gross-Pitaevskii equation, with time-varying scattering length and gain or loss, in both expulsive and regular parabolic confinement regimes. The consistency condition governing the soliton profiles is shown to map onto a linear Schrödinger eigenvalue problem, thereby enabling one to find analytically the effect of a wide variety of temporal variations in the control parameters, which are experimentally realizable. Corresponding to each solvable quantum mechanical system, one can identify a soliton configuration. These include soliton trains in close analogy to experimental observations of Streckeret al. [Nature (London) 417, 150 (2002)], spatiotemporal dynamics, solitons undergoing rapid amplification, collapse and revival of condensates, and analytical expression of two-soliton bound states, to name a few.

  7. Class of solitary wave solutions of the one-dimensional Gross-Pitaevskii equation

    SciTech Connect

    Atre, Rajneesh; Panigrahi, Prasanta K.; Agarwal, G. S.

    2006-05-15

    We present a large family of exact solitary wave solutions of the one-dimensional Gross-Pitaevskii equation, with time-varying scattering length and gain or loss, in both expulsive and regular parabolic confinement regimes. The consistency condition governing the soliton profiles is shown to map onto a linear Schroedinger eigenvalue problem, thereby enabling one to find analytically the effect of a wide variety of temporal variations in the control parameters, which are experimentally realizable. Corresponding to each solvable quantum mechanical system, one can identify a soliton configuration. These include soliton trains in close analogy to experimental observations of Strecker et al. [Nature (London) 417, 150 (2002)], spatiotemporal dynamics, solitons undergoing rapid amplification, collapse and revival of condensates, and analytical expression of two-soliton bound states, to name a few.

  8. An exact solution to the relativistic equation of motion of a charged particle driven by a linearly polarized electromagnetic wave

    NASA Technical Reports Server (NTRS)

    Shebalin, John V.

    1988-01-01

    An exact analytic solution is found for a basic electromagnetic wave-charged particle interaction by solving the nonlinear equations of motion. The particle position, velocity, and corresponding time are found to be explicit functions of the total phase of the wave. Particle position and velocity are thus implicit functions of time. Applications include describing the motion of a free electron driven by an intense laser beam..

  9. Incompressible SPH method based on Rankine source solution for violent water wave simulation

    NASA Astrophysics Data System (ADS)

    Zheng, X.; Ma, Q. W.; Duan, W. Y.

    2014-11-01

    With wide applications, the smoothed particle hydrodynamics method (abbreviated as SPH) has become an important numerical tool for solving complex flows, in particular those with a rapidly moving free surface. For such problems, the incompressible Smoothed Particle Hydrodynamics (ISPH) has been shown to yield better and more stable pressure time histories than the traditional SPH by many papers in literature. However, the existing ISPH method directly approximates the second order derivatives of the functions to be solved by using the Poisson equation. The order of accuracy of the method becomes low, especially when particles are distributed in a disorderly manner, which generally happens for modelling violent water waves. This paper introduces a new formulation using the Rankine source solution. In the new approach to the ISPH, the Poisson equation is first transformed into another form that does not include any derivative of the functions to be solved, and as a result, does not need to numerically approximate derivatives. The advantage of the new approach without need of numerical approximation of derivatives is obvious, potentially leading to a more robust numerical method. The newly formulated method is tested by simulating various water waves, and its convergent behaviours are numerically studied in this paper. Its results are compared with experimental data in some cases and reasonably good agreement is achieved. More importantly, numerical results clearly show that the newly developed method does need less number of particles and so less computational costs to achieve the similar level of accuracy, or to produce more accurate results with the same number of particles compared with the traditional SPH and existing ISPH when it is applied to modelling water waves.

  10. Analytical solutions for the seismic response of underground structures under SH wave propagation

    SciTech Connect

    Smerzini, C.; Aviles, J.; Sanchez-Sesma, F. J.

    2008-07-08

    A theoretical approach is presented to study the antiplane seismic response of underground structures subjected to the incidence of plane waves. The structure is assumed to be a circular inclusion embedded in a homogenous, isotropic and linear visco-elastic halfspace and its mathematical formulation is approached through the theory of multiple scattering and diffraction. The inclusion may consist either of a cavity, with or without a ring-shaped boundary, or it may be filled in with a linear-elastic material, without loss of generality. The seismic response of the inclusion and its influence on surface ground motions are analyzed in both frequency and time domains. The dependence of the transfer function amplitudes on several parameters, such as the angle of incident SH waves, the frequency content of the excitation, the impedance contrast between the inclusion and the surrounding medium and the position along the ground surface, is underlined. Considering the lack of analytical solutions for quantifying the modification of ground motions induced by subterranean inhomogeneities, the results of this study can be used, on one side, as benchmark for both geophysical investigations and numerical dynamic soil-structure interaction studies, and, on the other side, to support the formulation of simplified approaches and/or formulas for the seismic design and assessment of underground structures.

  11. Solitary wave solutions and modulational instability in a system of coupled complex Newell-Segel-Whitehead equations

    NASA Astrophysics Data System (ADS)

    Kelkar, Asawari; Yomba, Emmanuel; Djellouli, Rabia

    2016-12-01

    By virtue of the modulational instability (MI) and phase amplitude ansatz approach, a system of coupled complex Newell-Segel-Whitehead equations (NSWEs), which describes isotropic systems near a subcritical oscillatory instability, is investigated. The constraints that allow the MI procedure to transform the system under consideration into a study of the roots of a polynomial equation of the fourth degree are obtained. A number of examples are analyzed graphically, to overcome the complexity of the dispersion relation and its dependence on many parameters. The existence of a variety of MI gain spectrum is observed. The influence of the cubic-quintic nonlinearity and the magnitude of the plane wave solutions of the system on the MI are also analyzed. Various novel solitary-wave solutions of the system, such as bright-bright, dark-dark, and dark-bright wave solutions, are analytically obtained using direct approach under some constraint conditions.

  12. New topic of supercritical fluids: Local activity coefficients of supercritical solvent and cosolvent around solute

    NASA Astrophysics Data System (ADS)

    Hou, Minqiang; Zhang, Xiaogang; Han, Buxing; Song, Jiyuan; Liu, Gang; Zhang, Zhaofu; Zhang, Jianling

    2008-03-01

    The study of inhomogeneity in supercritical fluids (SCFs) is of great importance. In this work, we propose the concept of local activity coefficients in supercritical (SC) solutions, which link thermodynamics and inhomogeneity in SC systems. The local activity coefficients of CO2+acetonitrile+phenol blue and CO2+aceticacid+phenol blue systems are investigated at 308.15K in critical region and outside critical region. To do this, the local compositions of CO2+acetonitrile and CO2+acetic acid mixed solvents around phenol blue are first estimated using UV-visible spectroscopy. Then it is considered that there exist bulk phase and local phase around phenol blue in the systems. The activity coefficients of CO2 and the cosolvents (acetonitrile or acetic acid) in bulk phase are calculated using Peng-Robinson equation of state. The local activity coefficients of CO2 and the cosolvents are then calculated on the basis of thermodynamic principles. It is demonstrated that in the critical region the local activity coefficients differ from bulk activity coefficients significantly and are sensitive to pressure. This can explain many unusual phenomena in SC systems in critical region thermodynamically.

  13. New topic of supercritical fluids: local activity coefficients of supercritical solvent and cosolvent around solute.

    PubMed

    Hou, Minqiang; Zhang, Xiaogang; Han, Buxing; Song, Jiyuan; Liu, Gang; Zhang, Zhaofu; Zhang, Jianling

    2008-03-14

    The study of inhomogeneity in supercritical fluids (SCFs) is of great importance. In this work, we propose the concept of local activity coefficients in supercritical (SC) solutions, which link thermodynamics and inhomogeneity in SC systems. The local activity coefficients of CO(2)+acetonitrile+phenol blue and CO(2)+acetic acid+phenol blue systems are investigated at 308.15 K in critical region and outside critical region. To do this, the local compositions of CO(2)+acetonitrile and CO(2)+acetic acid mixed solvents around phenol blue are first estimated using UV-visible spectroscopy. Then it is considered that there exist bulk phase and local phase around phenol blue in the systems. The activity coefficients of CO(2) and the cosolvents (acetonitrile or acetic acid) in bulk phase are calculated using Peng-Robinson equation of state. The local activity coefficients of CO(2) and the cosolvents are then calculated on the basis of thermodynamic principles. It is demonstrated that in the critical region the local activity coefficients differ from bulk activity coefficients significantly and are sensitive to pressure. This can explain many unusual phenomena in SC systems in critical region thermodynamically.

  14. Overlapping local/global iteration framework for whole-core transport solution

    SciTech Connect

    Cho, N. Z.; Yuk, S.; Yoo, H. J.; Yun, S.

    2012-07-01

    In current practice of reactor design analysis, whole-core diffusion nodal method is used in which nodal parameters are provided by single-assembly lattice physics calculation with net current zero boundary condition. Thus, the whole-core solution is not transport, because the inter-assembly transport effect is not incorporated. In this paper, the overlapping local/global iteration framework is described that removes the limitation of the current method. It consists of two-level iterative computations: half-node overlapping local problems embedded in a global problem. The local problem can employ fine-group deterministic or continuous-energy stochastic (Monte Carlo) transport methods, while the global problem is an equivalent coarse-group transport model based on p-CMFD methodology. The method is tested on several highly heterogeneous multi-slab problems with encouraging results. (authors)

  15. Localization of small arms fire using acoustic measurements of muzzle blast and/or ballistic shock wave arrivals.

    PubMed

    Lo, Kam W; Ferguson, Brian G

    2012-11-01

    The accurate localization of small arms fire using fixed acoustic sensors is considered. First, the conventional wavefront-curvature passive ranging method, which requires only differential time-of-arrival (DTOA) measurements of the muzzle blast wave to estimate the source position, is modified to account for sensor positions that are not strictly collinear (bowed array). Second, an existing single-sensor-node ballistic model-based localization method, which requires both DTOA and differential angle-of-arrival (DAOA) measurements of the muzzle blast wave and ballistic shock wave, is improved by replacing the basic external ballistics model (which describes the bullet's deceleration along its trajectory) with a more rigorous model and replacing the look-up table ranging procedure with a nonlinear (or polynomial) equation-based ranging procedure. Third, a new multiple-sensor-node ballistic model-based localization method, which requires only DTOA measurements of the ballistic shock wave to localize the point of fire, is formulated. The first method is applicable to situations when only the muzzle blast wave is received, whereas the third method applies when only the ballistic shock wave is received. The effectiveness of each of these methods is verified using an extensive set of real data recorded during a 7 day field experiment.

  16. The influence of small additions of diethylenetriamine on the detonation waves stability for nitromethane/acetone solution

    NASA Astrophysics Data System (ADS)

    Mochalova, V.; Utkin, A.

    2014-05-01

    Instability of detonation front in the nitromethane/acetone (NM/A) solution was observed in our previous work: at 10% of acetone the amplitude of heterogeneities was about 20 microns and at 20% of acetone this size was 50 microns. It is known that small additions of diethylenetriamine (DETA) considerably increase the initial rate of chemical reaction in detonation waves for NM. It was expected that DETA would influence the stability of detonation waves in the NM/A solution too. To investigate this phenomenon the laser interferometer VISAR was used for the recording of particle velocity profiles in detonation waves for NM/A. It was found that at the addition of 0.5% DETA to NM/A 90/10 the oscillations in the velocity profile decreased several times over. At the addition of 1% DETA the profile is smooth, i.e. the heterogeneities disappear and detonation wave becomes steady-state. In NM/A 80/20 at the addition of 5% DETA the heterogeneities size is reduced by the order. The increase of detonation wave velocity of NM/A grater than 1% was observed at small concentrations of DETA. Thus it was found that small additions of DETA to the NM/A solution with an unstable detonation front resulted not only in the decrease of heterogeneities size but in their disappearance and stabilization of detonation waves.

  17. A family of exact travelling wave solutions of (2+1)-dimensional KdV4 equation

    NASA Astrophysics Data System (ADS)

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

    2017-01-01

    Nonlinear evolution equations have a wide range of applications in science and engineering. In recent years many power-ful methods to construct exact solutions of nonlinear evolution equations. In this paper we present (1/G' ) expansion method, extended simplest equation method (SEM) and the modification of the truncated expansion (MTEM) method for (2 + 1) dimensional KdV4 equation to establish new exact solutions. So periodic and hyperbolic function solutions are obtained for this equation. The effi-ciency of the these methods for finding travelling wave solutions of the high order nonlinear evolution equations is demonstrated.

  18. A note on free and forced Rossby wave solutions: The case of a straight coast and a channel

    NASA Astrophysics Data System (ADS)

    Graef, Federico

    2017-03-01

    The free Rossby wave (RW) solutions in an ocean with a straight coast when the offshore wavenumber of incident (l1) and reflected (l2) wave are equal or complex are discussed. If l1 = l2 the energy streams along the coast and a uniformly valid solution cannot be found; if l1,2 are complex it yields the sum of an exponentially decaying and growing (away from the coast) Rossby wave. The channel does not admit these solutions as free modes. If the wavenumber vectors of the RWs are perpendicular to the coast, the boundary condition of no normal flow is trivially satisfied and the value of the streamfunction does not need to vanish at the coast. A solution that satisfies Kelvin's theorem of time-independent circulation at the coast is proposed. The forced RW solutions when the ocean's forcing is a single Fourier component are studied. If the forcing is resonant, i.e. a free Rossby wave (RW), the linear response will depend critically on whether the wave carries energy perpendicular to the channel or not. In the first case, the amplitude of the response is linear in the direction normal to the channel, y, and in the second it has a parabolic profile in y. Examples of these solutions are shown for channels with parameters resembling the Mozambique Channel, the Tasman Sea, the Denmark Strait and the English Channel. The solutions for the single coast are unbounded, except when the forcing is a RW trapped against the coast. If the forcing is non-resonant, exponentially decaying or trapped RWs could be excited in the coast and both the exponentially ;decaying; and exponentially ;growing; RW could be excited in the channel.

  19. On the extension of solutions of the real to complex KdV equation and a mechanism for the construction of rogue waves

    NASA Astrophysics Data System (ADS)

    Abdel-Gawad, H. I.; Tantawy, M.; Abo Elkhair, R. E.

    2016-07-01

    Rogue waves are more precisely defined as waves whose height is more than twice the significant wave height. This remarkable height was measured (by Draupner in 1995). Thus, the need for constructing a mechanism for the rogue waves is of great utility. This motivated us to suggest a mechanism, in this work, that rogue waves may be constructed via nonlinear interactions of solitons and periodic waves. This suggestion is consolidated here, in an example, by studying the behavior of solutions of the complex (KdV). This is done here by the extending the solutions of its real version.

  20. Spreading speed and travelling wave solutions of a partially sedentary population

    NASA Astrophysics Data System (ADS)

    Volkov, Darko; Lui, Roger

    2007-12-01

    In this paper, we extend the population genetics model of Weinberger (1978, Asymptotic behavior of a model in population genetics. Nonlinear Partial Differential Equations and Applications (J. Chadam ed.). Lecture Notes in Mathematics, vol. 648. New York: Springer, pp. 47-98.) to the case where a fraction of the population does not migrate after the selection process. Mathematically, we study the asymptotic behaviour of solutions to the recursion un+1 = Qg[un], where ... In the above definition of Qg, K is a probability density function and f behaves qualitatively like the Beverton-Holt function. Under some appropriate conditions on K and f, we show that for each unit vector{xi} [isin] Rd, there exists a c*g({xi}) which has an explicit formula and is the spreading speed of Qg in the direction{xi} . We also show that for each c [≥] c*g({xi}), there exists a travelling wave solution in the direction{xi} which is continuous if gf '(0) [≤] 1.

  1. Tunable compression of template banks for fast gravitational-wave detection and localization

    NASA Astrophysics Data System (ADS)

    Chua, Alvin J. K.; Gair, Jonathan R.

    2016-06-01

    One strategy for reducing the online computational cost of matched-filter searches for gravitational waves is to introduce a compressed basis for the waveform template bank in a grid-based search. In this paper, we propose and investigate several tunable compression schemes for a general template bank. Through offline compression, such schemes are shown to yield faster detection and localization of signals, along with moderately improved sensitivity and accuracy over coarsened banks at the same level of computational cost. This is potentially useful for any search involving template banks, and especially in the analysis of data from future space-based detectors such as eLISA, for which online grid searches are difficult due to the long-duration waveforms and large parameter spaces.

  2. Master equation for a chemical wave front with perturbation of local equilibrium.

    PubMed

    Dziekan, P; Lemarchand, A; Nowakowski, B

    2011-08-28

    In order to develop a stochastic description of gaseous reaction-diffusion systems, which includes a reaction-induced departure from local equilibrium, we derive a modified expression of the master equation from analytical calculations based on the Boltzmann equation. We apply the method to a chemical wave front of Fisher-Kolmogorov-Petrovsky-Piskunov type, whose propagation speed is known to be sensitive to small perturbations. The results of the modified master equation are compared successfully with microscopic simulations of the particle dynamics using the direct simulation Monte Carlo method. The modified master equation constitutes an efficient tool at the mesoscopic scale, which incorporates the nonequilibrium effect without need of determining the particle velocity distribution function.

  3. Prospects for Gravitational Wave Searches for Core-Collapse Supernovae within the Local Universe

    NASA Astrophysics Data System (ADS)

    Gill, Kiranjyot; Branchesi, Marica; Zanolin, Michele; Szczepanczyk, Marek; LIGO Collaboration

    2017-01-01

    We present an updated estimate of the intrinsic (vs observed) core collapse supernovae (CCSNe) rate within 20 Mpc from Earth, which is roughly the largest distance of interest for the searches for gravitational waves (GWs) from CCSNe with laser interferometers. Recognizing that CCSN galaxy host models are morphologically dependent, we separate the galaxies within 20 Mpc into the local field and Virgo cluster and account for biases, such as galactic plane absorption. The improved estimation of the CCSNe rate within 20 Mpc is 430 +/- 21 CCSNe Century -1 Mpc-1. We also discuss the Feldman-Cousins and GRB methodologies for detecting CCSNe when there are multiple CCSNe optical triggers, as predicted for advanced LIGO data science runs. Illustrative examples of the sensitivity improvement with respect to the single-event current approaches are provided for rapidly rotating semi-analytical models of GW emissions and real (publicly released) LIGO data.

  4. Crustal shear-wave splitting from local earthquakes in the Hengill triple junction, southwest Iceland

    USGS Publications Warehouse

    Evans, J.R.; Foulger, G.R.; Julian, B.R.; Miller, A.D.

    1996-01-01

    The Hengill region in SW Iceland is an unstable ridge-ridge-transform triple junction between an active and a waning segment of the mid-Atlantic spreading center and a transform that is transgressing southward. The triple junction contains active and extinct spreading segments and a widespread geothermal area. We evaluated shear-wave birefringence for locally recorded upper-crustal earthquakes using an array of 30 three-component digital seismographs. Fast-polarization directions, ??, are mostly NE to NNE, subparallel to the spreading axis and probably caused by fissures and microcracks related to spreading. However, there is significant variability in ?? throughout the array. The lag from fast to slow S is not proportional to earthquake depth (ray length), being scattered at all depths. The average wave-speed difference between qS1 and qS2 in the upper 2-5 km of the crust is 2-5%. Our results suggest considerable heterogeneity or strong S scattering.

  5. Millimeter Wave Detection of Localized Anomalies in the Space Shuttle External Fuel Tank Insulating Foam

    NASA Technical Reports Server (NTRS)

    Kharkovsky, S.; Case, J. T.; Abou-Khousa, M. A.; Zoughi, R.; Hepburn, F.

    2006-01-01

    The Space Shuttle Columbia's catastrophic accident emphasizes the growing need for developing and applying effective, robust and life-cycle oriented nondestructive testing (NDT) methods for inspecting the shuttle external fuel tank spray on foam insulation (SOFI). Millimeter wave NDT techniques were one of the methods chosen for evaluating their potential for inspecting these structures. Several panels with embedded anomalies (mainly voids) were produced and tested for this purpose. Near-field and far-field millimeter wave NDT methods were used for producing images of the anomalies in these panels. This paper presents the results of an investigation for the purpose of detecting localized anomalies in several SOFI panels. To this end, reflectometers at a relatively wide range of frequencies (Ka-band (26.5 - 40 GHz) to W-band (75 - 110 GHz)) and utilizing different types of radiators were employed. The resulting raw images revealed a significant amount of information about the interior of these panels. However, using simple image processing techniques the results were improved in particular as it relate s to detecting the smaller anomalies. This paper presents the results of this investigation and a discussion of these results.

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

    NASA Astrophysics Data System (ADS)

    Yu, Fajun

    2017-02-01

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

  7. An alternative local collocation strategy for high-convergence meshless PDE solutions, using radial basis functions

    NASA Astrophysics Data System (ADS)

    Stevens, D.; Power, H.; Meng, C. Y.; Howard, D.; Cliffe, K. A.

    2013-12-01

    This work proposes an alternative decomposition for local scalable meshless RBF collocation. The proposed method operates on a dataset of scattered nodes that are placed within the solution domain and on the solution boundary, forming a small RBF collocation system around each internal node. Unlike other meshless local RBF formulations that are based on a generalised finite difference (RBF-FD) principle, in the proposed "finite collocation" method the solution of the PDE is driven entirely by collocation of PDE governing and boundary operators within the local systems. A sparse global collocation system is obtained not by enforcing the PDE governing operator, but by assembling the value of the field variable in terms of the field value at neighbouring nodes. In analogy to full-domain RBF collocation systems, communication between stencils occurs only over the stencil periphery, allowing the PDE governing operator to be collocated in an uninterrupted manner within the stencil interior. The local collocation of the PDE governing operator allows the method to operate on centred stencils in the presence of strong convective fields; the reconstruction weights assigned to nodes in the stencils being automatically adjusted to represent the flow of information as dictated by the problem physics. This "implicit upwinding" effect mitigates the need for ad-hoc upwinding stencils in convective dominant problems. Boundary conditions are also enforced within the local collocation systems, allowing arbitrary boundary operators to be imposed naturally within the solution construction. The performance of the method is assessed using a large number of numerical examples with two steady PDEs; the convection-diffusion equation, and the Lamé-Navier equations for linear elasticity. The method exhibits high-order convergence in each case tested (greater than sixth order), and the use of centred stencils is demonstrated for convective-dominant problems. In the case of linear elasticity

  8. Least squares collocation applied to local gravimetric solutions from satellite gravity gradiometry data

    NASA Technical Reports Server (NTRS)

    Robbins, J. W.

    1985-01-01

    An autonomous spaceborne gravity gradiometer mission is being considered as a post Geopotential Research Mission project. The introduction of satellite diometry data to geodesy is expected to improve solid earth gravity models. The possibility of utilizing gradiometer data for the determination of pertinent gravimetric quantities on a local basis is explored. The analytical technique of least squares collocation is investigated for its usefulness in local solutions of this type. It is assumed, in the error analysis, that the vertical gravity gradient component of the gradient tensor is used as the raw data signal from which the corresponding reference gradients are removed to create the centered observations required in the collocation solution. The reference gradients are computed from a high degree and order geopotential model. The solution can be made in terms of mean or point gravity anomalies, height anomalies, or other useful gravimetric quantities depending on the choice of covariance types. Selected for this study were 30 x 30 foot mean gravity and height anomalies. Existing software and new software are utilized to implement the collocation technique. It was determined that satellite gradiometry data at an altitude of 200 km can be used successfully for the determination of 30 x 30 foot mean gravity anomalies to an accuracy of 9.2 mgal from this algorithm. It is shown that the resulting accuracy estimates are sensitive to gravity model coefficient uncertainties, data reduction assumptions and satellite mission parameters.

  9. Local structure in the disordered solid solution of cis- and trans-perinones.

    PubMed

    Teteruk, Jaroslav L; Glinnemann, Jürgen; Heyse, Winfried; Johansson, Kristoffer E; van de Streek, Jacco; Schmidt, Martin U

    2016-06-01

    The cis- and trans-isomers of the polycyclic aromatic compound perinone, C26H12N4O2, form a solid solution (Vat Red 14). This solid solution is isotypic to the crystal structures of cis-perinone (Pigment Red 194) and trans-perinone (Pigment Orange 34) and exhibits a combined positional and orientational disorder: In the crystal, each molecular position is occupied by either a cis- or trans-perinone molecule, both of which have two possible molecular orientations. The structure of cis-perinone exhibits a twofold orientational disorder, whereas the structure of trans-perinone is ordered. The crystal structure of the solid solution was determined by single-crystal X-ray analysis. Extensive lattice-energy minimizations with force-field and DFT-D methods were carried out on combinatorially complete sets of ordered models. For the disordered systems, local structures were calculated, including preferred local arrangements, ordering lengths, and probabilities for the arrangement of neighbouring molecules. The superposition of the atomic positions of all energetically favourable calculated models corresponds well with the experimentally determined crystal structures, explaining not only the atomic positions, but also the site occupancies and anisotropic displacement parameters.

  10. Application of Local Time Dependent Ion Composition to Observations, Modeling, and Effects of Electromagnetic Ion Cyclotron Waves

    NASA Astrophysics Data System (ADS)

    Lee, J. H.; Angelopoulos, V.; Chen, L.; Thorne, R. M.

    2014-12-01

    Numerous global magnetospheric studies on electromagnetic ion cyclotron (EMIC) waves have revealed the typical wave properties observed throughout the Earth's magnetosphere. The observed trends in the wave properties at various geocentric distances and local time sectors, although in general agreement, elude satisfactory explanation without further details on the ambient plasma properties, the low-energy (few to ~100 eV) ions in particular. Recent studies also described techniques to deduce the presence and properties of low-energy ions and the application of such a technique to THEMIS (Time History of Events and Macroscale Interactions during Substorms) data has revealed the typical low-energy ion compositional properties throughout the Earth's magnetosphere. Motivated by the recent work on EMIC waves and low-energy ion composition, we analyze typical wave cases observed at each local time sector by the THEMIS satellites and apply the composition techniques or the statistical low-energy ion composition data to constrain the low-energy components in modeling of each wave case in the context of linear hot plasma theory. We find that the observed waves are modeled well with hot plasma theory and both are fully consistent with the composition of the ambient plasma. Our results suggest that combined ion composition and wave measurements are critical for further assessment of the effects of the waves on energetic particles. In the cases we report on here, we find the waves could resonantly interact with electrons at energies in excess of 2 MeV and therefore do not have an effect on the dominant trapped electron population.

  11. Global paths of time-periodic solutions of the Benjamin-Ono equation connecting arbitrary traveling waves

    SciTech Connect

    Ambrose, David M.; Wilkening, Jon

    2008-12-11

    We classify all bifurcations from traveling waves to non-trivial time-periodic solutions of the Benjamin-Ono equation that are predicted by linearization. We use a spectrally accurate numerical continuation method to study several paths of non-trivial solutions beyond the realm of linear theory. These paths are found to either re-connect with a different traveling wave or to blow up. In the latter case, as the bifurcation parameter approaches a critical value, the amplitude of the initial condition grows without bound and the period approaches zero. We propose a conjecture that gives the mapping from one bifurcation to its counterpart on the other side of the path of non-trivial solutions. By experimentation with data fitting, we identify the form of the exact solutions on the path connecting two traveling waves, which represents the Fourier coefficients of the solution as power sums of a finite number of particle positions whose elementary symmetric functions execute simple orbits in the complex plane (circles or epicycles). We then solve a system of algebraic equations to express the unknown constants in the new representation in terms of the mean, a spatial phase, a temporal phase, four integers (enumerating the bifurcation at each end of the path) and one additional bifurcation parameter. We also find examples of interior bifurcations from these paths of already non-trivial solutions, but we do not attempt to analyze their algebraic structure.

  12. Climate downscaling: Local mean sea-level rise, surge and wave modelling

    NASA Astrophysics Data System (ADS)

    Wolf, J.; Lowe, J.; Howard, T.

    2012-04-01

    The investigation of future climate impacts at the coast requires sufficiently detailed projections for the nearshore waves and sea levels in both the present day and a future climate scenario, to provide an offshore boundary condition. Here we discuss the future changes in surge and wave climate forced by winds and pressures from a version of the Met Office Hadley Centre Climate model, for various greenhouse gas emission scenarios and for various climate model parameter choices. The local spatial variation in mean sea level is also taken into account, incorporating deviations from global mean sea level change caused by regional variations in ocean density and circulation. Some parts of the UK are still subject to glacial isostatic readjustment after the last ice age, counter-acting sea level rise, although this will be overwhelmed by the projected effects of sea level rise due to global warming in the 21st century, for most future emission scenarios. Model downscaling from the global coupled atmosphere-ocean model using a regional climate model is needed to provide more realistic and detailed wind simulations over the NW European continental shelf. There is large uncertainty in projected changes in storminess for the NE Atlantic region, with different climate models providing conflicting results for the future. Results from this study show that large increases in mean sea level (even up to 5 metres) have very little effect on the dynamics of extreme surge events, the primary effect being on the speed of propagation of tide and surge (Howard et al., 2010). Increasing storminess is expected to increase surge heights but more direct effects can be attributed directly to increased mean sea level. Based on the wave model results, seasonal mean and annual maximum wave heights are generally expected to increase to the SW of the UK, reduce to the north of the UK and experience little change in the southern North Sea or eastern Irish Sea. This pattern is consistent with a

  13. Global classical solutions of the Vlasov-Fokker-Planck equation with local alignment forces

    NASA Astrophysics Data System (ADS)

    Choi, Young-Pil

    2016-07-01

    In this paper, we are concerned with the global well-posedness and time-asymptotic decay of the Vlasov-Fokker-Planck equation with local alignment forces. The equation can be formally derived from an agent-based model for self-organized dynamics called the Motsch-Tadmor model with noises. We present the global existence and uniqueness of classical solutions to the equation around the global Maxwellian in the whole space. For the large-time behavior, we show the algebraic decay rate of solutions towards the equilibrium under suitable assumptions on the initial data. We also remark that the rate of convergence is exponential when the spatial domain is periodic. The main methods used in this paper are the classical energy estimates combined with hyperbolic-parabolic dissipation arguments.

  14. Local toxicity of benzalkonium chloride in ophthalmic solutions following repeated applications.

    PubMed

    Okahara, Akihiko; Kawazu, Kouichi

    2013-01-01

    We performed repeated toxicity studies of benzalkonium chloride (BAK)-containing vehicles of ophthalmic solutions in monkeys and rabbits to assess the local toxicity of BAK after repeated applications on the ocular surface. Local toxicity of BAK was evaluated by toxicity studies in which a 0.01% BAK-containing vehicle was applied twice/day for 52 weeks, 4 times/day for 39 weeks, or 6 times/day for 13 weeks, or in which a 0.005% BAK-containing vehicle was applied 6 times/day for 52 weeks or twice/day for 4 weeks in monkeys. Local toxicity of BAK was also evaluated where a 0.01% BAK-containing vehicle was applied 6 times/day for 6 weeks, or a 0.005% BAK-containing vehicle was applied twice/day for 39 weeks or 8 times/day for 4 weeks in rabbits. These doses were chosen because BAK is generally used at concentrations up to 0.01% in ophthalmic solutions. The BAK-containing vehicle did not cause ophthalmological changes suggestive of irritation, allergy, or corneal damage. We also did not observe any histopathological changes in the eyeball, eyelid, lacrimal gland, and nasal cavity, with repeated applications of BAK for up to 52 weeks, up to 8 times/day, or at concentrations up to 0.01%, in monkeys and rabbits. Our results suggest that BAK in concentrations up to 0.01% in ophthalmic solution is non-toxic to the eyeball, its accessory organs, and the nasal cavity after long repeated applications.

  15. Estimation of seismic wave velocity at seafloor surface and sound source localization based on transmitted wave observation with an ocean bottom seismometer offshore of Kamaishi, Japan

    NASA Astrophysics Data System (ADS)

    Iwase, Ryoichi

    2016-07-01

    An in situ method of estimating the seismic wave velocity at the seafloor surface by observing the particle motion of a wave transmitted into the sediment is presented; this method uses a sound source whose location is known. Conversely, a sound source localization method using the obtained seismic velocities and involving particle motion observation is also presented. Although this method is applicable only when the sound source exists within the critical incidence angle range, it is expected to contribute to the tracing of vocalizing baleen whales, which are unknown around Japanese waters.

  16. The local properties of ocean surface waves by the phase-time method

    NASA Technical Reports Server (NTRS)

    Huang, Norden E.; Long, Steven R.; Tung, Chi-Chao; Donelan, Mark A.; Yuan, Yeli; Lai, Ronald J.

    1992-01-01

    A new approach using phase information to view and study the properties of frequency modulation, wave group structures, and wave breaking is presented. The method is applied to ocean wave time series data and a new type of wave group (containing the large 'rogue' waves) is identified. The method also has the capability of broad applications in the analysis of time series data in general.

  17. More than just an eyesore: local insights and solutions on vacant land and urban health.

    PubMed

    Garvin, Eugenia; Branas, Charles; Keddem, Shimrit; Sellman, Jeffrey; Cannuscio, Carolyn

    2013-06-01

    Vacant land is a significant economic problem for many cities, but also may affect the health and safety of residents. In order for community-based solutions to vacant land to be accepted by target populations, community members should be engaged in identifying local health impacts and generating solutions. We conducted 50 in-depth semi-structured interviews with people living in Philadelphia, Pennsylvania, a city with high vacancy, about the impact of vacant land on community and individual health and safety, as well as ideas for solutions to vacant land. Participants described a neighborhood physical environment dominated by decaying abandoned homes and overgrown vacant lots which affected community well-being, physical health, and mental health. Vacant land was thought to affect community well-being by overshadowing positive aspects of the community, contributing to fractures between neighbors, attracting crime, and making residents fearful. Vacant land was described as impacting physical health through injury, the buildup of trash, and attraction of rodents, as well as mental health through anxiety and stigma. Participants had several ideas for solutions to vacant land in their community, including transformation of vacant lots into small park spaces for the elderly and playgrounds for youth, and the use of abandoned homes for subsidized housing and homeless shelters. A few participants took pride in maintaining vacant lots on their block, and others expressed interest in performing maintenance but lacked the resources to do so. Public health researchers and practitioners, and urban planners should engage local residents in the design and implementation of vacant land strategies. Furthermore, municipalities should ensure that the health and safety impact of vacant land helps drive policy decisions around vacant land.

  18. Local, solvation pressures and conformational changes in ethylenediamine aqueous solutions probed using Raman spectroscopy.

    PubMed

    Cáceres, Mercedes; Lobato, Alvaro; Mendoza, Nubia J; Bonales, Laura J; Baonza, Valentín G

    2016-09-21

    Raman spectra of 1,2-ethylenediamine (EDA) in aqueous solutions are used to demonstrate that EDA molecules experience an anti-gauche conformational change resulting from the interactions with water. The observed Raman shift reveals a compressive (hydrophobic) effect of water on both methylene and amino groups of EDA. Raman spectra of EDA at high pressures are used as reference to quantify the intermolecular EDA-H2O interactions in terms of local pressures. These results are compared with macroscopic solvation pressures calculated from the cohesive energy parameter. We compare and discuss all our observations with available computational and experimental studies.

  19. Local Existence of Weak Solutions to Kinetic Models of Granular Media

    NASA Astrophysics Data System (ADS)

    Agueh, Martial

    2016-08-01

    We prove in any dimension {d ≥q 1} a local in time existence of weak solutions to the Cauchy problem for the kinetic equation of granular media, partial_t f+v\\cdot nabla_x f = {div}_v[f(nabla W *_v f)] when the initial data are nonnegative, integrable and bounded functions with compact support in velocity, and the interaction potential {W} is a {C^2({{R}}^d)} radially symmetric convex function. Our proof is constructive and relies on a splitting argument in position and velocity, where the spatially homogeneous equation is interpreted as the gradient flow of a convex interaction energy with respect to the quadratic Wasserstein distance. Our result generalizes the local existence result obtained by Benedetto et al. (RAIRO Modél Math Anal Numér 31(5):615-641, 1997) on the one-dimensional model of this equation for a cubic power-law interaction potential.

  20. Towards a unified solution of localization failure with mixed finite elements

    NASA Astrophysics Data System (ADS)

    Benedetti, Lorenzo; Cervera, Miguel; Chiumenti, Michele; Zeidler, Antonia; Fischer, Jan-Thomas

    2015-04-01

    Notwithstanding computational scientists made significant steps in the numerical simulation of failure in last three decades, the strain localization problem is still an open question. Especially in a geotechnical setting, when dealing with stability analysis of slopes, it is necessary to provide correct distribution of displacements, to evaluate the stresses in the ground and, therefore, to be able to identify the slip lines that brings to progressive collapse of the slope. Finite elements are an attractive method of solution thanks to profound mathematical foundations and the possibility of describing generic geometries. In order to account for the onset of localization band, the smeared crack approach [1] is introduced, that is the strain localization is assumed to occur in a band of finite width where the displacements are continuous and the strains are discontinuous but bounded. It is well known that this kind of approach poses some challenges. The standard irreducible formulation of FEM is known to be heavily affected by spurious mesh dependence when softening behavior occurs and, consequently, slip lines evolution is biased by the orientation of the mesh. Moreover, in the case of isochoric behavior, unbounded pressure oscillations arise and the consequent locking of the stresses pollutes the numerical solution. Both problems can be shown not to be related to the mathematical statement of the continuous problem but instead to its discrete (FEM) counterpart. Mixed finite element formulations represent a suitable alternative to mitigate these drawbacks. As it has been shown in previous works by Cervera [2], a mixed formulation in terms of displacements and pressure not only provides a propitious solution to the problem of incompressibility, but also it was found to possess the needed robustness in case of strain concentration. This presentation introduces a (stabilized) mixed finite element formulation with continuous linear strain and displacement

  1. Mapping displacement and deformation of the heart with local sine-wave modeling.

    PubMed

    Arts, T; Prinzen, Frits W; Delhaas, T; Milles, J R; Rossi, Alessandro C; Clarysse, Patrick

    2010-05-01

    The new SinMod method extracts motion from magnetic resonance imaging (MRI)-tagged (MRIT) image sequences. Image intensity in the environment of each pixel is modeled as a moving sine wavefront. Displacement is estimated at subpixel accuracy. Performance is compared with the harmonic-phase analysis (HARP) method, which is currently the most common method used to detect motion in MRIT images. SinMod can handle line tags, as well as speckle patterns. In artificial images (tag distance six pixels), SinMod detects displacements accurately (error < 0.02 pixels). Effects of noise are suppressed effectively. Sharp transitions in motion at the boundary of an object are smeared out over a width of 0.6 tag distance. For MRIT images of the heart, SinMod appears less sensitive to artifacts, especially later in the cardiac cycle when image quality deteriorates. For each pixel, the quality of the sine-wave model in describing local image intensity is quantified objectively. If local quality is low, artifacts are avoided by averaging motion over a larger environment. Summarizing, SinMod is just as fast as HARP, but it performs better with respect to accuracy of displacement detection, noise reduction, and avoidance of artifacts.

  2. Interpolation across a muffin-tin interstitial using localized linear combinations of spherical waves

    NASA Astrophysics Data System (ADS)

    Nohara, Yoshiro; Andersen, O. K.

    2016-08-01

    A method for 3D interpolation between hard spheres is described. The function to be interpolated could be the charge density between atoms in condensed matter. Its electrostatic potential is found analytically, and so are various integrals. Periodicity is not required. The interpolation functions are localized structure-adapted linear combinations of spherical waves, the so-called unitary spherical waves (USWs), ψR L(" close=")ɛn)">ɛ ,r , centered at the spheres R , where they have cubic-harmonic character L . Input to the interpolation are the coefficients in the cubic-harmonic expansions of the target function at and slightly outside the spheres; specifically, the values and the three first radial derivatives labeled by d =0 (value) and 1-3 (derivatives). To fit this, we use USWs with four negative energies, ɛ =ɛ1,ɛ2,ɛ3 , and ɛ4. Each interpolation function, ϱd R L(r ), is actually a linear combination of these four sets of USWs with the following properties. (1) It is centered at a specific sphere where it has a specific cubic-harmonic character and radial derivative. (2) Its value and the first three radial derivatives vanish at all other spheres and for all other cubic-harmonic characters, and is therefore highly localized, essentially inside its Voronoi cell. Value-and-derivative (v&d) functions were originally introduced and used by Methfessel [Phys. Rev. B 38, 1537 (1988), 10.1103/PhysRevB.38.1537], but only for the first radial derivative. Explicit expressions are given for the v&d functions and their Coulomb potentials in terms of the USWs at the four energies, plus ɛ0≡0 for the potentials. The coefficients, as well as integrals over the interstitial such as the electrostatic energy, are given entirely in terms of the structure matrix, SR L ,R'L', describing the slopes of the USWs at the five energies and their expansions in Hankel functions. For open structures, additional constraints are installed to pinpoint the interpolated

  3. The effects of the Asselin time filter on numerical solutions to the linearized shallow-water wave equations

    NASA Technical Reports Server (NTRS)

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

    1983-01-01

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

  4. Higher-order rational solitons and rogue-like wave solutions of the (2 + 1)-dimensional nonlinear fluid mechanics equations

    NASA Astrophysics Data System (ADS)

    Wen, Xiao-Yong; Yan, Zhenya

    2017-02-01

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

  5. Propagation and localization of electromagnetic waves in quasiperiodic serial loop structures

    NASA Astrophysics Data System (ADS)

    Aynaou, H.; El Boudouti, E. H.; El Hassouani, Y.; Akjouj, A.; Djafari-Rouhani, B.; Vasseur, J.; Benomar, A.; Velasco, V. R.

    2005-11-01

    We study the propagation of electromagnetic waves in one-dimensional quasiperiodic photonic band gap structures made of serial loop structures separated by segments. Different quasiperiodic structures such as Fibonacci, Thue-Morse, Rudin-Shapiro, and double period are investigated with special focus on the Fibonacci structure. Depending on the lengths of the two arms constituting the loops, one can distinguish two particular cases. (i) There are symmetric loop structures, which are shown to be equivalent to impedance-modulated mediums. In this case, it is found that besides the existence of extended and forbidden modes, some narrow frequency bands appear as defect modes in the transmission spectrum inside the gaps. These modes are shown to be localized within only one of the two types of blocks constituting the structure. 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 velocity of light. (ii) There are also asymmetric loop structures, where the loops play the role of resonators that may introduce transmission zeros and hence additional gaps unnoticed in the case of simple impedance-modulated mediums. A comparison of the transmission amplitude and phase time of Fibonacci systems with those of other quasiperiodic systems is also outlined. In particular, it was shown that these structures present similar behaviors in the transmission spectra inside the regions of extended modes, whereas they present different localized modes inside the gaps. Experiments and numerical calculations are in very good agreement.

  6. Systematic regularization of linear inverse solutions of the EEG source localization problem.

    PubMed

    Phillips, Christophe; Rugg, Michael D; Fristont, Karl J

    2002-09-01

    Distributed linear solutions of the EEG source localization problem are used routinely. Here we describe an approach based on the weighted minimum norm method that imposes constraints using anatomical and physiological information derived from other imaging modalities to regularize the solution. In this approach the hyperparameters controlling the degree of regularization are estimated using restricted maximum likelihood (ReML). EEG data are always contaminated by noise, e.g., exogenous noise and background brain activity. The conditional expectation of the source distribution, given the data, is attained by carefully balancing the minimization of the residuals induced by noise and the improbability of the estimates as determined by their priors. This balance is specified by hyperparameters that control the relative importance of fitting and conforming to prior constraints. Here we introduce a systematic approach to this regularization problem, in the context of a linear observation model we have described previously. In this model, basis functions are extracted to reduce the solution space a priori in the spatial and temporal domains. The basis sets are motivated by knowledge of the evoked EEG response and information theory. In this paper we focus on an iterative "expectation-maximization" procedure to jointly estimate the conditional expectation of the source distribution and the ReML hyperparameters on which this solution rests. We used simulated data mixed with real EEG noise to explore the behavior of the approach with various source locations, priors, and noise levels. The results enabled us to conclude: (i) Solutions in the space of informed basis functions have a high face and construct validity, in relation to conventional analyses. (ii) The hyperparameters controlling the degree of regularization vary largely with source geometry and noise. The second conclusion speaks to the usefulness of using adaptative ReML hyperparameter estimates.

  7. Studies on the spread of local anaesthetic solution in transversus abdominis plane blocks.

    PubMed

    Carney, J; Finnerty, O; Rauf, J; Bergin, D; Laffey, J G; Mc Donnell, J G

    2011-11-01

    The extent of analgesia provided by transversus abdominis plane blocks depends upon the site of injection and pattern of spread within the plane. There are currently a number of ultrasound-guided approaches in use, including an anterior oblique-subcostal approach, a mid-axillary approach and a more recently proposed posterior approach. We wished to determine whether the site of injection of local anaesthetic into the transversus abdominis plane affects the spread of the local anaesthetic within that plane, by studying the spread of a local anaesthetic and contrast solution in four groups of volunteers. The first group underwent the classical landmark-based transversus abdominis plane block whereby two different volumes of injectate were studied: 0.3 ml.kg(-1) vs 0.6 ml.kg(-1). The second group underwent transversus abdominis plane block using the anterior subcostal approach. The third group underwent transversus abdominis plane block using the mid-axillary approach. The fourth group underwent transversus abdominis plane block using the posterior approach, in which local anaesthetic was deposited close to the antero-lateral border of the quadratus lumborum. All volunteers subsequently underwent magnetic resonance imaging at 1, 2 and 4 h following each block to determine the spread of local anaesthetic over time. The studies demonstrated that the anterior subcostal and mid-axillary ultrasound approaches resulted in a predominantly anterior spread of the contrast solution within the transversus abdominis plane and relatively little posterior spread. There was no spread to the paravertebral space with the anterior subcostal approach. The mid-axillary transversus abdominis plane block gave faint contrast enhancement in the paravertebral space at T12-L2. In contrast, the posterior approaches, using both landmark and ultrasound identifications, resulted in predominantly posterior spread of contrast around the quadratus lumborum to the paravertebral space from T5 to L1

  8. On the Role of Osmosis for Non-Linear Shock Waves f Pressure and Solute in Porous Media

    NASA Astrophysics Data System (ADS)

    Kanivesky, Roman; Salusti, Ettore; Caserta, Arrigo

    2013-04-01

    A novel non-Osanger model focusing on non-linear mechanic and chemo-poroelastic coupling of fluids and solute in porous rocks is developed based on the modern wave theory. Analyzing in 1-D a system of two adjacent rocks with different conditions we obtain two coupled non-linear equations for fluid pressure and solute (salt or pollutants) concentration, evolving under the action of strong stress from one "source" rock towards the other rock. Their solutions allow to identify quick non-linear solitary (Burgers) waves of coupled fluid pressure and solute density, that are different from diffusive or perturbative solutions found in other analyses. The strong transient waves for low permeability porous media, such as clay and shale, are analyzed in detail. For medium and high-permeability porous media (sandstones) this model is also tentatively applied. Indeed in recent works of Alexander (1990) and Hart(2009) is supported the presence of small osmotic phenomena in other rocks where osmosis was previously ignored. An attempt to apply our model to soils in Calabria (Italy), such as clastic marine and fluvial deposits as well as discontinuous remnants of Miocene and Pliocene carbonate and terrigeneous deposits, is also discussed.

  9. Dark solitons, breathers, and rogue wave solutions of the coupled generalized nonlinear Schrödinger equations.

    PubMed

    Priya, N Vishnu; Senthilvelan, M; Lakshmanan, M

    2014-06-01

    We construct dark-dark soliton, general breather (GB), Akhmediev breather (AB), Ma soliton (MS), and rogue wave (RW) solutions of a coupled generalized nonlinear Schrödinger (CGNLS) equation. While dark-dark solitons are captured in the defocusing regime of the CGNLS system, the other solutions, namely, GB, AB, MS, and RW, are identified in the focusing regime. We also analyze the structures of GB, AB, MS, and RW profiles with respect to the four-wave mixing parameter. We show that when we increase the value of the real part of the four-wave mixing parameter, the number of peaks in the breather profile increases and the width of each peak shrinks. Interestingly, the direction of this profile also changes due to this change. As far as the RW profile is concerned the width of the peak becomes very thin when we increase the value of this parameter. Further, we consider the RW solution as the starting point, derive AB, MS, and GB in the reverse direction, and show that the solutions obtained in both directions match each other. In the course of the reverse analysis we also demonstrate how to capture the RW solutions directly from AB and MS.

  10. Solutions to Kuessner's integral equation in unsteady flow using local basis functions

    NASA Technical Reports Server (NTRS)

    Fromme, J. A.; Halstead, D. W.

    1975-01-01

    The computational procedure and numerical results are presented for a new method to solve Kuessner's integral equation in the case of subsonic compressible flow about harmonically oscillating planar surfaces with controls. Kuessner's equation is a linear transformation from pressure to normalwash. The unknown pressure is expanded in terms of prescribed basis functions and the unknown basis function coefficients are determined in the usual manner by satisfying the given normalwash distribution either collocationally or in the complex least squares sense. The present method of solution differs from previous ones in that the basis functions are defined in a continuous fashion over a relatively small portion of the aerodynamic surface and are zero elsewhere. This method, termed the local basis function method, combines the smoothness and accuracy of distribution methods with the simplicity and versatility of panel methods. Predictions by the local basis function method for unsteady flow are shown to be in excellent agreement with other methods. Also, potential improvements to the present method and extensions to more general classes of solutions are discussed.

  11. a Generic Probabilistic Model and a Hierarchical Solution for Sensor Localization in Noisy and Restricted Conditions

    NASA Astrophysics Data System (ADS)

    Ji, S.; Yuan, X.

    2016-06-01

    A generic probabilistic model, under fundamental Bayes' rule and Markov assumption, is introduced to integrate the process of mobile platform localization with optical sensors. And based on it, three relative independent solutions, bundle adjustment, Kalman filtering and particle filtering are deduced under different and additional restrictions. We want to prove that first, Kalman filtering, may be a better initial-value supplier for bundle adjustment than traditional relative orientation in irregular strips and networks or failed tie-point extraction. Second, in high noisy conditions, particle filtering can act as a bridge for gap binding when a large number of gross errors fail a Kalman filtering or a bundle adjustment. Third, both filtering methods, which help reduce the error propagation and eliminate gross errors, guarantee a global and static bundle adjustment, who requires the strictest initial values and control conditions. The main innovation is about the integrated processing of stochastic errors and gross errors in sensor observations, and the integration of the three most used solutions, bundle adjustment, Kalman filtering and particle filtering into a generic probabilistic localization model. The tests in noisy and restricted situations are designed and examined to prove them.

  12. Localization of finite frequency inertial Alfvén wave and turbulent spectrum in low beta plasmas

    NASA Astrophysics Data System (ADS)

    Rinawa, M. L.; Sharma, R. P.; Modi, K. V.

    2015-05-01

    In the present paper, we have investigated nonlinear interaction of inertial Alfvén wave with ion acoustic wave, for low β-plasma ( β≪ m e / m i ) where β is the thermal to magnetic pressure ratio. We have developed the dynamical equation of inertial Alfvén wave by considering the finite frequency as well as finite ion temperature correction. The dynamical equation of ion acoustic wave, propagating at an angle with respect to the background magnetic field, in the presence of ponderomotive nonlinearity due to inertial Alfvén wave is also derived. Numerical simulation has been carried out to study the effect of nonlinear coupling between these waves which results in the formation of localized structures and turbulent spectrum, applicable to auroral region. The result reveals that the localized structures become complex and intense in nature (quasi-steady state). Further, we have studied the turbulent spectrum which follows spectral index (˜ k -4.46) at smaller scales. Relevance of the obtained results has been shown with the observations reported by various spacecrafts like Hawkeye and HEOS-2 (Highly Eccentric Orbiting Satellite-2).

  13. Optical solutions for accommodating ELT LGS wave-front sensing to small format detectors

    NASA Astrophysics Data System (ADS)

    Gendron, E.

    2016-07-01

    Sodium laser guide stars (LGS) will be used on extremely large telescopes (ELT) for increasing the sky coverage of adaptive optics systems. The thickness of the sodium layer combined with a perspective effect makes the laser beacon to appear as an elongated plume when observed from a pupil location distant from the laser launch telescope. The wave-front sensing with a Shack-Hartmann on such a peculiar object requires a large number of pixels per sub-aperture in order to cope with the required field of view. As a large number of sub-apertures is required on an ELT, this leads to detector formats exceeding 1500 × 1500 pixels. It is worth noticing however that most of these numerous pixels are useless, as many of them won't receive any light due to the arrangement of the pattern of spots. We present in this article some potential optical solutions for relaxing the requirements of the detector format by a significant amount. This is obtained by re-arranging the pattern of the elongated spots in order to avoid any loss of space between them. Depending on the geometry of the system, a factor of ≍2 on the pixel count can be gained along both directions.

  14. P and S wave tomography of Japan subduction zone from joint inversions of local and teleseismic travel times and surface-wave data

    NASA Astrophysics Data System (ADS)

    Liu, Xin; Zhao, Dapeng

    2016-03-01

    We determined P and S wave velocity tomography of the Japan subduction zone down to a depth of 700 km by conducting joint inversions of a large number of high-quality arrival-time data of local earthquakes and teleseismic events which are newly collected for this study. We also determined 2-D phase-velocity images of fundamental mode Rayleigh waves at periods of 20-150 s beneath Japan and the surrounding oceanic regions using amplitude and phase data of teleseismic Rayleigh waves. A detailed 3-D S-wave tomography of the study region is obtained by jointly inverting S-wave arrival times of local and teleseismic events and the Rayleigh-wave phase-velocity data. Our inversion results reveal the subducting Pacific and Philippine Sea slabs clearly as dipping high-velocity zones from a 1-D starting velocity model. Prominent low-velocity (low-V) anomalies are revealed in the mantle wedge above the slabs and in the mantle below the Pacific slab. The distinct velocity contrasts between the subducting slabs and the surrounding mantle reflect significant lateral variations in temperature as well as water content and/or the degree of partial melting. The low-V anomalies in the mantle wedge are attributed to slab dehydration and corner flows in the mantle wedge. A sheet-like low-V zone is revealed under the Pacific slab beneath NE Japan, which may reflect hot upwelling from the deeper mantle and subduction of a plume-fed asthenosphere as well. Our present results indicate that joint inversions of different seismic data are very effective and important for obtaining robust tomographic images of the crust and mantle.

  15. Calculation of wave-functions with frozen orbitals in mixed quantum mechanics/molecular mechanics methods. II. Application of the local basis equation.

    PubMed

    Ferenczy, György G

    2013-04-05

    The application of the local basis equation (Ferenczy and Adams, J. Chem. Phys. 2009, 130, 134108) in mixed quantum mechanics/molecular mechanics (QM/MM) and quantum mechanics/quantum mechanics (QM/QM) methods is investigated. This equation is suitable to derive local basis nonorthogonal orbitals that minimize the energy of the system and it exhibits good convergence properties in a self-consistent field solution. These features make the equation appropriate to be used in mixed QM/MM and QM/QM methods to optimize orbitals in the field of frozen localized orbitals connecting the subsystems. Calculations performed for several properties in divers systems show that the method is robust with various choices of the frozen orbitals and frontier atom properties. With appropriate basis set assignment, it gives results equivalent with those of a related approach [G. G. Ferenczy previous paper in this issue] using the Huzinaga equation. Thus, the local basis equation can be used in mixed QM/MM methods with small size quantum subsystems to calculate properties in good agreement with reference Hartree-Fock-Roothaan results. It is shown that bond charges are not necessary when the local basis equation is applied, although they are required for the self-consistent field solution of the Huzinaga equation based method. Conversely, the deformation of the wave-function near to the boundary is observed without bond charges and this has a significant effect on deprotonation energies but a less pronounced effect when the total charge of the system is conserved. The local basis equation can also be used to define a two layer quantum system with nonorthogonal localized orbitals surrounding the central delocalized quantum subsystem.

  16. Elastic wave localization in two-dimensional phononic crystals with one-dimensional random disorder and aperiodicity

    NASA Astrophysics Data System (ADS)

    Yan, Zhi-Zhong; Zhang, Chuanzeng; Wang, Yue-Sheng

    2011-03-01

    The band structures of in-plane elastic waves propagating in two-dimensional phononic crystals with one-dimensional random disorder and aperiodicity are analyzed in this paper. The localization of wave propagation is discussed by introducing the concept of the localization factor, which is calculated by the plane-wave-based transfer-matrix method. By treating the random disorder and aperiodicity as the deviation from the periodicity in a special way, three kinds of aperiodic phononic crystals that have normally distributed random disorder, Thue-Morse and Rudin-Shapiro sequence in one direction and translational symmetry in the other direction are considered and the band structures are characterized using localization factors. Besides, as a special case, we analyze the band gap properties of a periodic planar layered composite containing a periodic array of square inclusions. The transmission coefficients based on eigen-mode matching theory are also calculated and the results show the same behaviors as the localization factor does. In the case of random disorders, the localization degree of the normally distributed random disorder is larger than that of the uniformly distributed random disorder although the eigenstates are both localized no matter what types of random disorders, whereas, for the case of Thue-Morse and Rudin-Shapiro structures, the band structures of Thue-Morse sequence exhibit similarities with the quasi-periodic (Fibonacci) sequence not present in the results of the Rudin-Shapiro sequence.

  17. Properties of Apolar Solutes in Alkyl Imidazolium-Based Ionic Liquids: The Importance of Local Interactions.

    PubMed

    Lesch, Volker; Heuer, Andreas; Holm, Christian; Smiatek, Jens

    2016-02-03

    The solvation and the dynamic properties of apolar model solutes in alkyl imidazolium-based ionic liquids (IL) are studied by using all-atom molecular dynamics simulations. In regards to specific IL effects, we focused on the often used 1-ethyl-3-methyl imidazolium cation in combination with the anions tetrafluoroborate, acetate, and bis(trifluoromethanesulfonyl)imide. Our findings reveal that the size of the anion crucially influences the accumulation behavior of the cations, which results in modified IL solvation properties. Deviations between the different alkyl imidazolium-based IL combinations can be also observed with regard to the results for the radial distribution functions, the number of surrounding molecules, and the molecular orientation. The analysis of the van Hove function further shows pronounced differences in the dynamic behavior of the solutes. The simulations verify that the solute mobilities are mainly influenced by the composition of the local solvent shell and the properties of the underlying Lennard-Jones interactions. Additional simulations with regard to modified short-range dispersion energies for alkyl imidazolium-based ILs validate our conclusions.

  18. Cosmological self-tuning and local solutions in generalized Horndeski theories

    NASA Astrophysics Data System (ADS)

    Babichev, Eugeny; Esposito-Farèse, Gilles

    2017-01-01

    We study both the cosmological self-tuning and the local predictions (inside the Solar System) of the most general shift-symmetric beyond Horndeski theory. We first show that the cosmological self-tuning is generic in this class of theories: By adjusting a mass parameter entering the action, a large bare cosmological constant can effectively be reduced to a small observed one. Requiring then that the metric should be close enough to the Schwarzschild solution in the Solar System, to pass the experimental tests of general relativity, and taking into account the renormalization of Newton's constant, we select a subclass of models which presents all desired properties: It is able to screen a big vacuum energy density, while predicting an exact Schwarzschild-de Sitter solution around a static and spherically symmetric source. As a by-product of our study, we identify a general subclass of beyond Horndeski theory for which regular self-tuning black hole solutions exist, in the presence of a time-dependent scalar field. We discuss possible future development of the present work.

  19. Four-wave-mixing spectroscopy of localized excitons in CdS 1- xSe x

    NASA Astrophysics Data System (ADS)

    Dinger, A.; Ell, R.; Reznitsky, A.; Klingshirn, C.

    2000-06-01

    We investigated the dephasing properties of excitons in CdS 1- xSe x in the compositional range 0.07≲ x≲0.80 by means of transient four-wave-mixing experiments. For 0.35≲ x≲0.80, the dephasing times of localized excitons are in the order of a few 100 ps up to 1 ns. Thereby, we observe a strong dependence of the dephasing times on the composition x, the localization depth and the spectral excitation width. For very short delay times (a few ps), a beat phenomenon is presented which is interpreted by multiple reflections of propagating exciton-polariton wave packets. In the compositional range 0.07≲ x≲0.35 the four-wave-mixing signal is strongly suppressed and the slowly dephasing signal is hardly observable or as in the most cases not measureable at all.

  20. The Multi-Scale Dynamics of Gravity Waves in Parameterizations: Central Issues and Solution Strategies

    NASA Astrophysics Data System (ADS)

    Achatz, U.; Becker, E.; Chau, J. L.; Doernbrack, A.; Harlander, U.; Horenko, I.; Klein, R.; Luebken, F. J.; Manzini, E.; Preusse, P.; Rapp, M.; Schmidt, H.; Spichtinger, P.; Zängl, G.; Zuelicke, C.

    2015-12-01

    A major source of uncertainty in current climate-chemistry models are internal gravity waves (GWs), represented by oversimplified parameterizations. A new German/Swiss research unit on the multiscale dynamics of GWs (MS-GWaves, https://ms-gwaves.iau.uni-frankfurt.de/index.php) is to formulate explicit models of GW excitation, propagation, and dissipation in a physically and mathematically consistent way. Both process-resolving numerical modeling and measurement campaigns will be critical in validating the approaches and improving them further. The improved GW parameterizations will be implemented into and tested in a global non-hydrostatic numerical weather-forecast model (ICON) that can locally resolve a major part of the GW spectrum. The presentation will discuss central questions addressed, and some early results. One focus will be on the modelling of the numerically stable two-way interaction between subgrid-scale GWs and the resolved flow. This will be extended depending on recent developments, e.g. with regard to spontaneous imbalance or the GW-tropopause interaction.

  1. Focused acoustic beam imaging of grain structure and local Young's modulus with Rayleigh and surface skimming longitudinal waves

    SciTech Connect

    Martin, R. W.; Sathish, S.; Blodgett, M. P.

    2013-01-25

    The interaction of a focused acoustic beam with materials generates Rayleigh surface waves (RSW) and surface skimming longitudinal waves (SSLW). Acoustic microscopic investigations have used the RSW amplitude and the velocity measurements, extensively for grain structure analysis. Although, the presence of SSLW has been recognized, it is rarely used in acoustic imaging. This paper presents an approach to perform microstructure imaging and local elastic modulus measurements by combining both RSW and SSLW. The acoustic imaging of grain structure was performed by measuring the amplitude of RSW and SSLW signal. The microstructure images obtained on the same region of the samples with RSW and SSLW are compared and the difference in the contrast observed is discussed based on the propagation characteristics of the individual surface waves. The velocity measurements are determined by two point defocus method. The surface wave velocities of RSW and SSLW of the same regions of the sample are combined and presented as average Young's modulus image.

  2. Experimental measurement of local displacement and chemical pair correlations in crystalline solid solutions

    SciTech Connect

    Sparks, C.L.; Ice, G.E.; Robertson, J.L.; Shaffer, L.B.

    1993-10-01

    Measurement of near-neighbor atomic arrangements in crystalline solid solutions is well established and provides meaningful values for chemical preference of atoms for their near neighbors to beyond the first ten neighboring shells. Static displacements (atomic size) between these atom pairs have mostly been either ignored in the recovery of the local pair preferences or removed by making use of the displacement scattering dependence on momentum transfer. With intense and energy tunable x-ray synchrotron sources, our ability to recover these static displacements between atoms has greatly improved. Data taken with multiple x-ray energies to obtain the contrast necessary to separate like from unlike neighbor pair distances are discussed for the two cases studied to date: A locally ordered Ni{sub 77.5}Fe{sub 22.5} crystal and a locally clustered Fe{sub 53}Cr{sub 47} crystal. Analysis of experimental parameters and data gives the systematic and statistical errors on the recovered parameters. Meaningful atomic displacements from the mean lattice can be measured and recovered. These displacements help us understand material properties and will provide theorists with tests for their calculations.

  3. Annihilation and creation of rotating waves by a local light pulse in a protoplasmic droplet of the Physarum plasmodium

    NASA Astrophysics Data System (ADS)

    Takagi, Seiji; Ueda, Tetsuo

    2010-06-01

    Pattern dynamics plays a fundamental role in biological functions from cell to organ in living systems, and the appearance of rotating waves can lead to pathological situations. Basic dynamics of rotating waves of contraction-relaxation activity under local perturbation is studied in a newly developed protoplasmic droplet of the Physarum plasmodium. A light pulse is applied by irradiating circularly a quarter of the droplet showing a single rotating wave. The oscillation pattern changes abruptly only when the irradiation is applied at a part of the droplet near the maximal contraction. The abrupt changes are as follows: the rotating wave disappears or is displaced when the irradiation area is very close to the center of the rotating wave, while new rotating waves are created when the irradiation area is far from the center of the rotating wave. These results support the hypothesis that the phase response curve has a discontinuous change (type 0 resetting) from delay to advance around the maximal contraction. The significance of the results is discussed in relation to “vulnerability” in excitable media and biological systems in general.

  4. PICKUP ION MEDIATED PLASMAS. I. BASIC MODEL AND LINEAR WAVES IN THE SOLAR WIND AND LOCAL INTERSTELLAR MEDIUM

    SciTech Connect

    Zank, G. P.; Hunana, P.; Mostafavi, P.; Goldstein, M. L.

    2014-12-20

    Pickup ions (PUIs) in the outer heliosphere and the local interstellar medium are created by charge exchange between protons and hydrogen (H) atoms, forming a thermodynamically dominant component. In the supersonic solar wind beyond >10 AU, in the inner heliosheath (IHS), and in the very local interstellar medium (VLISM), PUIs do not equilibrate collisionally with the background plasma. Using a collisionless form of Chapman-Enskog expansion, we derive a closed system of multi-fluid equations for a plasma comprised of thermal protons and electrons, and suprathermal PUIs. The PUIs contribute an isotropic scalar pressure to leading order, a collisionless heat flux at the next order, and a collisionless stress tensor at the second-order. The collisionless heat conduction and viscosity in the multi-fluid description results from a non-isotropic PUI distribution. A simpler one-fluid MHD-like system of equations with distinct equations of state for both the background plasma and the PUIs is derived. We investigate linear wave properties in a PUI-mediated three-fluid plasma model for parameters appropriate to the VLISM, the IHS, and the solar wind in the outer heliosphere. Five distinct wave modes are possible: Alfvén waves, thermal fast and slow magnetoacoustic waves, PUI fast and slow magnetoacoustic waves, and an entropy mode. The thermal and PUI acoustic modes propagate at approximately the combined thermal magnetoacoustic speed and the PUI sound speed respectively. All wave modes experience damping by the PUIs through the collisionless PUI heat flux. The PUI-mediated plasma model yields wave properties, including Alfvén waves, distinctly different from those of the standard two-fluid model.

  5. Soliton-like, periodic wave and rational solutions for a (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation in the incompressible fluid

    NASA Astrophysics Data System (ADS)

    Jia, Shu-Liang; Gao, Yi-Tian; Hu, Lei; Huang, Qian-Min; Hu, Wen-Qiang

    2017-02-01

    Under investigation in this paper is a (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation in the incompressible fluid. With the aid of the bilinear form, Nth-order soliton-like solutions are obtained via the Pffafian method, rational solutions are derived with the ansätz method and periodic wave solutions are constructed via the Riemann theta function. The analytic solutions obtained via the Pffafian method are similar to the kink solitons, while, the interaction regions with little peaks are different from those of the usual kink solitons. The rational solutions which have one upper lump and one down deep hole are the bright-dark solitary wave solutions. For the rational solutions which combine the kink solitary wave with breather-like wave, asymptotic behaviors show that the breather-like wave disappears with the evolution of t. Relations between the one-soliton solutions and one-periodic wave solutions are analysed, which exhibit the asymptotic behaviors of the periodic waves.

  6. P wave crustal velocity structure in the greater Mount Rainier area from local earthquake tomography

    USGS Publications Warehouse

    Moran, S.C.; Lees, J.M.; Malone, S.D.

    1999-01-01

    We present results from a local earthquake tomographic imaging experiment in the greater Mount Rainier area. We inverted P wave arrival times from local earthquakes recorded at permanent and temporary Pacific Northwest Seismograph Network seismographs between 1980 and 1996. We used a method similar to that described by Lees and Crosson [1989], modified to incorporate the parameter separation method for decoupling the hypocenter and velocity problems. In the upper 7 km of the resulting model there is good correlation between velocity anomalies and surface geology. Many focal mechanisms within the St. Helens seismic zone have nodal planes parallel to the epicentral trend as well as to a north-south trending low-velocity trough, leading us to speculate that the trough represents a zone of structural weakness in which a moderate (M 6.5-7.0) earthquake could occur. In contrast, the western Rainier seismic zone does not correlate in any simple way with anomaly patterns or focal mechanism fault planes, leading us to infer that it is less likely to experience a moderate earthquake. A ???10 km-wide low-velocity anomaly occurs 5 to 18 km beneath the summit of Mount Rainier, which we interpret to be a signal of a region composed of hot, fractured rock with possible small amounts of melt or fluid. No systematic velocity pattern is observed in association with the southern Washington Cascades conductor. A midcrustal anomaly parallels the Olympic-Wallowa lineament as well as several other geophysical trends, indicating that it may play an important role in regional tectonics. Copyright 1999 by the American Geophysical Union.

  7. Rogue-wave solutions for an inhomogeneous nonlinear system in a geophysical fluid or inhomogeneous optical medium

    NASA Astrophysics Data System (ADS)

    Xie, Xi-Yang; Tian, Bo; Jiang, Yan; Sun, Wen-Rong; Sun, Ya; Gao, Yi-Tian

    2016-07-01

    Under investigation in this paper is an inhomogeneous nonlinear system, which describes the marginally-unstable baroclinic wave packets in a geophysical fluid or ultra-short pulses in nonlinear optics with certain inhomogeneous medium existing. By virtue of a kind of the Darboux transformation, under the Painlevé integrable condition, the first- and second-order bright and dark rogue-wave solutions are derived. Properties of the first- and second-order bright and dark rogue waves with α(t), which measures the state of the basic flow, and β(t), representing the interaction of the wave packet and mean flow, are graphically presented and analyzed: α(t) and β(t) have no influence on the wave packet, but affect the correction of the basic flow. When we choose α(t) as a constant and linear function, respectively, the shapes of the first- and second-order dark rogue waves change, and the peak heights and widths of them alter with the value of β(t) changing.

  8. Slow waves on magnetic metamaterials and on chains of plasmonic nanoparticles: Driven solutions in the presence of retardation

    NASA Astrophysics Data System (ADS)

    Zhuromskyy, O.; Sydoruk, O.; Shamonina, E.; Solymar, L.

    2009-11-01

    Slow waves on chains or lattices of resonant elements offer a unique tool for guiding and manipulating the electromagnetic radiation on a subwavelength scale. Applications range from radio waves to optics with two major classes of structures being used: (i) metamaterials made of coupled ring resonators supporting magnetoinductive waves and (ii) plasmonic crystals made of nanoparticles supporting waves of near-field coupling. We derive dispersion equations of both types of slow waves for the case when the interelement coupling is governed by retardation effects, and show how closely they are related. The current distribution is found from Kirchhoff's equation by inverting the impedance matrix. In contrast to previous treatments power conservation is demonstrated in a form relevant to a finite structure: the input power is shown to be equal to the radiated power plus the powers absorbed in the Ohmic resistance of the elements and the terminal impedance. The relations between frequency and wave number are determined for a 500-element line for two excitations using three different methods. Our approach of retrieval of the dispersion from driven solutions of finite lines is relevant for practical applications and may be used in the design of metamaterials and plasmonic crystals with desired properties.

  9. Fully pseudospectral solution of the conformally invariant wave equation near the cylinder at spacelike infinity. II: Schwarzschild background

    NASA Astrophysics Data System (ADS)

    Frauendiener, Jörg; Hennig, Jörg

    2017-02-01

    It has recently been demonstrated (Frauendiener and Hennig 2014 Class. Quantum Grav. 31 085010) that the conformally invariant wave equation on a Minkowski background can be solved with a fully pseudospectral numerical method. In particular, it is possible to include spacelike infinity into the numerical domain, which is appropriately represented as a cylinder, and highly accurate numerical solutions can be obtained with a moderate number of gridpoints. In this paper, we generalise these considerations to the spherically-symmetric wave equation on a Schwarzschild background. In the Minkowski case, a logarithmic singularity at the future boundary is present at leading order, which can easily be removed to obtain completely regular solutions. An important new feature of the Schwarzschild background is that the corresponding solutions develop logarithmic singularities at infinitely many orders. This behaviour seems to be characteristic for massive space-times. In this sense this work is indicative of properties of the solutions of the Einstein equations near spatial infinity. The use of fully pseudospectral methods allows us to still obtain very accurate numerical solutions, and the convergence properties of the spectral approximations reveal details about the singular nature of the solutions on spacelike and null infinity. These results seem to be impossible to achieve with other current numerical methods. Moreover, we describe how to impose conditions on the asymptotic behaviour of initial data so that the leading-order logarithmic terms are avoided, which further improves the numerical accuracy.

  10. An improved solution of local window parameters setting for local singularity analysis based on Excel VBA batch processing technology

    NASA Astrophysics Data System (ADS)

    Zhang, Daojun; Cheng, Qiuming; Agterberg, Frits; Chen, Zhijun

    2016-03-01

    In this paper Excel VBA is used for batch calculation in Local Singularity Analysis (LSA), which is for the information extracting from different kinds of geoscience data. Capabilities and advantages of a new module called Batch Tool for Local Singularity Index Mapping (BTLSIM) are: (1) batch production of series of local singularity maps with different settings of local window size, shape and orientation parameters; (2) local parameter optimization based on statistical tests; and (3) provision of extra output layers describing how spatial changes induced by parameter optimization are related to spatial structure of the original input layers.

  11. Exact traveling wave solutions of the KP-BBM equation by using the new approach of generalized (G'/G)-expansion method.

    PubMed

    Alam, Md Nur; Akbar, M Ali

    2013-01-01

    The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. By means of this scheme, we found some new traveling wave solutions of the above mentioned equation.

  12. GENERAL: Periodic folded waves for a (2+1)-dimensional modified dispersive water wave equation

    NASA Astrophysics Data System (ADS)

    Huang, Wen-Hua

    2009-08-01

    A general solution, including three arbitrary functions, is obtained for a (2+1)-dimensional modified dispersive water-wave (MDWW) equation by means of the WTC truncation method. Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution, special types of periodic folded waves are derived. In the long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations. The interactions of the periodic folded waves and the degenerated single folded solitary waves are investigated graphically and found to be completely elastic.

  13. Effect of magnetic islands on the localization of kinetic Alfvén wave

    SciTech Connect

    Rai, Rajesh Kumar Sharma, Swati Yadav, Nitin; Sharma, R. P.; Goldstein, M. L.

    2015-12-15

    Recent studies have revealed an intimate link between magnetic reconnection and turbulence. Observations show that kinetic Alfvén waves (KAWs) play a very crucial role in magnetic reconnection and have been a topic of interest from decades in the context of turbulence and particle heating. In the present paper, we study the role that KAW plays in the formation of coherent structures/current sheets when KAW is propagating in the pre-existing fully developed chain of magnetic islands. We derived the dynamical equation of KAW in the presence of chain of magnetic islands and solved it using numerical simulations well as analytic tools. Due to pre-existing chain of magnetic islands, KAW splits into coherent structures and the scale size of these structures along transverse directions (with respect to background magnetic field) comes out to be either less than or greater than ion gyro radius. Therefore, the present work may be the first step towards understanding how magnetic reconnection generated islands may affect the KAW localization and eventually contribute to magnetic turbulence. In this way the present approach may be helpful to understand the interplay between magnetic reconnection and turbulence in ion diffusion region.

  14. THE DISTRIBUTION OF COALESCING COMPACT BINARIES IN THE LOCAL UNIVERSE: PROSPECTS FOR GRAVITATIONAL-WAVE OBSERVATIONS

    SciTech Connect

    Kelley, Luke Zoltan; Ramirez-Ruiz, Enrico; Zemp, Marcel; Diemand, Juerg; Mandel, Ilya

    2010-12-10

    Merging compact binaries are the most viable and best-studied candidates for gravitational-wave (GW) detection by the fully operational network of ground-based observatories. In anticipation of the first detections, the expected distribution of GW sources in the local universe is of considerable interest. Here we investigate the full phase-space distribution of coalescing compact binaries at z = 0 using dark matter simulations of structure formation. The fact that these binary systems acquire large barycentric velocities at birth ('kicks') results in merger site distributions that are more diffusely distributed with respect to their putative hosts, with mergers occurring out to distances of a few Mpc from the host halo. Redshift estimates based solely on the nearest galaxy in projection can, as a result, be inaccurate. On the other hand, large offsets from the host galaxy could aid the detection of faint optical counterparts and should be considered when designing strategies for follow-up observations. The degree of isotropy in the projected sky distributions of GW sources is found to be augmented with increasing kick velocity and to be severely enhanced if progenitor systems possess large kicks as inferred from the known population of pulsars and double compact binaries. Even in the absence of observed electromagnetic counterparts, the differences in sky distributions of binaries produced by disparate kick-velocity models could be discerned by GW observatories, within the expected accuracies and detection rates of advanced LIGO-in particular with the addition of more interferometers.

  15. Multi-site delamination detection and quantification in composites through guided wave based global-local sensing

    NASA Astrophysics Data System (ADS)

    Tian, Zhenhua; Leckey, Cara; Yu, Lingyu

    2017-02-01

    This paper presents a guided wave based global-local sensing method for rapid detection and quantification of multi-site delamination damage in large composite panels. The global-local approach uses a hybrid system consisting of a piezoelectric transducer (PZT) for generating guided waves and a non-contact scanning laser Doppler vibrometer (SLDV) for acquiring guided wave data. The global-local method is performed in two steps. First, a phased array configured of a small number of SLDV scan points (for example 10×10 points in a rectangular grid array) performs inspection over the entire plate to detect and locate damage. Local areas are identified as potential damage regions for the second step. Then high density wavefield measurements are taken over the identified areas and wavefield analysis is performed to quantitatively evaluate the damage. For the proof of concept in case with multi-site damage, the global-local approach is demonstrated on a carbon fiber reinforced polymer (CFRP) composite plate with two sites of impact-induced delamination damage. In the first step, the locations of two delamination sites are detected by the phased array method. In the second step, the delamination size and shape are evaluated using wavefield analysis. The detected delamination location, size and shape agree well with those of ultrasonic C-scan and the method led to a 93% reduction in inspection time compared to a full SLDV dense grid scan.

  16. DIRECT COMPARISON OF KINETIC AND LOCAL EQUILIBRIUM FORMULATIONS FOR SOLUTE TRANSPORT AFFECTED BY SURFACE REACTIONS.

    USGS Publications Warehouse

    Bahr, Jean M.; Rubin, Jacob

    1987-01-01

    Modeling transport of reacting solutes in porous media often requires a choice between models based on the local equilibrium assumption (LEA) and models involving reaction kinetics. Direct comparison of the mathematical formulations for these two types of transport models can aid in this choice. For cases of transport affected by surface reaction, such a comparison is made possible by a new derivation procedure. This procedure yields a kinetics-based formulation that is the sum of the LEA formulation and one or more kinetically influenced terms. The dimensionless form of the new kinetics-based formulation facilitates identification of critical parameter groupings which control the approach to transport behavior consistent with LEA model predictions. Results of numerical experiments demonstrate that criteria for LEA applicability can be expressed conveniently in terms of these parameter groupings. The derivation procedure is demonstrated for examples of surface reactions including first-order reversible sorption, Langmuir-type kinetics and binary, homovalent ion exchange.

  17. Elimination of spiral waves in a locally connected chaotic neural network by a dynamic phase space constraint.

    PubMed

    Li, Yang; Oku, Makito; He, Guoguang; Aihara, Kazuyuki

    2017-04-01

    In this study, a method is proposed that eliminates spiral waves in a locally connected chaotic neural network (CNN) under some simplified conditions, using a dynamic phase space constraint (DPSC) as a control method. In this method, a control signal is constructed from the feedback internal states of the neurons to detect phase singularities based on their amplitude reduction, before modulating a threshold value to truncate the refractory internal states of the neurons and terminate the spirals. Simulations showed that with appropriate parameter settings, the network was directed from a spiral wave state into either a plane wave (PW) state or a synchronized oscillation (SO) state, where the control vanished automatically and left the original CNN model unaltered. Each type of state had a characteristic oscillation frequency, where spiral wave states had the highest, and the intra-control dynamics was dominated by low-frequency components, thereby indicating slow adjustments to the state variables. In addition, the PW-inducing and SO-inducing control processes were distinct, where the former generally had longer durations but smaller average proportions of affected neurons in the network. Furthermore, variations in the control parameter allowed partial selectivity of the control results, which were accompanied by modulation of the control processes. The results of this study broaden the applicability of DPSC to chaos control and they may also facilitate the utilization of locally connected CNNs in memory retrieval and the exploration of traveling wave dynamics in biological neural networks.

  18. The relations among Shannon information entropy, quantum discord, concurrence and localization properties of one-dimensional single-electron wave functions

    NASA Astrophysics Data System (ADS)

    Gong, Longyan; Zheng, Yongcui; Wang, Haihong; Cheng, Weiwen; Zhao, Shengmei

    2014-09-01

    Shannon information entropy (SE), concurrence (CC), quantum discord (QD) and localization properties for various one-dimensional one-electron wave functions are intensively studied, respectively. They include Gaussian functions, power-law functions, and functions in the Anderson model and the Harper ones. For all these wave functions, we find that SE, CC and QD increase as the localization length of a wave function increases, respectively. There are linear or quadratic relationships between two of them. Therefore, we can confirm for the analyzed models that SE, CC and QD are statistically equivalent quantities to reflect the localization properties of wave functions though they are different measures of quantum information.

  19. Nonlinear Self-Adjointness, Conservation Laws and Soliton-Cnoidal Wave Interaction Solutions of (2+1)-Dimensional Modified Dispersive Water-Wave System

    NASA Astrophysics Data System (ADS)

    Xia, Ya-Rong; Xin, Xiang-Peng; Zhang, Shun-Li

    2017-01-01

    This paper mainly discusses the (2+1)-dimensional modified dispersive water-wave (MDWW) system which will be proved nonlinear self-adjointness. This property is applied to construct conservation laws corresponding to the symmetries of the system. Moreover, via the truncated Painlevé analysis and consistent tanh-function expansion (CTE) method, the soliton-cnoidal periodic wave interaction solutions and corresponding images will be eventually achieved. Supported by National Natural Science Foundation of China under Grant Nos. 11371293, 11505090, the Natural Science Foundation of Shaanxi Province under Grant No. 2014JM2-1009, Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009 and the Science and Technology Innovation Foundation of Xi’an under Grant No. CYX1531WL41

  20. Rapid convergence to the inverse solution regularized with Lorentzian distributed function for near-infrared continuous wave diffuse optical tomography.

    PubMed

    Pan, Min-Cheng; Pan, Min-Chun

    2010-01-01

    A promising method to achieve rapid convergence for image reconstruction is introduced for the continuous-wave near-infrared (NIR) diffuse optical tomography (DOT). Tomographic techniques are usually implemented off line and are time consuming to realize image reconstruction, especially for NIR DOT. Therefore, it is essential to both speed up reconstruction and achieve stable and convergent solutions. We propose an approach using a constraint based on a Lorentzian distributed function incorporated into Tikhonov regularization, thereby rapidly converging a stable solution. It is found in the study that using the proposed method with around five or six iterations leads to a stable solution. The result is compared to the primary method usually converging in approximately 25 iterations. Our algorithm rapidly converges to stable solution in the case of noisy (>20 dB) detected intensities.